Phase derivative estimation in digital holographic interferometry using a deep learning approach

Allaparthi Venkata Satya Vithin; Ankur Vishnoi; Rajshekhar Gannavarpu; Rajshekhar Gannavarpu

doi:10.1364/AO.455775

Applied Optics
Vol. 61,
Issue 11,
pp. 3061-3069
(2022)
•https://doi.org/10.1364/AO.455775

Phase derivative estimation in digital holographic interferometry using a deep learning approach

Allaparthi Venkata Satya Vithin, Ankur Vishnoi, and Rajshekhar Gannavarpu

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Allaparthi Venkata Satya Vithin, Ankur Vishnoi, and Rajshekhar Gannavarpu, "Phase derivative estimation in digital holographic interferometry using a deep learning approach," Appl. Opt. 61, 3061-3069 (2022)

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Table of Contents Category
- Instrumentation and Measurements
Optics & Photonics Topics
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About this Article
History
- Original Manuscript: February 10, 2022
- Revised Manuscript: March 14, 2022
- Manuscript Accepted: March 15, 2022
- Published: April 4, 2022

Abstract

In digital holographic interferometry, reliable estimation of phase derivatives from the complex interference field signal is an important challenge since these are directly related to the displacement derivatives of a deformed object. In this paper, we propose an approach based on deep learning for direct estimation of phase derivatives in digital holographic interferometry. Using a Y-Net model, our proposed approach allows for simultaneous estimation of phase derivatives along the vertical and horizontal dimensions. The robustness of the proposed approach for phase derivative extraction under both additive white Gaussian noise and speckle noise is shown via numerical simulations. Subsequently, we demonstrate the practical utility of the method for deformation metrology using experimental data obtained from digital holographic interferometry.

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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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S. No	Layer	Output Shape	Params Count	Inputs
01	Input layer	(256,256,1)	0
02	Down layer (256,256,[8;8;8])	(None,128,128,24)	1344	01
03	Down layer (128,128,[24;24;24])	(None,64,64,72)	15,912	02
04	Down layer (64,64,[72;72;72])	(None,32,32,216)	141,048	03
05	Down layer (32,32,[216;216;216])	(None,16,16,648)	1,262,952	04
06	Bridge layer (16,16,[678;678;256])	(None,32,32,256)	9,661,424	05
07	Up1 layer (32,32,[934;256;128])	(None,64,64,128)	10,052,462	(06, 05)
08	Up2 layer (32,32,[934;256;128])	(None,64,64,128)	10,052,462	(06, 05)
09	Up1 layer (64,64,[344;128;64])	(None,128,128,64)	1,537,720	(07, 04)
10	Up2 layer (64,64,[344;128;64])	(None,128,128,64)	1,537,720	(08, 04)
11	Up1 layer (128,128,[136;64;32])	(None,256,256,32)	264,392	(09, 03)
12	Up2 layer (128,128,[136;64;32])	(None,256,256,32)	264,392	(10, 03)
13	Up1 layer (256,256,[56;32;1])	(None,256,256,1)	45,091	(11, 02)
14	Up2 layer (256,256,[56;32;1])	(None,256,256,1)	45,091	(12, 02)

SNR		RMSE	SSIM	RMSE	SSIM
(dB)	Method	( $ϕ_{x}$ )	( $ϕ_{x}$ )	( $ϕ_{y}$ )	( $ϕ_{y}$ )
−4	ND	3.5118	$2.059 \times 10^{- 5}$	3.5171	$2.742 \times 10^{- 5}$
	WFT	0.0115	0.9724	0.0037	0.8688
	Proposed	0.0019	0.9964	0.0018	0.9786
0	ND	1.4577	$2.622 \times 10^{- 5}$	1.4631	$1.324 \times 10^{- 5}$
	WFT	0.0049	0.9527	0.0033	0.9526
	Proposed	0.0014	0.9960	0.0013	0.9911
4	ND	0.7476	0.0002	0.745	$9.821 \times 10^{- 5}$
	WFT	0.0081	0.9812	0.0035	0.9694
	Proposed	0.0011	0.9991	0.0011	0.9970

Speckle		RMSE	SSIM	RMSE	SSIM
Size (Pixels)	Method	( $ϕ_{x}$ )	( $ϕ_{x}$ )	( $ϕ_{y}$ )	( $ϕ_{y}$ )
2.5	ND	0.5664	0.0014	0.5667	0.0025
	WFT	0.0063	0.979	0.0068	0.9894
	Proposed	0.0011	0.9987	0.0014	0.9987
3	ND	0.4752	0.0005	0.4774	0.0002
	WFT	0.0034	0.9702	0.0026	0.9436
	Proposed	0.0009	0.9975	0.0009	0.9964
4	ND	0.654	0.0002	0.6522	0.0006
	WFT	0.0049	0.946	0.0088	0.9659
	Proposed	0.0010	0.9954	0.0013	0.9981

	RMSE	SSIM	RMSE	SSIM
Method	( $ϕ_{x}$ )	( $ϕ_{x}$ )	( $ϕ_{y}$ )	( $ϕ_{y}$ )
ND	3.9091	$6.81 \times 10^{- 6}$	3.9768	$6.11 \times 10^{- 8}$
WFT	0.0095	0.9565	0.0043	0.9330
Proposed	0.0016	0.9965	0.0019	0.9890

S. No	Layer	Output Shape	Params Count	Inputs
01	Input layer	(256,256,1)	0
02	Down layer (256,256,[8;8;8])	(None,128,128,24)	1344	01
03	Down layer (128,128,[24;24;24])	(None,64,64,72)	15,912	02
04	Down layer (64,64,[72;72;72])	(None,32,32,216)	141,048	03
05	Down layer (32,32,[216;216;216])	(None,16,16,648)	1,262,952	04
06	Bridge layer (16,16,[678;678;256])	(None,32,32,256)	9,661,424	05
07	Up1 layer (32,32,[934;256;128])	(None,64,64,128)	10,052,462	(06, 05)
08	Up2 layer (32,32,[934;256;128])	(None,64,64,128)	10,052,462	(06, 05)
09	Up1 layer (64,64,[344;128;64])	(None,128,128,64)	1,537,720	(07, 04)
10	Up2 layer (64,64,[344;128;64])	(None,128,128,64)	1,537,720	(08, 04)
11	Up1 layer (128,128,[136;64;32])	(None,256,256,32)	264,392	(09, 03)
12	Up2 layer (128,128,[136;64;32])	(None,256,256,32)	264,392	(10, 03)
13	Up1 layer (256,256,[56;32;1])	(None,256,256,1)	45,091	(11, 02)
14	Up2 layer (256,256,[56;32;1])	(None,256,256,1)	45,091	(12, 02)

Allaparthi Venkata Satya Vithin	https://orcid.org/0000-0002-3771-8679
Ankur Vishnoi	https://orcid.org/0000-0002-0136-3378
Rajshekhar Gannavarpu	https://orcid.org/0000-0002-4277-590X

Abstract

Data availability

Cited By

Figures (7)

Tables (4)

Equations (7)

Applied Optics