Real-time convolution method for generating light diffusion profiles of layered turbid media

Hoe-Min Kim; Kwang Hee Ko; Kwan H. Lee

doi:10.1364/JOSAA.28.001276

Journal of the Optical Society of America A
Vol. 28,
Issue 6,
pp. 1276-1284
(2011)
•https://doi.org/10.1364/JOSAA.28.001276

Real-time convolution method for generating light diffusion profiles of layered turbid media

Hoe-Min Kim, Kwang Hee Ko, and Kwan H. Lee

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Hoe-Min Kim, Kwang Hee Ko, and Kwan H. Lee, "Real-time convolution method for generating light diffusion profiles of layered turbid media," J. Opt. Soc. Am. A 28, 1276-1284 (2011)

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Related Topics
Table of Contents Category
- Medical Optics and Biotechnology
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Light propagation in tissues (170.3660)
- Turbid media (170.7050)
- Diffusion (290.1990)
- Multiple scattering (290.4210)

About this Article
History
- Original Manuscript: March 4, 2011
- Manuscript Accepted: March 24, 2011
- Published: May 27, 2011
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 6, Iss. 7

Abstract

In this paper we present a technique to obtain a diffusion profile of layered turbid media in real time by using the quasi fast Hankel transform (QFHT) and the latest graphics processing unit technique. We apply the QFHT to convolve the diffusion profiles of each layer so as to dramatically reduce the time for the convolution step while maintaining the accuracy. In addition, we also introduce an accelerated technique to generate individual discrete diffusion profiles for each layer through parallel processing. The proposed method is 2 orders of magnitude faster than the existing method, and we validate its efficiency by comparing it with Monte Carlo simulation and another relevant methods.

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$σ_{s}^{'}$	Reduced scattering coefficient
$σ_{a}$	Absorption coefficient
η	Relative refractive index between adjacent layers
$r_{s} (η)$	$- 0.4399 + \frac{0.7099}{η} - \frac{0.3319}{η^{2}} + \frac{0.0636}{η^{3}}$ , if $η < 1$ $- \frac{1.4399}{η^{2}} + \frac{0.7099}{η} + 0.6681 + 0.0636 η$ , if $η > 1$
$A_{top}$	$\frac{1 + r_{s} (η_{top})}{1 - r_{s} (η_{top})}$
$A_{bottom}$	$\frac{1 + r_{s} (η_{bottom})}{1 - r_{s} (η_{bottom})}$
D	$\frac{1}{3 (σ_{a} + σ_{s}^{'})}$
$z_{0}$	$\frac{1}{σ_{a} + σ_{s}^{'}}$
$z_{b, top}$	$2 A_{top} D$
$z_{b, bottom}$	$2 A_{bottom} D$
$z_{r, i}$	$2 i (d + z_{b, top} + z_{b, bottom}) + z_{0}$
$z_{v, i}$	$2 i (d + z_{b, top} + z_{b, bottom}) - z_{0} - z_{b, top}$
$α^{'}$	$\frac{σ_{s}}{σ_{s}^{'} + σ_{α}}$
$σ_{tr}$	$\sqrt{3 σ_{a}} (σ_{a} + σ_{s}^{'})$
$d_{r, i}$	$\sqrt{r^{2}} + z_{r, i}^{2} for R (r), \sqrt{r^{2}} + (d - z_{r, i})^{2} for T (r)$
$d_{v, i}$	$\sqrt{r^{2}} + z_{v, i}^{2} for R (r), \sqrt{r^{2}} + (d - z_{v, i})^{2} for T (r)$

Process \ Method	Monte Carlo ( $10 m$ photons)	Previous Method [15]	Proposed Method
Process \ Method	Monte Carlo ( $10 m$ photons)	Previous Method [15]		QFHT		QFHT+GPU
Sampling	−	46		46	⇒	6
Convolution	−	8584	⇒	10		10
Total time	$291 \times 10^{3}$	8630		56		16

$σ_{s}^{'}$	Reduced scattering coefficient
$σ_{a}$	Absorption coefficient
η	Relative refractive index between adjacent layers
$r_{s} (η)$	$- 0.4399 + \frac{0.7099}{η} - \frac{0.3319}{η^{2}} + \frac{0.0636}{η^{3}}$ , if $η < 1$ $- \frac{1.4399}{η^{2}} + \frac{0.7099}{η} + 0.6681 + 0.0636 η$ , if $η > 1$
$A_{top}$	$\frac{1 + r_{s} (η_{top})}{1 - r_{s} (η_{top})}$
$A_{bottom}$	$\frac{1 + r_{s} (η_{bottom})}{1 - r_{s} (η_{bottom})}$
D	$\frac{1}{3 (σ_{a} + σ_{s}^{'})}$
$z_{0}$	$\frac{1}{σ_{a} + σ_{s}^{'}}$
$z_{b, top}$	$2 A_{top} D$
$z_{b, bottom}$	$2 A_{bottom} D$
$z_{r, i}$	$2 i (d + z_{b, top} + z_{b, bottom}) + z_{0}$
$z_{v, i}$	$2 i (d + z_{b, top} + z_{b, bottom}) - z_{0} - z_{b, top}$
$α^{'}$	$\frac{σ_{s}}{σ_{s}^{'} + σ_{α}}$
$σ_{tr}$	$\sqrt{3 σ_{a}} (σ_{a} + σ_{s}^{'})$
$d_{r, i}$	$\sqrt{r^{2}} + z_{r, i}^{2} for R (r), \sqrt{r^{2}} + (d - z_{r, i})^{2} for T (r)$
$d_{v, i}$	$\sqrt{r^{2}} + z_{v, i}^{2} for R (r), \sqrt{r^{2}} + (d - z_{v, i})^{2} for T (r)$

Process \ Method	Monte Carlo ( $10 m$ photons)	Previous Method [15]	Proposed Method
Process \ Method	Monte Carlo ( $10 m$ photons)	Previous Method [15]		QFHT		QFHT+GPU
Sampling	−	46		46	⇒	6
Convolution	−	8584	⇒	10		10
Total time	$291 \times 10^{3}$	8630		56		16

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Journal of the Optical Society of America A

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