Light distribution modulated diffuse reflectance spectroscopy

: Typically, a diffuse reflectance spectroscopy (DRS) system employing a continuous wave light source would need to acquire diffuse reflectances measured at multiple source-detector separations for determining the absorption and reduced scattering coefficients of turbid samples. This results in a multi-fiber probe structure and an indefinite probing depth. Here we present a novel DRS method that can utilize a few diffuse reflectances measured at one source-detector separation for recovering the optical properties of samples. The core of innovation is a liquid crystal (LC) cell whose scattering property can be modulated by the bias voltage. By placing the LC cell between the light source and the sample, the spatial distribution of light in the sample can be varied as the scattering property of the LC cell modulated by the bias voltage, and this would induce intensity variation of the collected diffuse reflectance. From a series of Monte Carlo simulations and phantom measurements, we found that this new light distribution modulated DRS (LDM DRS) system was capable of accurately recover the absorption and scattering coefficients of turbid samples and its probing depth only varied by less than 3% over the full bias voltage variation range. Our results suggest that this LDM DRS platform could be developed to various low-cost, efficient, and compact systems for in-vivo superficial tissue investigation.


Introduction
Utilizing diffuse reflectance spectroscopy (DRS) to noninvasively estimate the absorption and scattering properties and physiological status of biological tissues has been successfully demonstrated by many groups [1][2][3][4]. In general, DRS systems can be categorized by the type of light source employed. For example, DRS systems employing pulse lasers [2,5], intensity modulated lasers [1,6], and CW light sources [4,7] are usually categorized as time-domain, frequency-domain, and steady-state techniques, respectively. DRS systems equipping with different types of light source have their unique advantages and disadvantages. For instance, time-domain DRS systems that utilize pulse lasers and time correlated single photon counting modules can trace pico-second level photon travel time in tissues. Although this type of systems have exceptional sensitivity to the absorption and scattering variation in tissues, their relatively high system cost hinders their wide spread use. On the other hand, spatially resolved DRS systems that use CW light sources can recover tissue optical properties from the diffuse reflectances measured at several source-detector separations. Since spatially resolved DRS systems typically employs CW light sources, they have relatively low system cost; however, the requirement of multiple source-detector pairs, whose separations are typically in the range from 1 to 20 mm, in the setup leads to a complex multiple-fiber configuration [8,9] and an indefinite overall sampling depth.
In this paper, we present a novel CW light source based DRS system which is capable of recovering sample optical properties from a few diffuse reflectances measured at a single source-detector separation. The key component of this system is a liquid crystal (LC) cell whose light scattering property can be adjusted by applying different bias voltages to the cell. By placing the LC cell in front of the light source, the light distribution in the sample could be modulated by the LC cell with various bias voltages, and this in turn results in the modulation of the measured diffuse reflectance. We will expound the configuration of this new light distribution modulated DRS (LDM DRS) system in Section 2. In Section 3, the characteristics of the LC cell and the performance of the LDM DRS system will be analyzed and discussed.

Light distribution modulated diffuse reflectance spectroscopy system
The schematic configuration of our LDM DRS system is illustrated in Fig. 1(a). The optical fibers employed in the system were low-OH multimode fibers that had diameter of 400 μm and numerical aperture of 0.22 (FG365LEC, Thorlabs, NJ). The source fiber was connected to a broadband tungsten halogen light source (HL2000, Ocean Optics, FL), and the detector fiber was connected to a spectrometer (PIXIS 256 and SP2300, Princeton Instruments, NJ).
An empty homemade LC cell was fabricated with two 1.1 mm thick glass substrates coated with indium tin oxide and a few 0.35 mm thick spacers. The device had external dimensions of 2.00 cm * 4.00 cm * 2.55 mm. Since we needed to measure the optical properties of the LC cell at various bias voltages using the integrating sphere measurements, the LC cell had to be large enough to cover the 1 cm diameter port of our integrating sphere. The LC was fabricated by mixing 50% of E7 liquid crystal ( = 1.7426 and o = 1.5216, Daily Polymer, Taiwan), 45% of NOA65 (n = 1.524, Norland Products, CA), and 5% of Tween-80 surfactant (Sigma-Aldrich, MO). The homemade LC cell was filled with the LC and then was irradiated with 365nm, 5mW/cm 2 UV light for 10 minutes. The LC cell was placed on the sample and was connected to a modulation voltage source. A 1 kHz square wave was generated from a function generator (33220A, Agilent, CA) and amplified by a voltage amplifier (HA-405, Pintek, Taiwan) to produce modulation signal in the range from 0 to 225 V to modulate the optical properties of LC cell. It is not suitable to bias the LC cell using a DC voltage since even a trace of impurity in the LC cell could be directed to either side of the cell substrates and lead to the device malfunction. Under 1 kHz AC voltage bias, the alternating speed of the electric field is fast enough so that the LC molecules cannot rotate with it and only equivalently see a constant bias voltage. Thus, the LC cell has constant optical properties when driving with a 1 kHz AC signal, and the diffuse reflectance detection does not require any form of synchronization. The optical properties of LC cell at various voltages will be discussed in Section 3.1.
The configuration of source and detector fibers was specially designed to achieve efficient light source distribution modulation as well as good sensitivity to sample optical property variation. The source fiber was placed on the LC cell and at a position 1.6 mm away from the LC cell's edge. The light employed in this study was not polarized, and the polarization of light would not be altered by the LC cell. The detector fiber was placed against the edge of the LC cell with its distal end in contact with the sample. The center-to-center separation between the source and the detector fibers was 2 mm. The picture of the measurement setup is shown in Fig. 1(b). Besides, for our system, the spectrometer integration time was set to 65 ms for acquiring diffuse reflectance spectra at all LC cell bias voltages.
In principle, optical properties of the LC cell can be adjusted by applying different bias voltages. By placing the LC cell between the light source and the sample, the light distribution in the sample could be modulated. The diffuse reflectances collected at various LC cell bias voltages are then utilized for the determination of the sample absorption and reduced scattering properties.

GPU-based Monte Carlo model and artificial neural network
In general, DRS techniques need to incorporate photon transport models to relate the measured reflectance to the sample optical properties. In a typical procedure of determining the sample optical properties, a photon transport model is iteratively used to generate diffuse reflectances to find a best fit to the measured diffuse reflectance and thus the optical properties of the sample can be determined. An important prerequisite for ensuring the robustness of this procedure is that the model relating optical properties to diffuse reflectances possesses one-to-one correspondence.
The photon transport model employed in this study was adopted from the GPU-based (Graphic Processing Unit) Monte Carlo model developed by Alerstam et al. [10]. The optical properties of the LC cell at a certain bias voltage were set to values according to our measurement results. The length, width, and thickness of the LC cell were set to 4 cm, 2 cm, and 2.55 mm, respectively. In the Monte Carlo model, the LC cell was composed of a 0.35 mm thick liquid crystal layer sandwiched by two 1.1 mm thick glass slabs of n = 1.45. The average index refraction of the liquid crystal layer was defined as φ and M φ were the fractions of LC and NOA65, respectively [11]. The source and detection areas both had diameter of 400 μm, NA = 0.22, and their center-to-center separation was 2 mm. In the code, the refractive index of sample was 1.4 and the radius and thickness of the sample were all set to 10 6 cm to simulate the semi-infinite sample geometry. Photon packets propagating in all media followed the Henyey-Greenstein phase function with the anisotropy factor g set to 0.8 [12]. In each run of simulation, a total number of 30,000,000 photon packets was launched. A typical simulation would take about a few seconds on a computer equipped with an Nvidia GTX 780-Ti graphic card. Although the computation speed of a GPU-based Monte Carlo model is usually faster than a conventional Monte Carlo model by about three orders, using such a model for real time (e.g., less than 1 second) sample optical property recovery is still not feasible. To achieve real time sample optical property recovery, we constructed an artificial neural network (ANN), which is trained by a database composed of numerous Monte Carlo simulation results, to efficiently determine the sample optical properties from the measured reflectance. The essential steps for constructing ANN models for this purpose were elaborated in our previous paper [13]. We employed the Matlab (Mathworks, MA) training function "trainbr" based on Bayesian regularization to update the weight and bias values according to Levenberg-Marquardt optimization. The Log-sigmoid transfer function "logsig" for the hidden layer was chosen to train the ANN models. We used 30 neurons for all ANN trainings, and the number of hidden layers was properly adjusted to optimize the ANN performance. A successful ANN training process could take a few hours depending on the complexity of the ANN structure. The ANNs can work in conjunction with a nonlinear optimization algorithm, such as the "lsqcurvefit" function in Matlab, to determine μ a and μ s ' of the sample under investigation from the diffuse reflectances measured at various bias voltages of the LC cell.

Silicone phantoms
We fabricated four homogeneous silicone phantoms to test the performance of our LDM DRS system. We used the black India ink as the absorbing agent and TiO2 powder as the scattering agent. By mixing the two-part silicone with different proportions of absorbing and scattering agents, four homogeneous silicone phantoms of different optical properties were fabricated. The benchmark optical properties of these phantoms were determined by inverse addingdoubling method [14]. The optical properties of the four silicone phantoms (SP1-SP4) at 700 nm are listed in Table 1.  One of the four silicone phantoms was employed as the calibration phantom to determine the system response. The process of calibration is described in detail in the following. First, the GPU-based Monte Carlo program was utilized to calculate the theoretical reflectance value of the calibration phantom SP4. Next, the experimental reflectance of the calibration phantom was divided by the theoretical reflectance to obtain the system response. The measured reflectance of other phantoms was assumed to be influenced by a system response that was the same as the one obtained in the previous step. The purpose of the calibration process was to calculate the experimentally measured reflectance of samples that was independent of the system response and this was achieved by dividing the measured sample reflectance by the system response. The calibrated diffuse reflectance of samples could then be sent to the nonlinear optimization routine to recover the sample optical properties.

Optical properties of the liquid crystal cell
The reflectance and transmittance of the LC cell at various applied voltages were measured using an integrating sphere, and they were further processed using the inverse addingdoubling (IAD) program developed by Prahl to derive the optical properties [14]. The optical properties of the LC cell in the wavelength range from 500 to 1000 nm at various biased voltage are illustrated in Fig. 2. It is shown in Fig. 2(a) that the absorption spectrum of the LC cell only slightly varied with the bias voltage. In contrast, the modulation of the reduced scattering spectrum of the LC cell by the bias voltage could be clearly seen in Fig. 2 To see how the optical property of the LC cell varied with the bias voltage in detail, the absorption and reduced scattering coefficients at 700 nm of the LC cell at various bias voltages were extracted from Fig. 2 and plotted in Fig. 3. It can be seen in Fig. 3(a) that the 700 nm absorption coefficient was barely modulated by the bias voltage. The maximum variation of the absorption coefficients at 700 nm was 14.8%. In contrast, the reduced scattering coefficient of the LC cell at 700 nm was varied from 6.41 mm −1 at 0V to 1.3 mm −1 at 225V as shown in Fig. 3(b).

ANN construction and validation
We aim to first demonstrate the use of the LDM DRS technique to recover the absorption and reduced scattering coefficients of samples at 700 nm. To this end, a mathematical model that relates the sample optical properties to the detected diffuse reflectances at various LC cell bias voltages is necessary. We constructed ANNs for this purpose. The essential steps of the construction and validation of these ANNs are very similar to those listed in our previous study [13] and are described in detail as follows.
Referring to the LC cell optical properties at 700 nm shown in Fig. 3, we generated 11 databases for 11 different LC cell bias voltages. Each database contained the diffuse reflectances corresponding to a range of sample optical property combinations. The sample optical properties were in the range from 0.02 to 0.18 mm −1 for μ a and from 0.8 to 2.5 mm −1 for μ s ' to account for the human skin optical properties variation range from 600 to 1000 nm [13,15,16]. We divided μ a and μ s ' ranges both into 60 equal steps to construct a training database containing the diffuse reflectances of 3600 optical property combinations. It generally would take about 2 hours to compute 3600 reflectances on a computer equipped with an Nvidia GTX 780-Ti graphic card The 11 databases corresponding to the 11 different LC cell bias voltages were used for the training of 11 ANNs. After the ANNs were successfully obtained, careful validation to the ANNs was carried out. In the first step of the validation process, 500 optical property combinations, excluding the optical property combinations employed in the training database, were randomly chosen in the optical property range of interest. These 500 optical property combinations were then sent to the ANNs to generate the diffuse reflectances. Finally, the percent differences between diffuse reflectances calculated using the ANNs and the GPUbased Monte Carlo model for these 500 optical property combinations were determined. The percent differences should be low enough to ensure that all ANNs were not over trained. For example, the validation results for two ANNs corresponding to 0V and 225V bias voltages are illustrated in Fig. 4. It can be seen in Fig. 4 that the ANNs can be used to accurately determine the diffuse reflectances with deviations of less than 0.35% from those generated from the GPU-base Monte Carlo model.  Once the 11 ANNs passed the validation process, we carried out the uniqueness test to ensure that any two distinct sample optical property combinations in the training database would not correspond to two indistinguishable diffuse reflectance sets generated from the 11 ANNs. We monitored the long term stability of our light source and found that the fluctuation of light intensity was within 0.5% in a 2-hour time frame. Thus we defined that any two sets of diffuse reflectances that had differences within 0.5% at all 11 bias voltages were not distinguishable. As the 11 ANNs passed the uniqueness test, they could be employed to work in conjunction with the Matlab nonlinear optimization algorithm "lsqcurvefit" to determine μ a and μ s ' of the sample under investigation from the 11 reflectance measured at 11 bias voltages of the LC cell at 700 nm.

Phantom measurement results
We carried out a phantom study to understand the experimental performance of the LDM DRS method. The fitting results are shown in Fig. 5. It can be seen that the reflectance intensity increases with the applied voltage and the fitting quality of the three phantoms is generally good. It is worth noting that for SP1 and SP2 whose differences in absorption and reduced scattering coefficients were 28% and 58%, respectively, calculated based on the values listed in Table 1, their diffuse reflectances were distinguishable only at bias voltages higher than 125V. On the other hand, referring to the benchmark values shown in Table 1, SP1 and SP3 had differences in absorption and reduced scattering coefficients for 215% and 4%, respectively, and it can be seen in Fig. 5 that their diffuse reflectances were distinct at all bias voltages. Our results shown here imply that, for samples of scattering properties that are not comparable, measurements carried out at low LC scattering (high bias voltage) are crucial for discerning their optical property difference. In contrast, for samples of comparable reduced scattering, diffuse reflectances measured at all LC cell bias voltages are effectively influenced by the sample absorption variation.
The recovered and reference absorption and reduced scattering coefficients at 700 nm are listed in Table 2. In addition, the percent deviations between the recovered and reference values were calculated and included in the table. The sample optical property recovery process employing the ANNs and nonlinear optimization routine took less than 1 second. It can be seen in Table 2 that the maximal deviations of the recovered optical properties from the benchmark values are 7.30% and 8.49% for μ a and μ s ', respectively. The results shown here verify the feasibility of LDM DRS. Since the phantoms employed here have optical

Interrogation depth of LDM DRS
We calculated the interrogation depths of the LDM DRS system shown in Fig. 1  simulation results for LC cell biased at 0V and 225V are plotted in Fig. 6. It can be seen in Fig. 6 that for a given bias voltage, the interrogation depth increases as the absorption and/or reduced scattering coefficients decrease. In addition, to quantify the change of interrogation depth induced by the increased bias voltage, we calculated the percent differences between the data displayed in Figs. 6(a) and 6(b) and plotted in Fig. 7. It can be found in Fig. 7 that the interrogation depth only slightly increases by 3% maximum as the bias voltage of the LC cell increases from 0V to 225V. This means that the probing depth of a preconfigured LDM DRS system depends majorly on the sample optical properties and could be fairly estimated by looking up a database such as the one shown in Fig. 6. In contrast, conventional spatially resolved DRS systems would employ multiple source-detector pairs whose separations could be in the range from 1 to 20 mm [8,9], and thus their interrogation depth cannot be clearly defined.
Furthermore, comparing to the maximum interrogation depth shown in Fig. 6, our simulation results revealed that decreasing the source-to-detector separation to 1 mm would result in the reduction of the maximum interrogation depth by 42~50% in the sample optical property range of interest here; on the other hand, increasing the source-to-detector separation to 3 mm would make the maximum interrogation depth deeper by 30~52%. Our data indicated that the interrogation depth of LDM DRS would depend on the source-to-detector separation, the optical properties of the LC cell, and the optical properties of the sample. It is also noteworthy that our additional simulation results (data not shown) revealed that due to the presence of the light scattering LC cell, the interrogation depth of LDM DRS is always shallower than that of a classical configuration DRS at a same source-to-detector separation.

Voltage range and voltage numbers required for LDM DRS
It is demonstrated in Section 3.3 that the employing 11 voltages ranging from 0 to 225V to modulate the optical properties of the LC cell enables us to accurately determine the sample optical properties from the 11 diffuse reflectance set. To understand the effect of changing the number of bias voltages used in the inverse fitting procedure on the recovery error of the sample optical properties, we gradually reduced the voltage number and determined the optical property recover errors. The results are listed in Table 3. All of the voltage combinations included the lowest (0V) and the highest (225V) bias voltages. It can be seen in this table that the reduction of the voltage number does not significantly affect the sample recovery errors. This implies that when the measurements can be accurately performed at all bias voltages, employing less bias voltages in the measurements would not greatly affect the optical property recovery accuracy of LDM DRS. In general, the larger the variation range of the light scattering properties of the LC cell is, the easier the one-to-one correspondence condition between the sample optical property and the diffuse reflectance set could be met. Nevertheless, it can be seen in Fig. 5 that one could very likely discern the sample optical property variation by employing only a few reflectances measured at high LC cell bias voltages near 225V. We deliberately employed diffuse reflectance set measured at the three lowest bias voltages as well as the three highest bias voltages for sample optical properties recovery. The recovered sample optical properties and percent deviations from the benchmark values are shown in Table 4. It can be observed in the table that choosing only the lowest 3 voltages or the highest 3 voltages cannot produce optical property recovery accuracy comparable to the accuracy level listed in Table 3. Generally speaking the performance of the 3 highest voltages group is better than the 3 lowest voltages group; this is reasonable since in Fig. 5 we observed that SP1 and SP2 cannot be distinguished using the reflectances measured at low bias voltages. We further speculate that although reflectances measured at high LC cell bias voltages are sensitive to the sample optical property variation, using these high voltages alone for sample optical property recovery would likely be affected by measurement artifacts. Thus, employing diffuse reflectances measured at both high and low voltage regions is advantageous than using either region alone. Moreover, we also tested using 7 reflectances measured at the bias voltages ranging from 0 to 137.5V for sample optical property recovery. The results shown in Table 4 indicate that the performance of the 0-137.5V bias voltage group is comparable to the 0-75V group. The merits of employing a larger bias voltage variation range to create a greater LC cell scattering property modulation can be clearly seen here.

Recovering broadband optical property spectra of turbid samples using LDM DRS
In Section 3.2, we presented the construction method of ANNs that could be employed to determine the sample absorption and reduced scattering coefficients at 700 nm. Phantom optical property recovery results from the LDM DRS measurements were demonstrated in Section 3.3 for the wavelength of 700 nm. It typically took 2 hours to obtain a database containing reflectances of 3600 optical property combinations and 1-2 hours for a successful ANN training on our Intel i7 4820K based computer equipped with an Nvidia GTX 780-Ti graphic card. Therefore, it needs about 1-2 days to produce 11 ANNs required for calculating the sample optical properties at a single wavelength using our computer.
Following similar procedures shown in Section 3.2, one could obtain ANNs for recovering sample optical properties at another wavelength of interest. By accumulating a proper amount of ANNs, it is possible to determine sample optical properties in a desired wavelength range and resolution. We constructed 451 ANNs for 41 wavelengths, which were used to recover sample optical properties in the wavelength range from 600 to 1000 nm with 10 nm wavelength resolution. The recovered optical properties for SP3 are plotted in Fig. 8. The average recovery errors in the 600-1000 nm wavelength region were 4.2% and 7.2% for μ a and μ s ', respectively. It can be seen in Fig. 8 that the recovered μ a and μ s ' slightly deviate from the benchmark values in the 600-750 nm and 800-1000 nm regions, respectively. We speculated that there could be several possible causes to this phenomenon. Since the current LDM DRS prototype employed relatively large size LC cell, the contact condition for each measurement could be slightly different; therefore, the measurement errors could be brought down by improving of the repeatability of the contact between the LC cell and the sample or further reducing the size of the LC cell to decrease the sample-LC cell contact area. In addition, as stated in Section 2.1, irradiating the LC device with UV light was an essential step in the device fabrication; thus, the uniformity of the UV light source could affect the homogeneity of the LC. If the optical properties of the LC device were not homogeneously distributed as they were assumed in the Monte Carlo model described in Section 2.2, the recovered optical properties could deviate from the benchmark values. We will further investigate methods for refining the fabrication processes of LC devices to enhance the performance of our LDM DRS system.

Conclusion
In this study, we proposed a novel LDM DRS measurement geometry that utilized a liquid crystal device to modulate the light distribution in the sample and to achieve the variation of diffuse reflectance measured at a single source-to-detector separation. We also developed ANNs that can rapidly calculate diffuse reflectances of a turbid sample for this special measurement geometry. We experimentally demonstrated that the ANNs can work with an optimization routine to determine the absorption and reduced scattering coefficients of samples from the measured diffuse reflectances in the 600-1000 nm wavelength region. Compared to the bulky light switching mechanism which is typically required by a conventional SRDRS system, the LC cell employed in a LDM DRS system could be low cost and flexible in physical dimensions. In addition, the interrogation depth is not greatly modulated by the variation of scattering property of the LC cell in a LDM DRS system. In contrast, a conventional SRDRS system would have very different interrogation region for different source-detector pairs. The design of LDM DRS is aimed to perform simple point reflectance spectroscopy for accurate determination of sample optical properties using only one source-detector pair. The results shown in this study suggest that LDM DRS could become a low-cost, efficient and compact platform for in-vivo superficial tissue investigation.