Spatially-resolved Diffuse Reflectance Research Articles

Photometric and Monte-Carlo modeling unified approach for the calculation of spatially-resolved correction coefficients linking simulated and experimental diffuse reflectance spectra.

The estimation of skin optical properties by means of inverse problem solving from spatially resolved diffuse reflectance (SR-DR) spectra is one way to exploit the acquired clinical signals. This method requires the comparison between the experimental spectra collected with a medical device, and spectra generated by the photons transport numerical simulations. This comparison is usually limited to spectral shape due to the absence of intensity standardization of the experimental DR spectra. This study proposes to theoretically (using photometric calculation) and experimentally (from experimental spectra acquired on optical phantom) establish a corrective factor to obtain common intensity unit for experimental and simulated signals.

Estimation of optical properties of turbid media using spatially resolved diffuse reflectance combined with LSTM-attention network.

The accurate estimation of the optical properties of turbid media by using a spatially resolved (SR) technique remains a challenging task due to measurement errors in the acquired spatially resolved diffuse reflectance (SRDR) and challenges in inversion model implementation. In this study, what we believe to be a novel data-driven model based on a long short-term memory network and attention mechanism (LSTM-attention network) combined with SRDR is proposed for the accurate estimation of the optical properties of turbid media. The proposed LSTM-attention network divides the SRDR profile into multiple consecutive and partially overlaps sub-intervals by using the sliding window technique, and uses the divided sub-intervals as the input of the LSTM modules. It then introduces an attention mechanism to evaluate the output of each module automatically and form a score coefficient, finally obtaining an accurate estimation of the optical properties. The proposed LSTM-attention network is trained with Monte Carlo (MC) simulation data to overcome the difficulty in preparing training (reference) samples with known optical properties. Experimental results of the MC simulation data showed that the mean relative error (MRE) with 5.59% for the absorption coefficient [with the mean absolute error (MAE) of 0.04 cm-1, coefficient of determination (R2) of 0.9982, and root mean square error (RMSE) of 0.058 cm-1] and 1.18% for the reduced scattering coefficient (with an MAE of 0.208 cm-1, R2 of 0.9996, and RMSE of 0.237 cm-1), which were significantly better than those of the three comparative models. The SRDR profiles of 36 liquid phantoms, collected using a hyperspectral imaging system that covered a wavelength range of 530-900 nm, were used to test the performance of the proposed model further. The results showed that the LSTM-attention model achieved the best performance (with the MRE of 14.89%, MAE of 0.022 cm-1, R2 of 0.9603, and RMSE of 0.026 cm-1 for the absorption coefficient; and the MRE of 9.76%, MAE of 0.732 cm-1, R2 of 0.9701, and RMSE of 1.470 cm-1for the reduced scattering coefficient). Therefore, SRDR combined with the LSTM-attention model provides an effective method for improving the estimation accuracy of the optical properties of turbid media.

Optical property recovery with spatially-resolved diffuse reflectance at short source-detector separations using a compact fiber-optic probe.

We describe a compact fiber-optic probe (2 mm outside diameter) that utilizes spatially-resolved diffuse reflectance for tissue optical property recovery. Validation was performed in phantoms containing Intralipid 20% as scatterer, and methylene blue (MB), MnTPPS, and/or India ink as absorbers. Over a range of conditions, the reduced scattering coefficient was recovered with a root mean square error (RMSE) of 0.86-2.7 cm-1 (average error = 3.8%). MB concentration was recovered with RMSE = 0.26-0.52 µM (average error = 15.0%), which did not vary with inclusion of MnTPPS (p=0.65). This system will be utilized to determine optical properties in human abscesses, in order to generate treatment plans for photodynamic therapy.

Assessment of the optical properties of peaches with fungal infection using spatially-resolved diffuse reflectance technique and their relationships with tissue structural and biochemical properties

This research measured the optical absorption (µa) and reduced scattering (μs') properties in peaches during quality deterioration, and determine the relationships of the optical parameters with select structural and biochemical parameters. Spatially resolved reflectance was measured for healthy and fungal infected peaches, followed by physical (the size and tissue color), structural [membrane permeability and SEM], and biochemical (Vc, soluble sugar, titratable acid, chlorophyll, total phenolic content) measurements. Both µa and µs' were correlated well with the cellulosic structural and biochemical parameters of peaches, and they had the best correlations with those quality parameters at 675 nm. The correlation of μs' with membrane permeability was the highest from −0.962–0.743, while μa had the best correlation with the chlorophyll content at 675 nm which is an indicator of plant maturation and senescence. These findings would be useful for further development of an effective optical technique for early disease detection of peach fruit.

A sequential method for estimating the optical properties of two-layer agro-products from spatially-resolved diffuse reflectance: Simulation

A sequential method for estimating the optical properties of two-layer biological tissues with spatially-resolved diffuse reflectance was proposed and validated using Monte Carlo simulations. The relationship between the penetration depth of detected photons and source-detector separation was first studied. Photons detected at larger source-detector separations generally penetrated deeper into the medium than those detected at small source-detector separations. The effect of each parameter involved in the two-layer diffusion model (i.e., the absorption and reduced scattering coefficients (μa and μs′) of each layer, and the thickness of top layer) on reflectance was investigated. It was found that the relationship between the optical properties and thickness of top layer was a critical factor in determining whether photons would have sufficient interactions with the top layer and also penetrate into the bottom layer. The constraints for the proposed sequential estimation method were quantitatively determined by the curve fitting procedure coupled with error contour map analyses. Results showed that the optical properties of top layer could be determined within 10% error using the semi-infinite diffusion model for reflectance profiles with properly selected start and end points, when the thickness of top layer was larger than two times its mean free path (mfp′). And the optical properties of the bottom layer could be estimated within 10% error by the two-layer diffusion model, when the thickness of top layer was <16 times its mfp′. The proposed sequential estimation method is promising for improving the estimation of the optical properties of two-layer tissues from the same spatially-resolved reflectance.

Noninvasive determination of fiber orientation and tracking 2-dimensional deformation of human skin utilizing spatially resolved reflectance of infrared light measurement in vivo

We propose a noninvasive method for determining Langer’s tension lines and tracking two-dimensional (2D) deformation of human skin utilizing spatially resolved diffuse reflectance (SRDR) of infrared (IR) light measurement in vivo. The anisotropic light propagation pattern of the skin was measured at several locations on the human body; then, the principal axis (i.e., eigenvector) of the radial plot of equi-distant intensity lines was obtained to determine the orientation of the scattering-induced anisotropic reflectance of IR light. The results indicate the proposed method is able to determine preferential orientation of filamentous fiber with a reasonable degree of prediction accuracy over the entire body. We validated the proposed method by comparing the detected orientations of fiber with a previous scattering model-based light propagation anisotropy analysis method. We measured temperature dependence and tensile stress-induced changes of the spatially resolved reflectance of IR light on the skin. The surface temperature affects the light transmittance almost isotopically on the propagation patterns. The main contribution of this work is tracking the direction of tension causing 2D deformation of human skin without visible markers. The proposed method is applicable to sensing facial gestures or skin movements induced by human motion of skeletal or facial muscles.

Quality assessment of tomato fruit by optical absorption and scattering properties

This paper reports on the measurement of optical properties of tomato fruit over the wavelength range of 550–300 nm by means of a spatially-resolved diffuse reflectance technique, for assessing the firmness, soluble solids content (SSC) and pH. Spatially resolved diffuse reflectance spectra of 600 ‘Sun Bright’ tomato samples harvested at six maturity stages were acquired using a newly developed spatially resolved spectroscopy (SRS) system, from which the reduced scattering (μ′s) and absorption (μa) coefficients were estimated using an inverse algorithm for the diffusion theory model. Tomato firmness was measured using two reference methods, i.e., compression and puncture, while SSC and pH were measured using the standard refractometry and pH meter. Partial least squares (PLS) models were developed, based on μ′s, μa and their combinations, for predicting the three quality parameters. While both μ′s and μa were correlated with tomato firmness, SSC and pH, better prediction results were obtained for the multiplication of μ′s and μa (i.e., μa×μ′s) except for puncture maximum force. PLS models gave good predictions of compression maximum force and puncture maximum force, slope and flesh firmness, with the correlation coefficients of 0.894, 0.915, 0.923, 0.835, respectively, while they had poor predictions of tomato SSC and pH with the correlation coefficients of 0.623 and 0.769, respectively. This research demonstrated that the SRS technique, along with the absorption and scattering coefficients, has potential for nondestructive measurement of quality attributes, especially firmness, of tomato fruit.

Modelling spatially-resolved diffuse reflectance spectra of a multi-layered skin model by artificial neural networks trained with Monte Carlo simulations.

A robust modelling method was proposed to extract chromophore information in multi-layered skin tissue with spatially-resolved diffuse reflectance spectroscopy. Artificial neural network models trained with a pre-simulated database were first built to map geometric and optical parameters into diffuse reflectance spectra. Nine fitting parameters including chromophore concentrations and oxygen saturation were then determined by solving the inverse problem of fitting spectral measurements from three different parts of the skin. Compared to the Monte Carlo simulation accelerated by a graphics processing unit, the proposed modelling method not only reduced the computation time, but also achieved a better fitting performance.

Improved algorithm for estimating the optical properties of food products using spatially-resolved diffuse reflectance

Understanding the optical properties of food products is essential to apply optical methods for quality detection. In this research, the inverse algorithm for estimating the optical properties of food products from spatially-resolved diffuse reflectance was optimized based on the reflectance profiles generated by Monte Carlo simulations. First, the start and end points, namely, the spatial region, of reflectance profiles for parameter estimation were optimized with the unit of mean free path (mfp’). Based on this optimal spatial region with recommended start and end points, an improved step-by-step method was proposed over conventional 1-step (C-1-step) method that used fixed start and end points. Furthermore, the C-1-step method was also modified by using the optimized end point of 16 mfp's and designated as M-1-step method. Results showed that the optimal start point decreased from 3 mfp's to 1.6 mfp's with the increase of μs′/μa value from 10 to 60, while the recommended end point was kept at 16 mfp's. Absolute values of relative errors for the best estimates of μa and μs′ using C-1-step and step-by-step methods were 8.7%, 5.6% and 3.5%, 2.3%, respectively, for a spatial resolution of 0.1 mm. The M-1-step method, with the spatial resolution of 0.1 mm, reduced the estimation errors to 3.8% and 3.7% for μa and μs′, representing 56% and 34% improvements over the C-1-step method. Based on the results of M-1-step method, the step-by-step method could also improve estimation accuracy. At last, the effectiveness of the proposed algorithm was validated with real mango samples. The mean absolute percentage errors for estimating μa and μs′ by a hyperspectral imaging system combined with the step-by-step method were 9.2% and 5.7%, respectively.

Characterizing pear tissue with optical absorption and scattering properties using spatially-resolved diffuse reflectance

Spatially-resolved diffuse reflectance (SRDR) technique, with simple instrumentation, fast measurement, and relatively cheap devices, offers great potential for measurement of optical absorption (µa) and scattering (µs′) properties of agro-products. In this study, a laboratory-based double-fiber-optical-probe system was established and developed for optical property measurement of pear samples in the spectral region of 500–1000 nm. The system, based on a simple two-source diffusion theory model, was able to acquire SRDR profiles, which were used to calculate the µa and µs′ via nonlinear fitting. 32 pear samples with three different measured surfaces were tested in this study. The SRDR profiles of 41 positions were acquired, from −1 to 1 cm at an interval of 0.05 cm. The values of µa ranged nearly from 0.10 to 0.61 cm−1 and peaked at 970 nm due to water absorption, while the µs′ decreased along wavelengths with its values from 12.5 to 9.5 cm−1. The results indicated that the optical properties of pear tissues were wavelength-dependent, and small discrepancies of µa and µs′ could be found for different measured surfaces. The creation of standard sample slicing procedure is in great demand, which is useful for improving the accuracy of optical property measurement.

Concentric Multipixel Silicon Photodiode Array Probes for Spatially Resolved Diffuse Reflectance Spectroscopy

Spatially resolved diffuse reflectance (SRDR) measurements provide photon path information, and enable depth-resolved tissue analysis. This paper introduces an innovative concentric multi-pixel photodiode array (CMPA) probe for SRDR measurements. The CMPA is a compact and densely packed semiconductor SRDR probe which was fabricated and tested on a 99% reflectance standard and two tissue mimicking liquid phantoms for probe validation. The experimental results agree well with forward Monte Carlo simulations.

Sensitivity of Delta-P1 approximation model to second-order parameter

The sensitivity of the second-order parameter of the Henyey-Greenstein phase function based on the spatially-resolved diffuse reflectance within the two-point-source approximation to the Delta-P1 approximation model is studied, and the analytical expression of the sensitivity is derived. The results show that the analytic solution of the Delta-P1 approximation model for reflectance contains the second-order parameter of the scattering phase function compared with the diffusion approximation model, and the second-order parameter has significant influence (the extreme value greater than 30%) on the analytic solution for spatially-resolved diffuse reflectance with small source-detector separations ( 1.5 mm) no matter whether the absorption is weak or strong. The research has theoretical significance for obtaining the optical information abour tissue with the second-order parameter .

Study of SP3 for spatially-resolved diffuse reflectance close to light source

Based on P3 approximate spatially-resolved diffuse reflectance theory for semi-infinite biological tissue, the simplified expression SP3 function for highly absorbing medium close to source is studied. The research result shows that function SP3 can better describe the spatially-resolved diffuse reflectance close to source for higher absorption; the inversion of the optical parameters of highly absorbing medium with function SP3 shows the existence of extreme values of the curves fitted with diffuse reflectance data for different start distances, and the inversion results near the extreme values are the most closest to the optical parameters of real tissues.

Quantification of the optical properties of two-layered turbid media by simultaneously analyzing the spectral and spatial information of steady-state diffuse reflectance spectroscopy

We applied hyperspectral imaging to measure spatially-resolved diffuse reflectance spectra in the visible range and an iterative inversion method based on forward Monte Carlo modeling to quantify optical properties of two-layered tissue models. We validated the inversion method using spectra experimentally measured from liquid tissue mimicking phantoms with known optical properties. Results of fitting simulated data showed that simultaneously considering the spatial and spectral information in the inversion process improves the accuracies of estimating the optical properties and the top layer thickness in comparison to methods fitting reflectance spectra measured with a single source-detector separation or fitting spatially-resolved reflectance at a single wavelength. Further development of the method could improve noninvasive assessment of physiological status and pathological conditions of stratified squamous epithelium and superficial stroma.

Quantification of the optical properties of two-layered turbid media by simultaneously analyzing the spectral and spatial information of steady-state diffuse reflectance spectroscopy

We applied hyperspectral imaging to measure spatially-resolved diffuse reflectance spectra in the visible range and an iterative inversion method based on forward Monte Carlo modeling to quantify optical properties of two-layered tissue models. We validated the inversion method using spectra experimentally measured from liquid tissue mimicking phantoms with known optical properties. Results of fitting simulated data showed that simultaneously considering the spatial and spectral information in the inversion process improves the accuracies of estimating the optical properties and the top layer thickness in comparison to methods fitting reflectance spectra measured with a single source-detector separation or fitting spatially-resolved reflectance at a single wavelength. Further development of the method could improve noninvasive assessment of physiological status and pathological conditions of stratified squamous epithelium and superficial stroma.

δ-P1 approximation model of biological tissues

A modified delta-P1 approximation is studied in this paper. An analytic solution Rδ-P1(ρ) of this model for reflectance in double source approximation is developed by taking the source series expansion terms to the first order. It is shown that when the source in extended to first order, a better description for high absorption and high scattering media will be developed. The new model can give satisfactory results in describing irradiance distribution close to source compared with the RSDA(ρ) of diffusion approximation. Moreover, Rδ-P1(ρ) provides the prediction of the second-order parameter γ, which is significant for developing the inversion algorithm to recover optical parameters from spatially-resolved diffuse reflectance by using smaller source-detector separations.

Optimization of inverse algorithm for estimating the optical properties of biological materials using spatially-resolved diffuse reflectance

Determination of the optical properties from intact biological materials based on diffusion approximation theory is a complicated inverse problem, and it requires proper implementation of inverse algorithm, instrumentation and experiment. This article was aimed at optimizing the procedure of estimating the absorption and reduced scattering coefficients of turbid homogeneous media from spatially-resolved diffuse reflectance data. A diffusion model and the inverse algorithm were first validated by Monte Carlo simulations. Sensitivity analysis was performed to gain an insight into the relationship between the estimated parameters and the dependent variables in the inverse algorithm for improving the parameter estimation procedure. Three data transformation and the relative weighting methods were compared in the nonlinear least squares regression. It is found that the logarithm and integral data transformation and relative weighting methods greatly improve estimation accuracy with the relative errors of 10.4%, 10.7% and 11.4% for the absorption coefficient, and 6.6%, 7.0% and 7.1% for the reduced scattering coefficient, respectively. Further statistical analysis shows that the logarithm transformation and relative weighting methods give more reliable estimations of the optical parameters. To accurately estimate the optical parameters, it is important to study and quantify the characteristics and properties of the mathematical model and its inverse algorithm.

Quantification of the optical properties of two-layer turbid materials using a hyperspectral imaging-based spatially-resolved technique

Recent research has shown that a hyperspectral imaging-based spatially-resolved technique is useful for determining the optical properties of homogenous fruits and food products. To better characterize fruit properties and quality attributes, it is desirable to consider fruit to be composed of two homogeneous layers of skin and flesh. This research was aimed at developing a nondestructive method to determine the absorption and scattering properties of two-layer turbid materials with the characteristics of fruit. An inverse algorithm along with the sensitivity coefficient analysis for a two-layer diffusion model was developed for the extraction of optical properties from the spatially-resolved diffuse reflectance data acquired using a hyperspectral imaging system. The diffusion model and the inverse algorithm were validated with Monte Carlo simulations and experimental measurements from solid model samples of known optical properties. The average errors of determining two and four optical parameters were 6.8% and 15.3%, respectively, for Monte Carlo reflectance data. The optical properties of the first or top layer of the model samples were determined with errors of less than 23.0% for the absorption coefficient and 18.4% for the reduced scattering coefficient. The inverse algorithm did not give acceptable estimations for the second or lower layer of the model samples. While the hyperspectral imaging-based spatially-resolved technique has the potential to measure the optical properties of two-layer turbid materials like fruits and food products, further improvements are needed in determining the optical properties of the second layer.

A preliminary study on skin phantoms to test spatially resolved–Diffuse Reflectance Spectroscopy as a tool to help diagnose cutaneous melanoma: A non-invasive measurement of Breslow index

Diagnosing malignant melanoma implies to evaluate its thickness also known as Breslow Index. Currently, Breslow Index is measured by the anatomopathologist after the visible tumour has been biopsied. Non-invasive measurement of Breslow Index using optical methods would turn the overall procedure into a one-step process thus reducing morbidity, cost and system burden. In the current study spatially-resolved Diffuse Reflectance (DR) Spectroscopy (using five Collection to Excitation Separations - CEFS) was evaluated as a tool to discriminate several Breslow Index simulated by phantoms. Those phantoms were made of two layers: the bottom and the top layers were made so as to simulate respectively dermis and melanoma optical coefficients optical coefficients. Dermis was considered as being mainly scattering (intralipids mixed with gelatin) and melanoma was considered as being both scattering and absorbing because of melanin (intralipids and coffee mixed within gelatin). Bottom layer's thickness was constant (6.3 mm) and top layers were either 2, 3, 4, 5 or 6 mm-thick. Our results show that absolute values of DR signal allow discrimination (p 0.92). Slopes of the decreasing signal allow discrimination (p<0.05) and that might be more robust to inter-individual variations of melanomas' absorption coefficients. A clinical trial needs to be carried out in order to confirm such an hypothesis.

Sensitivity of spatially-resolved diffuse reflectance to high-order optical parameters

Spatially resolved reflectance close to the source is dependent on high-order optical parameters of the media. In order to investigate the influence of high-order parameters on the diffuse reflectance, we define sensitivities of the spatially-resolved diffuse reflectance to the second- and third-order optical parameters. The sensitivity denotes the relative change of diffuse reflectance due to a change in the optical parameter. Expressions of the sensitivities are derived from P3 approximation theory, and numerical analyses are performed. We show that the sensitivity changes with source-detector separation and reaches a maximum in the region between one transport mean free path and two transport mean free paths, and is positive in the region beyond one transport mean free path. The influence of third-order optical parameter on the diffusing reflectance can be ignored in comparison with the influence of second-order optical parameter.