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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.)

The race for miniature color cameras using flat meta-optics has rapidly developed the end-to-end design framework using neural networks. Although a large body of work has shown the potential of this methodology, the reported performance is still limited due to fundamental limitations coming from meta-optics, mismatch between simulated and resultant experimental point spread functions, and calibration errors. Here, we use a HIL optics design methodology to solve these limitations and demonstrate a miniature color camera via flat hybrid meta-optics (refractive + meta-mask). The resulting camera achieves high-quality full-color imaging for a 5-mm aperture optics with a focal length of 5 mm. We observed a superior quality of the images captured by the hybrid meta-optical camera compared to a compound multi-lens optics of a mirrorless commercial camera.

End-to-end optimization of diffractive optical elements (DOEs) profile through a digital differentiable model combined with computational imaging have gained an increasing attention in emerging applications due to the compactness of resultant physical setups. Despite recent works have shown the potential of this methodology to design optics, its performance in physical setups is still limited and affected by manufacturing artefacts of DOE, mismatch between simulated and resultant experimental point spread functions, and calibration errors. Additionally, the computational burden of the digital differentiable model to effectively design the DOE is increasing, thus limiting the size of the DOE that can be designed. To overcome the above mentioned limitations, a co-design of hybrid optics and image reconstruction algorithm is produced following the end-to-end hardware-in-the-loop strategy, using for optimization a convolutional neural network equipped with quantitative and qualitative loss functions. The optics of the imaging system consists on the phase-only spatial light modulator (SLM) as DOE and refractive lens. SLM phase-pattern is optimized by applying the Hardware-in-the-loop technique, which helps to eliminate the mismatch between numerical modelling and physical reality of image formation as light propagation is not numerically modelled but is physically done. Comparison with compound multi-lens optics of a last generation smartphone and a mirrorless commercial cameras show that the proposed system is advanced in all-in-focus sharp imaging for a depth range 0.4-1.9 m.

In this paper, we detail a phase-shift implementation in a rotated plane-parallel plate (PPP). Considering the phase-shifting digital holography application, we provide a more precise phase-shift estimation based on PPP thickness, rotation, and mutual inclination of reference and object wavefronts. We show that phase retardation uncertainty implemented by the rotated PPP in a simple configuration is less than the uncertainty of a traditionally used piezoelectric translator. Physical experiments on a phase test target verify the high quality of phase reconstruction.

A power-balanced hybrid optical imaging system has a diffractive computational camera, introduced in this paper, with image formation by a refractive lens and multilevel phase mask (MPM). This system provides a long focal depth with low chromatic aberrations thanks to MPM and a high energy light concentration due to the refractive lens. We introduce the concept of optical power balance between the lens and MPM, which controls the contribution of each element to modulate the incoming light. Additional features of our MPM design are the inclusion of the quantization of the MPM's shape on the number of levels and the Fresnel order (thickness) using a smoothing function. To optimize the optical power balance as well as the MPM, we built a fully differentiable image formation model for joint optimization of optical and imaging parameters for the proposed camera using neural network techniques. We also optimized a single Wiener-like optical transfer function (OTF) invariant to depth to reconstruct a sharp image. We numerically and experimentally compare the designed system with its counterparts, lensless and just-lens optical systems, for the visible wavelength interval (400-700) nm and the depth-of-field range (0.5- ∞ m for numerical and 0.5-2 m for experimental). We believe the attained results demonstrate that the proposed system equipped with the optimal OTF overcomes its counterparts--even when they are used with optimized OTF--in terms of the reconstruction quality for off-focus distances. The simulation results also reveal that optimizing the optical power balance, Fresnel order, and the number of levels parameters are essential for system performance attaining an improvement of up to 5 dB of PSNR using the optimized OTF compared to its counterpart lensless setup.

A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier transform spectroscopy in the self-referencing optical setup and provides additional, beyond spectral intensity distribution, reconstruction of the investigated object's phase. The noise amplification Fellgett's disadvantage is relaxed by the application of a sparse wavefront noise filtering embedded in the proposed algorithm. The algorithm reliability is proved by simulation tests and by results of physical experiments for transparent objects. These tests demonstrate precise phase imaging and object depth (profile) reconstruction.

Design and optimization of lensless phase-retrieval optical system with phase modulation of free-space propagation wavefront is proposed for subpixel imaging to achieve super-resolution reconstruction. Contrary to the traditional super-resolution phase-retrieval, the method in this paper requires a single observation only and uses the advanced Super-Resolution Sparse Phase Amplitude Retrieval (SR-SPAR) iterative technique which contains optimized sparsity based filters and multi-scale filters. The successful object imaging relies on modulation of the object wavefront with a random phase-mask, which generates coded diffracted intensity pattern, allowing us to extract subpixel information. The system's noise-robustness was investigated and verified. The super-resolution phase-imaging is demonstrated by simulations and physical experiments. The simulations included high quality reconstructions with super-resolution factor of 5, and acceptable at factor up to 9. By physical experiments 3 μm details were resolved, which are 2.3 times smaller than the resolution following from the Nyquist-Shannon sampling theorem.

In this paper, we have applied a recently developed complex-domain hyperspectral denoiser for the object recognition task, which is performed by the correlation analysis of investigated objects' spectra with the fingerprint spectra from the same object. Extensive experiments carried out on noisy data from digital hyperspectral holography demonstrate a significant enhancement of the recognition accuracy of signals masked by noise, when the advanced noise suppression is applied.

The paper is devoted to a computational super-resolution microscopy. A complex-valued wavefront of a transparent biological cellular specimen is restored from multiple intensity diffraction patterns registered with noise. For this problem, the recently developed lensless super-resolution phase retrieval algorithm [Optica, 4(7), 786 (2017)] is modified and tuned. This algorithm is based on a random phase coding of the wavefront and on a sparse complex-domain approximation of the specimen. It is demonstrated in experiments, that the reliable phase and amplitude imaging of the specimen is achieved for the low signal-to-noise ratio provided a low dynamic range of observations. The filterings in the observation domain and specimen variables are specific features of the applied algorithm. If these filterings are omitted the algorithm becomes a super-resolution version of the standard iterative phase retrieval algorithms. In comparison with this simplified algorithm with no filterings, our algorithm shows a valuable improvement in imaging with much smaller number of observations and shorter exposure time. In this way, presented algorithm demonstrates ability to work in a low radiation photon-limited mode., Competing Interests: The authors declare that there are no conflicts of interest related to this article.

Recent works demonstrated that digital time-resolved holography is the prospective approach to study nonlinear light-matter interaction processes. In this Letter, we present a straightforward inline holographic approach for studying degenerate phase modulation induced by an inclined collimated pump beam in the isotropic sample. The method is based on a minimization of the difference between experimentally acquired data and simulated inline holograms obtained from a numerical model of pump-probe interaction in optical nonlinear media. A sophisticated experimental data processing algorithm is implemented to provide high sensitivity and a signal-to-noise ratio eligible for soft interaction with a collimated pump beam. The integral phase shift determined by our method can be used to estimate the nonlinear refractive index and the relaxation time for material with a low damage threshold. We validated our approach for the case of soda-lime and BK7 glasses.

Surface relief gratings and refractive index gratings are formed by direct holographic recording in amorphous chalcogenide nanomultilayer structures As 2 S 3 -Se and thin films As 2 S 3 . The evolution of the grating parameters, such as the modulation of refractive index and relief depth in dependence of the holographic exposure, is investigated. Off-axis digital holographic microscopy is applied for the measurement of the photoinduced phase gratings. For the high-accuracy reconstruction of the wavefront (amplitude and phase) transmitted by the fabricated gratings, we used a computational technique based on the sparse modeling of phase and amplitude. Both topography and refractive index maps of recorded gratings are revealed. Their separated contribution in diffraction efficiency is estimated.

A variational algorithm to object wavefront reconstruction from noisy intensity observations is developed for the off-axis holography scenario with imaging in the acquisition plane. The algorithm is based on the local least square technique proposed in paper [J. Opt. Soc. Am. A21, 367 (2004)]. First, multiple reconstructions of the wavefront are produced for various size and various directional windows applied for localization of estimation. At the second stage, a special statistical rule is applied in order to select the best window size estimate for each pixel of the image and for each of the directional windows. At the third final stage the estimates of the different directions obtained for each pixel are aggregated in the final one. Simulation experiments and real data processing prove that the developed algorithm demonstrate the performance of the extraordinary quality and accuracy for both the phase and amplitude of the object wavefront.

This work presents the new method for wavefront reconstruction from a digital hologram recorded in off-axis configuration. The main feature of the proposed algorithm is a good ability for noise filtration due to the original formulation of the problem taking into account the presence of noise in the recorded intensity distribution and the sparse phase and amplitude reconstruction approach with the data-adaptive block-matching 3D technique. Basically, the sparsity assumes that low dimensional models can be used for phase and amplitude approximations. This low dimensionality enables strong suppression of noisy components and accurate revealing of the main features of the signals of interest. The principal point is that dictionaries of these sparse models are not known in advance and reconstructed from given noisy observations in a multiobjective optimization procedure. We show experimental results demonstrating the effectiveness of our approach.

The two photon resonant, three photon ionization spectra of ArXe were recorded in the spectral region of 88,500-90,100 cm(-1). Seven new molecular band progressions dissociating to ArXe* → Ar(1)S0 + Xe* 7p[1/2]0, Xe* 7p[3/2]2, Xe* 6p'[3/2]2, Xe* 6p'[1/2]1, Xe* 6p'[1/2]0 have been selected and analyzed. The molecular constants for the excited states of ArXe* of these vibrational progressions were determined in the approximation of the anharmonic oscillator, the Morse potential and the Franck-Condon principle. The photoelectron spectra were recorded by several excited electronic-vibrational transitions of ArXe, the dissociation channels of the excited molecules were determined and extra information about the electron structure of the excited molecular states was obtained.