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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., Competing Interests: Conflict of interestThe authors declare no competing interests., (© The Author(s) 2024.)

We propose and demonstrate a holographic imaging scheme exploiting random illuminations for recording hologram and then applying numerical reconstruction and twin image removal. We use an in-line holographic geometry to record the hologram in terms of the second-order correlation and apply the numerical approach to reconstruct the recorded hologram. This strategy helps to reconstruct high-quality quantitative images in comparison to the conventional holography where the hologram is recorded in the intensity rather than the second-order intensity correlation. The twin image issue of the in-line holographic scheme is resolved by an unsupervised deep learning based method using an auto-encoder scheme. Proposed learning technique leverages the main characteristic of autoencoders to perform blind single-shot hologram reconstruction, and this does not require a dataset of samples with available ground truth for training and can reconstruct the hologram solely from the captured sample. Experimental results are presented for two objects, and a comparison of the reconstruction quality is given between the conventional inline holography and the one obtained with the proposed technique., (© 2023. The Author(s).)

The coherence holography offers an unconventional way to reconstruct the hologram where an incoherent light illumination is used for reconstruction purposes, and object encoded into the hologram is reconstructed as the distribution of the complex coherence function. Measurement of the coherence function usually requires an interferometric setup and array detectors. This paper presents an entirely new idea of reconstruction of the complex coherence function in the coherence holography without an interferometric setup. This is realized by structured pattern projections on the incoherent source structure and implementing measurement of the cross-covariance of the intensities by a single-pixel detector. This technique, named structured transmittance illumination coherence holography (STICH), helps to reconstruct the complex coherence from the intensity measurement in a single-pixel detector without an interferometric setup and also keeps advantages of the intensity correlations. A simple experimental setup is presented as a first step to realize the technique, and results based on the computer modeling of the experimental setup are presented to show validation of the idea., (© 2022. The Author(s).)