Diffuse photon remission associated with the center-illuminated-area-detection geometry. III.&#x00A0;Perspectives on the patterns of saturation

Daqing Piao; Tengfei Sun; Tengfei Sun; Nafiseh Farahzadi

doi:10.1364/AO.506514

Applied Optics
Vol. 63,
Issue 9,
pp. 2294-2305
(2024)
•https://doi.org/10.1364/AO.506514

Diffuse photon remission associated with the center-illuminated-area-detection geometry. III. Perspectives on the patterns of saturation

Daqing Piao, Tengfei Sun, and Nafiseh Farahzadi

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Daqing Piao, Tengfei Sun, and Nafiseh Farahzadi, "Diffuse photon remission associated with the center-illuminated-area-detection geometry. III. Perspectives on the patterns of saturation," Appl. Opt. 63, 2294-2305 (2024)

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Table of Contents Category
- Medical Optics, Microscopy, and Biotechnology
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About this Article
History
- Original Manuscript: September 20, 2023
- Revised Manuscript: February 20, 2024
- Manuscript Accepted: February 22, 2024
- Published: March 18, 2024

Abstract

Understanding scattering insensitiveness in diffuse reflectance spectroscopy (DRS) will be useful to enhancing the spectral specificity to absorption. In DRS based on center-illuminated-area-detection (CIAD), the scattering response can saturate as the relative strength of scattering with respect to the collection size, represented by a dimensionless reduced scattering, increases over a threshold. However, the formation of saturation versus the same range of dimensionless reduced scattering may differ between a fixed reduced scattering over an increasing collection size (case 1) and an increasing reduced scattering over a fixed collection size (case 2), due to the absorption. Part III demonstrates the differences of the scattering saturation as well as the effect of absorption on it in the CIAD geometry between the two cases while assessed over the same range of the dimensionless reduced scattering. A model allows predicting the absorption-dependent levels of saturation and the corner parameters of saturation transition. When assessed for the absorption coefficient to vary over $[{0.001},{0.01},{0.1},{1}]\;{{\rm mm}^{- 1}}$, the model-predicted levels of saturation agree with MC results with ${\le} 2.2\%$ error in both cases. In comparison, the model-predicted corner parameters of saturation show much different agreement with MC results in the two cases, suggesting that the saturation pattern is much better formed in one than in the other. Experiments conforming to the CIAD geometry support the discrepancy of the saturating patterns between the two cases.

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Supplementary Material (1)

Name	Description
Supplement 1	Supplemental Materials

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (36)

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Symbol	Description	Unit
$n_{t i s s}$	Refractive index
$ξ = - 1.44 n_{t i s s}^{- 2} + 0.71 n_{t i s s}^{- 1} + 0.668 + 0.0636 n_{t i s s}$	Coefficient #1 for BC
$μ_{a}$	Absorption coefficient	[ ${m m}^{- 1}$ ]
$μ_{s}$	Scattering coefficient	[ ${m m}^{- 1}$ ]
$g$	Anisotropy factor
$μ_{s}^{'} = μ_{s} (1 - g)$	Reduced scattering coefficient	[ ${m m}^{- 1}$ ]
$D = [3 (μ_{a} + μ_{s}^{'})]^{- 1}$	Diffusion coefficient	[mm]
$μ_{e f f} = \sqrt{μ_{a} / D}$	Effective attenuation coefficient	[ ${m m}^{- 1}$ ]
$z_{a} = [μ_{s}^{'}]^{- 1}$	Reduced scattering pathlength	[mm]
$A = (1 + ξ) / (1 - ξ)$	Coefficient #2 for BC
$β = (2 / 3) A$	Coefficient #3 for BC
$z_{b} = β z_{a}$	A distance to displace due to BC	[mm]
$η = [g \cdot \exp (1 - g)]^{\frac{1}{10}}$	Coefficient 1 for the slave source
$α = (1 - g)^{2} (1 - η)$	Coefficient 2 for the slave source
$z_{a}^{*} = α z_{a}$	The depth of the slave source	[mm]
$S^{*} = η \cdot \exp [- μ_{e f f} z_{a} (\frac{1 + α}{2})]$	The strength of the slave source	[ ${m m}^{- 3}$ ]
$r_{i n n e r} = δ z_{a}$	Inner radius of CIAD	[mm]
$r_{a r e a} = ζ z_{a}$	Outer radius of CIAD	[mm]
$d_{a r e a} = 2 r_{a r e a}$	Diameter of CIAD	[mm]

	$μ_{s}^{'} [{m m}^{- 1}]$	$g$	$d_{a r e a}$ mm	$μ_{a} [{m m}^{- 1}]$
1	1.0	0.9	$[10^{- 2}, 10^{3}]$	[0.001, 0.01, 0.1, 1]
2	$[10^{- 2}, 10^{3}]$	0.9	1.0	[0.001, 0.01, 0.1, 1]
3	1.0	0.5	$[10^{- 2}, 10^{3}]$	0.01
		0.7
		08
		0.95
4	$[10^{- 2}, 10^{3}]$	0.5	1.0	0.01
		0.7
		08
		0.95

Symbol	Description	Unit
$n_{t i s s}$	Refractive index
$ξ = - 1.44 n_{t i s s}^{- 2} + 0.71 n_{t i s s}^{- 1} + 0.668 + 0.0636 n_{t i s s}$	Coefficient #1 for BC
$μ_{a}$	Absorption coefficient	[ ${m m}^{- 1}$ ]
$μ_{s}$	Scattering coefficient	[ ${m m}^{- 1}$ ]
$g$	Anisotropy factor
$μ_{s}^{'} = μ_{s} (1 - g)$	Reduced scattering coefficient	[ ${m m}^{- 1}$ ]
$D = [3 (μ_{a} + μ_{s}^{'})]^{- 1}$	Diffusion coefficient	[mm]
$μ_{e f f} = \sqrt{μ_{a} / D}$	Effective attenuation coefficient	[ ${m m}^{- 1}$ ]
$z_{a} = [μ_{s}^{'}]^{- 1}$	Reduced scattering pathlength	[mm]
$A = (1 + ξ) / (1 - ξ)$	Coefficient #2 for BC
$β = (2 / 3) A$	Coefficient #3 for BC
$z_{b} = β z_{a}$	A distance to displace due to BC	[mm]
$η = [g \cdot \exp (1 - g)]^{\frac{1}{10}}$	Coefficient 1 for the slave source
$α = (1 - g)^{2} (1 - η)$	Coefficient 2 for the slave source
$z_{a}^{*} = α z_{a}$	The depth of the slave source	[mm]
$S^{*} = η \cdot \exp [- μ_{e f f} z_{a} (\frac{1 + α}{2})]$	The strength of the slave source	[ ${m m}^{- 3}$ ]
$r_{i n n e r} = δ z_{a}$	Inner radius of CIAD	[mm]
$r_{a r e a} = ζ z_{a}$	Outer radius of CIAD	[mm]
$d_{a r e a} = 2 r_{a r e a}$	Diameter of CIAD	[mm]

	$μ_{s}^{'} [{m m}^{- 1}]$	$g$	$d_{a r e a}$ mm	$μ_{a} [{m m}^{- 1}]$
1	1.0	0.9	$[10^{- 2}, 10^{3}]$	[0.001, 0.01, 0.1, 1]
2	$[10^{- 2}, 10^{3}]$	0.9	1.0	[0.001, 0.01, 0.1, 1]
3	1.0	0.5	$[10^{- 2}, 10^{3}]$	0.01
		0.7
		08
		0.95
4	$[10^{- 2}, 10^{3}]$	0.5	1.0	0.01
		0.7
		08
		0.95

Abstract

Supplementary Material (1)

Data availability

Cited By

Figures (9)

Tables (2)

Equations (36)

Applied Optics