In the recent past, optical spectroscopy and imaging methods for biomedical diagnosis and target enhancing have been widely researched. The challenge to improve the performance of these methods is to know the sensitive depth of the backwards detected light well. Former research mainly employed a Monte Carlo method to run simulations to statistically describe the light sensitive depth. An experimental method for investigating the sensitive depth was developed and is presented here. An absorption plate was employed to remove all the light that may have travelled deeper than the plate, leaving only the light which cannot reach the plate. By measuring the received backwards light intensity and the depth between the probe and the plate, the light intensity distribution along the depth dimension can be achieved. The depth with the maximum light intensity was recorded as the sensitive depth. The experimental results showed that the maximum light intensity was nearly the same in a short depth range. It could be deduced that the sensitive depth was a range, rather than a single depth. This sensitive depth range as well as its central depth increased consistently with the increasing source-detection distance. Relationships between sensitive depth and optical properties were also investigated. It also showed that the reduced scattering coefficient affects the central sensitive depth and the range of the sensitive depth more than the absorption coefficient, so they cannot be simply added as reduced distinct coefficients to describe the sensitive depth. This study provides an efficient method for investigation of sensitive depth. It may facilitate the development of spectroscopy and imaging techniques for biomedical diagnosis and underwater imaging.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
In recent decades, in many research areas like biomedical optics or underwater target imaging, backwards detected light is frequently used to detect or enhance a target which is below the surface of a turbid medium. Spectroscopy like reflected spectroscopy (RS) , diffuse optical spectroscopy (DOS) , and light scattered spectroscopy (LSS)  were developed for disease diagnosis in breast, esophagus, colon, prostate, skin, and other tissues. These technologies can be used for better understanding of the morphologic and pathological information of the tissue. Imaging methods like polarization difference imaging (PDI)  and range-gated imaging (RGI)  were developed for target enhancement under water or in fog. These can be used for car driver’s vision enhancement in bad weather or for monitoring of military targets.
However, the performance of these approaches is mainly dependent on the precise description of the light transport in turbid media which has been effectively provided by the radiative transport theory (RTT) . Because of the difficulty of resolving the RTT equation, Monte Carlo (MC) method was most commonly used to simulate light transport in tissue which has been treated as “golden standard” . The light arrives at the detector after transporting in turbid medium, carrying information along photons’ migration paths. Hence, to meet the challenge of enhancing the performance of these techniques the depth information of the light should be known better. It can be used for judging the optimal valid ranges of the different methods .
In early years, researchers focused on studying the penetration depth of the detected light which restricted the maximum detection depth. J. Eichler measured the light penetration depth in a tissue in 1977  using transmitted light. The transmitted light along the incident direction attenuated basically following the Beer-Lambert Law. However, usually the medium is addressed in reflectance geometry, in which the light is injected and collected from same surface. Hence, it is more valuable to study the penetration depth in reflectance geometry.
The research dealing with reflected light depth information has many different names including “penetration depth” , “sampling depth” , “look-ahead distance” , “path length distribution” , and “interrogation depth” .
The first three kinds basically mean the same. It is the maximum depth which can be reached by the photons detected at the surface of the medium at a distance ρ from the incident point . This kind of depth information can be called “penetration depth” (PDep, ) uniformly. It was useful for estimating the limit depth of the pathological changes which can be detected. In MC method, it was described by calculating the weighted mean value of the maximum depth reached by each detected photon.
The last two are mainly studied by MC method. It basically implies the average scattering depth . In MC method, it can be described as the weighted mean value of each photon packet’s average “scattering depth” in which the photon’s scattering events occurred . can be called as “sensitive depth” (SDep) uniformly. Compared to the penetration depth which can only describe the limit of the detection, sensitive depth can be used for estimating the optimal range of depth in which the detected light would be most sensitive to the abnormities.
The penetration depth had already been studied by several groups in the last two decades while studies on sensitive depth were much less. Moreover, the penetration depth can be deduced from the equations while the sensitive depth can only be statistically calculated by the MC method. Although the MC method has proven to be efficient for the light transport simulation, the accuracy of the sensitive depth calculating algorithm requires experimental estimation which is lacking till now. Experimental study on penetration depth has been undertaken through inverting the modified Beer–Lambert expression  or by using a two-layer phantom . However, the sensitive depth cannot be studied experimentally as yet.
In this study, an absorption plate based method is introduced to experimentally study the sensitive depth of the backwards detected light in small source-detection distance. By moving the absorption plate from the surface of the probe in which the light could be totally absorbed to the deep of the phantom, light distribution along the depth can be recorded and then the sensitive depth can be derived from the results. We also built many phantoms with different absorption coefficients and reduced scattering coefficients to investigate their relationship with the sensitive depth.
2.1 Fundamental theory
In order to experimentally measure the sensitive depth of the backwards detected light, we used an absorption plate to abandon the photons which can transport deeper than the location of the absorption plate. As shown in Fig. 1, the penetration depths of three photons were marked as point A, B, and C and hence the corresponding three photons could be marked as Photon A, B, and C. The solid and dotted black lines in the figure represent two potential positions of the absorption plate. When the plate is positioned on the dotted black line, photons B and C would be absorbed while photon A could be transported into the collection fiber. If the plate moved to the solid black line, photon B would also be collected.
The depth of the plate from probe is increased from 0 mm to the depth in which the intensity of the measured light became invariant. In each movement of the absorption plate, the intensity of backwards detected light is recorded. By differentiating the measured results with respect to the depth, we can get the distribution of the backwards detected light intensity along the depth dimension. The backwards detected photons in small source-detection distance (SD) usually go through only a few scattering events. So the backwards detected photons must suffer a back-scattering. Thus the depth of the backwards detected light can be seen as the place in which a back-scattered event occurs. Consequently the depth with the maximum intensity distribution can represent the sensitive depth.
2.2 Experimental setup
The experimental setup is shown in Fig. 2.
The source fiber was connected to a 670 nm wavelength laser diode module (LDM670, Thorlabs Inc., Newton, New Jersey, USA) and the detecting fiber was connected to a Si transimpedance amplified photodetector (PDA100Aa, Thorlabs Inc., Newton, New Jersey, USA) along with a Digital Oscilloscope (DS2000A, Rigol, Beijing, China). The instrument system also included a Translation Stage (GCM-125401AM, Daheng Optics, Beijing, China) and an 850 nm Longpass Colored Glass Filter (FGL850S, Thorlabs Inc., Newton, New Jersey, USA). The Colored Glass Filter was used as an absorbing plate at 670 nm. It was rigid enough to keep horizontal during the experiments. Its surface was smooth enough to keep it flat in several micrometers. A fiber probe (see the cross section in Fig. 2) was fixed on the translation stage. All the fibers were silica optical fibers and had a numerical aperture of 0.22, core diameter of 400 μm, and coating diameter of 500 μm.
The phantom was made using deionized water, Indian-ink and 20% Intralipid. Indian-ink was diluted to 0.1%, after which the transmittance ratio in 670 nm wavelength was 0.3% as measured by a spectrophotometer (721, Yue Feng Inc., Shang Hai, China). The absorption coefficient ( mm−1) was calculated using Beer-Lambert Law and was found to be 0.58 mm1. The scattering coefficient ( mm−1) and the anisotropic factor (g) of 20% intralipid was calculated  by Mie theory as20].
The basic phantom’s optical coefficients were initially set to 0.01 mm−1 for the absorption coefficient and 1 mm−1 for the reduced scattering coefficient. The reduced transport mean free path was approximated to 1 mm. The detection fiber connecting to the photodetector can be switched to alter the SD from 1 mm to 5 mm with 1 mm increment. The probe was fixed vertically under the surface of the phantom while the absorption plate could be moved vertically by the translation stage to change the distance between the probe and the plate. The translation resolution of the stage was 1 μm and the step size in the experiments was set to be 50 μm.
In addition, a series of phantoms were made in order to study the relationship between depth information and the optical properties. For studying the relationship between sensitive depth and absorption coefficient, the absorption coefficient was set to be 0.01, 0.02, 0.04, 0.06, 0.08, 0.1, and 0.15 mm−1 by adding specified quantity of Indian ink while the reduced scattering coefficient remained 1 mm−1. For studying the relationship between sensitive depth and reduced scattering coefficient, the reduced scattering coefficient was set to be 0.1, 0.5, 0.8 1, 1.5, and 2 mm−1 by adding specified quantity of Intralipid. Indian ink was also added to make sure that the absorption coefficient remained 0.01 mm−1.
3.1 Sample result
The light collected by the detection fiber was transported to the photodetector, then measured by the oscilloscope, and displayed in the form of voltage. The voltage recorded when the absorption plate and probe tip were close to each other was subtracted from each recorded voltage in order to avoid the influence of the detector’s dark count. The light intensity collected by the fiber at 1 mm SD could be 100 times higher than that collected by the fiber at 5 mm SD. In order to compare the results of five fibers with different values of SD in one chart, the voltage was normalized respectively by the maximum voltage of each curve. The recorded normalized intensity (NI) of the phantom with basic set of optical properties are shown in Fig. 3.
In the beginning, the probe and the absorption plate were positioned close to each other. As the absorption plate went down, the depth of the absorption plate (DA) increased. The detected intensity increased consistently with increasing DA because less light would be absorbed as the plate goes deeper. Figure 3 also shows that higher value of SD led to slower increase of the detected light intensity which resulted in higher value of the maximum reached depth. In order to achieve the sensitive depth, the derivative of each curve in Fig. 3 was determined asFig. 4. The normalized slope of each curve represents the detected light intensity distribution along the depth dimension.
Figure 4 shows the backwards detected light distribution along the depth. The peak of each curve represents the sensitive depth in which the backwards detected light was relatively high. But there existed a flat peak with fluctuation in each curve. Hence, it can be derived that there exists a range of depth which mostly affects the reflected light intensity. The central value of the range was recorded as the central sensitive depth. The bandwidth of the range was recorded as the range of the sensitive depth. The results are tabulated in Table 1. C stands for the central sensitive depth and R stands for the range of the sensitive depth.
According to Table 1, the central sensitive depth and the range of sensitive depth increased consistently with increasing SD.
3.2 Sensitive depths in mediums with different optical properties
In order to investigate the relationship between the sensitive depth and the optical properties, more phantoms were prepared and studied. The results were calculated following the former method. The normalized slopes of the measured curves are shown in Fig. 5 and Fig. 6.
The results for SD = 5 mm with 0.15 mm−1 absorption coefficient could hardly be recorded due to the resolution limit of the instruments. Hence the data were abandoned. The central sensitive depths and the ranges of sensitive depths exhibited a consistent decrease with increasing absorption coefficient.
The results for SD from 2 mm to 5 mm with 0.1 mm−1 reduced scattering coefficient could hardly be recorded due to the sensitivity limit of the instruments. They could hardly be detected. According to the Table 3, the central sensitive depths and the ranges of sensitive depths exhibited a consistent decrease with increasing reduced scattering coefficient.
There still lack of study on sensitive depth of the backwards detected light which does not satisfy the diffusion approximation. In order to verify the experimental results, the penetration depth of the backwards detected light was calculated as , where NS is the Normalized Slope. The PDeps for SDs from 1 mm to 5 mm was 0.95 mm, 1.45 mm, 2.30 mm, 3.05 mm, and 3.90 mm. Comparing with the results from MC , the PDeps calculated from our experimental results are about 10% bigger than the PDeps from MC. In MC the incident light is pencil beam. But in the experiments, source fiber’s core diameter and numerical aperture cannot be ignored. These factors will enlarge the incident range and angle leading to deeper penetration of the light which satisfy the experimental results. Hence the experimental results are reliable.
The sensitive depth of the diffused light has been well studied using MC. It can be approximately calculated as half the penetration depth . But for the backwards detected light which does not satisfy the diffusion approximation, the sensitive depth is bigger than half of the penetration depth. For instance, the single scatted photons’ sensitive depth should be equal to the penetration depth. The results show that for bigger SD like 5 mm, the central sensitive depth is more close to half the penetration depth because the light has more scattering events. But for the smaller SD like 1mm, the central sensitive depth is more close to the penetration depth because the light only has a few scattering events.
The range of the sensitive depth may be partly caused by the source fiber’s core diameter and numerical aperture. The core diameter will vary the SD while the numerical aperture will vary the incident angle. So the results should be the sum of incident photons with different incident place and angle. But for guiding the application of the backwards detected light, a sensitive range would be more useful than a sensitive depth. Since the experimental method cannot be used for investigating the sensitive depth for the diffused light. Further studies on the scattering depth distribution will be done by MC to investigate on the “sensitive range” for the diffused light in future work.
The results tabulated in Table 2 show that the range of sensitive depth and the central sensitive depth decrease with the increasing absorption coefficient. It can be easily deduced from the Beer-lambert Law. The results tabulated in Table 3 show that the range of the sensitive depth and the central sensitive depth also decrease with the increasing reduced scattering coefficient. For the backwards detected light in small SD which only has a few scattering events, the photons must suffer a back-scattering event before they can go backwards. So the sensitive depth for the back-scattered light in small SD is dominated by the scattering coefficient. As the reduced scattering coefficient increasing, the scattering event will occur in a shorter distance away from the surface and resulting smaller light travelling depth. So the sensitive depth will decrease with the increasing reduced scattering coefficient. According to Table 2 and Table 3, the reduced scattering coefficient affect the sensitive depth more than the absorption depth. In many other studies, researchers have often used reduced extinction coefficient to describe the penetration depth . However, for further research of the sensitive depth, the absorption coefficient and reduced scattering coefficient should be studied separately.
In this study, an experimental method for investigating the sensitive depth of the backwards detected light in turbid media was developed. It employed an absorption plate to remove all the light which can travel deeper than the plate. By moving the plate and recording the light intensity and related depth between the probe and plate, the detected intensity distribution along the depth dimension can be achieved. According to the results of the experiments, the sensitive depth was a range rather than a single number. The central sensitive depth and the range of the sensitive depth were all seen to be increasing with the SD. It also showed that the reduced scattering coefficient affects the central sensitive depth and the range of the sensitive depth more than the absorption coefficient. This research provided an experimental method to measure the sensitive depth. It is valuable for researchers to further investigate the sensitive depth of the backwards detected light. In the sensitive range, the abnormities or target could mostly affect the detected light intensity and then be detected or recognized. If spectroscopy or imaging techniques are working in the sensitive range, the signal to noise ratio of the detected light would be the highest. The data postprocessing would be more effective. So a clearly known sensitive depth may facilitate the application of the related spectroscopy and imaging techniques.
National Natural Science Foundation of China (NSFC) (51727811); China Postdoctoral Science Foundation (CPSF) (2016M592788).
The authors would like to acknowledge financial support from the National Natural Science Foundation of China and the China Postdoctoral Science Foundation.
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