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High quality of an absolute phase reconstruction for coherent digital holography with an enhanced anti-speckle deep neural unwrapping network

Wei Lu, Yue Shi, Pan Ou, Ming Zheng, Hanxu Tai, Yuhong Wang, Ruonan Duan, Mingqing Wang, and Jian Wu

Open Access Open Access

Abstract

It is always a challenge how to overcome speckle noise interference in the phase reconstruction for coherent digital holography (CDH) and its application, as this issue has not been solved well so far. In this paper, we are proposing an enhanced anti-speckle deep neural unwrapping network (E-ASDNUN) approach to achieve high quality of absolute phase reconstruction for CDH. The method designs a special network-based noise filter and embeds it into a deep neural unwrapping network to enhance anti-noise capacity in the image feature recognition and extraction process. The numerical simulation and experimental test on the phase unwrapping reconstruction and the image quality evaluation under the noise circumstances show that the E-ASDNUN approach is very effective against the speckle noise in realizing the high quality of absolute phase reconstruction. Meanwhile, it also demonstrates much better robustness than the typical U-net neural network and the traditional phase unwrapping algorithms in reconstructing high wrapping densities and high noise levels of phase images. The E-ASDNUN approach is also examined and confirmed by measuring the same phase object using a commercial white light interferometry as a reference. The result is perfectly consistent with that obtained by the E-ASDNUN approach.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

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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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Figures (6)
Fig. 1.
Fig. 1. A diagram of the E-ASDNUN network architecture, in which Conv, BN and ReLU denote the convolution, the batch normalization and the rectified linear unit, respectively.

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Fig. 2.
Fig. 2. A test wrapped-phase image with σ = 0.5 and its feature maps before and after undergoing the anti-noise module at Epoch 1, Epoch 50 and Epoch 100 of network training.

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Fig. 3.
Fig. 3. Numerical simulation of the phase reconstruction with the E-ASDNUN, the U-net, the PUMA and the DCT-LS approaches. (a), (b), (c) are a random phase object, its wrapped phase image and the phase distribution within one cross-section located at 80 pixels, respectively. The max wrapping number of the object is nM= 4 and the noise level is σ= 0.1. (d)-(f), (g)-(i), (j)-(l), (m)-(o) are the phase reconstruction results with the E-ASDNUN, the PUMA, the DCT-LS and the U-net approaches, respectively. (e), (h), (k). (n) are the error maps between the reconstructed phase images and the object. The blue and red curves in (f), (i), (l), (o) are the phase distributions within one fixed cross-section at 80 pixels from the object and the reconstructed images, respectively.

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Fig. 4.
Fig. 4. PSNRs and SSIMs of the reconstructed phase images for different noise levels of σ = 0.1-0.5 and different wrapping densities of n = 2-10 of the object, where the red, black, blue and green curves are corresponding to the reconstruction approaches of the E-ASDNUN network, the U-net network, the PUMA and the DCT-LS algorithms, respectively.

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Fig. 5.
Fig. 5. The noise suppression and image reconstruction of a stem cell with severe noise interference using the E-ASDNUN network approach based on the same network training sets and conditions. (a)-(c) show the wrapped cell images with noise standard deviation of σ = 0.5, 0.7 and 0.9, respectively. (d)-(f) show the reconstructed cell images. (g)-(i) show the error plots between the reconstructed cell image and the ground truth.

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Fig. 6.
Fig. 6. Experimental demonstration of phase reconstruction and speckle noise suppression in laser digital holography. The sample is a micro-lens array product (Thorlabs, model MLA150-7AR) and laser wavelength is 632.8 nm (a)-(b) are the reconstructed image and its truth height plot of phase cross-section using the white light interferometer (model: SmartWLI-prime). (c)-(d), (e)-(f) and (g)-(h) are the reconstructed images and their cross-section phase plots with DCT-LS, PUMA and E-ASDNUN approaches, respectively, where the red curves in (d), (f), (h) are the truth height plots of a phase cross-section (marked by black dash lines). The black curves in (b), (d), (f), (h) are the truth height plots of the same cross-section phase of the image measured with SmartWLI-prime.

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Tables (3)

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Table 1. The variance of feature maps before undergoing the anti-noise module at Epoch 1, Epoch 50 and Epoch 100.

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Table 2. The PSNR and SSIM of the reconstructed cell images

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Table 3. Height and width parameters of the reconstructed micro-lens array with different methods

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Equations (9)

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U ~ ( x , y ) = A ( x , y ) e j [ φ ( x , y ) + 2 π n ( x , y ) ] = A 0 ( x , y ) e j [ φ 0 ( x , y ) + 2 π n ( x , y ) ] ⋅ [ 1 + N ~ ( x , y ) ]
N ~ ( x , y ) = A n ( x , y ) e j [ φ n ( x , y ) ]
φ ( x , y ) = a r c t a n { s i n φ 0 ( x , y ) + σ n R ( x , y ) ⋅ s i n [ φ 0 ( x , y ) + σ n I ( x , y ) ] c o s φ 0 ( x , y ) + σ n R ( x , y ) ⋅ c o s [ φ 0 ( x , y ) + σ n I ( x , y ) ] }
P S N R = 10 ⋅ log 10 ( M A X φ o r i g 2 M S E )
S S I M ( φ Re , φ o r i g ) = ( 2 μ Re μ o r i g + C 1 ) ( 2 σ Re o r i g + C 2 ) ( μ Re 2 + μ o r i g 2 + C 1 ) ( σ Re 2 + σ o r i g 2 + C 2 )
U ~ ( m , n ) = I F F T { T ( ξ , η ) F F T [ H ( k , l ) ] }
H ( k , l ) = H ( x , y ) r e c t ( x M Δ x , y N Δ y ) × ∑ k M ∑ l N δ ( x − k Δ x , y − l Δ y )
T ( ξ , η ) = exp ⁡ { j 2 π λ d [ 1 − ( λ ( ξ − M / 2 ) ) 2 − ( λ ( η − N / 2 ) ) 2 ] 1 / 2 }
φ ( m , n ) = arctan ⁡ { Im [ U ~ ( m , n ) ] Re [ U ~ ( m , n ) ] }
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