Fig 1.
Schematic of the two-layer scattering medium including locations of the source and the detector.
Here, and
are the absorption and reduced scattering coefficients,
is the transport mean free path, and
is the absorption mean free path, for the respective layers where n = 1–2. The top layer is the solid layer with finite thickness (d1), the bottom layer is the liquid layer with semi-infinite geometry (d2).
Fig 2.
Schematic of the custom DCS system and setup for the two-layer phantom experiment with a single source fiber and four detection fibers at 10 mm, 15 mm, 20 mm and 25 mm from the source fiber.
The top and bottom layers are solid and liquid phantom layers respectively.
Fig 3.
(a) g2 from homogenous phantom P0 to two-layer phantom P7, where d1 is the thickness of the top layer phantom, shown for SD = 20 mm. (b) Corresponding g1 curves calculated from g2 in (a).
Fig 4.
(a-d) Photon count rate vs. top layer thickness (P0-P7) for SD1-SD4 respectively.
Fig 5.
Measured and fitted g1 at SD3 (20 mm) for homogenous phantoms P0.
Purple: measured g1 with standard deviation. Green with circle: Eq (14) with n = 1. Orange: conventional single-layer model (Eq (2)).
Fig 6.
(a-d) Measured and fitted g1 at SD3 (20 mm) for two-layer phantoms P1 (2.01 mm), P3 (3.87 mm), P5 (4.99 mm), P7 (8.08 mm). Purple: measured g1 with standard deviation. Green with circle: two-layer model. Orange: single-layer model (Eq (2)).
Fig 7.
(a) Comparison between fitted and true d1 for various top layer thicknesses at each SD distance. Bule: SD1 = 10 mm. Red: SD2 = 15 mm. Orange: SD3 = 20 mm. Green: SD4 = 25 mm. Mean and standard deviation of fitted d1 were derived from ten repeated measurements. (b) Percent differences between layered phantom (P1-P7) and P0 in αDB using the single-layer model (triangle), and DB2 using the two-layer model (circle) vs. true d1 values. Mean and standard deviation of fitted flow were derived from ten repeated measurements.
Fig 8.
RSS between the fitted and measured g1 by varying d1 from 1 mm to 9 mm, and DB2 from 0.5×10−9 cm2/s to 7.5×10−9 cm2/s.
(a-d) Example RSS of one out of ten repeated measurements for P1 = 2.01 mm, P3 = 3.28 mm, P5 = 4.99 mm, and P7 = 8.08 mm respectively at SD3 = 20 mm. Red cross: Global minimum.
Fig 9.
Influence of uncertainties in layer optical properties on fitted d1.
Purple: baseline. Blue: first layer increased by 20%. Red: first layer decreased by 20%. Yellow: second layer increased by 20%. Green: second layer decreased by 20%. (a-d) Influence of layer μa, SD1-SD4. (e-h) Influence of layer , SD1-SD4.
Fig 10.
Influence of uncertainties in layer optical properties on fitted DB2.
Purple: baseline. Blue: first layer increased by 20%. Red: first layer decreased by 20%. Yellow: second layer increased by 20%. Green: second layer decreased by 20%. (a-d) Influence of layer μa, SD1-SD4. (e-h) Influence of layer , SD1-SD4.