Single-shot fringe pattern phase retrieval using improved period-guided bidimensional empirical mode decomposition and Hilbert transform

Roadmap on computational methods in optical imaging and holography [invited]

Computational methods have been established as cornerstones in optical imaging and holography in recent years. Every year, the dependence of optical imaging and holography on computational methods is increasing significantly to the extent that optical methods and components are being completely and efficiently replaced with computational methods at low cost. This roadmap reviews the current scenario in four major areas namely incoherent digital holography, quantitative phase imaging, imaging through scattering layers, and super-resolution imaging. In addition to registering the perspectives of the modern-day architects of the above research areas, the roadmap also reports some of the latest studies on the topic. Computational codes and pseudocodes are presented for computational methods in a plug-and-play fashion for readers to not only read and understand but also practice the latest algorithms with their data. We believe that this roadmap will be a valuable tool for analyzing the current trends in computational methods to predict and prepare the future of computational methods in optical imaging and holography.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00340-024-08280-3.

High space-time bandwidth product imaging in low coherence quantitative phase microscopy

Current low coherence quantitative phase microscopy (LC-QPM) systems suffer from either reduced field of view (FoV) or reduced temporal resolution due to the short temporal coherence (TC) length of the light source. Here, we propose a hybrid, experimental and numerical approach to address this core problem associated with LC-QPM. We demonstrate high spatial resolution and high phase sensitivity in LC-QPM at high temporal resolution. High space-time bandwidth product is achieved by employing incoherent light source for sample illumination in QPM to increase the spatial resolution and single-shot Hilbert spiral transform (HST) based phase recovery algorithm to enhance the temporal resolution without sacrificing spatial resolution during the reconstruction steps. The high spatial phase sensitivity comes by default due to the use of incoherent light source in QPM which has low temporal coherence length and does not generate speckle noise and coherent noise. The spatial resolution achieved by the HST is slightly inferior to the temporal phase-shifting (TPS) method when tested on a specimen but surpasses that of the single-shot Fourier transform (FT) based phase recovery method. Contrary to HST method, FT method requires high density fringes for lossless phase recovery, which is difficult to achieve in LC-QPM over entire FoV. Consequently, integration of HST algorithm with LC-QPM system makes an attractive route. Here, we demonstrate scalable FoV and resolution in single-shot LC-QPM and experimentally corroborate it on a test object and on both live and fixed biological specimen such as MEF, U2OS and human red blood cells (RBCs). LC-QPM system with HST reconstruction offer high-speed single-shot QPM imaging at high phase sensitivity and high spatial resolution enabling us to study sub-cellular dynamic inside U2OS for extended duration (3 h) and observe high-speed (50 fps) dynamics of human RBCs. The experimental results validate the effectiveness of the present approach and will open new avenues in the domain of biomedical imaging in the future.

State-space modeling approach for fringe pattern demodulation

A spatial carrier fringe demodulation technique is proposed based on a state-space modeling approach for phase estimation. The fringe background intensity, carrier frequency, and phase quadrature components are considered to be the elements of the state vector, which are estimated simultaneously. The state estimation is performed using the extended Kalman filter. The simulation and experimental results are provided to demonstrate the performance comparison of the proposed method with popular and state-of-the-art methods in terms of noise robustness and phase estimation accuracy.

Single-shot fringe pattern phase retrieval using improved period-guided bidimensional empirical mode decomposition and Hilbert transform

Fringe pattern analysis is the central aspect of numerous optical measurement methods, e.g., interferometry, fringe projection, digital holography, quantitative phase microscopy. Experimental fringe patterns always contain significant features originating from fluctuating environment, optical system and illumination quality, and the sample itself that severely affect analysis outcome. Before the stage of phase retrieval (information decoding) interferogram needs proper filtering, which minimizes the impact of mentioned issues. In this paper we propose fully automatic and adaptive fringe pattern pre-processing technique - improved period guided bidimensional empirical mode decomposition algorithm (iPGBEMD). It is based on our previous work about PGBEMD which eliminated the mode-mixing phenomenon and made the empirical mode decomposition fully adaptive. In present work we overcame key problems of original PGBEMD - we have considerably increased algorithm's application range and shortened computation time several-fold. We proposed three solutions to the problem of erroneous decomposition for very low fringe amplitude images, which limited original PGBEMD significantly and we have chosen the best one among them after comprehensive analysis. Several acceleration methods were also proposed and merged to ensure the best results. We combined our improved pre-processing algorithm with the Hilbert Spiral Transform to receive complete, consistent, and versatile fringe pattern analysis path. Quality and effectiveness evaluation, in comparison with selected reference methods, is provided using numerical simulations and experimental fringe data.