Twin image removal with deep learning for multi-wavelength digital in-
#,1Aditya Chandra Mandal* ,2Abhijeet Phatak* and 3
1Department of Mining Engineering, Indian Institute of Technology (Banaras Hindu University,
Varanasi - 221005, India
2245 W California Ave #6, Sunnyvale, California 94085, USA:
3Department of Physics, Indian Institute of Technology (Banaras Hindu University), Varanasi -
*These authors contributed equally to this work
Abstract: Phase of an object plays a crucial role in retrieving the complete information. Digital in-line
holography is a simple and effective technique to retrieve the phase information and 3D features of object.
However the twin image formation limits the total information that can be obtained using in-line holography.
Here in this paper, we show how deep learning can be leveraged to reconstruct the inline hologram to
remove the twin image and thus preserve the amplitude and phase information of the object.
Digital hologram (DH) has played a significant role in the quantitative phase imaging (QPI) and the technique
has emerged as an effective tool for imaging of transparent microscopic and macroscopic objects [1,2]. The
DH relies on the principle of optically recording the complex wavefront of the light diffracted from the object
as an interference pattern and subsequently applying the digital reconstruction method to the recorded
interference pattern. Several experimental systems have been developed for the DH and significant among
them are in-line, off-axis and phase shifting methods. In-line geometry has been proved to be a very
powerful method due to its compactness and simplicity. This method has many practical applications in
biology, metrology applications, multiple 3D image encryption etc. However, reconstruction quality of such in-
line holograms is constrained by twin image formation . Previously proposed solutions to twin image
removal were demonstrated by Rivenson, Yair, et al. , Latychevskaia, Tatianaet, et al. . In this paper,
the twin image removal is explored for multi-wavelength digital in-line holography  using an unsupervised
deep neural network with encoder-decoder architecture , the so-called auto-encoder. Two different light
sources (532nm and 632nm wavelengths) were used to illuminate the object sequentially and the separate
holograms were reconstructed with corresponding wavelengths.
2. Basic principle
DH makes use of an interference between object and reference beam. This interference pattern, between
two coherent beams namely object and reference, is represented as
() = () + ()2
() = ()()+()()+()2+()2 (1)
Where R and O are reference and object waves respectively. The spatial coordinate at the recording plane is
represented by .
Recorded interference pattern, as represented by Eq. (1), is digitally reconstructed using appropriate
propagation algorithm. For instance, reconstruction can be achieved via a Kirchhoff- Helmholtz transform as
=2 (exp 2
Realization of the Eq. (2) provided mainly three terms and all these three terms are spatially merged hiding
any useful information. In in-line holography, simultaneous real and virtual images of the object in the same
line of sight and also accompanied by a coherent background are produced . This is referred to as the twin
In order to remove this artifact in the reconstruction of in-line holography, we present here our investigation
based on deep learning. The reconstruction includes the following steps. (i) Formation of the input complex
Manisha, Rakesh Kumar Singh
field as (), where the is amplitude which is always given by the square root of the normalized
hologram and the initial phase of the hologram is calculated using Gerchberg-Saxton (GS) algorithm . (ii)
Then the complex field () is back propagated to the object plane and the back-propagated
amplitude and phase were the input to the auto-encoder. Fig1. describes the learning steps of the
Fig 1. The overall block diagram of our learning procedure. After feeding a fixed input (as the initial guess) into the network, the network
reconstructs the image. The reconstructed result is propagated to the hologram plane by the transmission, depending on the optical
parameters. The network updates its weights by minimizing the pixel-wise error between the forward-propagated result and the captured
3. Results and Discussion:
For demonstration of our approach, we have considered two simulated in-line holograms of the letter “A” for
two different wavelengths (532nm, 632nm) and these holograms are subjected to a reconstruction algorithm
guided by a deep learning model. The structural similarity index (SSIM) and mean squared error (MSE) were
calculated between of ground truth and reconstructed object amplitude. Results based on with twin image
and without twin-image are shown in Fig. 2.
Fig. 2 (i) Reconstruction for 532 nm (ii) Reconstruction for 632 nm (a),(c) Back propagated amplitude and phase respectively in
presence of twin-image (b),(d) Reconstructed amplitude and phase respectively with twin-image removed by auto-encoder model
The SSIM and MSE were 0.9840 and 0.0027 and 0.9759 and 0.0075 for 532 nm and 632 nm respectively.
Issue of twin image in in-line holography is examined and addressed by a deep learning approach.
Simulation results based on deep learning approach show potential of this technique in the reconstruction of
the in-line holography with multi-wavelength illumination.
 J. W. Goodman, Fourier Optics, Viva Books Pvt. Ltd, New Delhi 2007
 W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, PNAS 98 , 11301-11305 (2001).
 Rivenson, Yair, Yibo Zhang, Harun Günaydın, Da Teng, and Aydogan Ozcan, Light: Science & Applications 7, no. 2 (2018):
 Latychevskaia, Tatiana, and Hans-Werner Fink. , Physical review letters 98.23 (2007):
 Velaquez D, Garcia-Sucerquia J. InDigital Holography and Three-Dimensional Imaging 2012 Apr 28 (pp. DTu1C-4). Optical
Society of America.
 Li, H., Chen, X., Chi, Z., Mann, C., & Razi, A. (2020). IEEE Access, 8, 202648-202659.
 Denis, L., Fournier, C., Fournel, T., & Ducottet, C. (2005, September). In Wavelets XI (Vol. 5914, p. 59140J). International
Society for Optics and Photonics.