The Surface-Roughness Effects on Light Beam Interactions between the CsI Phosphor and Optical Sensing Materials

Abstract

In digital phosphor-based imaging modalities, one important intermediate stage is the optical coupling between the phosphor material and the optical sensor. The performance of the optical compatibility is affected by surface-roughness issues, for which further research should be paid. This paper investigates the surface-roughness influence between the CsI phosphor material and the optical sensing materials (i.e., the silicon dioxide-SiO2, the indium tin oxide-ITO, and the indium gallium arsenide-InGaAs) employed in several image devices. Results showed that for all sensing materials, the transmission factor t of the optical signal follows qualitatively the variation of their refractive indexes and quantitatively the variation of the surface roughness and the incident polar angle. Finally, with respect to light wavelength, the curve of variation was found to be continuous for ITO and SiO2 sensing materials; however, lower and sharper variations were observed in the first case.

Full text

Crystals 2020, 10, 174; doi:10.3390/cryst10030174 www.mdpi.com/journal/crystals
Article
The Surface-Roughness Effects on Light Beam
Interactions between the CsI Phosphor and
Optical Sensing Materials
P. Liaparinos
1,
* and S. David
1,2
1
Radiation Physics, Materials Technology and Biomedical Imaging Laboratory, Department of Biomedical
Engineering, University of West Attica, 12210 Athens, Greece
2
Department of Medical Physics, University of Patras, 26504 Rion, Greece;
* Correspondence: liapkin@uniwa.gr
Received: 11 February 2020; Accepted: 4 March 2020; Published: 5 March 2020
Abstract: In digital phosphor-based imaging modalities, one important intermediate stage is the
optical coupling between the phosphor material and the optical sensor. The performance of the
optical compatibility is affected by surface-roughness issues, for which further research should be
paid. This paper investigates the surface-roughness influence between the CsI phosphor material
and the optical sensing materials (i.e., the silicon dioxide—SiO
2
, the indium tin oxide—ITO, and the
indium gallium arsenide—InGaAs) employed in several image devices. Results showed that for all
sensing materials, the transmission factor t of the optical signal follows qualitatively the variation
of their refractive indexes and quantitatively the variation of the surface roughness and the incident
polar angle. Finally, with respect to light wavelength, the curve of variation was found to be
continuous for ITO and SiO
2
sensing materials; however, lower and sharper variations were
observed in the first case.
Keywords: surface roughness; light interactions; phosphor materials; optical sensors
1. Introduction
Optical sensors are devices, usually incorporating a sensing material, which convert the light
quanta into electronic signals. They are often used to measure physical quantities (e.g., pressure,
flow, temperature) of an instrument by detecting and translating the characteristics of light (e.g.
frequency, wavelength, polarization), or by performing measurements of light variations (e.g.,
intensity, distribution). Optical sensors are used in numerous applications, either for research or
commercial purposes, and their technology has found significant implementations in various
scientific fields such as: environmental monitoring, metrology, particle counting and
characterization, pharmaceuticals, biotechnology, etc.
In the field of biomedical imaging, the optical sensor is considered as a required and significant
tool in the imaging chain, which is generally located at the position of the system where the final
image is formed. In particular, in indirect digital medical systems, the optical sensor is part of the
phosphor-based radiation detector, which consists of a serial chain of signal components, such as
phosphors, fiber optics or lenses, image intensifiers and the sensor pixel array. The phosphor, either
the CsI columnar structure or the Gd
2
O
2
S powder synthesis [1], converts the ionizing radiation (e.g.,
the X-rays) into optical signals, a sensing material (e.g., a photodiode) detects and transforms the
optical signals to electron carries, and finally a readout pixel array system produces the gray-scale
image with respect to the integration of the electron flow intensity. Today, several devices have been
developed that implement various types of digital optical sensors, including: (a) commercial
systems, such as: (i) charge-coupled devices (CCD) devices, (ii) thin-film transistor (TFT) devices,

Crystals 2020, 10, 174 2 of 11
(iii) complementary metal-oxide-semiconductor (CMOS) devices [2–5], and (b) forward-looking
systems, such as: (i) digital integration sensors (DIS), and (ii) quantum image sensors (QIS) [6]. The
advantages, disadvantages, limitations, and further challenges of each image sensor have
extensively been analyzed [2–6].
In most, if not all, cases, different detector technologies necessitate compromises among the
following factors: field coverage, geometrical characteristics, quantum efficiency, sensitivity,
dynamic range, uniformity, acquisition speed, the power consumption and supply, electronic read
out mechanisms, frame rate, and cost [2,3]. Based on the necessities of the imaging task, crucial
factors in the digitization process can also be considered to be the pixel size and the bit depth, which
affect the spatial resolution and noise characteristics. However, since the image quality is related to
light characteristics, a lot of attention has been focused on either phosphor improvement (i.e., the
synthesis of new materials of optimized chemical [7,8], optical [9–11], and structural properties [11–
13] or advanced optical sensor development. Particular research has also been carried out on the
optical compatibility [14] (i.e., the optical matching) between the phosphor material and the optical
sensor. Although several studies have been performed for a variety of issues, as described above,
further investigation discussing the effects of the roughness of surface between the phosphor
material and the sensing material of the optical sensor is required. In general, different modeling
approaches have been employed for the determination of surface-roughness effects on: (i) light
scattering modeling [15], (ii) optical properties and sensitivity [16], (iii) reflectance [17], (iv)
transmission capacities of optical fibers [18], and (v) the overall performance of a sensor [19]. On the
other hand, several instrumentation technologies (laser-based [20,21], LED-based [22], or reflective
[23] fiber-optic sensors) and different methodologies [24,25] have been developed to measure,
assess, and finally characterize the properties of surface roughness.
The aim of this manuscript is to use a simple model and provide a wider understanding of
roughness effects on optical coupling especially observed in phosphor-based imaging systems. The
present examination considered the coupling of CsI phosphor with three cases of sensing materials:
(i) silicon dioxide (SiO2) material employed in charge-coupled devices (CCD), (ii) indium tin oxide
(ITO) material used in thin-film transistor (TFT) devices, and (iii) indium gallium arsenide (InGaAs)
applied in complementary metal-oxide-semiconductor (CMOS) devices.
2. Materials and Methods
2.1. Evaluation of Diffuse Intensity Reflectance and Transmittance
In digital imaging systems, during the light detection process, light photons are emitted from
the phosphor material and thereafter are recorded by the optical detector. However, during this
procedure, when light photons hit one of the phosphor layer boundaries, they may either pass to the
optical sensor or internally be reflected.
2.2. The Case of Surface Smoothness
In the case of surface smoothness (the interface between the phosphor and the optical sensor is
smooth as shown in Figure 1a), the angle of transmission ω is calculated as a function of the angle of
incidence θ with the help of Snell’s law according to the following formula:
()
θθ
coscos 1−
= and








=−
θω
sinsin 1
receiving
origin
n
n
(1)
where norigin is the refractive index of the origin medium (the phosphor layer) and nreceiving is the
refractive index of the receiving medium (the optical sensor). Using Fresnel’s formulas, the
probability of the optical reflectance Rs and transmittance Ts is evaluated as follows [26–28]:

Crystals 2020, 10, 174 3 of 11
() ()
()








+
−
+
+
−
=
ωθ
ωθ
ωθ
ωθ
2
2
2
2
tan
tan
)(sin
sin
2
1
Rs
and RTs −= 1
(2)
taking into account the average of the reflectances for the two orthogonal polarization directions
[29]:
)(tan
)(tan
2
2
ωθ
ωθ
+
−
=IIR
and )(sin
)(sin
2
2
ωθ
ωθ
+
−
⊥=R
(3)
2.3. The Effect of Surface Roughness
In the case of surface roughness (the interface between the phosphor and the optical sensor is
rough as shown in Figure 1b), the Fresnel’s formulas are modified by taking into account a factor
that depends on the granularity of the interface and the evaluation of reflectance Rr and
transmittance Tr is given below [30–33]:
















−−=
2
cos
4
exp1
θ
λ
δπ
origin
n
r
and RsrRr =
(4)
and
()















−
−−=
2
cos
4
exp1
θ
λ
δπ
receivingorigin nn
t
and TstTr =
(5)
where δ is the surface roughness expressing the area of surface irregularities profile per unit of
length, λ is the light wavelength, norigin is the refractive index of the medium of origin, nreceiving is the
refractive index of the receiving medium, and θ is the incident angle. Values of r and t near to unity
imply reflectance and transmittance similar to those of surface smoothness. It is of significance to
note that equations (4) and (5) have suitably been modified so as to provide results for particular
angles.
(a) Smoothness surface (b) Roughness effect
Figure 1. The figure illustrates the light ray interaction with the surface (the interface between the
phosphor and the optical sensor) in case of: (a) smooth surface and (b) rough surface.
2.4. Set Up of Phosphor–Optical Detector Combinations
In the present study, the surface-roughness effects between the phosphor and optical sensor
were evaluated for the most widely used phosphor material in indirect phosphor-based medical

Crystals 2020, 10, 174 4 of 11
imaging detectors, which is the CsI phosphor (i.e., the geometry of the detector consists of CsI
phosphor coupled with the sensing layer of the optical sensor, as illustrated in Figure 2).
Figure 2. The figure illustrates the geometry of the present study (the configuration between the
phosphor and the optical sensor).
Its columnar (needle-like) structure is employed in imaging systems to improve the X-ray
quanta detection while controlling lateral dispersion of the signal due to optical transport [29]. In
addition, this property allows the CsI layer to be made thicker than other phosphor layers (i.e., for
the same amount of spatial spread of the signal), the increased thickness allows higher X-ray
absorption and as a result CsI generally produces equivalent image quality at lower X-ray exposure
levels than Gd2O2S-based detectors [1].
Figure 3. The refractive index as a function of light wavelength (400–700 nm). Figure depicts the
refractive index of CsI phosphor and the corresponding refractive indices of three sensing materials:
(1) SiO2 (employed in charge-coupled devices (CCD)), (2) ITO (employed in thin-film transistor (TFT)
devices) and (3) InGaAs (employed in complementary metal-oxide-semiconductor (CMOS) devices).
Thus, the CsI phosphor provides excellent resolution, through reduced scattering, since each
column acts as a light pipe channeling the visible light to the optical sensor. The aforementioned
conditions make the CsI phosphor prevalent and provide an advantage over the traditional, popular
and cost-effective gadolinium oxysulfide (Gd2O2S) granular phosphor, although its technology is
well-known, and its size, thickness, and flexibility can be handled easily [34]. Due to the slightly
hydroscopic nature, columnar crystalline structures are obtained via a deposition process on
specially treated substrates, and coatings are often encapsulated against moisture ingress, which
also eliminate damage from transit and handling. Last but not least, the CsI phosphor can be readily
deposited by thermal evaporation onto a readout pixel array without degrading the properties of
active devices in the array. This direct deposition avoids the use of the optical coupling agents, such
as optical grease or coupling fluid, between the scintillator and the readout pixel array [34]. The

Crystals 2020, 10, 174 5 of 11
value of CsI refractive index is often given stable (value equal to 1.8) in literature; however, in the
present study, it was considered to vary with light wavelength, as shown in Figure 3 [35].
Below the phosphor material, the compatibility with the optical sensors is mainly served by a
photodiode. This device is capable of converting light into electric current and thus being able to
sense light intensity (i.e., as light hits the photodiode, free electrons will be generated and the current
flowing in the circuit will increase) [36]. Three cases of sensing materials were assumed as the
intermediate stage between the phosphor and the readout pixel array system: (1) silicon dioxide
(SiO2) material employed in charge-coupled devices (CCD), (2) indium tin oxide (ITO) material used
in thin-film transistor (TFT) devices, and (3) indium gallium arsenide (InGaAs) applied in
complementary metal-oxide-semiconductor (CMOS) devices. The variation of refractive indexes as a
function of light wavelength (400–700 nm) is also provided in Figure 3 for all sensing materials
[37,38]. The surface-roughness effects were examined in the range from 10 nm up to 100 nm. Three
different cases were examined based on the angle of the incident light photons at the exit surface of
the phosphor and the entrance surface of the sensing material: (a) θ = 0°, (b) θ = 15°, and (c) θ = 45°.
3. Results and Discussion
The effects of surface roughness on light reflection and transmission on the intermediate surface
between the CsI phosphor and the sensing materials are provided in figures 4–6.
(a) (b)
(c) (d)
Figure 4. Figure depicts the variation of the reflection r (case a) and the tranmission t (cases b–d) as a
function of light wavelength (400–700 nm). Figures correspond to three cases of confuguration
geometries between CsI phosphor and three sensing materials: SiO2 (employed in CCD), ITO

Crystals 2020, 10, 174 6 of 11
(employed in TFT), and InGaAs (employed in CMOS), respectively. Results are provided for incident
polar angle θ equal to 0°.
In particular, the results were obtained by using equation 4 (evaluation of the reflection factor r)
and equation 5 (evaluation of the transmission factor t) and are analyzed and classified as follows.
Each figure depicts four cases: (a) the first case shows the variation of the reflection factor r as a
function of light wavelength (400–700 nm) for surface roughness δ values from 5 nm up to 35 nm, (b)
the second case corresponds to SiO2 sensing material and shows the variation of the transmission
factor t as a function of light wavelength (400–700 nm) for surface roughness δ values from 10 nm up
to 100 nm, (c) the third case corresponds to ITO sensing material and shows the variation of the
transmission factor t as a function of light wavelength (400–700 nm) for surface roughness δ values
from 10 nm up to 100 nm, and (d) the fourth case corresponds to InGaAs sensing material and shows
the variation of the transmission factor t as a function of light wavelength (400–700 nm) for surface
roughness δ values from 10 nm up to 100 nm. Results are provided in figures 4–6 for incident polar
angle θ equal to to 0°, 15°, and to 45°, respectively.
Examining and comparing the reflection factor r under similar and specific conditions, it was
found to vary: (i) from 0.03 (surface roughness of 5 nm) up to 0.71 (surface roughness of 35 nm) at
700 nm light wavelength and polar angle 0°, (ii) from 0.98 (light wavelength 400 nm) down to 0.71
(light wavelength 700 nm) for surface roughness of 35 nm and polar angle 0°, and (iii) from 0.71
(polar angle 0°) down to 0.29 (polar angle 45°) at 700 nm light wavelength and surface roughness of
35 nm. As a result, the following conclusions can be drawn. The reflection factor r: (i) increases with
surface-roughness value, (ii) decreases with light wavelength, and (iii) decreases with incident polar
angle.
Regarding the transmission factor t, by analyzing and comparing the performance of the three
sensing materials under similar conditions, general observations can be underlined.
In the case of SiO2 sensing material: there may be observed a continuous decrease of
transmission factor t from an initial value (at 400 nm) down to lower values (at 700 nm). Identically
with the case of ITO sensing material, the variation of the transmission factor t is continuous,
however the SiO2 exhibits higher values under similar surface-roughness conditions. More
specifically, the transmission factor t varies: (i) from 0.76 down to 0.28 for the highest value of
surface roughness (100 nm). Data are provided for polar angle 0°, (ii) from 0.56 down to 0.17 for the
highest value of surface roughness (100 nm). Data are provided for polar angle 15° and (iii) from 0.20
down to 0.05 (at 600 nm) for the highest value of surface roughness (100 nm). Data are provided for
polar angle 45°.
In the case of ITO sensing material: there may be observed a continuous decrease of
transmission factor t from an initial value (at 400 nm) down to zero value. The initial value is higher
for high values of surface roughness and low values of polar angle. For example, the initial value
takes: (i) the value of 0.49 for surface roughness 100 nm and 0.007 for surface roughness of 10 nm
(polar angle 0°). Below 0.01 is achieved approximately around 650 nm for all cases of
surface-roughness values, (ii) the value of 0.33 for surface roughness of 100 nm and 0.004 for surface
roughness of 10 nm (polar angle 15°). Below 0.01 is achieved approximately around 650 nm for all
cases of surface-roughness values and (iii) the value of 0.17 for surface roughness of 100 nm and
0.001 for surface roughness of 10 nm (polar angle 45°). Below 0.01 is achieved approximately around
600 nm for all cases of surface-roughness values.

Crystals 2020, 10, 174 7 of 11
(a) (b)
(c) (d)
Figure 5. The figure depicts the variation of the reflection r (case a) and the tranmission t (cases b–d)
as a function of light wavelength (400–700 nm). Figures correspond to three cases of configuration
geometries between CsI phosphor and three sensing materials: SiO2 (employed in CCD), ITO
(employed in TFT), and InGaAs (employed in CMOS), respectively. Results are provided for incident
polar angle θ equal to 15°.
In the case of InGaAs sensing material: there may be observed a variation of transmission factor
t where initially there is an increase up to a maximum value and thereafter follows a decrease with
light wavelength. However, this observation concerns particular surface-roughness values, which
change also with the polar angle value. In particular, (i) for polar angle 0° the transmission factor t:
(a) increases from 0.21 up to 0.36 (light wavelength 500 nm) and thereafter decreases down to 0.13,
regarding the surface roughness of 10 nm, and (b) increases from 0.76 up to 0.94 (light wavelength
500 nm) and thereafter decreases down to 0.58, regarding the surface roughness of 25 nm. For higher
values of surface roughness (i.e., 50 nm, 75 nm and 100 nm) the transmission factor t was found to be
stable and almost equal to unity, (ii) for polar angle 150 the transmission factor t: (a) increases from
0.13 up to 0.23 (light wavelength 500 nm) and thereafter decreases down to 0.08, regarding the
surface roughness of 10 nm, and (b) increases from 0.57 up to 0.80 (light wavelength 500 nm) and
thereafter decreases down to 0.39, regarding the surface roughness of 25 nm. For higher values of
surface roughness (i.e., 75 nm and 100 nm) the transmission factor t was found to be stable and
almost equal to unity, apart from the surface value 50 nm, where a decrease occurred from unity
down to 0.86 (above 550 nm up to 700 nm), and (iii) for polar angle 45° the transmission factor t: (a)

Crystals 2020, 10, 174 8 of 11
increases from 0.06 up to 0.12 (light wavelength 500 nm) and thereafter decreases down to 0.04,
regarding the surface roughness of 10 nm, (b) increases from 0.33 up to 0.54 (light wavelength 500
nm) and thereafter decreases down to 0.21, regarding the surface roughness of 25 nm, and (c)
increases from 0.80 up to 0.96 (light wavelength 500 nm) and thereafter decreases down to 0.61,
regarding the surface roughness of 50 nm. For higher values of surface roughness (i.e., 100 nm) the
transmission factor t was found to be stable and almost equal to unity, apart from the surface value
75 nm, where a decrease occurred from unity down to 0.88 (above 550 nm up 700 nm).
(a) (b)
(c) (d)
Figure 6. The figure depicts the variation of the reflection r (case a) and the tranmission t (cases b–d)
as a function of light wavelength (400–700 nm). Figures correspond to three cases of configuration
geometries between CsI phosphor and three sensing materials: SiO2 (employed in CCD), ITO
(employed in TFT), and InGaAs (employed in CMOS), respectively. Results are provided for incident
polar angle θ equal to 45°.
Based on the aforementioned analysis, for the variation of transmission factor t the following
main outcomes can be drawn: (a) for all sensing materials the variation of transmission factor t
follows qualitatively the variation of their refractive indexes with light wavelength, as shown in
Figure 3; (b) for all sensing materials the variation of transmission factor t follows quantitatively the
variation of: (i) surface roughness, and (ii) incident polar angle; (c) the curve of variation was found
to be continuous for ITO and SiO2 sensing materials. Between the two cases, ITO exhibited lower
values and the curve of variation was sharper than in the SiO2 case. This section may be divided by
subheadings. It should provide a concise and precise description of the experimental results, their
interpretation as well as the experimental conclusions that can be drawn.

Crystals 2020, 10, 174 9 of 11
Table 1. The table provides the variation of the tranmission factor t between CsI phosphor and the
corresponding sensing materials SiO2, ITO, and InGaAs, respectively. Results are provided for
incident polar angles θ equal to 0°, 15°, and 45° and surface roughness (10, 25, 50, 75, 100 nm). Data are
shown for light wavelength 550 nm (the approximate emission peak of CsI phosphor doped with
thallium activator).
Light Wavelength: 550 nm
Surface Roughness (nm) Transmission (t) - CsI / SiO2
θ = 00 θ = 150 θ = 450
10 0.01 0.00 0.00
25 0.04 0.02 0.01
50 0.14 0.08 0.04
75 0.28 0.17 0.09
100 0.44 0.29 0.15
Transmission (t) - CsI / ITO
θ = 00 θ = 150 θ = 450
10 0.00 0.00 0.00
25 0.01 0.00 0.00
50 0.02 0.01 0.01
75 0.05 0.03 0.01
100 0.08 0.05 0.02
Transmission (t) - CsI / InGaAs
θ = 00 θ = 150 θ = 450
10 0.28 0.17 0.09
25 0.87 0.69 0.43
50 1.00 0.99 0.89
75 1.00 1.00 0.99
100 1.00 1.00 1.00
Finally, table 1 summarizes the variation of the tranmission factor t with incident polar angles θ
and surface roughness between CsI phosphor and the corresponding sensing materials SiO2, ITO,
and InGaAs, respectively. Results are provided for light wavelength equal to 550 nm (the
approximate emission peak of CsI phosphor doped with thallium activator). In particular, and for
surface roughness in the range 10–100 nm, the transmission factor increases: (a) from 0.01 up to 0.44
for SiO2, from 0 up to 0.08 for ITO, and from 0.28 up to 1 for InGaAs, considering polar angle 00; (b)
from 0 up to 0.29 for SiO2, from 0 up to 0.05 for ITO and from 0.17 up to 1 for InGaAs, considering
polar angle 150; and (c) ) from 0 up to 0.15 for SiO2, from 0 up to 0.02 for ITO and from 0.09 up to 1
for InGaAs, considering polar angle 450. Considering surface roughness of 100 nm, there was found
to be a decrease of (i) 10 % for the first configuration CsI/SiO2 (angle range 00–450) and (ii) 75 % for
the second configuration CsI/ITO (angle range 00–450). For the third configuration CsI/InGaAs, no
variation was observed.
4. Conclusions
Research and development in digital optical devices have become ubiquitous over the past
decade with the purpose of presenting new and advanced high-performance displays for a variety
of applications. Within the framework of image acquisition research, the optimization of the imaging
system can be accomplished by improving the surface-roughness effects of the components
embedded in the imaging chain. Regarding the surface-roughness influence between the widely
used CsI phosphor material and the sensing materials (i.e., the silicon dioxide—SiO2, the indium tin
oxide—ITO, and the indium gallium arsenide—InGaAs) employed correspondingly in CCD, TFT,
and CMOS image devices, the following major conclusion can be drawn: the transmission factor t of

Crystals 2020, 10, 174 10 of 11
the optical signal follows qualitatively the variation of their refractive indexes and quantitatively the
variation of the surface roughness and the incident polar angle.
Author Contributions: Conceptualization, P.L. and S.D.; methodology, P.L. and S.D.; software, P.L.; validation,
P.L.; formal analysis, P.L.; investigation, P.L. and S. D.; writing—original draft preparation, P.L.;
writing—review and editing, P.L. and S.D.; visualization, P.L.; supervision, P.L. All authors have read and
agreed to the published version of the manuscript.
Funding: “This research received no external funding”
Conflicts of Interest: “The authors declare no conflict of interest.”
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