Depth-selective method for time-domain diffuse reflectance measurements: validation study of the dual subtraction technique

Abstract

Research on the spatial distribution of sensitivity of time-domain near infrared diffuse reflectance measurement is reported in this paper. The main objective of the investigation is to validate theoretically calculated sensitivity profiles for a measurement geometry with two detectors and two sources in which sensitivity profiles of statistical moments of distributions of time of flight of photons (DTOFs) are spatially restricted to a region underneath the detectors. For this dual subtraction method, smaller sensitivities to changes appearing in the superficial layer of the medium were observed compared to the single distance and single subtraction methods. Experimental validation of this approach is based on evaluation of changes in the statistical moments of DTOFs measured on a liquid phantom with local absorption perturbations. The spatial distributions of sensitivities, depth-related sensitivity and depth selectivities were obtained from the dual subtraction method and compared with those from single distance and single subtraction approaches. Also, the contrast to noise ratio (CNR) was calculated for the dual subtraction technique and combined with depth selectivity in order to assess the overall performance (product of CNR and depth selectivity) of the method. Spatial sensitivity profiles from phantom experiments are in a good agreement with the results of theoretical studies and feature more locally restricted sensitivity volume with the point of maximal sensitivity located deeper. The highest value of overall performance was obtained experimentally for the second statistical moment in the dual subtraction method (∼10.8) surpassing that of the single distance method (∼8.7). This confirms the advantage of dual subtraction measurement geometries in the suppression of optical signals originated in the superficial layer of the medium.

Fig. 1.

Schematic of the experiment setup consisting of a time-resolved NIRS system with semiconductor laser heads LH1 and LH2, photomultiplier tubes PMT for light detection, preamplifiers AMP and time-correlated single photon counting TCSPC cards for recording of DTOFs

Fig. 2.

Illustration of the experimental setup: two sources (red arrows with labels “right” and “left”) and two detectors (green arrows with labels 1 and 2) were located on one wall of the fish tank. A black cylinder with a diameter of 3 mm and a height of 5 m was immersed into the phantom by a thin pipe (0.15 mm thickness) which was fixed on a 3D stepper motor.

Fig. 3.

Spatial distributions of changes in the statistical moments of DTOF (number of photons, mean time of flight and variance) obtained for source-detector separation of 3 cm along X axis presented on three coordinate planes for a phantom with µ_a≈0.1 cm^-1 and µ_s’≈5 cm^-1.

Fig. 4.

Spatial distributions of changes in the statistical moments of DTOF obtained for source-detector separation of 3 cm for µ_a≈0.1 cm^-1 and three different µ_s’≈5, 10 and 20 cm^-1.

Fig. 5.

Spatial distributions of changes in statistical moments of DTOF for a phantom with µ_a≈0.1 cm^-1 and µ_s’≈5 cm^-1. Top row: single subtraction for the source located on the right side and pair of detectors. Bottom row: sum of subtractions obtained for two sources located on the right and left sides of the pair of detectors.

Fig. 6.

Spatial distributions of the dual subtractions method for three statistical moments of DTOFs obtained for a phantom with µ_a≈0.1 cm^-1 and three different values of reduced scattering coefficients µ_s’≈5,10 and 20 cm^-1.

Fig. 7.

Normalized depth-dependent sensitivities of statistical moments to absorption change appearing a layer of 2 mm thickness for a single-distance method with source-detector separation of 3 cm (µ_a≈0.1 cm^-1 and µ_s’≈10 cm^-1) and the single and dual subtraction methods with large source-detector separation of 3 cm and small source-detector separation of 2.5 cm.

Fig. 8.

Depth selectivity of statistical moments for single-distance method with source-detector separation of 3 cm and dual subtraction method (µ_a≈0.1 cm^-1 and µ_s’=10 cm^-1) with large source detector separation of 3 cm and small source-detector separation of 2.5 cm.

Fig. 9.

Comparison of the overall performance of single distance and dual subtraction methods. Values of the product of depth selectivity and CNR (both unitless parameters) are shown beside each point. The dashed lines show all the points in the graph wi with the same value of the product of CNR and depth selectivity. The thickness of the top layer is around 15 mm for the phantom with µ_a≈0.1 cm^-1 and µ_s’≈10 cm^-1.