Simple demodulation method for optical property extraction in spatial frequency domain imaging

Liyu Dai; Yifeng Luo; Xiaping Fu

doi:10.1364/AO.430937

Applied Optics
Vol. 60,
Issue 26,
pp. 7878-7887
(2021)
•https://doi.org/10.1364/AO.430937

Simple demodulation method for optical property extraction in spatial frequency domain imaging

Liyu Dai, Yifeng Luo, and Xiaping Fu

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Liyu Dai, Yifeng Luo, and Xiaping Fu, "Simple demodulation method for optical property extraction in spatial frequency domain imaging," Appl. Opt. 60, 7878-7887 (2021)

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Table of Contents Category
- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: May 10, 2021
- Revised Manuscript: July 28, 2021
- Manuscript Accepted: August 3, 2021
- Published: September 2, 2021

Abstract

Different demodulation methods affect the efficiency and accuracy of spatial frequency domain imaging (SFDI). A simple and effective method of sum-to-product identities (STPI) demodulation was proposed in this study. STPI requires one fewer image than conventional three-phase demodulation (TPD) at a spatial frequency. Numerical simulation and phantom experiments were performed. The result proved the feasibility of STPI and showed that STPI combined with subtraction can achieve high-precision demodulation in the low spatial frequency domain. Through extraction of phantom optical properties, STPI had similar accuracy compared with other demodulation methods in extracting optical properties in phantoms. STPI was also used to extract the optical properties of milk, and it had highly consistent results with TPD, which can distinguish milk with different fat content. The demodulation effect of this method in the low spatial frequencies is better than other fast demodulation methods.

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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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Milk Type	Fat Content (g/100 ml)	Protein Content (g/100 ml)
Skim	0	3.6
Low fat	1.5	3.0
Full fat	3.5	3.6

Pixel Frequency	GSO Filtering	GSO Subtracting	Hilbert Filtering	Hilbert Subtracting	STPI Filtering	STPI Subtracting	TPD
0.001	0.11960	0.04735	0.16809	0.15768	0.12805	0.00522	0.00403
0.0025	0.06488	0.01862	0.09981	0.09819	0.05995	0.00554	0.00403
0.005	0.02747	0.01045	0.06594	0.06177	0.00871	0.00562	0.00402
0.01	0.01759	0.00590	0.04893	0.04901	0.01617	0.00572	0.00403
0.025	0.00719	0.00607	0.02612	0.02614	0.00478	0.00571	0.00403
0.05	0.00477	0.00577	0.01896	0.01913	0.00468	0.00571	0.00402
0.1	0.00391	0.00577	0.01536	0.01561	0.00364	0.00570	0.00403
0.25	0.00362	0.00572	0.01491	0.01517	0.00332	0.00555	0.00394

Optical	High Spatial	GSO	GSO	Hilbert	Hilbert	STPI	STPI
Property	Frequency ( ${m m}^{- 1}$ )	Filtering	Subtracting	Filtering	Subtracting	Filtering	Subtracting	TPD
$μ_{a}$	0.112	9.84%	11.11%	9.94%	9.63%	10.52%	11.56%	10.52%
	0.14	8.93%	10.86%	9.60%	8.86%	8.66%	10.20%	9.10%
	0.1667	9.43%	9.59%	9.50%	8.73%	9.23%	9.24%	9.48%
	0.2	9.46%	7.28%	9.73%	8.27%	9.43%	7.08%	9.69%
	0.25	10.72%	7.60%	10.59%	10.21%	10.68%	7.77%	10.95%
	0.3333	12.62%	11.54%	12.60%	12.46%	12.87%	12.13%	12.98%
$μ_{s}^{'}$	0.112	7.92%	8.35%	7.85%	7.38%	7.79%	8.39%	7.83%
	0.14	6.79%	7.00%	7.08%	6.84%	6.92%	6.63%	6.87%
	0.1667	5.96%	5.47%	5.91%	5.20%	6.36%	5.50%	6.26%
	0.2	5.75%	4.74%	5.73%	4.56%	5.76%	5.46%	5.94%
	0.25	5.64%	5.23%	5.56%	4.86%	5.32%	5.37%	5.57%
	0.3333	5.28%	5.88%	5.22%	4.82%	5.24%	5.61%	5.30%

Optical Property	Milk Type	Demodulation Method	$0.112 {m m}^{- 1}$	$0.14 {m m}^{- 1}$	$0.1667 {m m}^{- 1}$	$0.2 {m m}^{- 1}$	$0.25 {m m}^{- 1}$	$0.3333 {m m}^{- 1}$
$μ_{a} ({m m}^{- 1})$	skim	TPD	0.0083	0.0120	0.0117	0.0117	0.0122	0.0127
		STPI-filtering	0.0083	0.0120	0.0117	0.0117	0.0122	0.0128
		STPI-subtracting	0.0083	0.0120	0.0117	0.0117	0.0123	0.0130
	Low fat	TPD	0.0066	0.0107	0.0103	0.0103	0.0108	0.0112
		STPI-filtering	0.0066	0.0107	0.0103	0.0103	0.0108	0.0112
		STPI-subtracting	0.0066	0.0107	0.0103	0.0103	0.0108	0.0113
	Full fat	TPD	0.0066	0.0107	0.0103	0.0102	0.0107	0.0112
		STPI-filtering	0.0066	0.0107	0.0103	0.0102	0.0107	0.0112
		STPI-subtracting	0.0066	0.0107	0.0103	0.0102	0.0107	0.0112
$μ_{s}^{'} ({m m}^{- 1})$	Skim	TPD	0.9297	0.8459	0.8632	0.8716	0.8533	0.8220
		STPI-filtering	0.9320	0.8494	0.8700	0.8786	0.8591	0.8386
		STPI-subtracting	0.9289	0.8467	0.8656	0.8861	0.8755	0.9266
	Low fat	TPD	1.9160	1.6397	1.6962	1.7346	1.7226	1.6773
		STPI-filtering	1.9155	1.6429	1.7032	1.7454	1.7232	1.6883
		STPI-subtracting	1.9141	1.6417	1.6953	1.7481	1.7415	1.7670
	Full fat	TPD	3.5264	2.9410	3.0373	3.1502	3.1772	3.1619
		STPI-filtering	3.5078	2.9477	3.0412	3.1609	3.1708	3.1728
		STPI-subtracting	3.5193	2.9460	3.0286	3.1379	3.1800	3.2015

Milk Type	Fat Content (g/100 ml)	Protein Content (g/100 ml)
Skim	0	3.6
Low fat	1.5	3.0
Full fat	3.5	3.6

Abstract

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Tables (5)

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Applied Optics