CC BY
53B-O-4
One-step phase reconstruction using deep learning in off-axis holography
G. Dardikman-Yoffe1, N. Shaked1
1Tel Aviv University, Biomedical Engineering, Tel Aviv, Israel
Phase contrast images supply inherently good contrast for isolated cells in vitro without the need for staining, along with valuable information regarding both the internal geometrical structure and the RI distribution of the sample [1]. Digital holography can capture a sample complex wavefront by recording the interference pattern between a sample beam, interacting with the sample, and a reference beam [2]. In off-axis holography [3], one of the interfering beams is slightly tilted relative to the other beam, creating a linear shift that allows separation of the field intensity from the two complex-conjugate wave front terms in the spatial-frequency domain (SFD), and thus reconstruction of the complex wave front from a single hologram. Nevertheless, even upon successful extraction of the wavefront from the SFD, as can be done by cropping one of the cross correlation terms in the SFD [4], the reconstruction of the final phase profile from the recorded wavefront is a complicated task, including five main steps:
1) Initial extraction: the initial estimate of the phase is extracted from the wavefront using a simple four-quadrant arctangent function.
2) Beam referencing: the phase profile of a sample-free wavefront is subtracted from the initial phase estimate.
3) Phase unwrapping: the unwrapped phase is restored from its modulo 2n function (where the quotient is unknown); this can be done using a variety of algorithms [5], where a good choice requires certain expertise.
4) Linear slope correction: the unwrapped phase is fitted numerically in an iterative process, to find the parasitic tilted plain, such that it can be removed.
5) Background noise attenuation: finally, to get a clean image with a completely flat background, various heuristic thresholding and morphological operations have to be applied.
In the past couple of years, the concept of deep learning has emerged as a gold-standard solution to many types of problems in endless fields [6]. Specifically in the field of image processing, deep convolutional neural networks have revolutionized problems ranging from basic classification and segmentation to complex inverse problems in imaging. For the latter case of inverse problems, the residual neural network (ResNet) architecture [7], which adds short-term memory to each layer, has taken the lead due to its ability to force the network to learn new information in every layer beyond what is already encoded in the network. Here, we exploit this concept to train a neural network able to perform steps 2-5 at once, with only the initial estimate of the phase extracted from the sample wavefront as input; this not only eliminates the need to acquire a sample-free wavefront, but also removes the heuristics and inconsistency involved in phase reconstruction, and allows a faster, iteration-free and fully-automated phase reconstruction process.
References
[1] G. Dardikman and N. T. Shaked, "Review on methods of solving the refractive index-thickness coupling problem in digital holographic microscopy of biological cells," Optics Communications 422 (2018): 8-16.
[2] C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
[3] N. T. Shaked, "Quantitative phase microscopy of biological samples using a portable interferometer," Opt. Lett. 37, 2016-2018 (2012).
[4] P. Girshovitz and N. T. Shaked, "Real-time quantitative phase reconstruction in off-axis digital holography using multiplexing," Opt. Lett. 39, 2262-2265 (2014).
[5] D. C. Ghihlia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
[6] Y. LeCun, Y. Bengio, and G. Hinton, "Deep learning," Nature 521, 436-444 (2015).
[7] K. He, X. Zhang, S. Ren, and J. Sun, "Deep residual learning for image recognition," IEEE Conference on Computer Vision and Pattern Recognition, 770-778 (2016).
