Generalized freespace diffuse photon transport model based on the influence analysis of a camera lens diaphragm.
ABSTRACT The camera lens diaphragm is an important component in a noncontact optical imaging system and has a crucial influence on the images registered on the CCD camera. However, this influence has not been taken into account in the existing freespace photon transport models. To model the photon transport process more accurately, a generalized freespace photon transport model is proposed. It combines Lambertian source theory with analysis of the influence of the camera lens diaphragm to simulate photon transport process in free space. In addition, the radiance theorem is also adopted to establish the energy relationship between the virtual detector and the CCD camera. The accuracy and feasibility of the proposed model is validated with a MonteCarlobased freespace photon transport model and physical phantom experiment. A comparison study with our previous hybrid radiosityradiance theorem based model demonstrates the improvement performance and potential of the proposed model for simulating photon transport process in free space.

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ABSTRACT: A novel method is presented for accurately reconstructing a spatially resolved map of diffuse light flux on a surface using images of the surface and a model of the imaging system. This is achieved by applying a modelbased reconstruction algorithm with an existing forward model of light propagation through free space that accounts for the effects of perspective, focus, and imaging geometry. It is shown that flux can be mapped reliably and quantitatively accurately with very low error, <3% with modest signaltonoise ratio. Simulation shows that the method is generalizable to the case in which mirrors are used in the system and therefore multiple views can be combined in reconstruction. Validation experiments show that physical diffuse phantom surface fluxes can also be reconstructed accurately with variability <3% for a range of object positions, variable states of focus, and different orientations. The method provides a new way of making quantitatively accurate noncontact measurements of the amount of light leaving a diffusive medium, such as a small animal containing fluorescent or bioluminescent markers, that is independent of the imaging system configuration and surface position.Journal of the Optical Society of America A 12/2013; 30(12):257284. · 1.67 Impact Factor 
Article: Alloptical quantitative framework for bioluminescence tomography with noncontact measurement
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ABSTRACT: In this contribution, we present an alloptical quantitative framework for bioluminescence tomography with noncontact measurement. The framework is comprised of four indispensable steps: extraction of the geometrical structures of the subject, light flux reconstruction on arbitrary surface, calibration and quantification of the surface light flux and internal bioluminescence reconstruction. In particular, the geometrical structures are retrieved using a completely optical method and captured under identical viewing conditions with the bioluminescent images. As a result, the proposed framework avoids the utilization of computed tomography or magnetic resonance imaging to provide the geometrical structures. On the basis of experimental measurements, we evaluate the performance of the proposed alloptical quantitative framework using a mouse shaped phantom. Preliminary result reveals the potential and feasibility of the proposed framework for bioluminescence tomography.International Journal of Automation and Computing 02/2012; 9(1).  SourceAvailable from: Jon Frampton[Show abstract] [Hide abstract]
ABSTRACT: A multimodal optical imaging system for quantitative 3D bioluminescence and functional diffuse imaging is presented, which has no moving parts and uses mirrors to provide multiview tomographic data for image reconstruction. It is demonstrated that through the use of transilluminated spectral nearinfrared measurements and spectrally constrained tomographic reconstruction, recovered concentrations of absorbing agents can be used as prior knowledge for bioluminescence imaging within the visible spectrum. Additionally, the first use of a recently developed multiview optical surface capture technique is shown and its application to modelbased image reconstruction and freespace light modelling is demonstrated. The benefits of modelbased tomographic image recovery as compared to twodimensional (2D) planar imaging are highlighted in a number of scenarios where the internal luminescence source is not visible or is confounding in 2D images. The results presented show that the luminescence tomographic imaging method produces 3D reconstructions of individual light sources within a mousesized solid phantom that are accurately localized to within 1.5 mm for a range of target locations and depths, indicating sensitivity and accurate imaging throughout the phantom volume. Additionally the total reconstructed luminescence source intensity is consistent to within 15%, which is a dramatic improvement upon standard bioluminescence imaging. Finally, results from a heterogeneous phantom with an absorbing anomaly are presented, demonstrating the use and benefits of a multiview, spectrally constrained coupled imaging system that provides accurate 3D luminescence images.Measurement Science and Technology 09/2013; 24(10):105405. · 1.44 Impact Factor
Page 1
Generalized freespace diffuse photon transport model
based on the influence analysis of a
camera lens diaphragm
Xueli Chen,1,2Xinbo Gao,1 ,* Xiaochao Qu,2Duofang Chen,2Xiaopeng Ma,2
Jimin Liang,2and Jie Tian2,3
1Video and Image Processing System Laboratory, School of Electronic Engineering, Xidian University,
Xi’an, Shaanxi 710071, China
2Life Sciences Research Center, School of Life Sciences and Technology, Xidian University,
Xi’an, Shaanxi 710071, China
3Institute of Automation, Chinese Academy of Science, Beijing 100190, China
*Corresponding author: tian@ieee.org
Received 28 April 2010; revised 21 August 2010; accepted 11 September 2010;
posted 13 September 2010 (Doc. ID 127716); published 7 October 2010
The camera lens diaphragmis an important component in a noncontact optical imaging system and has a
crucial influence on the images registered on the CCD camera. However, this influence has not been
taken into account in the existing freespace photon transport models. To model the photon transport
process more accurately, a generalized freespace photon transport model is proposed. It combines Lam
bertian source theory with analysis of the influence of the camera lens diaphragm to simulate photon
transport process in free space. In addition, the radiance theorem is also adopted to establish the energy
relationship between the virtual detector and the CCD camera. The accuracy and feasibility of the pro
posed model is validated with a MonteCarlobased freespace photon transport model and physical
phantom experiment. A comparison study with our previous hybrid radiosityradiance theorem based
model demonstrates the improvement performance and potential of the proposed model for simulating
photon transport process in free space.© 2010 Optical Society of America
OCIS codes:
110.2970, 170.3880, 170.5280, 170.7050.
1.
Optical imaging has attracted much more attention
in recent years due to its reasonable spatial and tem
poral resolution and affordable cost [1–4]. In particu
lar, its noncontact measurement has become a
valuable tool for the noninvasive detection because
of its significant advantages in detection sensitivity,
image quality, and system simplicity [5–8]. In non
contact optical imaging, the photon transport process
can be divided into two parts—photon transport in
tissues and in free space. Many numerical algo
rithms [9–11] have been proposed to simulate the
Introduction
photon transport process in biological tissues with
high efficiency and good applicability, but they can
not simulate photon transport process in free space.
As a goldstandard algorithm, the Monte Carlo (MC)
method can handle the photon transport process
both in biological tissues and in free space [12,13].
However, it is timeconsuming and needs a large
number of photons to obtain an acceptable result.
In addition, the method cannot be applied to the in
verse process of photon transport in free space, which
describes the reconstruction of light flux distribution
on tissue surfaces from noncontact measurement on
a CCD camera. Because of the complexity of the op
tical system and the Lambertian characteristics of
the escaped photons, it is difficult to develop an
00036935/10/29565411$15.00/0
© 2010 Optical Society of America
5654APPLIED OPTICS / Vol. 49, No. 29 / 10 October 2010
Page 2
effective model for freespace diffuse photon trans
port in such a noncontact measurement.
To handle this problem, Ripoll et al. successfully
proposed an effective freespace photon transport
model that first demonstrated the possibility of rea
lizing qualitative noncontact optical imaging [14].
However, this model is limited to modeling the image
aberrations, perspective, and depthoffield effects.
Based on the proposed model, Schulz et al. put for
ward an improved and simplified model using the
perspective projection method by replacing the cam
era lens with a virtual pinhole [15]. However, the im
proved model neglects the depthoffield effects and
can only apply to the case of a small aperture camera
lens. In our previous study [16], a hybrid radiosity
radiance theorem (HRRT) based model has been pro
posed to simulate the photon transport process,
which analyzed the influence of the camera lens and
modeled it as a thin lens. The model reduced the in
fluence of image aberrations, perspective, and depth
offield effects by using the virtual detector, camera
lens simplification model, radiance theorem, and the
improvement of visibility factor. However, this model
can only apply to the case of the large aperture cam
era lens effectively because it does not consider the
influence of the camera lens diaphragm, which is also
neglected in the existing models presented in Refs.
[14,15]. The camera lens diaphragm is an inevitable
component of the camera lens and plays an impor
tant role in a noncontact optical imaging system. Im
age quality is affected greatly by the camera lens
diaphragm, such as in image range, image definition,
and image intensity. Thus, to accurately model the
photon transport process in free space, analysis of
the camera lens diaphragm is absolutely necessary
and important.
In this paper, a generalized freespace photon
transport model is developed based on the influence
analysis of the camera lens diaphragm, which is an
improved version of the previous HRRT model [16].
Similarly, a propagation formula derived from the
Lambertian source theory is used to describe the en
ergy transformation when a photon propagates in
free space. In the model, the camera lens is modeled
as a combination of a thin lens and a camera lens
diaphragm. Thus, the radiance theorem based on
the thinlens model can also be utilized to depict
the energy relationship between the virtual detector
and the CCD camera. In addition, the introduction of
the camera lens diaphragm can further improve the
depthoffield effects so that we can obtain more
accurate simulation images. The performance of
the proposed generalized model is validated with
MonteCarlobased freespace photon transport (MC
FSPT) model and physical phantom experiment. A
comparison study with the HRRT model presents
the improvement performance of the proposed gener
alized model and demonstrates its feasibility and po
tential for simulating the photon transport process in
free space.
2. Theory and Method
A.
According to the knowledge of infrared physics, dif
fuse photons would act as a new Lambertian source
once they have escaped from the diffuse medium and
registered at the medium surface [17]. It is well
acknowledged that the Lambertian source is a radia
tion source that irradiates to the surrounding space
isotropically. Thus, the microunit power dPðrdÞ of a
detector at position rdof the differential area and or
ientation dA emitted from a medium surface point r
of differential area and orientation dS, in direction s
within a solid angle dΩ, is given by [14]
Lambertian Source Theory
dPðrdÞ ¼1
πJnðrÞðns• sÞdΩdS;
ð1Þ
where JnðrÞ is the surface flux density and is calcu
lated by considering the mismatched boundary con
dition; nsis the unit normal vector of dS and dS is the
corresponding area. Considering the definition of the
solid angle dΩ ¼ −ðdA • sÞ=jrd− rj2, where s always
points to rdand integrates Eq. (1) over all the med
ium surface points, we obtain the total power PðrdÞ at
rdas
PðrdÞ ¼1
π
Z
SJnðrÞξðr;rdÞcosθscosθd
jrd− rj2
dAdS;
ð2Þ
where cosθs¼ ns• s is the cosine dependence of
Lambert’s law; cosθd¼ −ðdA • sÞ=dA accounts for
the detector orientation with respect to the direction
s; dA is the area of the differential detector unit; and
ξðr;rdÞ is a visibility factor that discards surface
points invisible from the differential detector. Equa
tion (2) distinctively depicts the transport character
istic of diffuse photons in free space emitted from the
Lambertian source as the case shown in Fig. 1.
B.
Imaging System
In the optics design of a camera lens, designers
should be concerned not only with the relevant issues
of Gaussian optics, such as the magnification ratio of
the camera lens and the conjugate distribution of ob
ject image, but also other crucial issues on imaging,
such as image range, image definition, and image in
tensity. An actual camera lens is not a simple combi
nation of several lenses, but a system consisting of
various optical components, including a lens system
and several diaphragms [18]. They are important
optical function elements in a camera lens. The lens
system puts emphasis on the transformation of the
light beam, and the diaphragms focus on the receiv
ing constraint of the line of sight [19]. Analysis of
the lens system has been introduced in a previous pa
per [16], so this contribution presents only the
analysis of the camera lens diaphragm.
The diaphragm aims to restrict the light beam en
teredintothecameralens,thatis,usefullinesofsight
Camera Lens Diaphragms in an Optical
10 October 2010 / Vol. 49, No. 29 / APPLIED OPTICS5655
Page 3
are imaged in the camera lens and others are ob
structed. Generally speaking, there are two basal
types of diaphragms in any optical system: aperture
diaphragmandfielddiaphragm[19,20].Theaperture
diaphragm, also named “effective diaphragm,” is a
crucial concept in the camera lens and is used to de
termine the size of the imaging beam, which varies
with the size of aperture diaphragm and affects the
luminance on the imaging plane. In an actual optical
system,thesizeoftheaperturediaphragmisadjusted
by changing the aperture value, which satisfies the
following equation:
D ¼
F
fnum
;
ð3Þ
where D is the size of the aperture diaphragm called
effectiveapertureinoptics,asshowninFig.2;F isthe
focus of the camera lens; and fnum is the aper
ture value.
The function of the field diaphragm is to restrict
the range of image. Image range can be limited by
various physical borders, such as the border of dia
phragm, the border of lens, and the physical bound
ary of image sensor. These physical borders all work
as the field diaphragm. Figure 2 presents two con
ventional positions of the diaphragm, at both sides
of the lens system. In the case of Fig. 2(a), the dia
phragm border acts as both the aperture diaphragm
and the field diaphragm; in Fig. 2(b), the field dia
phragm is performed by the border of the lens system
[21]. Because the camera lens adopted in our optical
imaging system is equipped with a diaphragm lo
cated at the back of the lens system, the following
subsection just presents the influence analysis of the
camera lens diaphragm shown in Fig. 2(b).
C.
Optical Imaging System
According to the simplification theory of the imaging
objective, the lens system adopted in an ideal optical
system can be modeled as a thinlens model [22,23].
However, this simplification considers only the Gaus
sian optics characteristic of the camera lens and
neglects its physical factors, such as diaphragms.
Modeling Camera Lens Diaphragm in a Simplified
Fig. 1.Schematic diagram of the characteristic of diffuse photons transport in free space emitted from a Lambertian source.
Fig. 2.
behind the lens system.
Two types of diaphragms in any camera lens: (a) diaphragm located at the front of the lens system and (b) diaphragm located
5656APPLIED OPTICS / Vol. 49, No. 29 / 10 October 2010
Page 4
To accurately simulate the photon transport process
in free space, we should take both influences into
account in simplifying the camera lens. According
to the aforementioned description of diaphragm,
the camera lens adopted in the optical imaging sys
tem can be equivalently modeled as a simplified thin
lens and a diaphragm. Therein, the diaphragm is vir
tual and located at the same position as the thin lens,
as shown in Fig. 3, where AB shows the lens system
and CG represents the virtual diaphragm.
In Fig. 3, the border of the lens system acts as the
field diaphragm, and the virtual diaphragm as the
aperture diaphragm. The lens system works to deter
mine the range of image, and the virtual diaphragm
is used to restrict the light beam entered into the
camera lens. Assuming that S is the surface profile
of the object and Ω0is the virtual detection space that
is a focal space (a space constructed by the focal
plane) of the detection space Ω, we can determine
the effective virtual detection space Ω0
the relationship between the lens system and the
surface profile, as shown in Fig. 3. Once the effective
virtual detection space is obtained, we can further
define a field visibility factor to restrict the range
of image as
Eby analyzing
αðr;rvdÞ ¼
?1
Ifðrvd∈ Ω0
Otherwise;
EÞ
AND
ðsr→rvd∩S ¼ frgÞ;
0
ð4Þ
where αðr;rvdÞ is the field visibility factor, r is a point
on the surface profile and satisfies r ∈ S,rvd∈ Ω0is a
point at the virtual detection space and satisfies the
lens law with the point rdat the detection space, Ω0
is the effective virtual detection space and has the
relationship of Ω0
from r to rvd.
The virtual diaphragm performs the function of
aperture diaphragm and forms an effective aperture
space ΩD. Making use of Eq. (3), we can obtain the
size of the effective aperture space. An effective
E
E⊂Ω0, and sr→rvdis the line of sight
visibility factor can be introduced to determine the
size of imaging beam as
βðr;rd;ΩDÞ ¼
?1
If sr→rvd∩ΩD≠ ∅;
If sr→rvd∩ΩD¼ ∅;
0
ð5Þ
where βðr;rd;ΩDÞ is the effective visibility factor and
ΩDis the effective aperture space and has a circular
area with a diameter D, calculated by Eq. (3). The ex
pression sr→rvd∩ΩD≠ ∅ can be interpreted that the
line just passes through the effective aperture space,
as Line 1, shown in Fig. 3; similarly, sr→rvd∩ΩD¼ ∅
shows that the intersection point between the line
and effective aperture space is out of the range of
the effective aperture space, as Line 2, shown in
Fig. 3.
D.
Model and Numerical Implementation
Based on the derivation of the radiance theorem, the
photon flux registered at the detector plane is equal
to that at its conjugated virtual detector plane when
an ideal optical imaging system is considered [16].
Thus, the corresponding relationship of energy be
tween a detection point rdand a medium surface
point r can be expressed as
Generalized FreeSpace Diffuse Photon Transport
PðrdÞ ¼1
π
Z
SJnðrÞξðr;rdÞ
cosθscosθd
????rd− r −
l
cosθs0
????
2
dAd
t2dS; ð6Þ
where PðrdÞ is the total power of a differential de
tection area dAdcentered at rd; l is the object image
distance between the virtual detector plane and de
tector plane; s0represents the direction from rvdto rd;
θ is the angle between the direction s0and optical
axis; θsis the angle between the differential medium
surface normal and direction sr→rvd; θdis the angle
between the normal of the virtual detector plane
and direction −sr→rvd; t is the magnification ratio of
the optical imaging system; and dAdis a differential
Fig. 3.Schematic diagram of modeling the camera lens diaphragm in the simplification of noncontact optical imaging system.
10 October 2010 / Vol. 49, No. 29 / APPLIED OPTICS5657
Page 5
detection area at the detector plane and satisfies
dAd¼ t2dAvd, where dAvdis a differential detection
area at the virtual detector plane. Therein, the detec
tion point rd and the virtual detection point rvd
satisfy the following equation:
rd¼ rvdþ
l
cosθs0:
ð7Þ
In Eq. (6), ξðr;rdÞ is the visibility factor that takes
into account the influence of the camera lens dia
phragm presented in Eqs. (4) and (5). As a result,
we obtain a generalized formula for diffuse photon
transport in free space that takes into account the
influence of the camera lens diaphragm as
PðrdÞ ¼1
π
Z
SJnðrÞTðr;rdÞdS;
ð8Þ
where a function that accounts for diffuse photon
transport in free space has been introduced:
Tðr;rdÞ ¼ α
?
????rd− r −
r;rd−
l
cosθs0
?
????
βðr;rd;ΩDÞ
dAd
t2;
×
cosθscosθd
l
cosθs0
2
r ∈ S:
ð9Þ
The flux distribution at the detector plane can be ob
tained directly by the proposed model described in
Eqs. (8) and (9). Compared with the published meth
ods in Refs. [14–16], the proposed model concentrates
more on modeling the camera lens, especially on the
camera lens diaphragm. Furthermore, the proposed
model will reduce to the pinhole model presented in
Ref. [15] if the effective aperture is small enough to
allow one line of sight to pass through for each sur
face point. If the effective aperture can be compar
able to the size of the lens system, the proposed
model would be performed as the thinlens model
presented in Ref. [16]. As a result, the proposed mod
el is a generalized formula for the simulation of
diffuse photon transport in free space.
3.
In this section, three groups of verification experi
ments were designed and performed to evaluate the
performance of the proposed model in this paper.
First,numericalsimulationandphysicalphantomex
periments were conducted to validate the accuracy of
theproposedmodelwithafixedaperturevalue.Then,
a series of optical imaging experiments were carried
out to illustrate the influence of camera lens dia
phragmonimageperformanceandshowtheeffective
ness of the proposed model in the case of different
aperture values. Finally, a comparison experiment
with our previous HRRT model was conducted to
demonstrate the improved performance of the pro
posed model.
Experiments and Results
In the optical imaging experiments, a nylon cylind
rical homogeneous phantom of 15mm radius and
30mm height was designed and utilized. One small
hole of 1mm radius and 16mm depth from the top
surface of the phantom was drilled with a distance
of 8mm from the center to emplace a light source,
as presented in Ref. [16]. The light source was made
of luminescent solution that was extracted from a red
luminescent light stick (Glow Products, Canada).
Because the central wavelength of the luminescence
light generated by the luminescent solution is about
650nm, the optical properties of the phantom used
the values measured at the wavelength of about
660nm by a timecorrelated single photon counting
system [24]. The absorption coefficient is μa¼
0:0138mm−1and the reduced scattering coefficient
is μ0s¼ 0:91mm−1. After injecting the light source,
the free volume of the small hole was filled with
the same material solid stick to avoid leakage of
light, and then the phantom was mounted on a 360°
rotation stage. By rotating the phantom three 90°,
luminescence light was registered by a liquidwater
cooled backilluminated CCD camera (Princeton
Instruments/Acton, 2048B) coupled with a Nikkor
Micro 55mm f=2:8 camera lens.
In order to evaluate the performance of the pro
posed model, the mean error (ME) and correlation
factor (CF) are introduced as presented in [16,25]
? e ¼
X
X
× =ððN − 1ÞσðPcalÞσðPstdÞÞ;
where? e and ρ are the value of the mean error and the
correlation factor, respectively; the superscript cal
represents the flux at the detector plane calculated
by the proposed model, and std shows the flux ob
tained by the standard methods that are used to
evaluate the performance of the proposed model;?P
and σ are the mean value and the standard deviation
of the flux distribution at the detector plane that can
be either Pcator Pstd; N is the total sample number at
the detector plane; and PðiÞis the power of the ith
sample. The CF indicates the degree of correlation
between the calculated and the standard flux, while
the ME describes the discrepancy of them. Accord
ingly, the closer the CF gets to unity and the closer
the ME gets to zero, the better the performance of the
proposed model.
N
i¼1
N
jPcalðiÞ− PstdðiÞj=N;
ρ ¼
i¼1
ðPcalðiÞ−?PcalÞðPstdðiÞ−?PstdÞ
A.
In the experiment verifications, the MCFSPT model
and the real experiment were used as the standard
methods to validate the accuracy of the proposed
model. Results of the MCFSPT model were obtained
by the platform of Molecular Optical Simulation
Environment(MOSE),which
Experiment Verifications
isan MCbased
5658 APPLIED OPTICS / Vol. 49, No. 29 / 10 October 2010
Page 6
simulation platform [26,27] and can be accessed
freely on the website: http://www.mosetm.net/. Re
sults of the real experiment were measured by the
aforementioned noncontact optical imaging system
with a fixed aperture value of fnum¼ 8.
TheexperimentalsetupisshowninFig.4.Therein,
Fig. 4(a) presents the physical phantom used in the
optical imaging experiment; Fig. 4(b) describes four
perspectives for the CCD camera to register the out
going luminescence light, including the front, left,
back, and right perspective; and Fig. 4(c) shows the
numerical phantom utilized in the calculation frame
work of the proposed model and the MCFSPT model.
In the calculation framework of the proposed model,
the surface flux distribution Jnwas obtained by
MOSEafterconsideringamismatchedboundarycon
dition and then interpolated linearly between all the
adjacent points to obtain a refined flux distribution.
Once the refined surface flux distribution was ob
tained, we used the proposed model to calculate the
flux distribution at the detector plane. For the MC
FSPT model, a one hundred million photon simula
tion was performed, which was 100 times as many
as that used in determining the surface flux distribu
tion for the calculation of the proposed model.
In view of the fact that the photon flux registered
in the right perspective has the same trends in dis
tribution as that in the left perspective, flux distribu
tions of the front, left, and back perspective were
examined in this subsection. All the flux was normal
ized to the maximum value versus the detection po
sitions. Figure 5 shows the comparison results for the
detector at z position: zd¼ 0:0, 2.0, and 4:0mm.
Therein, Figs. 5(a)–5(c) present the comparison re
sults between the calculated flux of the proposed
model and the simulated flux of the MCFSPT model.
Figures 5(d)–5(f) show comparisons between the cal
culated flux of the proposed model and the measured
flux of the real experiment. In Fig. 5, the solid lines
show the standard flux from the MCFSPT model or
real experiment, and the asterisks represent the cal
culated results of the proposed model. Furthermore,
the ME and CF of the three perspectives were also
calculated and listed in Table 1. Similar tendency
and good agreement were observed in the cases ex
amined, with average ME and CF being about
0.0219 and 0.9698. From Figs. 5(c) and 5(f), we find
that the calculated flux of the proposed model seems
a bit sparse, which was intrinsically caused by the
inadequate spatial resolution of the refined surface
flux. However, compared with the simulated flux of
the MCFSPT model, the sparsity of the calculated
flux was a little better, which can also be seen from
the ME and CF listed in Table 1. The comparison re
sults indicated that the proposed model worked well
in simulating the photon transport process in free
space and appeared in good agreement with both
the MCFSPT model and the real experiment.
B.
Image Quality
To illustrate the influence of the camera lens dia
phragm on images registered at the CCD camera
and the capability of the proposed model to simulate
that influence, a group of experiments with different
aperture values were conducted using the aforemen
tioned noncontact optical imaging system. The ex
perimental setup employed in the experiments was
the same as that described in Subsection 3.A, except
that the light source was a bit larger—about 6mm in
length. It should be noted that images registered
on the CCD camera were captured under the same
conditions, except for the aperture value. Left
perspective images on the CCD camera captured un
der different aperture values were observed, and four
of them are presented in Figs. 6(a)–6(d). Using the
proposed model, the corresponding calculated results
are shown in Figs. 6(e)–6(h). As presented in
Fig. 6(h), there was a little sparse in the calculated
results when the aperture value was bigger than a
certain value (about fnum¼ 16 in this experiment),
which was probably caused by the inadequate spatial
resolution of the refined surface flux distribution.
Particularly, the degree of sparse for the results dee
pened with the increase of the aperture value under
the condition of using the same surface flux distribu
tion. If the spatial resolution of the surface flux dis
tribution were adequately refined with the increase
of aperture value, the sparse of the results would
be improved. Nevertheless, compared with the
Influence of the Camera Lens Diaphragm on
Fig. 4.
experiment, (b) four perspectives for the CCD camera to register escaped photons, (c) the numerical phantom used in the simulation
and calculation.
(Color online) Experimental setup for comparison experiment showing (a) the physical phantom used in the optical imaging
10 October 2010 / Vol. 49, No. 29 / APPLIED OPTICS 5659
Page 7
experimental results, similar tendency and compar
able distribution were addressed in all cases
examined.
From Fig. 6 and no presented results, we find that
two phenomena happen as the aperture value in
creases or as the size of the aperture diaphragm de
creases in both the captured and the calculated
images. First, the intensity becomes weaker and the
definitiongetsworse.Becausethefunctionoftheaper
turediaphragmistodeterminethesizeoftheimaging
beam, a smaller aperture diaphragm will lead to less
light entered into the camera lens and imaged at the
CCD camera. As a result, the intensity and signalto
noise ratio of the image will decrease. Figure 7
presents a downtrend of the intensity as the aperture
value increases. Figure 7(a) shows the downtrend of
peak intensity, and Fig. 7(b) is the average intensity.
Therein, the square lines represent the experimental
data and the asterisks show the calculated results.
From Fig. 7, we determine that both the peak and the
average intensity become smaller as the aperture va
lue increases and the proposed model wellsimulated
the changes with extremely small discrepancies. The
MEforthepeakintensitycomparisonwas0.0166,and
the normalized ME for the average intensity compar
isonwas0.0097.Furthermore,arelativequantitative
relationship between the intensity and the aperture
value was also observed where the intensity will de
crease by almost half once the aperture value in
creases a scale, particularly as shown in Fig. 7(b).
Second, the distributional pattern of each image is
different. To illustrate this difference, a distance
from the position of the peak intensity point to the
image border of the research object was used, as
described in Fig. 8(a). By increasing the aper
ture value, the distance was gradually reduced.
Fig. 5.
zd¼ 0:0, 2.0, and 4:0mm. (a)–(c) Comparison of flux between the proposed model and the MCFSPT model; (d)–(f) comparison of flux
between the proposed model and the real experiment. (a) and (d) front perspective, (b) and (e) left perspective, (c) and (f) back perspective.
(Color online) Comparison results between the calculated (asterisk lines) and standard flux (solid lines) at the detection position:
Table 1.Error Comparison between the Calculated and the Standard Fluxa
Proposed Model Comparison
ME CF
FrontLeft Back Front LeftBack
MCFSPT model
Real experiment
0.0104
0.0176
0.0179
0.0113
0.0468
0.0271
0.9968
0.9917
0.9844
0.9141
0.9606
0.9711
aThe second row presents the comparison of flux between the proposed model and the Monte Carlo method based on the freespace
photon transport model; the third row shows the comparison between the proposed model and the real experiment. ME is defined as
the mean error between the two compared objects; CF is the correlation factor of the two compared objects. The symbols front, left,
and back represent the three different perspectives.
5660APPLIED OPTICS / Vol. 49, No. 29 / 10 October 2010
Page 8
Figure 8(b) presents the trend of the distance varia
tion as the aperture value increases. Although there
was a little difference between the calculated and
the experimental results, the downtrend of them
was consistent, with an average distance of 0.625
pixels.
As a result, we conclude that the performance of
images registered at the CCD camera was factually
affected by the camera lens diaphragm, such as
image intensity and definition, image range, and in
tensity distribution. The comparisons between the
calculated and the experimental results demon
strated that the proposed model can wellsimulate
the influence of the camera lens diaphragm. If a
small aperture diaphragm is used in the imaging ex
periment and a larger aperture diaphragm or no
aperture diaphragm is adopted in the calculation,
an image of bad boundary will be obtained.
C.
Accordingtotheaforementionedillustrationofthein
fluence of camera lens diaphragm on image perfor
mance, we infer that the HRRT model presented in
our previous study [16] would work poorly when a
smallaperturediaphragmisusedintheexperiments.
However,theproposedmodelinthispaperovercomes
this problem because of the consideration of the cam
era lens diaphragm. A comparison experiment was
conducted in this subsection to present the improved
performance of the proposed model compared with
the HRRT one. The experimental setup is also pre
sented in Fig. 4, and the experimental conditions
are identical. In the comparison experiment, the sur
facefluxdistributionsutilizedinthetwomodelswere
both obtained by MOSE and then interpolated line
arly to approach a refined surface flux distribution.
Improved Performance Demonstration
Fig. 6.
CCD camera captured with different aperture values (top row) in the left perspective. (a)–(d) captured images at the CCD camera; (e)–(h)
calculated results of the proposed model. For (a) and (e), fnum¼ 2:8; (b) and (f), fnum¼ 5:6; (c) and (g), fnum¼ 11; (d) and (h), fnum¼ 22.
(Color online)Comparisonsbetweenthecalculatedresultsof theproposedmodel(bottomrow)andthe experimentalimageson the
Fig.7.
results (asterisk lines) and the experimental data (square lines). (a) Curve for variation of the peak intensity with the different aperture
values. (b) Curve for variation of the average intensity with the different aperture values.
(Coloronline)Correspondingrelationshipbetweentheintensityvariationandthedifferent aperturevaluesfor boththecalculated
10 October 2010 / Vol. 49, No. 29 / APPLIED OPTICS5661
Page 9
Figure 9 presents the comparison images between
the two models and the real experiment. The experi
mental result is shown in Fig. 9(a), and the corre
sponding calculated results obtained by the HRRT
model and the proposed model are presented in Figs.
9(b) and 9(c). Moreover, the factors of the ME and CF
were also calculated and listed in Table 2. From
Fig. 9 and Table 2, we find that the proposed model
performed better than the HRRT model in handling
the boundary aberrations of the imaging region,
which was intrinsically caused by no consideration
of the camera lens diaphragm in the HRRT model.
If the HRRT model is considered from the aspect
of the camera lens diaphragm, it can be viewed as a
model with an effective aperture equaling the size of
the camera lens. Thus, the equivalent effective aper
ture will be much larger than the real one used in the
experiment. Therefore, the HRRT result presented
in Fig. 9(b) is comprehensible, according to the afore
mentioned illustration of the influence of the camera
lens diaphragm. On the other hand, the improved
performance for the frontperspective images is not
significant, which can be seen from the values of
the ME listed in Table 1 of this contribution and
Table 2 of the previous study [16]. For the front per
spective, the outgoing luminescence light registered
at the detector plane is mainly gathered at the center
of imaging region so that the intensity at the sur
rounding boundary area is extremely low. Thus, we
conclude that the proposed model exhibited a well
improved performance on the boundary aberrations
in the modeling photon transport process in free
space. In conclusion, the proposed model greatly im
proved the simulation images on image range and
flux distribution and provided much accurate simu
lated detection results for the simulation of optical
imaging experiments.
4.
In this paper, a generalized freespace diffuse photon
transportmodel wasdeveloped for the noncontact de
tection measurement. Similar to our previous study
[16], this model also employed the hybrid radiosity
radiancetheoremtodepicttheenergytransformation
for photon transports in a noncontact detection
system. Furthermore, the influence analysis of the
camera lens diaphragm was incorporated into the
simplification model of the camera lens, which made
the model suitable for processing image aberrations
anddepthoffieldeffects.Comparedwiththeexisting
Discussion and Conclusion
Fig. 8.
results (first column) and the experimental data (second column). (a) Schematic diagram of the definition of pixel distance. (b) Curve for
variation of the pixel distance with the different aperture values.
(Color online) Corresponding relationship between the pixel distance and the different aperture values for both the calculated
Fig. 9.
experimental results, (b) calculations of the HRRT model, (c) calculations of the proposed mode.
(Color online) Comparisons of flux distribution at the detector plane between the calculation models and the real experiment: (a)
5662APPLIED OPTICS / Vol. 49, No. 29 / 10 October 2010
Page 10
models, the proposed model has the following
features.
First, simplified model of the camera lens dia
phragm is applied to describe the photon transport
process in free space for the first time, to the best
of our knowledge, which has a great influence on
images registered at the CCD camera, such as the
image range, image definition, and image intensity,
and especially the quality of the image boundary. The
proposed generalized model can be better used to
handle the boundary aberrations of the image region
than the existing models. In addition, the introduc
tion of virtual detector plane and radiance theorem
contributes to eliminate the perspective effects.
Therefore, simulated images are more comparable
to the images captured by the CCD camera.
Second, the proposed model is a generalized for
mula for simulating the photon transport process
in free space, which contains two extreme cases, that
is, a pinhole lens based model [15] and a thinlens
based model [16]. If the effective aperture is so small
that only one line of sight can pass through for each
surface point, the model is reduced to the pinhole
lens based model. Otherwise, if the effective aperture
is comparable to the size of the lens system, the mod
el would be performed as the thinlens based model.
Furthermore, the depthoffield effects of the optical
imaging system are relevant to the effective aper
ture, which is determined by the size of the aperture
diaphragm. Thus, the proposed generalized model
can be better to process the problem of depth of field.
On the otherhand, the proposed generalizedmodel
is accurate to a great extent, but it is a little time
consuming. To achieve a smoother simulation result,
we must interpolate the surface flux distribution to
guarantee the adequately refined surface spatial re
solution. As a result, it makes the computation much
more timeconsuming. Fortunately, with the devel
opment of technology, the parallel strategy and the
graphics processing unit (GPU) technique can be
adopted to speed up the proposed generalized model.
And the corresponding work is ongoing. In addition,
the proposed model is developed based on the
assumption that the photons escaping from the
medium surface are diffuse. If the surface light dis
tribution is not diffuse but anisotropic, the resulting
transport function from the medium surface to the
CCD camera should be far more complicated because
of the angle dependency.
In conclusion, we have presented a generalized
freespace diffuse photon transport model based on
the influence analysis of a camera lens diaphragm
in this paper. Preliminary experimental results de
monstrated the feasibility and potential of the pro
posed generalized model. Our future work will
concentrate on the acceleration of the generalized
model based on the GPUbased technique and mod
eling the far more complicated transport function.
The corresponding results will be reported later.
This work is supported by the Program of the
National Basic Research and Development Program
of China (973 Program) under grants 2006CB705700
and2011CB707702, the
Sciences (CAS) Hundred Talents Program, the Na
tional Natural Science Foundation of China (NSFC)
under grants 81090272, 81000632, 30900334, and
60771068, the Shaanxi Provincial Natural Science
Foundation Research
2009JQ8018, and the Fundamental Research Funds
for the Central Universities.
Chinese Academyof
Projectundergrant
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