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One step accurate phase demodulation from a closed fringe pattern with the convolutional neural network HRUnet

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Abstract

Retrieving a phase map from a single closed fringe pattern is a challenging task in optical interferometry. In this paper, a convolutional neural network (CNN), HRUnet, is proposed to demodulate phase from a closed fringe pattern. The HRUnet, derived from the Unet model, adopts a high resolution network (HRnet) module to extract high resolution feature maps of the data and employs residual blocks to erase the gradient vanishing in the network. With the trained network, the unwrapped phase map can be directly obtained by feeding a scaled fringe pattern. The high accuracy of the phase map obtained from HRUnet is demonstrated by demodulation of both simulated data and actual fringe patterns. Compared results between HRUnet and two other CNNS are also provided, and the results proved that the performance of HRUnet in accuracy is superior to the two other counterparts.

© 2023 Optica Publishing Group

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Supplementary Material (1)

NameDescription
Code 1       Source code

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. Source codes of the HRUnet network presented in this paper are available in Code 1, Ref. [43].

43. R. Guo, S. Lu, M. Zhang, et al., “HRUney/py,” figshare (2023), https://doi.org/10.6084/m9.figshare.24624246.

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Figures (10)

Fig. 1.
Fig. 1. Flow chart of the demodulation method.
Fig. 2.
Fig. 2. Flow diagram of (a) network training and (b) network testing.
Fig. 3.
Fig. 3. Part of simulated data. (a) Fringe patterns; (b) corresponding phase maps. The unit of each picture is pixel.
Fig. 4.
Fig. 4. Network structure of HRUnet. (a) Overall structure; (b) structure of HRnet module in the HRUnet; (c) Stage2 used in HRnet.
Fig. 5.
Fig. 5. Loss function during training.
Fig. 6.
Fig. 6. Statistical results for HRUnet, HCNN, and Unet on simulated data. (a) Histograms of RMSE values of the error maps; (b) histograms of PV values of the three error maps.
Fig. 7.
Fig. 7. Demodulation results of simulated fringe patterns. (a) Fringe patterns; (b) ground truth unwrapped phase maps; (c) phase map predicted by the HRUnet; (d) error map between the reconstructed phase shown in (c) and the ground truth values; (e) phase map predicted by the HCNN and (f) its error map; (g) phase map predicted by the Unet and (h) its error map.
Fig. 8.
Fig. 8. Demodulation results of simulated fringe patterns containing higher order Zernike polynomials. (a) Fringe patterns; (b) corresponding ground truth unwrapped phase maps; (c) phase maps predicted by HRUnet; (d) error maps between phase map shown in (c) and that in (b).
Fig. 9.
Fig. 9. Noise level test results for simulated fringe patterns. (a1)–(a3) Fringe patterns with added noises with 40 dB, 30 dB, and 20 dB, respectively. (b1)–(b3) Corresponding errors maps.
Fig. 10.
Fig. 10. Demodulation results of actual fringe patterns. (a) Fringe patterns; (b) unwrapped phase maps reconstructed by the ZYGO interferometer; (c) phase map predicted by the HRUnet; (d) error map between the reconstructed phase shown in (c) and that in (b); (e) phase map predicted by the HCNN and (f) its error map; (g) phase map predicted by the Unet and (h) its error map.

Tables (1)

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Table 1. Training Strategy

Equations (5)

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ϕ ( x , y ) = i = 1 10 c i Z i ( x , y ) ,
I ( x , y ) = a ( x , y ) + b ( x , y ) cos ( ϕ ( x , y ) ) + p ( x , y ) ,
I cos = 2 ( I min ( I ) max ( I ) min ( I ) 1 ) ,
M A E = 1 n i = 1 n | ϕ i ϕ i | ,
M S E = 1 n i = 1 n | ϕ i ϕ i | 2 .
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