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We investigated the peculiarities of the terahertz pulse time-domain holography principle in the case of raster scanning with the balance detection system. The noise in this system represents a Skellam distribution model, which differentiates it from systems based on a photoconductive antenna. We analyzed this Skellam model and provided both numerical and experimental investigations. We found that the variance of the noise in the balance detection system does not depend on the true signal. Complex-domain images obtained in this model are filtered by block-matching algorithms adapted for spatio-temporal and spatiospectral volumetric data. We presented a new cube complex-domain filter algorithm that uses block matching in all 3D data sets simultaneously in spatial and frequency coordinates. A combination of temporal and complex-domain filters allows us to expand the dynamic range of terahertz frequencies for which we can obtain amplitude/phase information. Experimental data demonstrate an improvement in the quality of the resultant images both in the time domain and complex-spectral domain. The simulation and experimental results are in good agreement.

We investigated data denoising in hyperspectral terahertz pulse time-domain holography. Using the block-matching algorithms adapted for spatio-temporal and spatio-spectral volumetric data we studied and optimized parameters of these algorithms to improve phase image reconstruction quality. We propose a sequential application of the two algorithms oriented on work in temporal and spectral domains. Experimental data demonstrate the improvement in the quality of the resultant time-domain images as well as phase images and object's relief. The simulation results are proved by comparison with the experimental ones.

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.

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.

We consider reconstruction of a wave field distribution in an input/object plane from data in an output/diffraction (sensor) plane. We provide digital modeling both for the forward and backward wave field propagation. A novel algebraic matrix form of the discrete diffraction transform (DDT) originated in Katkovnik et al. [Appl. Opt. 47, 3481 (2008)] is proposed for the forward modeling that is aliasing free and precise for pixelwise invariant object and sensor plane distributions. This "matrix DDT" is a base for formalization of the object wave field reconstruction (backward propagation) as an inverse problem. The transfer matrices of the matrix DDT are used for calculations as well as for the analysis of conditions when the perfect reconstruction of the object wave field distribution is possible. We show by simulation that the developed inverse propagation algorithm demonstrates an improved accuracy as compared with the standard convolutional and discrete Fresnel transform algorithms.

A discrete diffraction transform (DDT) is a novel discrete wavefield propagation model that is aliasing free for a pixelwise invariant object distribution. For this class of distribution, the model is precise and has no typical discretization effects because it corresponds to accurate calculation of the diffraction integral. A spatial light modulator (SLM) is a good example of a system where a pixelwise invariant distribution appears. Frequency domain regularized inverse algorithms are developed for reconstruction of the object wavefield distribution from the distribution given in the sensor plane. The efficiency of developed frequency domain algorithms is demonstrated by simulation.