Biological phase sample study using variational Hilbert imaging technique

Abstract

Quantitative phase imaging (QPI) measurement is achieved by interference, e.g., in digital holographic microscopy and interference microscopy, where the fringe pattern (hologram/interferogram) phase distribution stores information about the refractive index structure of studied transparent biological samples. In this contribution we report the base for new endto- end QPI computational technique named the Variational Hilbert Imaging (VHI). It can be divided into two steps: hologram filtration using modified variational image decomposition (mVID) approach and phase map (sample-induced optical path delay) extraction using the Hilbert spiral transform (HST). The mVID employs new denoising approach and reliable criterion for determination of the end of calculations with careful investigation of proper parameter values. Quality of obtained results is therefore significantly increased ensuring acceleration and automation of calculations combined with remarkable robustness to different strongly varying hologram characteristics, i.e., local fringe period and orientation, background intensity, contrast deteriorations and noise. Additionally the HST makes it possible to retrieve phase from single hologram, even in case of closed fringes, providing efficient means for biological events characterization in dynamic regime. The VHI algorithm enables analysis of variety of biological samples without user’s meddling and loss of the accuracy. It is an important step to simplify optical measurement of complicated and fragile biological samples. Investigated VHI algorithm is tested on simulated and experimental data (i.e., swine spermatozoon). Phase decoding results are compared with reference algorithms, i.e., the Hilbert-Huang and Fourier transforms. Versatility of the proposed method and its potentially ubiquitous applications in full-field optical metrology are highlighted.