Available via license: CC BY 4.0
Content may be subject to copyright.
Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier 10.1109/ACCESS.2024. XXXXXXX
LED degradation monitoring using a
multi-channel spectral sensor
PAUL MYLAND1, ALEXANDER HERZOG1, SEBASTIAN BABILON2, WILLEM D. VAN
DRIEL3,4 , and TRAN QUOC KHANH1
1Laboratory of Adaptive Lighting Systems and Visual Processing, Department of Electrical Engineering and Information Technology, Technical University of
Darmstadt, Germany
2Arnold & Richter Cine Technik GmbH & Co. Betriebs KG, Stephanskirchen, Germany
3EEMCS Faculty, Delft University of Technology, The Netherlands
4Signify, 5656 AE Eindhoven, The Netherlands
Corresponding author: Paul Myland (e-mail: myland@lichttechnik.tu-darmstadt.de).
We acknowledge support by the Deutsche Forschungsgemeinschaft (DFG – German Research Foundation) and the Open Access
Publishing Fund of Technical University of Darmstadt.
ABSTRACT This study explores a novel approach to monitor the spectral emission of LEDs by estimating
the spectral power distribution from the spectral sensor responses during an accelerated ageing experiment.
Two methods for reconstructing the actual LED spectra from sensor responses are presented and tested, one
solely requires sensor datasheet information and the other uses a full spectral characterisation of the sensor’s
spectral sensitivities. The reconstruction results show that a spectral sensor can provide accurate spectral
estimates even after severe LED degradation. Only for an LED that suffered a phosphor crack, affecting its
spatial radiation characteristics, limited ability to estimate the true spectral power distribution without prior
assumptions about the spectral changes must be reported. Overall, the use of a spectral sensor, even without
detailed characterisation of the sensor itself, allows for an accurate monitoring of the true emission of LEDs,
with a maximum radiometric error of 0.73 %, a maximum colormetric error of 0.0017 ∆u′v′and a maximum
spectral nRMSE error of 0.0097 compared to a spectroradiometric measurement. This advance holds great
promise for improving lighting technology, particularly in applications that require constant radiometric
output and stable color.
INDEX TERMS Sensor feedback, spectral sensing, LED degradation, spectral reconstruction, closed loop,
spectral power distribution, constant radiometric output, constant light output, stable lighting color, LED
maintenance.
I. INTRODUCTION
THE research and development of light emitting diodes
(LEDs) is closely related to LED lifetime modelling and
the associated dependence on operating conditions [1]–[4].
Today, there are standardized and established approaches de-
scribed in the ANSI/IES TM-21 to approximate, model, and
extrapolate the radiant flux as a function of operating time,
temperature, and current [5]. However, modeling the spectral
characteristics is much more complex [6]–[8], and significant
luminous flux, colorimetric, and spectral errors between state
of the art modelling approaches and real degradation data
can be observed [9]–[19], showing heterogeneity even within
sample groups [20]. As a consequence, it is currently unfeasi-
ble to use the modeled spectral degradation for proper aging
compensation in multi-channel LED systems.
While models could be or already have been developed for
the in-situ estimation of LED radiant flux decrease from diode
parameters on a chip level [21], [22] or from the electrical
and optical small-signal modulation responses [23], there are
currently limited possibilities to determine the ageing effects
that occur in the package from monitoring only the electrical
parameters. However, with the improvements in crystal qual-
ity, device efficiency, and thermal management, the lifetime
limiting factors have shifted from the semiconductor chip
towards the package elements of the LED system [3]. Defects
that may occur on a package level are e.g. delamination,
encapsulant yellowing and cracking, tarnishing of the silver
reflector, phosphor effects, or cracks [24]. In particular, oper-
ation at higher temperatures and low wavelength radiation is
known to be associated with decreasing phosphor conversion
efficiency and degradation of polymer encapsulants [25].
This paper tackles the issue of LED degradation prediction
from a different perspective and addresses the question of
whether the actual spectral power distribution (SPD) of a
VOLUME 11, 2023 1
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
degrading LED can be estimated with sufficient spectral and
colorimetric accuracy for lighting applications from spectral
sensor responses.
The use of information captured with spectral sensors has
already been investigated for various lighting applications.
Most of the previous work found in the literature considered
RGB-like sensors for modelling and predicting trichromatic
responses and/or integral measures of lighting quality: Trinh
et al. [26] demonstrated the possibility to estimate the circa-
dian effectiveness of light sources in terms of the circadian
stimulus (CS) metric from an RGB color sensor. Agudo et
al. [27] developed a portable low-cost color-picking device
for non-self-luminous surfaces by combining an RGB color
sensor with an integrated high-power white LED. Botero el
al. [28] proposed a method to estimate the correlated color
temperature (CCT) from RGB sensor responses by using
linear regression for the transformation from RGB responses
to CIE XYZ tristimulus values together with McCamy’s
CCT approximation method [29]. Later, in order to classify
artificial light sources into illuminant categories and estimate
color temperature and color rendition measures, Botero el al.
[30] employed a k-nearest neighbor algorithm and category-
specific regression models. Breniuc et al. [31] used the raw
sensor readouts of an RGBC (RGB + clear silicon channel)
sensor to calculate illuminance and CCT values for a tunable-
white LED luminaire. Chew et al. [32] and Maiti and Roy
[33] both used data from color sensors to model human
trichromatic responses directly in the feedback loop of a
multi-luminaire lighting system. Ashibe et al. [34] developed
a lighting control scheme for a room with 15 RGB luminaires
based on color-sensor feedback that allows for the realization
of target illuminances and chromaticities at different locations
in the room.
As an advancement from simple RGB color sensors, multi-
band (i.e., with considerably more than three spectral chan-
nels) sensors emerged to fill the gap between (trichromatic)
color and spectral information, resolving the spectral energy
distribution in greater detail. Botero et al. [35] for exam-
ple developed an alternative to a spectrometer for low-cost
spectral light measurements using a multilayer perceptron
(artificial neural network) for the relative SPD reconstruction
from spectral sensor responses. Amirazar et al. [36] applied
this principle to build a device for monitoring a person’s indi-
vidual lighting exposure from an 18-channel spectral sensor,
again relying on an artificial neural network for the SPD
reconstruction. Instead of an SPD reconstruction, Botero et
al. [37] also investigated the feasability of directly estimating
certain color rendition features, such as TM 30-18 Rfand
Rgvalues or the CIE Racolor rendering index, from spectral
sensor responses.
None of the published works so far have considered to
investigate in detail to which extent a spectral sensor is able
to resolve the spectral changes occurring with the degradation
of an LED over its lifetime. Such knowledge including an
adequate proof-of-concept would open the door to the de-
velopment of sensor-based multi-channel luminaires that are
capable of internally compensating for age-related changes
in individual LED channels. As a result, these luminaires
could achieve significantly improved color, spectral, and ra-
diant flux consistency over the lifetime of the fixture for
factory-calibrated light settings, such as pre-calculated chan-
nel mixtures for various CCTs. Here, the current work can
be considered to lay the foundation for achieving this goal,
firstly, by subjecting four different LEDs to accelerated aging
operating conditions while the spectral emission is monitored
with a spectroradiometer and a spectral sensor, secondly, by
comparing the occurring radiometric, colorimetric, and spec-
tral changes in the LED spectra to the corresponding sensor
responses while analyzing potential relationships, and thirdly,
by evaluating two different methods for reconstructing the
LED spectra from the sensor responses differing in the level
of required a priori knowledge about the spectral sensitivities
of the sensor. Based on these contributions, the present work
demonstrates for the first time the potential in using spectral
sensors for monitoring LED degradation.
II. EXPERIMENTAL SETUP AND SAMPLES
A schematic overview of the experimental setup is shown
in Figure 1. The LEDs are surface mounted to individual
aluminium core printed circuit boards, which are in turn fixed
on a copper mounting plate backed by a peltier element, heat
sink and fan. The solder point temperature of the LED boards
is sensed with a PT100 resistance temperature sensor and
controlled via a THORLABS (Newton, New Jersey, United
States) ITC4020 Laser Diode / Temperature Controller. A
Keithley (Solon, Ohio, United States) 2651A High Power
System SourceMeter is used to drive the LEDs. A switching
unit consisting of multiple relays is used to connect the LEDs
with the source meter: For optical measurements the switch-
ing unit is configured to power one LED at a time, while
for the operation condition the LEDs under test are driven
in series with constant current. Optical measurements are
therefore performed iteratively with only one LED powered
in constant current mode by the SourceMeter (switching unit
configured to connect the anode and cathode of a single LED
to the SourceMeter), while for accelerated aging with con-
stant stress current, the switching unit is configured to create
a series connection of all LEDs under test with the anode
of the first LED and the cathode of the last LED connected
to the SourceMeter. Spectral measurements are performed
with an Instrument Systems (Munich, Germany) CAS 140D
spectroradiometer together with an EOP-120 optical probe.
The optical probe is facing the LED mounting plate with a
distance of 45 cm. The spectral sensor AS7343 from ams-
OSRAM AG (Premstaetten, Austria) is mounted with a lateral
offset of its optical axis of 5.5 cm to the optical axis of the
optical probe.
Since both the sensor and the optical probe approximate
a cosine-corrected and diffused angular response (the sensor
uses a diffuser foil, the optical probe uses an integrated co-
2VOLUME 11, 2023
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
FIGURE 1. Hardware setup with the temperature-stabilized LEDs being oriented towards and aligned with the spectrometer measuring probe and the
spectral sensor, all shieled by a black housing. Outside the housing are the temperature controller, the spectrometer, the power source for operating the
LEDs and a unit for controlling the circuitry (serial/single) of the LEDs for measurements.
sine corrector and diffuser in its glass body), a lateral offset
between the sensor and the optical probe could result in a
difference in the registered irradiance at the probe and at the
sensor position. However, since both SPD estimation methods
compute their estimates relative to the initial SPD and the
initial sensor response, this difference is already accounted
for in the estimation process, making the measurements from
the optical probe and the estimates computed from the sensor
responses absolutely comparable. This also applies for any
color (change) over angle effects of the LEDs. Only if the
geometry or directional emission of the LEDs were to change
during the experiment would this offset cause errors in the
estimation results. The optical components are placed in a
matte black housing to shield them from external irradiation.
Four commercially available high power LEDs (one green,
one warm white, two neutral white) are subjected to 2000 h of
accelerated aging under operating conditions of 1.1 A stress
current and a case temperature Tcof 75 °C. Additionally, a
fifth LED is acting as a reference, being measured at the same
intervals as each of the other LEDs but not being powered the
rest of the time and mounted on a separate peltier element
with Tc= 25 °C.
Table 1 gives the initial irradiance, illuminance, chromatic-
ity, CCT and Duv (distance of the light source chromaticity to
the Plankian locus), while Figure 2 depicts the initial spectral
power distributions of the different LEDs with 30mA mea-
surement current at 30 °C measurement temperature. While
data was also collected for higher measurement currents,
only the 30 mA condition is investigated in this paper, since
the effects of defect associated chip-level LED degradation
are more pronounced for lower measurement currents [22],
[38], [39]. The lowest measurement current is therefore the
most challenging condition to test the sensor based spectral
monitoring of LED degradation. The measurement cycles
are performed in a pulsed manner, where the measurement
current is only applied for the duration of the optical measure-
ment defined by the time of collecting the read-outs from both
the spectrometer and the spectral sensor. The impact of sensor
temperature was disregarded for this experiment, it is not
expected to have a significant impact due to relatively stable
conditions (mean 30.15 °C and sample standard deviation
1.64 °C, which were measured using an integrated temper-
ature sensor on the spectral sensor’s PCB. Additionally, the
sensor was operated with an internal dark current correction
utilizing covered photodiodes.
TABLE 1. Initial characteristics (irradiance, illuminance, chromaticity
coordinate, and where applicable CCT and Duv) of the examined LEDs,
measured at 30 mA operating current and 30 °C case temperature Tc. The
spectral power distributions are given in Figure 2.
LED Er/W Ev/lx u′v′CCT/K Duv
Green 0.0529 29.9 0.0801 0.5797 - -
WW 0.0587 18.4 0.2562 0.5148 2902 -0.0061
NW1 0.0574 17.2 0.2210 0.4820 4609 -0.0079
Ref 0.0346 10.9 0.2550 0.5175 2916 -0.0039
NW2 0.0234 7.0 0.2205 0.4758 4824 -0.0106
400 500 600 700 800
Wavelength in nm
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
Spectral irradiance
in W/(nm m2)
Green
WW
NW1
Ref
NW2
FIGURE 2. Spectral irradiance of the investigated LEDs for the 30mA, 30 °C
measurement condition. The photometric parameters are listed in Table 1.
III. SPD ESTIMATION FROM SPECTRAL SENSOR
RESPONSES
The electro-optical response of a multi-channel spectral sen-
sor can mathematically be described using Equation (1) [40].
The output value ckof the kth sensor channel is determined by
a non-linear function F, which depends on the sensor’s gain
factor κ, on the integration time e, and the response signal R.
The response signal Ris obtained by integrating the product of
the spectral irradiance ϕ(λ)and the channel’s spectral sensi-
VOLUME 11, 2023 3
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
tivity function rk(λ). Additionally, the term nkin Rrepresents
the contribution of additive noise to the response signal.
ck=F(κ, e,R),
R=Zϕ(λ)·rk(λ) dλ+nk.(1)
In this work, the AS7343 optical sensor from ams-OSRAM
AG (Premstaetten, Austria) with 11 spectral channels in the
visible range, an additional clear, and a near-infrared (NIR)
channel is used as the monitoring device for the LED degra-
dation. The available evaluation kit of the sensor comes with
a diffusion foil attached to the sensor’s circuit board. Fig-
ure 3 shows the relative spectral sensitivities of the optical
sensor system. These sensitivities were determined using an
MSH 300 monochromator setup (Quantum Design GmbH,
Darmstadt, Germany) with a 300 W xenon arc lamp from
370 nm to 780nm in steps of ∆λ=1 nm, with probe stimuli of
approximately 3 nm full-width at half-maximum (FWHM),
see e.g. Myland et al. [41] or Trinh et al. [26] for further
details.
The sensor features multiple analog gain levels and an
adjustable integration time. For the experiment, the gain of
512x was used together with integration times that ensured a
sensor saturation of the clear channel of at least 20 %. For the
30 mA measurement current, this implied integration times in
the range of 6 s to 25 s depending on the specific LED under
test.
400 500 600 700 800
Wavelength in nm
0.0
0.2
0.4
0.6
0.8
1.0
Rel. sensitivity
FIGURE 3. Relative sensor sensitivities of the used spectral sensor
(AS7343, ams-OSRAM AG). According to the datasheet, the maximum
sensitivities of the sensor channels are: 405 nm (actually 401 nm), 425 nm
(423 nm), 450 nm (451 nm), 475 nm (475 nm), 515nm (516 nm), 550 nm
(544 nm), 555 nm (560 nm), 600 nm (594nm), 640 nm (631nm), 690 nm
(687nm), 745 nm (746 nm). The actual sensitivities were measured on a
monochromator with 3 nm full-width at half-maximum (FWHM) and in
steps of 1 nm.
Only little preliminary work exist in the literature on
reconstructing SPDs from sensor responses and none of them
dealt with the reconstruction of spectral, age-related shifts
of LEDs. Botero et al. [35] used a multi-layer perceptron
(MLP) artificial neural network to reconstruct the SPD of
fluorescence, tungsten, and LED spectra mixtures from sim-
ulated sensor responses (10 bands distributed in the visible
spectrum) to an SPD with a wavelength resolution of 5nm.
The reconstructions are evaluated in terms of SSE R-value,
RMSE, NRMSE, CCT error, and multiple color rendition
metrics. In summary, NRMSE errors lower than 2 % are re-
ported. Amirazar et al. [36] also made use of an MLP model to
reconstruct the SPDs of different light sources from 14 sensor
responses to an SPD of 3.5 nm resolution in the wavelength
range between 410 nm and 760 nm. NRMSE errors lower than
1 % are reported on simulated sensor data, but errors in a
real world validation are considerably higher ranging from
11 up to 40 %. The authors attribute these discrepancies to
insufficient training data for the real world application [36].
In a previous work, the authors of the present paper
demonstrated the in-field applicability of spectral sensors for
spectral reconstruction in real-world lighting scenarios [42],
where, on average, spectral deviations of less than 1.6% in
terms of nRMSE, colorimetric error smaller than 0.001 ∆u′v′,
and illuminance errors below 2.7 % could be achieved.
Nonetheless, all these preliminary works assume that rep-
resentative training data for sensor-based SPD estimation are
available. In a general illumination scenario, where perfect
reconstruction of individual LED spectra is not crucial, but
rather the overall satisfactory color and spectral capture of
mixtures is of importance, this assumption is justifiable.
However, this approach appears inadequate when it comes
to accurately reconstructing subtle degradation of individual
LEDs without prior knowledge of their aging process for
training purposes.
Therefore, a different approach is under evaluation in this
work: It basically exploits all the information available in the
initial state to enable accurate reconstruction of the specific
LED SPDs during operation, but does not include any a priori
knowledge about possible degradation of the LEDs. For this
purpose, two reconstruction variants should be compared, i.e.,
the estimation via a Wiener filter, which requires knowledge
of the spectral sensor sensitivities, and a minimal knowledge
approach that works only with key parameters taken from
the sensor’s datasheet and polynomial-based interpolation be-
tween the sensor responses. Both reconstruction variants use
the knowledge of the initial SPD of each LED together with
the corresponding sensor response to estimate the spectral
changes between the initial state SPD and the SPD after a
certain number of operating hours under stress conditions.
This drastically reduces the complexity of the otherwise ill-
posed reconstruction problem of the spectral irradiance for
wavelengths between 370 nm and 780 nm from eleven sensor
responses.
A. DIFFERENCE ESTIMATION WITH WIENER FILTER
The Wiener filter [43] approach is an established method for
reconstructing spectral reflectance from RGB camera images,
when the SPD of the illumination (possibly multiple SPDs
time-multiplexed to increase the dimensionality of the cap-
tured information) and the camera channel sensitivities are
known [44]–[52]. Furthermore, the approach has been applied
extensively in the field of sensor sensitivity reconstruction
4VOLUME 11, 2023
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
from known reflectances and SPDs [53]. In general, the
Wiener filter is based on a linear sensor model as described
in Equation 2.
c=Rϕ+n.(2)
The sensor response vector cresults from the product of
the spectral irradiance ϕ=ϕ(λ)and the sensitivity matrix R
according to the sensor model from equation (1). nmodels
additive noise on the sensor responses. The estimation from
the Wiener filter is then given by
ˆ
ϕ=Wc,(3)
where the filter matrix Wis computed from the covariance
matrix of the SPD to be reconstructed Kϕϕ =⟨ϕϕT⟩, the
sensor sensitivity matrix R, and the system noise matrix
Knn =⟨nnT⟩according to
W=KϕϕRT(RKϕϕ RT+Knn)−1.(4)
Since the Wiener Filter is a linear estimator, Equation 3
can also be formulated to estimate the spectral difference
∆ˆ
ϕfrom the sensor response difference ∆c. This uses the
knowledge of the initial SPD ϕinit so that only the (compared
to the full spectral power distribution) much smaller spectral
differences have to be estimated from the sensor response, as
shown in Equation 5.
∆c=c−cinit,(5)
∆ˆ
ϕ=W∆c,(6)
ˆ
ϕ=ϕinit + ∆ ˆ
ϕ.(7)
Assuming statistical independence of the noise in the chan-
nels of the spectral sensor, Knn can be constructed as a
diagonal matrix with the variance of the sensor responses on
the diagonal. The covariance matrix Kϕϕ is often calculated
from a dataset - in case of the reflectance estimation task
a dataset of spectral reflectances [45], [49], [52], [54]. The
reconstruction quality depends on how well the spectral quan-
tity to be reconstructed can be described by the covariance of
the data set, therefore, methods were proposed to weight or
select the database entries before reconstruction [55]–[60].
Since it is unclear how a data set for a reconstruction of the
spectral degradation of an LED should be compiled without
already knowing the spectral degradation progression, a more
general approach to the construction of the matrix Kϕϕ is
investigated in this paper. This makes use of a matrix with
Toeplitz structure according to equation (8) [47], [51], [61],
[62].
Kϕϕ =
1ρ ρ2· · · ρn−1
ρ1ρ· · · ρn−2
ρ2ρ1.
.
.
.
.
..
.
....ρ
ρN−1ρN−2· · · ρ1
.(8)
The parameter ρof the Toeplitz matrix can be understood to
set the expected correlation between the interpolation points
in the spectral distribution. Its optimum value depends on the
wavelength resolution and the smoothness of the curves to
be reconstructed [53]. In order to incorporate the knowledge
about the initial SPD’s covariance into the Wiener filter esti-
mation, the matrix Kϕϕ can be transformed by multiplication
of the initial SPD from the left and right as given by Equa-
tion (9). This approach equates to weighting the covariance
of different wavelengths with their respective power in the
initial SPD.
Kϕϕ,init =ϕinitKϕϕ ϕT
init (9)
In the literature regarding the reflectance estimation with
a Toeplitz-structured estimation matrix, ρis chosen without
further explanation to be 0.97 in two separate studies [47],
[51]. For the reconstruction of the spectral sensitivity of a
camera, on the other hand, ρis chosen to be 0.99 [53], which is
justified by the smoothness of the expected sensitivity curves
of the monochrome sensor and the transmission curves of
the filters and by the high wavelength sampling rate of 1 nm
steps. In a pre-simulation of the Wiener filter approach for
the reconstruction of spectral shifts using spectra composed
of up to two Gaussian functions (roughly simulating "white"
and monochromatic LEDs), practical values for ρin the range
of 0.79 to 0.91 could be determined (slightly depending on the
LED type to be reconstructed). Since LED spectra in general
show sharper peaks and, thus, are less smooth than camera
spectral sensitivities, such a reduction in optimal ρvalues
compared to reflectance or sensitivity estimation could be
expected. Hence, for this study, ρ= 0.85 was used for further
computations.
The variances of the sensor response on the diagonal of
Knn are dominated by photon noise in regular operating
conditions of the sensor and, thus, depend on the signal level
of each channel [50]. The photon transfer curve (i.e., the
variance of the sensor response as a function of the mean
sensor response when considering a stable light source) was
determined in a separate measurement setup for the given
sensor and then used to compute the entries of Knn based
on the sensor response input to the Wiener filter.
B. DIFFERENCE ESTIMATION WITH SENSOR RESPONSE
INTERPOLATION
The aforementioned Wiener filter approach requires knowl-
edge of the spectral sensitivities of the sensor, which can only
be accurately determined through elaborated procedures us-
ing expensive measurement techniques [41]. Although there
are methods in the literature, as mentioned earlier, to estimate
the sensitivities of a sensor from more practical setups, it
requires to carefully consider how the errors in this sensitivity
estimations would affect the reconstruction quality. There-
fore, as an alternative method to the Wiener filter, an approach
is being investigated that relies solely on basic information
about the sensor itself, i.e., the typical peak wavelengths of the
individual sensor channels obtained from the manufacturer’s
VOLUME 11, 2023 5
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
datasheet. This is, of course, an imprecise piece of informa-
tion. However, it is worth noting that the sensor channels
already have a certain spectral width that is larger than the
specified ranges of variation for the peak wavelengths. Thus,
using the information from the datasheet, a rough estimation
of the incident energy in specific wavelength ranges can be
made from the sensor channels. Between these data points
comprising the datasheet peak wavelengths of the channels
and the output sensor values, a very rough estimation of the
incident power distribution can be obtained by interpolation.
However, this would result in an inaccurate estimate of the
SPD which is rather inadequate for further use in colori-
metric applications. A potential solution is to consider the
interpolated sensor responses relative to the initial state of the
SPD and the corresponding sensor responses. The spectral
changes can be determined as multiplicative factors relative
to the initial state by calculating the ratio between the initial
interpolated sensor response and any subsequent interpolated
sensor response as observed during the aging process. This
spectral quotient curve can then be applied to the initial SPD
to get an estimate of the SPD at a later time under stress
conditions. Even though this approach does not allow for
resolving narrowband changes in the power distribution, it
still provides a very intuitive method for capturing light output
degradation, which is capable of describing at least power
redistributions from one broader wavelength range to another,
e.g., when examining the excitation peak in relation to the
phosphor emission of phosphor-converted LEDs.
Mathematically, the approach can be summarized in a
few steps, as given by Algorithm 1. Firstly, interpolation
is performed between the eleven sensor responses cτat a
given time τto match the wavelengths of the spectrometer
measurements. Subsequently, the quotient tτ(λ)is calculated
between this interpolation ˜
cτ(λ)and the sensor response
interpolation of the initial state ˜
c0(λ)for each wavelength.
Finally, the initial spectrum ϕ0(λ)is multiplied with this spec-
tral "transmission" quotient to obtain the estimated spectral
power distribution ˆ
ϕτ(λ).
Algorithm 1 Estimation of Spectral Power Distribution
1: ˜
cτ(λ)←Interpolate cτto match wavelengths of ϕ0(λ),
with the peak channel sensitivity wavelength λkas the
assumed wavelength of each channel response ck
2: tτ(λ)←˜
cτ(λ)
˜
c0(λ)
3: ˆ
ϕτ(λ)←ϕ0(λ)·tτ(λ)
A plethora of interpolation methods could be employed in
step 1 of the algorithm. The classical Sprague interpolation
method (according to the CIE recommendation for interpo-
lating spectral data [63]) is not suitable in this case because
it assumes that the independent variable is equally spaced.
The Sprague interpolation is based on a spline interpolation
using 5th-degree polynomials, where the gradients and curva-
ture are constrained to match the neighboring points. Among
the various other spline interpolation methods available, the
piecewise cubic hermite interpolating polynomial (PCHIP)
[64] appears advantageous. It preserves monotonicity, ensur-
ing that no new maxima or minima are created during the
interpolation process besides the known data points. Figure 4
shows the described procedure on example data. As can
be seen in the caption of Figure 3 the sensor used in this
work shows some deviations from the typical channel peak
wavelengths given in the datasheet. The effects of the as-
sumed wavelengths and the applied interpolation method are
analyzed in the discussion section, showing that the PCHIP
interprolation with assumption of the datasheet peak wave-
lengths is an adequate approach for a minimal knowledge
spectral reconstruction. The investigation of this approach
aims at determining the quality achievable in the spectral
reconstruction of LED degradation without specific sensor
characterization.
IV. RESULTS
First, the ageing of the LEDs themselves and the associated
sensor responses in the raw state are considered. In partic-
ular, the question arises as to whether the sensor is at all
capable of detecting changes in spectral emission with its
significantly reduced wavelength resolution. Figure 5 shows
how the photometric quantities irradiance, illuminance, chro-
maticity, and RMSE of the normalized spectra (nRMSE) have
changed over 2000h of operation under stress conditions for
the individual LEDs. In terms of irradiance and illuminance,
the curves are very similar. The green and NW2 LEDs show
the strongest degradation of up to 25 % and 10 %, respec-
tively. The other two LEDs under stress conditions, on the
other hand, degraded only in the lower single-digit percentage
range. Regarding the observed color and spectral deviations,
calculated by the distance ∆u′v′to the start condition in
the CIE 1976 UCS and the RMSE between normalized start
condition and relative SPDs at later times, there are again
similarities in terms of curvature shapes. While the reference
LED, as expected, has not undergone any visible changes, the
green LED and the warm white LED show slight color and
spectral shifts below ∆u′v′= 0.0015 and nRMSE= 0.006.
The NW1 LED exhibits a steep spectral change within the
first 100 h of operating time, which is then continuing with
a slower pace and reaches ∆u′v′= 0.0083 and nRMSE=
0.037 at 2000 h. The NW2 LED shows a steep increase in
the first hours, followed by decreasing color and spectral
deviations compared to the initial state, while rising steeply
again towards the end of the test reaching a high level of
∆u′v′= 0.0108 and nRMSE= 0.048 at 2000 h. This can
be explained by crack forming in the phosphor layer applied
to the LED chip.
The recorded relationship between these spectral changes
and the sensor responses of the spectral sensor is visualized in
the next three figures. For the sake of clarity, only the LEDs
with the greatest ageing are depicted: Green, NW1, and NW2.
For the green LED, in addition to the differences in spectra
and the differences in sensor responses as compared to its
initial state, the relative changes given by the actual state
6VOLUME 11, 2023
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
400 450 500 550 600 650 700 750
0.000
0.005
0.010
Sensor Response
in DN/ s
Sensor Response
Initial
2000h
400 450 500 550 600 650 700 750
0.0000
0.0005
0.0010
0.0015
Spectral irradiance
in W/(nm m2)
Initial Spectral Power Distribution
Initial
2000h
400 450 500 550 600 650 700 750
0.000
0.005
0.010
Sensor Response
in DN/ s
Interpolation
Initial
2000h
400 450 500 550 600 650 700 750
Wavelength in nm
1.00
1.05
Spectral quotient
Quotient from initial to sensor response at t=2000 h
400 450 500 550 600 650 700 750
Wavelength in nm
0.0000
0.0005
0.0010
0.0015
Spectral irradiance
in W/(nm m2)
Applied quotient for SPD estimation
estimated 2000h
2000h
FIGURE 4. Computation steps for the estimation of spectral power distributions from interpolated spectral sensor responses. The interpolation is
performed between the sensor responses at a given time. Next, the spectral quotient between this interpolation and the sensor response interpolation of
the initial state is computed for each wavelength. Finally, the initial spectrum is multiplied with this spectral quotient to obtain the estimated spectral
power distribution.
divided by the initial state are also shown in Figure 6. As
could be seen in Figure 5, ageing mainly affects this LED
in the form of a decrease in radiant flux. When comparing
the differences in spectra to the differences in sensor values,
it is clear that this decrease is also detected by the sensor.
The relative observation of the spectral changes then shows
a minimal shift of the spectral emission towards longer
wavelengths, which can also be recognized in the sensor
responses. However, it already becomes clear here that the
correct interpretation of the sensor data alone (without the
knowledge of the causing spectrum) is not trivial. Although
the relative changes in the spectra roughly match the relative
changes in the sensor responses in terms of their shape, the
wavelength range apparently affected by the sensor seems
much larger than the SPD changes actually are. This is mainly
due to the width of (some) sensor channels (see Figure 3).
Nevertheless, the detectable, apparent correlations between
measured SPDs and observed sensor responses suggest great
potential for spectrally reconstructing the degradation dynam-
ics of the green LED.
For the NW1 LED the ratio changes between the light com-
ponent of the blue excitation chip and the orange component
re-emitted by the phosphor over 2000h of operation. As can
be seen from Figure 7, the blue peak of the SPD actually in-
creases with increasing operating time, while the emission of
the phosphor in the longer wavelength range decreases. This
behavior is also captured by the spectral sensor, which again
suggests that the spectral ageing process can successfully be
reconstructed from the sensor data.
The NW2 LED shows the biggest spectral variations. Es-
sentially, the curves can be divided into two phases: First,
the blue part of the spectrum decreases in relation to the
phosphor-converted part, until blue light isincreasingly emit-
ted directly from the chip of the LED due to crack formation
in the phosphor. This is accompanied by a decrease of the
phosphor emission, so that after 2000 h more blue and, at
the same time, less yellow light than in the initial state make
up the total emission. These two ageing phases can also be
recognized in the differences of the sensor responses with
respect to the start condition. However, the crack-related
elevation of the blue peak in the second phase of ageing as
detected by the spectrometer is not reflected in the sensor
data. This can be explained by the fact that the strong spectral
change of the emission due to the crack in the phosphor may
also be accompanied by a change in the spatial radiation
characteristics. During a test run of the final state of the LED,
a clear directional dependence of the light color of the emis-
sion could be observed. It is therefore reasonable to assume
that the observed discrepancy in the detection of the spectral
change between the spectrometer and the sensor is partly due
to the spatial distance (5.5 cm, see section II) between the
receiver surface of the spectrometer head and the sensor, as
the sensor was quite capable of detecting such changes in
the blue peak for the NW1 LED. In addition, the changes
of the peak at NW2 concern an even narrower wavelength
range and are surrounded on both sides by negative spec-
tral differences, which additionally complicates the correct
VOLUME 11, 2023 7
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
25
20
15
10
5
0
rel.
Er
in %
25
20
15
10
5
0
rel.
Ev
in %
0.000
0.002
0.004
0.006
0.008
0.010
u'v'
0 250 500 750 1000 1250 1500 1750 2000
Stress time in h
0.00
0.01
0.02
0.03
0.04
0.05
nRMSE
LEDType
Green WW NW1 Ref NW2
FIGURE 5. Overview over radiometric, photometric, color difference and
nRMSE development between the initial measurement at the start of the
experiment and later times. The green and NW2 LEDs show the strongest
radiometric degradation with up to 25 % and 10 % respectively. The
reference LED has not undergone any visible changes, the green LED and
the warm white LED show slight, the NW1 LED big color and spectral
shifts. The NW2 LED shows a very dynamic curve of color and spectral
deviations.
resolving with regard to the already mentioned width of the
sensor channels. The NW2 LED therefore is a challenging
case for the spectral reconstruction approaches presented in
this work, since a very drastic change in the SPD occurred
during the experiment. At the same time, most of the spectral
degradation is actually captured in the sensor data suggesting
that, even in this case, much of the spectral ageing process
can be successfully reconstructed from the sensor responses.
After presenting the raw data of the ageing experiment,
the following subsections are dedicated to the analysis of the
spectral differences reconstructed from the sensor data with
the different methods and their errors.
400 450 500 550 600 650 700 750
0.0000
0.0005
0.0010
Spectral irradiance
in W/(nm m2)
Spectral power distribution
400 450 500 550 600 650 700 750
0.000
0.002
0.004
Sensor response
in DN/ s
Sensor response
400 450 500 550 600 650 700 750
0.0003
0.0002
0.0001
0.0000
Spectral irradiance
in W/(nm m2)
Difference to initial SPD
400 450 500 550 600 650 700 750
0.0010
0.0005
0.0000
Sensor response
in DN/ s
Difference to initial sensor response
400 450 500 550 600 650 700 750
0.02
0.00
0.02
Rel. SPD
Difference to initial SPD (normed)
400 450 500 550 600 650 700 750
Wavelength in nm
0.02
0.00
Rel. sensor response
Difference to initial sensor response (normed)
LED under test: Green
FIGURE 6. Spectral power distributions and corresponding sensor
responses for the green LED over the course of the 2000 h stress
operation. Also visualized are the differences in spectra and the
differences in the sensor responses compared to the initial LED emission
at 0 h. A correlation with potential for reconstruction is evident between
the sensor responses and the observed spectral behavior.
A. ESTIMATES OF SPECTRAL DIFFERENCES: GREEN LE D
For the green LED, the upper left graph of Figure 9 shows the
deviations from the initial spectrum as calculated from the
spectrometer measurements. The following graphs in the left
column illustrate the reconstruction results using the Wiener
filter with a simple Toeplitz matrix Kϕϕ, the Wiener filter
with the covariance matrix adjusted via Equation 9), and
the PCHIP interpolation approach, which operates without a
8VOLUME 11, 2023
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
400 450 500 550 600 650 700 750
0.00000
0.00025
0.00050
Spectral irradiance
in W/(nm m2)
Spectral power distribution
400 450 500 550 600 650 700 750
0.000
0.002
Sensor response
in DN/ s
Sensor response
400 450 500 550 600 650 700 750
0.0
2.5
5.0
Spectral irradiance
in W/(nm m2)
1e 5 Difference to initial SPD
400 450 500 550 600 650 700 750
Wavelength in nm
0.0001
0.0000
0.0001
Sensor response
in DN/ s
Difference to initial sensor response
LED under test: NW1
FIGURE 7. Spectral power distributions and corresponding sensor
responses for the NW1 LED over the course of the 2000 h stress
operation. Also visualized are the differences in spectra and the
differences in the sensor responses compared to the initial LED emission
at 0 h. A correlation with potential for reconstruction is evident between
the sensor responses and the observed spectral behavior.
measurement of the spectral sensitivities of the sensor. It can
be seen directly that the generic Wiener filter approach (which
knows the spectral sensitivities of the sensor, but apart from
the covariance matrix with Toeplitz structure and ρ= 0.85
nothing about the difference spectra to be reconstructed)
can only estimate the spectral shape of the differences very
roughly. Both, the width of the affected area and the position
of the actual maximum are reconstructed with considerable
errors, as shown in the corresponding residual error graphs
depicted in the right column of Figure 9. In contrast, the
reconstruction results from both the Wiener filter adjusted
to the start spectrum and the PCHIP interpolation are much
closer to the ground truth of the true difference spectra. How-
ever, neither method can fully track the minimal sideways
motion of the emission maximum. This limitation can also
be found in the relative ratios of the sensor responses (see
Figure 6). The most distinct component of the ageing process
of the green LED in the form of a decrease in optical power
is estimated from the sensor data with little observable error.
The overall performances of the various spectral recon-
struction approaches discussed above are visualized in Fig-
400 450 500 550 600 650 700 750
0.0000
0.0001
0.0002
Spectral irradiance
in W/(nm m2)
Spectral power distribution
400 450 500 550 600 650 700 750
0.000
0.001
Sensor response
in DN/ s
Sensor response
400 450 500 550 600 650 700 750
1
0
1
Spectral irradiance
in W/(nm m2)
1e 5 Difference to initial SPD
400 450 500 550 600 650 700 750
Wavelength in nm
0.0001
0.0000
Sensor response
in DN/ s
Difference to initial sensor response
LED under test: NW2
FIGURE 8. Spectral power distributions and corresponding sensor
responses for the NW2 LED over the course of the 2000 h stress
operation. Also visualized are the differences in spectra and the
differences in the sensor responses compared to the initial LED emission
at 0 h. Two ageing phases can be identified from the differences in the
sensor responses and spectra compared to the initial LED state. However,
the elevation of the blue peak in the second phase of ageing as detected
by the spectrometer is not reflected in the sensor data.
ure 10 using suitable error metrics. In addition, the error
evolution between the initial SPD and the degraded SPDs is
given for reference. This basically reflects the current state of
most commercial luminaires where no ageing compensation
from sensor feedback or predetermined by the manufacturer
is used. With a similar behavior being observed for radiomet-
ric vs. photometric degradation and colorimetric vs. spectral
degradation, as shown by Figure 5, the following analysis
focuses on irradiance and colorimetric errors only. With re-
gard to the irradiance calculated from the reconstructions, the
distance to the initial state (shown in red) increases with time,
where after the 2000 h of stress condition the optical power
of the green LED actually decreased by approx. 31 %. With
the generic Wiener filter, an underestimation of the optical
power of up to 19% (shown in blue) is observed. In contrast,
the irradiance error for the adjusted Wiener filter (shown in
orange) and the PCHIP interpolation (shown in green) are
much closer to zero. The maximum estimation error in |∆Er|
of the adjusted Wiener filter is 0.6%, while for the PCHIP
interpolation a maximum error of 0.73 % is observed.
VOLUME 11, 2023 9
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
400 500 600 700
0.0002
0.0000
W/(nm m2)
Difference to initial SPD
400 500 600 700
0.0002
0.0000
W/(nm m2)
Wiener estimated difference (Toeplitz
K
)
400 500 600 700
0.0001
0.0000
Spectral errors
400 500 600 700
0.0002
0.0000
W/(nm m2)
Wiener estimated difference (custom
K
)
400 500 600 700
0.0001
0.0000
400 500 600 700
Wavelength in nm
0.0002
0.0000
W/(nm m2)
PCHIP estimated difference
400 500 600 700
Wavelength in nm
0.0001
0.0000
LED under test: Green
FIGURE 9. Differences to the initial spectrum for the green LED shown
together with the spectral reconstruction results for the different
reconstruction methods in the left column. The right column shows the
spectral errors of the reconstructions compared to the spectrometer
measurements at each time. While the generic Wiener Filter with the
synthetic Toeplitz covariance matrix can only give a rough estimate of the
spectral shapes, the spectral errors of the PCHIP approach and the
customized Wiener filter are small.
The green LED undergoes only minimal color changes
during this ageing experiment so that a maximum error of
0.0012∆u′v′is made when neglecting the LED degradation.
The generic Wiener filter continuously estimates the actual
spectrum of the green LED with a larger colorimetric error
of 0.0023∆u′v′at its maximum. The colorimetric error of
the adjusted Wiener filter reconstruction, on the other hand,
is slightly smaller compared to neglecting the degradation.
Here, a maximum of 0.001∆u′v′is observed. Finally, the
PCHIP interpolation achieves the best reconstruction result
in terms of residual colorimetric errors showing a maximum
of only 0.0006∆u′v′.
For the intuitive analysis of ageing processes, a represen-
tation of the color coordinates over time as illustrated in
Figure 11 is useful [65]. The color coordinates are depicted in
CIE 1976 u′v′color space, where the results of the different
reconstruction methods, demarcated by color and marker
type, are compared to the spectrometer measurements. The
time component is visualized by an increasing marker size
representing increasing test time. In addition, a scale marker
20
0
20
rel.
Er
in %
0 250 500 750 1000 1250 1500 1750 2000
Stress time in h
0.0000
0.0005
0.0010
0.0015
0.0020
u'v'
LED under test: Green
method
Wiener (Toeplitz
K
)
Wiener (custom
K
)
PCHIP
neglect degrad.
FIGURE 10. Evaluation of the different spectral reconstruction methods
compared to neglecting the degradation over the course of the
experiment for the green LED. The radiometric error for the adjusted
Wiener filter (shown in orange) and the PCHIP interpolation (shown in
green) are close to zero at all times. The PCHIP interpolation achieves the
best reconstruction result with respect to color deviations.
is inserted in the lower left corner with its edge lengths mea-
suring exactly 0.001∆u′v′to ensure an easy visual assessment
of the color distances in the diagram.
As expected from the analysis of the spectral data, the color
coordinates of the green LED move roughly on a straight line
due to the slight shift of the peak wavelength in the course of
the ageing experiment. All reconstruction methods correctly
estimate the direction of the color changes, but extend towards
this direction to different degrees. While the PCHIP approach
does not fully track the color shift, the Wiener filters overes-
timate the shift by indicating higher u′values. Looking at
the distance ratios between the starting color coordinates, the
final color coordinates, and the estimated color coordinates of
all reconstruction methods raises the question of whether an
increasingly larger estimation error would be expected with
an increasing shift of the LED over time for times beyond
2000 h, where a divergence of the estimates occurs. This
question should be investigated as part of future work and
can be probed using e.g. a reconstruction experiment looking
into current-induced shifts of several nm for a monochromatic
LED.
B. ESTIMATES OF SPECTRAL DIFFERENCES: NW1 LED
For the NW1 LED, the spectral reconstruction results and
estimation errors are given in Figure 12. The generic Wiener
10 VOLUME 11, 2023
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
0.0800 0.0808 0.0816 0.0824 0.0832
u'
0.5784
0.5792
0.5800
0.5808
v'
0.001
hour
0
400
800
1200
1600
2000
method
Wiener (Toeplitz
K
)
Wiener (custom
K
)
PCHIP
neglect degrad.
spectrometer
LED under test: Green
FIGURE 11. The color coordinates of the green LED over the course of the
ageing experiment. The slight shift of the peak wavelength visible in
Figure 6 causes a move of the color coordinates roughly along a straight
line towards the direction of orange. All reconstruction methods correctly
estimate the direction of the color change. However, the PCHIP approach
does not fully track the color shift, whereas the Wiener filters
overestimate the shift by indicating higher u′values.
filter again provides only a very inaccurate estimate of the
spectral differences, with significant over- and underestima-
tions especially with regard to the width of the blue peak
and its changes. The adjusted Wiener filter shows very small
spectral errors in its estimation of the difference spectra,
but the largest deviations occur around the maximum of the
blue peak. Apart from the blue spectral region, the PCHIP
interpolation offers a comparably good reconstruction of
the difference spectra, however, the sensor data representing
the behavior of the blue peak are interpreted less accurate
compared to the adjusted Wiener filter.
The evaluation of the error metrics for the spectral re-
construction of the ageing of the NW1 LED is visualized
in Figure 13. From the error curves resulting from simply
neglecting the degradation it can be seen (similar to Figure 5)
that the optical power initially increases slightly and only in
the middle progression of the ageing experiment a decrease
of the optical power occurs.
By neglecting the degradation, maximum relative irradi-
ance errors of 1.65 % are made. Note that the curve shape
suggests a further degradation and, thus, increasing errors by
neglecting the degradation of the LED for operating times
beyond the 2000 h. The reconstruction results obtained by
400 500 600 700
0.0
2.5
5.0
W/(nm m2)
1e 5
Difference to initial SPD
400 500 600 700
0.0
2.5
5.0
W/(nm m2)
1e 5
Wiener estimated difference (Toeplitz
K
)
400 500 600 700
0
2
1e 5 Spectral errors
400 500 600 700
0.0
2.5
5.0
W/(nm m2)
1e 5
Wiener estimated difference (custom
K
)
400 500 600 700
0
2
1e 5
400 500 600 700
Wavelength in nm
0.0
2.5
5.0
W/(nm m2)
1e 5
PCHIP estimated difference
400 500 600 700
Wavelength in nm
0
2
1e 5
LED under test: NW1
FIGURE 12. Differences to the initial spectrum for the NW1 LED shown
together with the spectral reconstruction results for the different
reconstruction methods in the left column. The right column shows the
spectral errors of the reconstructions compared to the spectrometer
measurements at each time. While the generic Wiener Filter with the
synthetic Toeplitz covariance matrix only achieves a rough estimate of the
spectral shapes, the spectral errors of both the PCHIP and the customized
Wiener filter approach are much smaller and mainly located around the
blue peak, where the latter exhibits the least overall spectral errors.
using the generic Wiener filter suffers from an overestimation
of the optical power in terms of irradiance by a maximum
of 1.27 % over large parts of the ageing experiment. Both
the adjusted Wiener filter and the PCHIP interpolation yield
considerably better reconstruction results with a maximum
deviation in relative Ervalues of 0.55 % for the adjusted
Wiener filter and a slightly smaller maximum deviation of
0.4 % for the PCHIP approach. The corresponding relative Er
error curves exhibit a similar behavior and virtually lie on top
of each other. Thus, the reconstruction estimates obtained for
both the adapted Wiener filter and the PCHIP interpolation
approach show much smaller errors than those of neglecting
the degradation.
Concerning the colorimetric errors, the latter in comparison
to the various sensor-based approaches also yields signifi-
cantly larger deviations of up to ∆u′v′= 0.0083. Here,
even the generic Wiener filter is capable of providing smaller
colorimetric errors with a maximum ∆u′v′= 0.046. The
error curves for the reconstruction via PCHIP interpolation
VOLUME 11, 2023 11
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
1
0
1
rel.
Er
in %
0 250 500 750 1000 1250 1500 1750 2000
Stress time in h
0.000
0.002
0.004
0.006
0.008
u'v'
LED under test: NW1
method
Wiener (Toeplitz
K
)
Wiener (custom
K
)
PCHIP
neglect degrad.
FIGURE 13. Evaluation of the different spectral reconstruction methods
compared to neglecting the degradation for the NW1 LED. The irradiance
error for the adjusted Wiener filter and the PCHIP interpolation are
between 0 and 1 % for all times. The adjusted Wiener filter achieves a
spectral reconstruction result with almost no colorimetric errors
compared to a spectroradiometer measurement. The observed
phenomenon of an increase in irradiance compared to the initial state
during the first 1750 h of the experiment is possibly related to the
activation of Mg acceptors in the p-region of the diode [39].
are even lower, here maximum colorimetric errors of ∆u′v′=
0.0017 are achieved. By far the lowest colorimetric and spec-
tral errors are observed for the adapted Wiener filter approach,
where a maximum deviation of only ∆u′v′= 0.0004 can be
reported.
Again, the color shifts of the NW1 LED follow an ap-
proximately straight line oriented towards the blue part of the
color space. As can be seen from Figure 14, all reconstruction
methods correctly predict this shift direction. However, the
generic Wiener filter overestimates the color coordinates of
the LED as being further shifted towards blue than they
actually are. The PCHIP reconstruction, on the other hand,
again remains a little bit too conservative in its shift estimates,
whereas the adjusted Wiener filter follows the course of the
spectrometer measurements very closely with an average
∆u′v′<< 0.001.
C. ESTIMATES OF SPECTRAL DIFFERENCES: NW2 LED
For the NW2 LED, it can be seen from Figure 15 that,
as expected, all methods have difficulties in capturing the
dynamics of the blue peak in the difference spectra. In ad-
dition, the generic Wiener filter also exhibits difficulties in
correctly reconstructing the spectral changes of the phosphor-
converted light component from the sensor data. Again, the
0.213 0.216 0.219 0.222 0.225
u'
0.471
0.474
0.477
0.480
v'
0.001
hour
0
400
800
1200
1600
2000
method
Wiener (Toeplitz
K
)
Wiener (custom
K
)
PCHIP
neglect degrad.
spectrometer
LED under test: NW1
FIGURE 14. The color coordinates of the NW1 LED as a function of time
over the course of the ageing experiment. The changing ratio between the
blue chip emission and the phosphor fluorescence moves the color
coordinates towards the direction of blue. All reconstruction methods
correctly estimate the direction of the color change. While the PCHIP
approach slightly underestimates the color shift, the adjusted Wiener
filter tracks it accurately.
main difference between the adapted Wiener filter and the
PCHIP interpolation is in the area of the blue peak. As a
result, larger over- and underestimations can be observed for
the PCHIP approach when compared to the adjusted Wiener
filter.
The erratic nature of the degradation of the NW2 LED
is also reflected in the error curves of the different recon-
struction methods shown in Figure 16. When considering
the Ererrors, neglecting the degradation first leads to an
underestimation and later, from about hour 250 onwards, to
an overestimation of the irradiance with an error of 11.41%.
Again, the generic Wiener filter is unsuitable for determining
irradiance with appreciably smaller errors than neglecting the
degradation. Here, the reconstruction results of the adjusted
Wiener filter and PCHIP interpolation likewise show a tran-
sition between the low error start of the experiment and a
fairly constant error towards the end of approx. 2 %, where the
transition between the two phases can probably be attributed
to the cracking of the phosphor.
With regard to the color errors, high variability can be
observed. In the initial phase (up to about 250 h), the errors
of the reconstruction methods behave in a similar manner
as for LED NW1. At this point, the first serious damage to
the phosphor appears to set in. Colorwise, the emission of
12 VOLUME 11, 2023
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
400 500 600 700
2
0
W/(nm m2)
1e 5
Difference to initial SPD
400 500 600 700
2
0
W/(nm m2)
1e 5
Wiener estimated difference (Toeplitz
K
)
400 500 600 700
2
0
1e 5 Spectral errors
400 500 600 700
2
0
W/(nm m2)
1e 5
Wiener estimated difference (custom
K
)
400 500 600 700
2
0
1e 5
400 500 600 700
Wavelength in nm
2
0
W/(nm m2)
1e 5
PCHIP estimated difference
400 500 600 700
Wavelength in nm
2
0
1e 5
LED under test: NW2
FIGURE 15. Differences to the initial spectrum for the NW2 LED shown
together with the spectral reconstruction results for the different
reconstruction methods in the left column. The right column shows the
spectral errors of the reconstructions compared to the spectrometer
measurements at each time. None of the reconstruction methods are
capable of delivering an estimate of the later SPDs without notable
spectral errors. While the errors of the PCHIP and adjusted Wiener filter
approach are mainly around the blue peak of the LED emission due to
underestimation, the generic Wiener filter shows spectral errors
distributed over the whole wavelength range of emission.
the NW2 LED then consolidates towards the initial state (up
to approx. hour 600) and, finally, drifts away with contin-
uously increasing errors. The maximum deviations between
the initial and final state amount to ∆u′v′= 0.0108. PCHIP
reconstruction and adjusted Wiener filter show a quite similar
behavior, where the adjusted Wiener filter reconstructs with
smaller errors. In the final state, the color difference between
reconstruction and spectrometer measurement is ∆u′v′=
0.0062 and ∆u′v′= 0.0049 for the PCHIP interpolation and
the adjusted Wiener filter, respectively.
Even though the generic Wiener filter reconstructs the
SPDs of the NW2 LED with the largest errors of all recon-
struction methods for the first 250 h, the situation reverses
for longer operation and the generic filter achieves very good
error metrics at 2000 h. The largest spectral changes were
observed with the NW2 LED, which are also reflected in the
largest color shifts among the test LEDs as seen from Fig-
ure 17. The color coordinates obtained from the spectrometer
5
0
5
10
rel.
Er
in %
0 250 500 750 1000 1250 1500 1750 2000
Stress time in h
0.0000
0.0025
0.0050
0.0075
0.0100
u'v'
LED under test: NW2
method
Wiener (Toeplitz
K
)
Wiener (custom
K
)
PCHIP
neglect degrad.
FIGURE 16. Evaluation of the different spectral reconstruction methods
compared to neglecting the degradation for the NW2 LED. The radiometric
error of the adjusted Wiener filter and the PCHIP interpolation are
between 0 and 2 % for all times. In general, the adjusted Wiener filter and
the PCHIP approach achieve a spectral reconstruction result with at least
half the colorimetric error compared to neglecting the degradation, but
the asymptotic color distance is greater than the human perception
threshold of 3 standard deviation of color matching (SDCM) often applied
in LED binning (corresponding to a distance of about 0.003 in u′v′). The
generic Wiener filter appears to outperform the other reconstruction
approaches in terms of color estimation error for the later times.
measurements initially run towards the direction of yellow be-
fore taking an almost 180°turn leading to a steady movement
towards the direction of blue until the end of the experiment
while almost intersecting with the starting color coordinates.
This course fits the observed splitting of the phosphor. As al-
ready analyzed spectrally and ranked accordingly,the generic
Wiener filter delivers the smallest color distances for the later
ageing phase, while the other reconstruction methods perform
better before the observed U-turn in color coordinates.
D. ESTIMATES OF SPECTRAL DIFFERENCES: REFERE NCE
LED
The reference LED shows no noticeable color shifts
(∆u′v′<< 0.001) over the 2000h of experiment, as can
be observed from Figure 18. The PCHIP results are very
narrowly scattered around the spectrometer measurements.
The adjusted Wiener filter shows minimal deviations from
the LED chromaticity coordinates, while the generic Wiener
filter shows ∆u′v′errors of about 0.001.
E. ESTIMATES OF SPECTRAL DIFFERENCES: WW LED
The WW LED follows a right-hand curve in the u′v′color
space, see Figure 19, by first drifting towards blue and then
VOLUME 11, 2023 13
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
0.215 0.220 0.225 0.230
u'
0.465
0.470
0.475
0.480
0.485
v'
0.001
hour
0
400
800
1200
1600
2000
method
Wiener (Toeplitz
K
)
Wiener (custom
K
)
PCHIP
neglect degrad.
spectrometer
LED under test: NW2
FIGURE 17. The color coordinates of the NW2 LED over the course of the
ageing experiment. The changing ratio between chip and phosphor as
well as a crack in the phosphor cause a dynamic movement of the color
coordinates. The color locations initially run towards the direction of
yellow, then take a sharp U-turn to move towards direction of blue. While
the other reconstruction methods perform better before this U-turn, the
generic Wiener filter delivers the closest color estimates to ground truth
for the later ageing phase.
turning towards yellow. All applied methods are capable of
reconstructing this course, where, however, an increasing
distance of the PCHIP estimates from the true chromaticity
coordinates as well as from the chromaticity coordinates of
the Wiener filter estimates can be observed.
F. RESULT OVERVIEW
The numerical results for all examined LEDs are presented
in Table 2. As expected, only smallest changes, which can
be interpreted as measurement uncertainties of the spectrom-
eter, occur with the reference LED. Maximal deviations in
Erof 0.38 % and a maximum ∆u′v′= 0.000132 can be
reported. The reconstructions of the reference LED sensor
data provide almost identical results with the generic Wiener
filter showing the largest errors (∆u′v′= 0.0011). The
WW LED also exhibits only small ageing effects, where the
maximum deviations from the initial state are 2.18 % for Er
and ∆u′v′= 0.0013 in color coordinates. Nonetheless, all
reconstruction methods provide considerably more accurate
reconstruction estimates than assuming the initial state to be
constant (neglecting degradation). Here, a similar pattern as
already observed for the other LEDs can be noticed: The
0.2536 0.2544 0.2552 0.2560 0.2568
u'
0.5160
0.5168
0.5176
0.5184
v'
0.001
hour
0
400
800
1200
1600
2000
method
Wiener (Toeplitz
K
)
Wiener (custom
K
)
PCHIP
neglect degrad.
spectrometer
LED under test: Ref
FIGURE 18. The color coordinates of the reference LED over the 2000h of
the experiment. The spectrometer measurements scatter within a very
small area (deviations << 0.001 in u′or v′). The corresponding
reconstructions of the PCHIP approach show only a marginally bigger
spread. The adjusted Wiener filter shows minimal deviations of the LED
chromaticity coordinates, while the generic Wiener filter experiences
larger deviations in the same directions as the adjusted one.
generic Wiener filter gives the worst results, the PCHIP
interpolation yields the smallest errors with respect to Er
and Evand the adapted Wiener filter provides the smallest
colorimetric and spectral errors.
For lighting applications with a perspective of compensat-
ing for the LED ageing that occurs for example in a multi-
channel LED system, it is rather relevant which errors the
reconstruction methods cause or by how much the reconstruc-
tion estimates deviate from the ground truth in the worst case.
Therefore, for the evaluation of the reconstruction results, the
maximum errors are discussed. Comparing with the results
obtained for the other LEDs from this experiment, the very
good color and spectral performance of the generic Wiener
filter for the NW2 LED seems to be a coincidence here, which
will be reasoned in the discussion section.
V. DISCUSSION
The reconstruction results from the previous section provide
room for discussion. For the results of the green LED the
generic Wiener filter is limited in its ability to estimate
the spectral degradation because a covariance matrix with
Toeplitz structure and constant correlation parameter ρover
the whole wavelength range is assumed. This is a severe
14 VOLUME 11, 2023
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
0.2544 0.2552 0.2560 0.2568
u'
0.5136
0.5144
0.5152
0.5160
0.5168
v'
0.001
hour
0
400
800
1200
1600
2000
method
Wiener (Toeplitz
K
)
Wiener (custom
K
)
PCHIP
neglect degrad.
spectrometer
LED under test: WW
FIGURE 19. The color coordinates of the WW LED over the course of the
ageing experiment. The color coordinates first move towards blue and
then turn towards yellow. All applied methods are capable of
reconstructing this course, but the PCHIP results show an increasing
distance to the spectrometer measurement after the turn.
disadvantage, because the actual LED emission is situated
in a very narrow wavelength range, and the spectral changes
resulting from the degradation are also very narrow. On the
other hand, there is a wide sensor channel (peak approx.
555 nm, FWHM approximately 100 nm) and neighboring
channels whose sensitivities only intersect at the edges with
the emission of the green LED. The generic filter is therefore
set up (from the Toeplitz-covariance matrix) in such a way
that the changes in the sensor responses from the initial
measurement, are estimated to happen over the entire range
of sensitivities of the sensor channels registering the LED
emission, which leads to the overshoots and undershoots in
the estimated difference spectra in Figure 9 for the generic
Wiener filter. The generic filter simply lacks the information
to provide a better estimate: The spectral changes to be
reconstructed are too narrow compared to the width and
number of sensor channels observing these changes, and
the unadjusted (generic) covariance matrix does not help
to narrow down where in the spectral range the spectral
changes are located. The adjusted (covariance) Wiener filter
in comparison is mathematically constructed to estimate the
spectral changes to occur in regions where the initial SPD
had the most power, which in the case of the green LED
reduces the estimation errors for the Wiener filter greatly.
The even still slightly better performance of the PCHIP
approach for the green LED can be reasoned by the fact that
TABLE 2. Maximum errors of irradiance, illuminance, color and spectral
distribution between a sensor-based reconstruction and a spectrometer
measurement, broken down by method and LED type.
LED method \
|∆Er|/% \
|∆Ev|/% \
∆u′v′·10−3\
nRMSE
Green PCHIP 0.728 0.983 0.636 0.005
Green Wiener (Toepl.) 19.235 17.432 2.228 0.049
Green Wiener (custom) 0.601 0.189 0.997 0.007
Green negl. degr. 31.688 31.036 1.158 0.006
NW1 PCHIP 0.402 0.854 1.711 0.010
NW1 Wiener (Toepl.) 1.267 1.230 4.571 0.013
NW1 Wiener (custom) 0.545 0.555 0.372 0.003
NW1 negl. degr. 1.653 3.058 8.307 0.037
NW2 PCHIP 1.404 0.451 6.213 0.031
NW2 Wiener (Toepl.) 8.125 7.977 3.365 0.012
NW2 Wiener (custom) 2.034 0.714 4.859 0.018
NW2 negl. degr. 11.413 15.069 10.805 0.048
Ref PCHIP 0.350 0.385 0.183 0.001
Ref Wiener (Toepl.) 0.321 0.308 1.085 0.008
Ref Wiener (custom) 0.341 0.331 0.327 0.003
Ref negl. degr. 0.384 0.384 0.132 0.001
WW PCHIP 0.484 0.272 0.644 0.003
WW Wiener (Toepl.) 0.455 0.388 0.488 0.004
WW Wiener (custom) 0.597 0.497 0.329 0.002
WW negl. degr. 2.177 1.648 1.310 0.004
almost no spectral (sideways) shifts occur, and that the simple
interpolation of sensor responses introduces smaller errors
than an ill posed (eleven sensor channels to 401 wavelengths)
Wiener estimation for this case. Nevertheless, the latter two
reconstruction methods show a very good spectral traceability
of the ageing of the green LED via the output values of the
spectral sensor.
In the case of the NW1 LED, the adapted Wiener filter
approach can show its benefits from knowledge of the spectral
sensitivity curves of the sensor and, thus, in addition to low
errors with regard to Erand Ev, also achieves an excellent
spectral estimation of the actual SPD of the LED after severe
ageing. The results of the PCHIP interpolation, on the other
hand, are also still in a very good range, i.e., << 2 SDCM,
which would be classified as a barely perceptible difference
in the context of LED binning.
Unfortunately, concerning the results of the NW2 LED,
it is not possible to determine from the data of the exper-
iment by how much the phosphor crack affects the spatial
radiation characteristics of the LED. Thus, in addition to the
error stemming from the applied reconstruction method itself,
an unclear impact of potentially different irradiances on the
spectrometer head and the spectral sensor is to be expected.
The observation that the reported errors for the illuminance
estimates are small and almost without any visible impact
from the phases of the phosphor crack can be explained by
the fact that the reconstruction errors in Figure 15 are found
to especially occur in the blue region, which basically has not
much relevance for the V(λ)weighted illuminance.
Regarding the results of the NW2 LED, the surprisingly
VOLUME 11, 2023 15
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
good performance of the generic Wiener filter approach
in terms of color and spectral errors demands for further
discussion: The good performance of the generic Wiener
filter for the NW2 LED appears to be a coincidence, be-
cause for all other LEDs this method offers by far the worst
estimation results. Even for the NW2 LED, looking at the
residual spectral errors (Figure 15), it is not apparent that the
generic Wiener filter provides a better spectral reconstruction
(compared to the other methods). Only when the colorimetric
integrals are evaluated in terms of ∆u′v′the generic wiener
filter pulls clearly ahead. This can be explained from the
trichromaticity of human color perception, where color is
assumed to be describable by a relation between radiation in
the short (around 450 nm), medium (around 555 nm) and long
(around 600 nm) regions in the visible spectrum. Comparing
the different spectral residual errors between the estimation
methods in Figure 15 it becomes apparent, that the error of
the generic Wiener filter is distributed over the whole visible
region, while the errors of the adjusted Wiener filter and
PCHIP approach are concentrated in a sharp peak around
460 nm. The generic Wiener filter clearly overestimates the
changes in the yellow-orange light component as the es-
timated spectral differences in Figure 15 are clearly more
negative than calculated from the measured ground truth
or from the other reconstruction methods. These different
error distributions lead to a smaller colorimetric error for
the generic Wiener filter compared to the other methods,
because the ratio between the three tristimulus values is
less effected from the more evenly distributed spectral error
of the generic Wiener filter. Comparing this performance
with the performance on the other LEDs it is clear that
the generic Wiener filter is generally more imprecise in it’s
spetcral reconstruction than the other methods (broader error
distributions). Only for the NW2 LED this coincidentally
results in a smaller colorimetric error, that is accompanied by
a large radiometric error. In principle, however, it is of course
possible that the generic approach provides better results for
LED changes that cannot be described with the covariance
matrix adjusted to the initial state. Further investigations with
other LEDs and scenarios are required in a follow-up to this
work to reveal whether the more unspecific reconstruction of
the unadjusted Wiener filter can actually be an advantage in
certain cases.
The comparison of the results from both Wiener filter
variants frequently shows similar directions in terms of
deviations, possibly caused by inaccuracies in the spectral
characterization which are manifested here. This represents
a reopening of an old topic, as the spectral characterization
of cameras has been the subject of extensive research in
numerous publications in the past [66]–[69]. Simultaneously,
spectral sensors for spectral reconstruction significantly raise
the bar for required characterization accuracy. When consid-
ering camera sensitivities, there can be a general assumption
of a certain smoothness in the spectral sensitivities, as the
sensitivities of different channels are realized through pig-
ments or dyes, rather than nano-optical interference filters, as
it is the case for most spectral sensors. Moreover, the spectral
sensor sensitivities exhibit much steeper slopes compared to
most RGB cameras. At this point, it is very convenient for
the practical application that the PCHIP approach based only
on the datasheet properties of the sensor was already able to
reconstruct the degraded spectral emission of all LEDs in this
experiment very well.
To analyze the impact of deviations in real channel peak
wavelengths from the datasheet on the accuracy of the min-
imal knowledge approach (PCHIP) the assumed peak wave-
lengths are varied in 5 nm steps within ±10 nm of the typical
value for all sensor channels in the NW1 LED’s radiation
range, resulting in 390625 combinations of peak wavelengths.
The resulting errors of different assumptions of peak sensitiv-
ity wavelengths are given in table Table 3. Assuming different
peak locations can lead to smaller or larger errors in individual
metrics compared to using measured peak wavelengths or
typical values from the datasheet, while no peak wavelength
assumption minimizes all evaluation metrics at the same time.
The datasheet values provide a performance close to the me-
dian of all possible combinations; for the actual sensor used in
this experiment, there is no observable benefit in using the la-
boriously measured true peak locations. The PCHIP approach
is therefore limited by the width and number of the sensor
channels, the (in)correct assumption of the datasheet channel
peak sensitivity wavelengths only has a minor influence on
the performance of the PCHIP approach for the given sensor.
The assumption of the typical peak sensitivity wavelengths
(datasheet) offer close to median performance of all possible
assumptions.
TABLE 3. Monitoring result variations caused by assumption of different
channel peak wavelengths for the PCHIP approach in reconstructing the
NW1 LED after 2000h stress operation. Given are the minimal, median
and maximum resulting error in comparison to the results of using the
datasheet peak locations and the measured peak locations of the actual
sensor (Figure 3).
∆Er/% ∆Ev/% ∆u′v′·10−3nRMSE
Minimum -0.27 0.34 0.0012 0.0057
Median 0.17 0.67 0.0017 0.0088
Maximum 0.61 1.06 0.0022 0.0107
True peaks 0.19 0.68 0.0016 0.0086
Datasheet peaks 0.17 0.66 0.0017 0.0087
The impact of the interpolation method can be discussed
on the basis of Table 4, where the mean and maximum value
for the evaluation metrics are shown for minimal knowledge
spectral reconstructions from senor data of all LEDs under
stress conditions after 2000 h using different algorithms for
the interpolation step. A simple form of interpolation can be
achieved through polynomial regression from the sensor re-
sponses as dependant variables and the assumed peak channel
sensitivities as independents. The evaluation metrics for using
such a polynomial interpolation of order 1, 3, 7 and 11 are
given in the table.
16 VOLUME 11, 2023
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
TABLE 4. Result variations caused by using different interpolation algorithms in reconstructing the LEDs under stress after 2000h operation with the
minimal knowledge approach (without knowing the exact spectral sensitivities). Given are the mean and maximum resulting error metrics to compare the
performance of the used interpolation method (polynomial and spline interpolations of varying order, piecewise cubic hermite interpolating polynomial).
Interpolation method |∆Er|/% \
|∆Er|/% |∆Ev|/% \
|∆Ev|/% ∆u′v′·10−3\
∆u′v′·10−3nRMSE
\
nRMSE
PCHIP 0.5134 1.2691 0.4494 0.6615 0.0022 0.0060 0.0114 0.0306
Poly1 0.6292 1.6218 0.9572 1.9073 0.0047 0.0097 0.0212 0.0451
Poly3 0.6814 1.7600 0.7867 1.5562 0.0041 0.0091 0.0185 0.0428
Poly7 0.4868 1.2460 0.3677 0.4842 0.0021 0.0059 0.0112 0.0319
Poly11 0.3004 0.5417 0.4306 0.6100 0.0021 0.0060 0.0126 0.0336
piecewise linear 0.5000 1.2715 0.4534 0.6535 0.0022 0.0061 0.0114 0.0312
piecewise quadratic 0.5193 1.2852 0.4341 0.6001 0.0021 0.0059 0.0110 0.0302
piecewise cubic 0.5235 1.2937 0.4362 0.6039 0.0021 0.0059 0.0110 0.0301
As introduced in the methods section of this work, the CIE
recommendation for interpolating spectral data [63]) is based
on spline interpolation, so for comparison of interpolation
methods for sensor responses, linear, quadratic, and cubic
spline interpolation are evaluated here. While both PCHIP
and cubic spline interpolation use cubic polynomials for
interpolation, the key difference lies therein that PCHIP is
preserving monotonicity. PCHIP can therefore be understood
as a conservative choice for interpolation of spectral sensor
data, since no new maxima or minima are created during the
interpolation process besides the sensor data points. In view
of the curves (number of minima/maxima/saddle points) in
the difference spectra to be estimated (Figure 6 - 8), it is clear
why the simple 1st and 3rd order polynomials cannot keep
up with the other methods, which perform very close to each
other; depending on the metric considered, the ranking of the
interpolation methods changes only slightly. The higher order
polynomials provide slightly better radiometric or photomet-
ric results, although this is at the expense of colorimetric and
spectral accuracy. The piecewise interpolation methods pro-
vide practically equivalent results. Therefore, the preservation
of monotonicity by the PCHIP method does not provide clear
advantages for the monitoring of the tested LEDs, degradation
processes and the sensor used, but it is also not inferior to
other methods.
From the data of the experiment presented here, a con-
clusion can be drawn to the question which method is best
suited for monitoring LEDs with different ageing properties:
For LEDs that only loose flux without major spectral shifts,
the PCHIP approach is predestined, as it does not require any
complex sensor calibration and still shows excellent recon-
struction results for these LEDs. For LEDs that are expected
to have spectral shifts at wavelengths where there are also
high radiation components in the initial spectrum, the Wiener
filter adapted to the initial state provides the best reconstruc-
tion results. As long as these spectral shifts are wide enough,
i.e., in the order of magnitude of the sensor channel width, the
reconstruction results of the PCHIP approach are still suitable
for application. For LEDs whose age-related spectral changes
do not occur where there is a lot of radiant power in the
initial spectrum or where anomalies, such as phosphor cracks,
are observed, the conclusion is more difficult. Although the
use of a spectral sensor provides an estimate of the actual
LED emission that provides at least a halving of the color
and a reduction of the relative radiometric error by at least
87 % compared to neglecting the degradation, the limit of
this methodology for the reconstruction of color and spectral
information from sensor data is reached.
The projection from SPD to sensor response that occurs
inside a spectral sensor is a drastic reduction in dimension
and information (401 wavelengths to a few sensor channels).
Each sensor channel has a spectral width of its sensitivity,
so the output of a sensor channel not only corresponds to
the SPD at the peak wavelength, but it is a weighted (with
the channel sensitivity) integral of the SPD. This introduces
the problem of sensor metamerism: Different SPDs can
cause the same sensor response, and therefore the inverse
projection (sensor response to SPD) is not unique. Given
a sensor response, accurate reconstruction of the original
SPD (interpretation of the sensor response) therefore requires
additional (a priori) information about the SPD, even if the
sensor channel sensitivities are known. The task of extract-
ing this a priori information and incorporating it into the
reconstruction, but keeping the degree of estimation freedom
large enough to have generalization and not create an overfit
to the observed data (data used for modeling / information
extraction) is not trivial. The only solution to make interpre-
tation / reconstruction from sensor data less challenging is
to reduce the dimensionality mismatch of the inversion task.
There are two evident possibilities: Increasing the spectral
resolution of the sensor (more channels, reduced width of
channels) or reducing the dimensionality of the SPD (possibly
through parametric modeling of LED spectra) without loss
of information. However, this would require SPD models
capable of describing individual spectral LED degradation
with a few unambiguous parameters and without noticeable
errors. Unfortunately, such models do not exist today.
One constraint in the application of the spectral sensor used
in this work is that the resolving power is closely related to
the integration time. For very small emission changes of a
very low-light LED, very long integration times are needed
to achieve a usable signal-to-noise ratio. During this time, the
luminaire emission and, if applicable, the ambient lighting
must not change. Another limitation becomes relevant when
several LED channels in a luminaire are to be monitored. The
VOLUME 11, 2023 17
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
approaches presented in this paper assume that the sensor
responses to each LED are acquired individually. In an ap-
plication with multiple LED channels, sequential acquisition
of the individual channels would therefore be necessary. Al-
ternatively, each LED channel could be captured via its own
sensor or hardware-based solutions could be developed that
ensure that iteratively only the light of a specific LED channel
falls onto the sensor. A software solution is also conceivable
that can determine the proportions of the individual LED
channels from a detected light mixture, e.g., over several
measurements with slight variations.
Ambient light, which may enter the luminaire from outside
falling onto the sensor, poses no hard limitation as long as
the signal to be measured is not completely overpowered
by the ambient light. Either the ambient and luminaire mea-
surements can be directly offset against each other (e.g.,
ambient measurement with the luminaire switched off, sub-
tracting from the sum measurement) or spectral unmixing
algorithms could be developed to determine the ambient light
contributions to the sensor response for subtraction before the
estimation of the LED SPD.
VI. CONCLUSION
One key area of LED research is modelling the lifetime
under different operating conditions. While standardized ap-
proaches exist for estimating the radiant flux as a function
of time, temperature, and current, the modelling of spectral
emission as a function of these influencing variables is com-
plex and, according to the current state of research, subject
to large errors compared to real degradation. It is therefore
currently not practicable to use modeled spectral degradation
for ageing compensation in multi-channel LED systems.
Such compensations, however, could achieve significantly
improved color and radiant flux consistency increasing the
lifetime of the fixture for factory-calibrated light settings
(e.g., pre-calculated channel mixtures for various correlated
color temperatures). This work, in contrast to a priori mod-
eling, thus investigated a different approach: The estimation
of the actual spectral power distribution of a degrading LED
from spectral sensor responses.
Four different LEDs were subjected to accelerated aging
operating conditions and the spectral emission was measured
with a spectroradiometer and simultaneously captured with a
spectral sensor. The comparison of degradation spectra and
sensor responses showed that most of the spectral degra-
dation is actually captured in the sensor data, even though
the spectral resolution of the sensor is much lower than that
of the spectroradiometer. Over the four LEDs (green, warm
white, and two neutral white) under stress conditions (2000 h,
1.1 A, 75°) the maximum radiometric error of neglecting the
appearing degradation would have been 7.2% and 20.5 %
at the end of the experiment, respectively. The mean and
maximum colorimetric (spectral) error from that same com-
parison were 0.00284 (0.0126) and 0.01080 (0.0484) in terms
of ∆u′v′(nRMSE). Two methods for reconstruction of the
actual LED spectra from the sensor responses were presented
and tested on the collected data. While the adjusted Wiener
filter approach, which makes use of spectral characterization
of the sensor sensitivities, was able to basically reconstruct
the degraded SPDs with a smaller colorimetric error, the
PCHIP approach, only making use of datasheet information
about peak sensitivity wavelengths of the sensor channels,
resulted in only minimally larger colorimetric misestimations
but also excellent radiometric estimates. Even without spec-
tral characterization of the sensor the PCHIP approach could
thus provide estimates of the same SPDs with a maximum
radiometric error (compared to a spectroradiometer measure-
ment) of 1.4 %, maximum colorimetric error of 0.0062 ∆u′v′,
and maximum nRMSE of 0.0310. Knowledge of specific
sensor sensitivities used in an adjusted Wiener filter for recon-
struction resulted in a maximum radiometric error of 2.0 %,
maximum colorimetric error of 0.00486 ∆u′v′, and maximum
nRMSE of 0.0177.
In all cases, the estimation errors were smaller than neglect-
ing the degradation. These results demonstrate that a spectral
sensor is capable of providing spectral estimates after heavy
degradation with very little errors compared to measurements
of a spectroradiometer. The highest errors here are caused by
a single LED developing a phosphor crack which influenced
the spatial radiation characteristics as well as the spectral
emission. While being easily identifiable from the sensor
responses (e.g. for a damage warning to the user) such an
unforeseeable event limits the ability to estimate the actual
SPD from the sensor responses without the a priori knowledge
of the causing spectral changes. If this event, which is cer-
tainly unlikely in practical applications with safely designed
operating parameters, is not taken into account, the adjusted
Wiener filter (the PCHIP approach) achieves a maximum
radiometric error of 0.6 % (0.73 %), a maximum colormetric
error of 0.001 (0.0017) ∆u′v′, and a maximum spectral
nRMSE error of 0.0071 (0.0097) compared to the spectrora-
diometric ground truth monitoring of the LED degradation. In
summary, it can be stated that by using a spectral sensor, even
without a detailed characterization of the sensor itself, the
actual condition of LEDs can be monitored more accurately
than what human perception would be able to differentiate.
Subsequent work should investigate more closely how well
spectrally narrow changes can in particular be estimated via a
sensor, for example using different (beyond green) monochro-
matic, non-phosphor-converted LEDs. In addition, the ques-
tion must be answered how a spectral sensor should be used in
practical applications to best record the emission that actually
leaves the luminaire, especially when it comes to devices that
do not have a mixing chamber but create a highly directional
emission. In this context, the findings from the bursting of
the phosphor in LED NW2 and the associated change in the
spatial radiation characteristics must be taken into account.
At the same time, when developing a commercial luminaire,
the operating conditions would be specified in such a way
that such drastic damage should not be possible. However, an
18 VOLUME 11, 2023
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
integrated spectral sensor provides important information in
any case that the spectral emission has changed drastically.
Depending on the application, this is useful even if no perfect
reconstruction of the degraded spectral emission (and thus
only limited compensation by other LED channels in a multi-
channel system) is possible, e.g. for automated maintenance
warnings or anomaly detection.
It is also interesting to consider the use case of having a
sensor in the luminaire while carrying out long-term tests
in the factory. This approach would allow manufacturers to
develop specific solutions (such as Wiener filters) that could
be programmed as firmware updates in case of unexpected
degradation. These custom solutions could be used to re-
motely calibrate luminaires that exhibit similar behavior in
terms of the temporal response of the sensors in the field,
thereby resolving any issues that may arise.
While no sensor drift was observed in this experiment,
which clearly demonstrated the feasibility and potential of
spectral sensor feedback to track spectral emission during
the degradation of an LED, dedicated tests should explicitly
focus on the optical stability of the sensors. Ideally, these
new ageing tests should be carried out on complete light
engines with an integrated sensor, in order to be able to
take into account all possible interactions (e.g. chemical
reactions, humidity, temperature, spatial dislocations, etc.) of
the components under the stress conditions.
Compared to competing technologies for compensation
of ageing phenomena of LEDs, spectral sensors offer big
advantages. The so-called constant light output (CLO), which
some electronic ballasts offer as an option, does not take
into account the actual LED condition (LED emission) but
uses a pre-programmed curve to compensate for the expected
decrease in luminous flux depending on the LED operating
time. Because field data is generally not available and labo-
ratory degradation data (most notably LM-80 reports, where
measurements are made with LEDs operating continuously
in a controlled and stable temperature environment [70]) is
in contrast to typical real-world usage patterns that include
degradation accelerated by thermal cycling [71], any pre-
dictions based on LM-80 (laboratory) data may differ from
real-world performance [70]. This translates to the possibility
of open-loop compensation (CLO) models greatly over- or
under-compensating the actual LED degradation. Integrated
spectral sensors could not only collect these field data for
modelling, but could also be used directly for requirement-
oriented re-adjustment (closed loop compensation).
A single photodiode (e.g. luminance sensor) can only de-
tect an integral quantity and cannot deal with spectral shifts,
i.e., as soon as the sensor is not perfectly matched in terms
of sensitivity (radiometric or photometric), spectral shifts
also cause radiometric or photometric errors. This problem
does not affect a spectral sensor, because due to the multiple
spectral channels an estimation of the integral quantity can
be achieved with small errors (below 2% even for extreme
degradation events such as phosphor cracks).
Finally, the initially formulated goal should of course be
pursued further in subsequent work: The compensation of
spectral and colorimetric errors in mixtures of several LED
channels, when the SPDs of the individual channels in the
current operating state are estimated by spectral sensor feed-
back. Such a self-monitoring (and possibly self-calibrating)
multi-LED channel light engine could be of great use in
all applications where constant radiometric output and color
(spectral) quality is required, for example in museums, film
sets, sample lighting, and automated color inspection. In
museums, accurate color representation of artifacts and ex-
hibits is critical. On film sets, maintaining consistent lighting
during shooting is essential for seamless color correction and
visual effects in post-production. Automated color inspection
systems would greatly benefit from such a self-monitoring
and self-calibrating light engine. These systems require pre-
cise and consistent color illumination to ensure accurate and
reliable color measurements in industries such as printing,
textiles, and product quality control. In conclusion, the further
pursuit of LED monitoring using multi-channel spectral sen-
sors could significantly advance lighting technology, offering
innovative solutions for applications requiring consistent ra-
diometric output and impeccable color quality.
REFERENCES
[1] W. D. van Driel, M. Schuld, B. Jacobs, F. Commissaris, J. van der Eyden,
and B. Hamon, ‘‘Lumen maintenance predictions for led packages,’’ Mi-
croelectronics Reliability, vol. 62, pp. 39–44, 2016.
[2] G. Bobashev,N. G. Baldasaro, K. C. Mills, and J. L. Davis, ‘‘An efficiency-
decay model for lumen maintenance,’’ IEEE Transactions on Device and
Materials Reliability, vol. 16, no. 3, pp. 277–281, 2016.
[3] M. Buffolo, A. Caria, F. Piva, N. Roccato, C. Casu, C. de Santi, N. Trivellin,
G. Meneghesso, E. Zanoni, and M. Meneghini, ‘‘Defects and reliability of
gan–based leds: Review and perspectives,’’ physica status solidi (a), vol.
219, no. 8, p. 2100727, 2022.
[4] M. S. Ibrahim, J. Fan, W. K. Yung, Z. Wu, and B. Sun, ‘‘Lumen degradation
lifetime prediction for high-power white leds based on the gamma process
model,’’ IEEE Photonics Journal, vol. 11, no. 6, pp. 1–16, 2019.
[5] Illuminating Engineering Society, Technical Memorandum: Projecting
Long-Term Luminous, Photon, and Radiant Flux Maintenance of LED
Light Sources. ANSI/IES TM-21-21. New York: IES, 2021.
[6] F. Reifegerste and J. Lienig, ‘‘Modelling of the temperature and current
dependence of led spectra,’’ Journal of Light & Visual Environment, vol. 32,
no. 3, pp. 288–294, 2008.
[7] A. Vaskuri, P. Kärhä, H. Baumgartner, O. Kantamaa, T. Pulli, T. Poikonen,
and E. Ikonen, ‘‘Relationships between junction temperature, electrolu-
minescence spectrum and ageing of light-emitting diodes,’’ Metrologia,
vol. 55, no. 2, pp. S86–S95, 2018.
[8] A. Vaskuri, H. Baumgartner, P. Kärhä, G. Andor, and E. Ikonen, ‘‘Modeling
the spectral shape of ingaalp-based red light-emitting diodes,’’ Journal of
Applied Physics, vol. 118, no. 20, p. 203103, 2015.
[9] B.-M. Song and B. Han, ‘‘Spectral power distribution deconvolution
scheme for phosphor-converted white light-emitting diode using multiple
gaussian functions,’’ Applied optics, vol. 52, no. 5, pp. 1016–1024, 2013.
[10] Z. Guo, T. Shih, Y. Gao, Y. Lu, L. Zhu, G. Chen, Y. Lin, J. Zhang,
and Z. Chen, ‘‘Optimization studies of two-phosphor-coated white light-
emitting diodes,’’ IEEE Photonics Journal, vol. 5, no. 2, p. 8200112, 2013.
[11] A. Keppens, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, ‘‘Modeling
high power light-emitting diode spectra and their variation with junction
temperature,’’ Journal of Applied Physics, vol. 108, no. 4, p. 043104, 2010.
[12] M. E. Raypah, M. Devarajan, and F. Sulaiman, ‘‘Modeling spectra of low-
power smd leds as a function of ambient temperature,’’ IEEE Transactions
on Electron Devices, vol. 64, no. 3, pp. 1180–1186, 2017.
VOLUME 11, 2023 19
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
[13] W. Chen, J. Fan, C. Qian, B. Pu, X. Fan, and G. Zhang, ‘‘Reliability assess-
ment of light-emitting diode packages with both luminous flux response
surface model and spectral power distribution method,’’ IEEE Access,
vol. 7, pp. 68 495–68 502, 2019.
[14] H. Chen and S. Y. Hui, ‘‘Dynamic prediction of correlated color temper-
ature and color rendering index of phosphor-coated white light-emitting
diodes,’’ IEEE Transactions on Industrial Electronics, vol. 61, no. 2, pp.
784–797, 2014.
[15] J. Fan, M. G. Mohamed, C. Qian, X. Fan, G. Zhang, and M. Pecht, ‘‘Color
shift failure prediction for phosphor-converted white leds by modeling
features of spectral power distribution with a nonlinear filter approach,’’
Materials (Basel, Switzerland), vol. 10, no. 7, 2017.
[16] J. Fan, Y. Li, I. Fryc, C. Qian, X. Fan, and G. Zhang, ‘‘Machine-learning
assisted prediction of spectral power distribution for full-spectrum white
light-emitting diode,’’ IEEE Photonics Journal, vol. 12, no. 1, pp. 1–18,
2020.
[17] J. Fan, W. Chen, W. Yuan, X. Fan, and G. Zhang, ‘‘Dynamic prediction of
optical and chromatic performances for a light-emitting diode array based
on a thermal-electrical-spectral model,’’ Optics express, vol. 28, no. 9, pp.
13 921–13 937, 2020.
[18] C. Qian, J. Fan, X. Fan, and G. Zhang, ‘‘Prediction of lumen depreciation
and color shift for phosphor-converted white light-emitting diodes based
on a spectral power distribution analysis method,’’ IEEE Access, vol. 5, pp.
24 054–24 061, 2017.
[19] S. Benkner, A. Herzog, S. Klir, W. D. van Driel, and T. Q. Khanh,
‘‘Advancements in spectral power distribution modeling of light-emitting
diodes,’’ IEEE Access, vol. 10, pp. 83 612–83619, 2022.
[20] J. Hegedüs, G. Hantos, and A. Poppe, ‘‘Lifetimemodelling issues of power
light emitting diodes,’’ Energies, vol. 13, no. 13, p. 3370, 2020.
[21] Z. Vaitonis, A. Miasojedovas, A. Novičkovas, S. Sakalauskas, and A.
Žukauskas, ‘‘Effect of long-term aging on series resistance and junction
conductivity of high-power ingan light-emitting diodes,’’ Lithuanian Jour-
nal of Physics, vol. 49, no. 1, pp. 69–74–69–74, 2009.
[22] A. Herzog, M. Wagner, and T. Q. Khanh, ‘‘Monitoring the optical degra-
dation of green light-emitting diodes on the basis of measured electrical
characteristics,’’ Microelectronics Reliability, vol. 121, p. 114147, 2021.
[23] A. Alexeev, J.-P. Linnartz, G. Onushkin, K. Arulandu, and G. Martin,
‘‘Dynamic response-based leds health and temperature monitoring,’’ Mea-
surement, vol. 156, p. 107599, 2020.
[24] W. D. van Driel and X. J. Fan, Eds., Solid state lighting reliability: Compo-
nents to systems, ser. Solid state lighting technology and application series
(Print). New York: Springer, 2013.
[25] M. Buffolo, C. de Santi, M. Meneghini, D. Rigon, G. Meneghesso, and
E. Zanoni, ‘‘Long-term degradation mechanisms of mid-power leds for
lighting applications,’’ Microelectronics Reliability, vol. 55, no. 9-10, pp.
1754–1758, 2015.
[26] V. Q. Trinh, S. Babilon, P. Myland, and T. Q. Khanh, ‘‘Processing rgb color
sensors for measuring the circadian stimulus of artificial and daylight light
sources,’’ Applied Sciences, vol. 12, no. 3, p. 1132, 2022.
[27] J. E. Agudo, P. J. Pardo, H. Sánchez, Á. L. Pérez, and M. I. Suero, ‘‘A
low-cost real color picker based on arduino,’’ Sensors (Basel, Switzerland),
vol. 14, no. 7, pp. 11 943–11 956, 2014.
[28] J. Botero-Valencia, F. López-Giraldo, and J. Vargas-Bonilla, ‘‘Calibration
method for correlated color temperature (cct) measurement using RGB
color sensors,’’ in Proceedings of the Symposium of Signals, Images and
Artificial Vision—2013: STSIVA, 11–13 September 2013, Bogota, Colom-
bia, 2013, pp. 3–8.
[29] C. S. McCamy, ‘‘Correlated color temperature as an explicit function of
chromaticity coordinates,’’ Color Research & Application, vol. 17, no. 2,
pp. 142–144, 1992.
[30] J. Botero-Valencia, F. López-Giraldo, and J. Vargas-Bonilla, ‘‘Classifica-
tion of artificial light sources and estimation of color rendering index using
RGB sensors, k nearest neighbor and radial basis function,’’ International
Journal on Smart Sensing and Intelligent Systems, vol. 8, no. 3, pp. 1505–
1524, 2015.
[31] L. Breniuc, C.-G. Haba, C.-D. Galatanu, D. Petrisor, and R. Hertanu,
‘‘Correlated color temperature measuring and adjustment system,’’ in 2019
- 11th International Symposium on Advanced Topics in Electrical Engi-
neering (ATEE). [Piscataway, NJ]: IEEE, 2019, pp. 1–6.
[32] I. Chew, V. Kalavally, C. P. Tan, and J. Parkkinen, ‘‘A spectrally tunable
smart LED lighting system with closed-loop control,’’ IEEE Sensors Jour-
nal, vol. 16, no. 11, pp. 4452–4459, 2016.
[33] P. K. Maiti and B. Roy, ‘‘Evaluation of a daylight-responsive, itera-
tive, closed-loop light control scheme,’’ Lighting Research & Technology,
vol. 52, no. 2, pp. 257–273, 2020.
[34] M. Ashibe, M. Miki, and T. Hiroyasu, ‘‘Distributed optimization algorithm
for lighting color control using chroma sensors,’’ in Systems, Man and
Cybernetics, 2008. SMC 2008. IEEE International Conference on. Los
Alamitos: IEEE Computer Society, 2008, pp. 174–178.
[35] J.-S. Botero-Valencia, J. Valencia-Aguirre, D. Durmus, and W. Davis,
‘‘Multi-channel low-cost light spectrum measurement using a multilayer
perceptron,’’ Energy and Buildings, vol. 199, pp. 579–587, 2019.
[36] A. Amirazar, M. Azarbayjani, M. Molavi, and M. Karami, ‘‘A low-cost and
portable device for measuring spectrum of light source as a stimulus for the
human’s circadian system,’’ Energy and Buildings, vol. 252, p. 111386,
2021.
[37] J.-S. Botero, J. Valencia Aguirre, and J.-F. Vargas Bonilla, ‘‘Estimation
of light source color rendition with low-cost sensors using multilayer
perceptron and extreme learning machine,’’ LEUKOS, vol. 17, no. 3, pp.
280–290, 2021.
[38] A. Herzog, M. Wagner, and T. Q. Khanh, ‘‘Efficiency droop in green
ingan/gan light emitting diodes: Degradation mechanisms and initial char-
acteristics,’’ Microelectronics Reliability, vol. 112, p. 113792, 2020.
[39] A. Herzog, S. Benkner, B. Zandi, M. Buffolo, W. D. van Driel, M. Menegh-
ini, and T. Q. Khanh, ‘‘Lifetime prediction of current-and temperature-
induced degradation in silicone-encapsulated 365 nm high-power light-
emitting diodes,’’ IEEE Access, vol. 11, pp. 19 928–19940, 2023.
[40] P. L. Vora, J. E. Farrell, J. D. Tietz, and D. H. Brainard, Digital color
cameras-1-Response models. Hewlett-Packard Laboratories, 1997.
[41] P. Myland, S. Babilon, and T. Q. Khanh, ‘‘Tackling heterogeneous color
registration: Binning color sensors,’’ Sensors, vol. 21, no. 9, 2021.
[42] P. Myland, S. Fischer, T. Hegemann, S. Klir, and T. Q. Khanh, ‘‘Recon-
struction of spectral irradiance in a real application with a multi-channel
spectral sensor using convolutional neural networks,’’ Optics Express, jun
2023.
[43] W.Pratt, ‘‘Digital image processing: PIKS inside,’’ John Wiley & Sons, Inc,
2001.
[44] N. Shimano, ‘‘Recovery of spectral reflectances of objects being imaged
without prior knowledge,’’ IEEE transactions on image processing : a
publication of the IEEE Signal Processing Society, vol. 15, no. 7, pp. 1848–
1856, 2006.
[45] P. Stigell, K. Miyata, and M. Hauta-Kasari, ‘‘Wiener estimation method in
estimating of spectral reflectance from rgb images,’’ Pattern Recognition
and Image Analysis, vol. 17, no. 2, pp. 233–242, 2007.
[46] P. Urban, M. R. Rosen, and R. S. Berns, ‘‘A spatially adaptive wiener filter
for reflectance estimation,’’ Color and Imaging Conference, vol. 16, no. 1,
pp. 279–284, 2008.
[47] P. Urban, M. R. Rosen, and R. S. Berns, ‘‘Spectral image reconstruction
using an edge preserving spatio-spectral wiener estimation,’’ Journal of
the Optical Society of America A, vol. 26, no. 8, pp. 1865–1875, 2009.
[48] I. Nishidate, T.Maeda, K. Niizeki, and Y. Aizu, ‘‘Estimation of melanin and
hemoglobin using spectral reflectance images reconstructed from a digital
rgb image by the wiener estimation method,’’ Sensors (Basel, Switzerland),
vol. 13, no. 6, pp. 7902–7915, 2013.
[49] S. Babilon, P. Myland, J. Klabes, J. Simon, and T. Q. Khanh, ‘‘Spectral
reflectance estimation of organic tissue for improved color correction of
video-assisted surgery,’’ Journal of ElectronicImaging, vol. 27, no. 05, p. 1,
2018.
[50] A. Mahmoudi Nahavandi, ‘‘Noise segmentation for improving perfor-
mance of wiener filter method in spectral reflectance estimation,’’ Color
Research & Application, vol. 43, no. 3, pp. 341–348, 2018.
[51] F. Sippel, J. Seiler, N. Genser, and A. Kaup, ‘‘Structure-preserving spec-
tral reflectance estimation using guided filtering,’’ Journal of the Optical
Society of America A, vol. 37, no. 11, pp. 1695–1710, 2020.
[52] V. Kitanovski, J.-B. Thomas, and J. Yngve Hardeberg, ‘‘Reflectance es-
timation from snapshot multispectral images captured under unknown
illumination,’’ Color and Imaging Conference, vol. 29, no. 1, pp. 264–269,
2021.
[53] J. Klein, J. Brauers, and T. Aach, ‘‘Methods for spectral characterization of
multispectral cameras,’’ in Digital Photography VII, ser. SPIE Proceedings,
F. H. Imai and F. Xiao, Eds. SPIE, 2011, p. 78760B.
[54] Y. Murakami, K. Fukura, M. Yamaguchi, and N. Ohyama, ‘‘Color repro-
duction from low-snr multispectral images using spatio-spectral wiener
estimation,’’ Optics express, vol. 16, no. 6, pp. 4106–4120, 2008.
[55] H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and
Y. Miyake, ‘‘System design for accurately estimating the spectral re-
20 VOLUME 11, 2023
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
Myland et al.: LED degradation monitoring using a multi-channel spectral sensor
flectance of art paintings,’’ Applied Optics, vol. 39, no. 35, pp. 6621–6632,
2000.
[56] H.-L. Shen and J. H. Xin, ‘‘Spectral characterization of a color scanner by
adaptive estimation,’’ Journal of the Optical Society of America A, vol. 21,
no. 7, pp. 1125–1130, 2004.
[57] H.-L. Shen, J. H. Xin, and S.-J. Shao, ‘‘Improved reflectance reconstruc-
tion for multispectral imaging by combining different techniques,’’ Optics
express, vol. 15, no. 9, pp. 5531–5536, 2007.
[58] S. Chen and Q. Liu, ‘‘Modified wiener estimation of diffuse reflectance
spectra from rgb values by the synthesis of new colors for tissue measure-
ments,’’ Journal of biomedical optics, vol. 17, no. 3, p. 030501, 2012.
[59] J.-H. Yoo, W.-J. Kyung, H.-G. Ha, and Y.-H. Ha, ‘‘Estimation of reflectance
based on properties of selective spectrum with adaptivewiener estimation,’’
in Color Imaging XVIII: Displaying, Processing, Hardcopy, and Applica-
tions, ser. SPIE Proceedings, R. Eschbach, G. G. Marcu, and A. Rizzi, Eds.
SPIE, 2013, p. 86520D.
[60] S. Tominaga and H. Sakai, ‘‘Spectral reflectance estimation from camera
responses using local optimal dataset,’’ Journal of imaging, vol. 9, no. 2,
2023.
[61] W. K. Pratt, ‘‘Generalized wiener filtering computation techniques,’’ IEEE
Transactions on Computers, vol. C-21, no. 7, pp. 636–641, 1972.
[62] U. Spagnolini, Statistical signal processing in engineering. Hoboken, NJ:
John Wiley & Sons, Inc, 2018.
[63] CIE, ‘‘Recommended practice for tabulating spectral data for use in colour
computations,’’ International Commission on Illumination, Vienna, Tech.
Rep. CIE 167:2005, 2005.
[64] K. A. Novak, Numerical methods for scientific computing: The definitive
manual for math geeks, 2nd ed. Virginia: Equal Share Press, 2022.
[65] S. Benkner, S. Babilon, A. Herzog, and T. Q. Khanh, ‘‘Combined method-
ology for accurate evaluation of distance and direction of chromaticity
shifts in LED reliability tests,’’ IEEE Transactions on Device and Materials
Reliability, vol. 21, no. 4, pp. 500–507, 12 2021.
[66] P. L. Vora, J. E. Farrell, J. D. Tietz, and D. H. Brainard, Digital color
cameras—2—Spectral response. Hewlett-Packard Laboratories, 1997.
[67] B. Jähne, ‘‘EMVA 1288 standard for machine vision,’’ Optik & Photonik,
vol. 5, no. 1, pp. 53–54, 4 2010.
[68] G. Finlayson, M. M. Darrodi, and M. Mackiewicz, ‘‘Rank-based camera
spectral sensitivity estimation,’’ Journal of the Optical Society of America
A, vol. 33, no. 4, pp. 589–599, 2016.
[69] Y. Ji, Y. Kwak, S. M. Park, and Y. L. Kim, ‘‘Compressive recovery of
smartphone rgb spectral sensitivity functions,’’ Optics Express, vol. 29,
no. 8, pp. 11 947–11961, 2021.
[70] L. Davis and M. Hansen, ‘‘Led luminaire reliability: Impact of color
shift,’’ U.S. Department of Energy, last accessed on 28.09.2023.
[Online]. Available: https://www.energy.gov/sites/prod/files/2019/10/f67/
lsrc_colorshift_apr2017.pdf
[71] M. P. Royer, ‘‘Lumen and chromaticity maintenance of led par38
lamps operated in steady-state conditions,’’ U.S. Department of Energy,
12 2014, last accessed on 28.09.2023. [Online]. Available: https:
//doi.org/10.2172/1170114
PAUL MYLAND received his M.S. degree in
electrical engineering and information technology
from the Technical University of Darmstadt, Ger-
many, in 2019. Since then, he has been working
at the Laboratory of Adaptive Lighting Systems
and Visual Processing as a research assistant and
doctoral candidate. His current work is focused on
applications for spectral sensors in lighting control.
His broader research interests include color and
lighting quality, color perception, museum lighting
and multidimensional lighting optimisation.
ALEXANDER HERZOG received the B.Sc.,
M.Sc., and Ph.D. degrees in electrical engineer-
ing from the Technische Universität Darmstadt, in
2012, 2015, and 2020, respectively. He is currently
a Postdoctoral Researcher and a research group
Leader with the Laboratory of Adaptive Light-
ing Systems and Visual Processing, Technische
Universität Darmstadt. His research interests in-
clude lifetime prediction, reliability analysis, dig-
ital twins of light-emitting diodes, temporal light
artifacts, and spectral optimization of metameric spectra.
SEBASTIAN BABILON received his Ph.D. in elec-
trical engineering from the Technische Universität
Darmstadt in 2018. His work mainly focused on
color perception and the modelling of color rendi-
tion in relation to memory colors. After three years
of being appointed as a Postdoctoral Researcher,
he moved on to industrial R&D. Currently, he
is employed at Arnold & Richter Cine Technik
GmbH & Co. Betriebs KG as a Development Engi-
neer being responsible for the colorimetric design
and optimization of lighting fixtures for the movie and television industry.
WILLEM D. VAN DRIEL graduated the degree in
mechanical engineering from the Technical Uni-
versity of Eindhoven, and the Ph.D. degree from
the Delft University of Technology, The Nether-
lands. He has more than 25 years of track record
in the reliability domain. Application areas range
from healthcare, gas and oil explorations, and
semiconductors. He is currently a Fellow Scientist
with Signify (formerly Philips Lighting). Besides
that, he holds a professor position with the Univer-
sity of Delft, The Netherlands. He has authored and coauthored more than
350 scientific publications, including, journals and conference papers, book
or book chapters, and invited keynote lectures. His research interests include
solid state lighting, microelectronics and microsystems technologies, virtual
prototyping, virtual reliability qualification, and designing for reliability
of microelectronics and microsystems. He is the Chair of the Organizing
Committee of the IEEE Conference EuroSimE.
TRAN QUOC KHANH is a university professor
and head of the Laboratory of Adaptive Lighting
Systems and Visual Processing at the Technical
University of Darmstadt, Germany. He graduated
in optical technologies and obtained a doctoral
degree in lighting engineering from the Techni-
cal University of Ilmenau, Germany. Before being
appointed as a professor, he gathered industrial
experience as a project manager at Arnold and
Richter Cine Technik AG in Munich, Germany. His
research interests cover all aspects of modern lighting technology, including
LEDs, colorimetry, mesopic vision, glare, photometry, and color science
related topics.
VOLUME 11, 2023 21
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3378101
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
