Terahertz diffractive imaging with saturated data inpainting.

Multiplane iterative phase retrieval is a promising approach to diffraction imaging, which accurately determines the topographic and internal characteristics of various objects. Nevertheless, the detection systems used often have a limited dynamic range, resulting in overexposure of recorded intensity distributions. In this Letter, we present a novel, to the best of our knowledge, reconstruction algorithm that inpaints saturated areas on the measured intensity datasets and reliably retrieves wave complex amplitude. The proposed technique can be used in various spectral ranges, while we have tested it in the terahertz frequency range, where the problem of sources and detectors is most acute. We show that retrieved amplitude and phase distributions have a quality comparable to that of the images reconstructed from the reference high dynamic range technique. Herewith, the proposed approach seriously simplifies the process of data acquisition, what expands the possibilities in the design of measurement tools and studies of dynamic scenes.

Analog-to-digital conversion of information archived in display holograms: I. discussion.

This discussion paper highlights the potential of display holograms in the storage of information about objects' shape. The images recorded and reconstructed from holograms have high visual appeal, and the holographic carrier has far higher information capacity than other storage media. One hindrance to the application of display holograms is the inadequate development of techniques for digitizing information from them, which is compounded by insufficient analysis and discussion of existing approaches. In this review, we provide a historical retrospective of the use of display holography to save comprehensive information on object morphology. We also discuss existing and emerging technologies for converting information into a digital format, addressing one of the most serious challenges to the widespread use of display holography. Potential applications of these technologies are also analyzed.

Analog-to-digital conversion of information archived in display holograms: II. photogrammetric digitization.

We demonstrate the opportunities of photogrammetry in digitizing information about objects by acquiring a set of photographic images captured from three-dimensional scenes, which are reconstructed from volume reflection holograms. The corresponding requirements are determined for both recording the display hologram and digitizing the information reconstructed from it by photogrammetry. They include the choice of the radiation source used to reconstruct the object wave from the hologram; requirements for object positioning when recording a display hologram relative to the recording medium; and requirements for the glare minimization procedure during the construction of a photogrammetric three-dimensional model.

Optimization of DMD-based independent amplitude and phase modulation by analysis of target complex wavefront.

The paper presents the results of a comprehensive study on the optimization of independent amplitude and phase wavefront manipulation which is implemented using a binary digital micromirror device. The study aims to investigate the spatial resolution and quantization achievable using this approach and its optimization based on the parameters of the target complex wave and the modulation error estimation. Based on a statistical analysis of the data, an algorithm for selecting parameters (carrier frequency of binary pattern and aperture for the first diffraction order filtering) that ensures the optimal quality of the modulated wavefront was developed. The algorithm takes into account the type of modulation, that is, amplitude, phase, or amplitude-phase, the size of the encoded distribution, and its requirements for spatial resolution and quantization. The results of the study will greatly contribute to the improvement of modulated wavefront quality in various applications with different requirements for spatial resolution and quantization.

Phase Retardation Analysis in a Rotated Plane-Parallel Plate for Phase-Shifting Digital Holography.

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.

Investigation of Nonlinear Optical Properties of Quantum Dots Deposited onto a Sample Glass Using Time-Resolved Inline Digital Holography.

We report on the application of time-resolved inline digital holography in the study of the nonlinear optical properties of quantum dots deposited onto sample glass. The Fresnel diffraction patterns of the probe pulse due to noncollinear degenerate phase modulation induced by a femtosecond pump pulse were extracted from the set of inline digital holograms and analyzed. The absolute values of the nonlinear refractive index of both the sample glass substrate and the deposited layer of quantum dots were evaluated using the proposed technique. To characterize the inhomogeneous distribution of the samples' nonlinear optical properties, we proposed plotting an optical nonlinearity map calculated as a local standard deviation of the diffraction pattern intensities induced by noncollinear degenerate phase modulation.

Open-source 3D-printed terahertz pulse time-domain holographic detection module.

We present a holographic detection module to measure the spatially resolved distribution of pulsed terahertz field in a single scan by a motorized translation stage, responsible for the time delay. All mounts of the optical elements of the module are easily reproduced by 3D printing and attached to the optical cage system. The latter greatly simplifies the measurement procedure, allowing the experimenter to move and adjust the detection system as a single device. The developed mounts are made universal and can be used in other setups. We have made 3D models available as open-source hardware. The module is based on an electro-optical detection scheme with wide-aperture ZnTe crystal, crossed polarizers, and a matrix photodetector. The validation of its operability was performed with two experiments to measure the spatial distribution of the unperturbed field from the generator and the vortex field formed by the spiral phase plate. Optical vortices with multiple topological charges of 2-4 were detected on spectral components in the range from 0.3 to 1.1 THz. In addition, we have detailed the alignment process of terahertz imaging systems.

Noncollinear degenerate phase modulation in samples with inhomogeneous optical nonlinear properties [Invited].

Digital inline pump-probe holography can be applied to estimate parameters of samples' optical nonlinear properties. Here we propose a mathematical model to describe noncollinear degenerate phase modulation in samples with inhomogeneities of nonlinear refractive index over all three dimensions, namely, two-layered samples and samples with local impurities. The impact of sample parameters in the considered configurations is analyzed. We show that analysis of inline digital holograms obtained by time-resolved inline digital holography can be successfully used for rapid detection and characterization of various types of nonlinear refractive index inhomogeneities.

Terahertz phase retrieval imaging in reflection.

Terahertz phase retrieval is a promising technique able to assess the complex diffracted wave properties through an iterative processing algorithm. In this Letter, we demonstrate the implementation of this technique in reflection geometry with a continuous wave acquisition system working at 0.287 THz. To ensure a high signal-to-noise ratio in the measured dataset, we proposed a double parallel recording scheme with one detector and two lock-in amplifiers operating with the complimentary sensitivity setting. This provided a higher numerical aperture than conventional raster-scanning focal plane imaging. A specialized digital interferometric postprocessing procedure was applied to obtain a surface height map from the reconstructed phase distribution in the object's irradiated area.

Terahertz pulse time-domain holography with balance detection: complex-domain sparse imaging.

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.

Resolution and contrast in terahertz pulse time-domain holographic reconstruction.

Here, we present a comprehensive study of the reconstruction quality in terahertz (THz) pulse time-domain holography. We look into single wavelength reconstructions, as well as broadband recovery enabled by the ultrabroadband nature of radiation and coherent detection enabled by electro-optic or photoconductive sensing. We demonstrate the transverse resolution dependence for amplitude and phase objects on the solid angle of the inline recorded time-domain THz hologram, and then turn to the contrast of reconstructed binary amplitude objects, and further to longitudinal resolution of phase objects. We show that transverse resolution can reach values comparable to the wavelength of the radiation used, and longitudinally, phase objects can be resolved with even greater precision. We compare the obtained resolution with theoretical estimates and show that THz pulse time-domain holography is a powerful non-contact imaging tool.

Effect of object thickness on ultrashort pulse diffraction.

When calculated in the spectral domain, the propagation of an ultrashort optical pulse may suffer from inaccuracy due to the finite thickness of the object it diffracts on. Unlike monochromatic radiation, ultrashort pulse interaction with an object in the time domain depends on the pulse longitudinal coordinate. Here, we propose an algorithm to study the effect of the object thickness on ultrashort pulse diffraction on amplitude, phase, and three-dimensional highly scattering objects. The algorithm comprises a stepwise approach to simulating the diffraction of ultrashort pulses on apertures or scatterers having a finite thickness. We confirm the applicability of the approach and convergence of the result upon reducing the simulation step. We compare the simulation results obtained with traditionally calculated wavefields and the updated results obtained with the proposed approach. We reveal a discrepancy of about 7% for pulsed radiation with λ=800nm on a 1 mm thick object. Then, we demonstrate the dependence of this mismatch on the object thickness and show that for non-Gaussian vortex beams, this effect is even more pronounced. We reveal that spatiotemporal coupling effects depend on the pulse-object interaction simulation approach as well. The obtained results demonstrate that applicability of the single-layer representation of the simulated object strongly depends on its specific features, and inaccuracy of such an approach strongly depends on individual characteristics of the object.

Spectral Object Recognition in Hyperspectral Holography with Complex-Domain Denoising.

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.

Hyperspectral data denoising for terahertz pulse time-domain holography.

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.

Spatio-temporal and spatiospectral metrology of terahertz broadband uniformly topologically charged vortex beams.

A comprehensive characterization of the diffraction properties of terahertz (THz) pulsed broadband vortex beams consisting of several electromagnetic field oscillations requires state-of-the-art techniques for studying the evolution of a wavefront as it propagates. For this purpose, we have applied the capabilities offered by THz pulse time domain holography. Accurate metrological study of pulsed single-period THz field propagation allowed us to reveal the spatio-temporal and spatiospectral couplings in broadband uniformly topologically charged vortex beams. Here, we reveal dynamics of such beam propagation in a free space as well as in the experiment with edge diffraction with 50% blocking of the beam focal waist. In this study, we compare the dynamics of freely propagating and edge-diffracted THz vortex. Despite the fact that in the amplitude representation one can observe the emergence of strong asymmetry, analysis of the spectral trajectory of the singular point at some distance from the obstacle and the visualization of phase distribution for individual spectral components testify to the conservation of transverse energy circulation. Similar to the edge diffraction of monochromatic optical vortices, it can be interpreted as self-reconstruction of vortex properties. The given term has not previously been used for the case of pulsed broadband THz beams, to the best of our knowledge.

Increasing the resolution of the reconstructed image in terahertz pulse time-domain holography.

In this paper, we present a novel numerical approach for increasing the resolution of retrieved images of objects after their diffraction patterns are recorded via terahertz pulse time-domain holography (THz PTDH). THz PTDH allows for spectrally resolved imaging with high spatial resolution and does not require the fine alignment of complex optics in the THz path. The proposed data post-processing method opens up the possibility to reconstruct holograms recorded with spatially restricted THz detectors, and overcome the diffraction limit even for the lower-frequency spectral components. The method involves an iterative procedure of backward-forward wavefront propagation to simulate the field distribution beyond the initially recorded hologram area. We show significant improvement in both the object reconstruction and contrast across the whole spectrum, with qualitative resolution enhancement at lower frequency spectral components.

Super-resolution microscopy for biological specimens: lensless phase retrieval in noisy conditions.

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.

On terahertz pulsed broadband Gauss-Bessel beam free-space propagation.

Terahertz pulse time-domain holography is the ultimate technique allowing the evaluating a propagation of pulse broadband terahertz wavefronts and analyze their spatial, temporal and spectral evolution. We have numerically analyzed pulsed broadband terahertz Gauss-Bessel beam's both spatio-temporal and spatio-spectral evolution in the non-paraxial approach. We have characterized two-dimensional spatio-temporal beam behavior and demonstrated all stages of pulse reshaping during the propagation, including X-shape pulse forming. The reshaping is also illustrated by the energy transfer dynamics, where the pulse energy flows from leading edge to trailing edge. This behavior illustrates strong spatio-temporal coupling effect when spatio-temporal distribution of Bessel beam's wavefront depends on propagation distance. The spatio-temporal and spatio-spectral profiles for different spectral components clearly illustrate the model where the Bessel beam's wavefront at the exit from the axicon can be divided into radial segments for which the wave vectors intersect. Phase velocity via propagation distance is estimated and compared with existing experimantal results. Results of the phase velocity calculation depend strongly on distance increment value, thus demonstrating superluminal or subluminal behavior.

Correlation Characterization of Particles in Volume Based on Peak-to-Basement Ratio.

We propose a new express method of the correlation characterization of the particles suspended in the volume of optically transparent medium. It utilizes inline digital holography technique for obtaining two images of the adjacent layers from the investigated volume with subsequent matching of the cross-correlation function peak-to-basement ratio calculated for these images. After preliminary calibration via numerical simulation, the proposed method allows one to quickly distinguish parameters of the particle distribution and evaluate their concentration. The experimental verification was carried out for the two types of physical suspensions. Our method can be applied in environmental and biological research, which includes analyzing tools in flow cytometry devices, express characterization of particles and biological cells in air and water media, and various technical tasks, e.g. the study of scattering objects or rapid determination of cutting tool conditions in mechanisms.

High-accuracy off-axis wavefront reconstruction from noisy data: local least square with multiple adaptive windows.

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.