Towards a more practical analysis of Newton’s rings using deep learning

Tianshan Zhang; Ming-Feng Lu; Jin-Min Wu; Wenjie He; Feng Zhang; Ran Tao

doi:10.1364/AO.511173

Applied Optics
Vol. 63,
Issue 7,
pp. 1854-1866
(2024)
•https://doi.org/10.1364/AO.511173

Towards a more practical analysis of Newton’s rings using deep learning

Tianshan Zhang, Ming-Feng Lu, Jin-Min Wu, Wenjie He, Feng Zhang, and Ran Tao

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Tianshan Zhang, Ming-Feng Lu, Jin-Min Wu, Wenjie He, Feng Zhang, and Ran Tao, "Towards a more practical analysis of Newton’s rings using deep learning," Appl. Opt. 63, 1854-1866 (2024)

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Abstract

As a typical form of optical fringes with a quadratic phase, Newton’s ring patterns play an important role in spherical measurements and optical interferometry. A variety of methods have been used to analyze Newton’s ring patterns. However, it is still rather challenging to fulfill the analysis. We present a deep-learning-based method to estimate the parameters of Newton’s ring patterns and fulfill the analysis accordingly. The experimental results indicate the excellent accuracy, noise robustness, and demodulation efficiency of our method. It provides another applicable approach to analyzing Newton’s ring patterns and brings insights into fringe analysis and interferometry-based measurements.

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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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Training Configuration	Reference Value
Number of samples	10,000
Optimizer	AdamW [33]
Cost function	Mean squared error
Base learning rate	$1 \times 10^{- 3}$
Weight decay	0.1
Learning rate schedule	Cosine decay [34]
Batch size	128
Training epochs	150

Training Configuration	Reference Value
Number of samples	100,000
Optimizer	AdamW [33]
Cost function	Mean squared error
Base learning rate	$2 \times 10^{- 4}$
Weight decay	0.1
Learning rate schedule	Cosine decay [34]
Batch size	1024
Training epochs	400

Networks	Center RMSE	Radius Relative MAE	Training Time	Demodulation Time (using CPU)	Demodulation Time (using GPU)
VGG with single head [30]	51.06 pixels	82.47%	12.98 h	82.42 ms	4.98 ms
VGG with multiple heads	46.58 pixels	16.70%	11.55 h	81.15 ms	3.63 ms
Residual network with single head	66.27 pixels	112.15%	11.03 h	39.22 ms	5.88 ms
Residual network with multiple heads (current work)	0.23 pixels	0.15%	10.12 h	38.87 ms	6.67 ms

Example	Image Scale ( $µ m$ /pixel)	Center Ground Truth	Radius Ground Truth (m)	Center Estimation	Radius Estimation without MLP (m)	Radius Estimation with MLP (m)
Fig. 7(a)	15.171	(20, 107)	1.6698	(20, 107)	1.8348	1.6754
Fig. 7(b)	16.667	(20, 107)	1.6698	(20, 107)	1.6649	1.6649
Fig. 7(c)	19.541	(20, 107)	1.6698	(20, 107)	1.4217	1.6724

Example	Image Scale ( $µ m$ /pixel)	Center Ground Truth	Radius Ground Truth (m)	Center Estimation	Radius Relative MAE
Fig. 8(a)	15.685	(82, 106)	0.855	(81, 105)	2.89%
Fig. 8(b)	21.053	(110, 94)	1.443	(111, 94)	1.59%
Fig. 8(c)	15.685	(73, 118)	1.443	(73, 118)	0.37%

Example	Image Scale ( $µ m$ /pixel)	Center Ground Truth	Radius Ground Truth (m)	Center Estimation	Radius Relative MAE
Fig. 11(a)	15.685	(73, 118)	1.443	(73, 118)	0.37%
Fig. 11(b)	17.538	(138, 139)	1.443	(139, 137)	2.23%
Fig. 11(c)	17.538	(118, 131)	1.443	(117, 133)	4.51%

Setups	Center RMSE	Radius Relative MAE
Trained without noise	11.34 pixels	8.28%
Trained with noise	0.34 pixels	0.24%

Example	Center Ground Truth	Radius Ground Truth (m)	Center Estimation	Radius Relative MAE
Fig. 13(a)	(114, 206)	1.6092	(114, 205)	0.04%
Fig. 13(b)	(173, 189)	1.1145	(173, 188)	0.69%
Fig. 13(c)	(70, 62)	1.5889	(70, 62)	0.11%

SNR(dB)	Center Estimation	Radius Relative MAE
$\infty$	(114, 206)	0.09%
30	(114, 206)	0.15%
25	(114, 206)	0.20%
20	(114, 206)	0.11%
15	(114, 206)	0.07%
10	(114, 206)	0.14%
5	(114, 206)	0.10%
0	(114, 206)	0.04%
-5	(114, 205)	0.04%

Abstract

Data availability

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Figures (16)

Tables (11)

Equations (2)

Applied Optics