Nikolay V. Petrov

Holography and phase retrieval in terahertz imaging

In this paper, we present review and latest results obtained in the scope of terahertz holographic and other methods for phase retrieval in terahertz imaging. Not only accurate change of amplitude, but also rigorous phase retrieval is essential for precise calculation of optical parameters of the samples in terahertz range. Pulse terahertz holography introduced some years ago shows itself as perfect method for overall-object phase retrieval technique, but in the same time it allows measurement with low signal to noise that leads to less precise derivation of sample optical parameters. And certainly just point-by-point terahertz time-domain spectroscopy provides the most precise information of sample phase, but it is rather time consuming and has low spatial resolution as well. The other possible way assumes, in contrary to pulse terahertz holography and spectroscopy, using narrow-band continuous terahertz source, which tunability might also make the measurement process easier. And diffraction patterns registered with microbolometer array or any other terahertz intensity sensor placed at several different distances from the object and/or taken for several different terahertz frequencies are used for phase retrieval in this case. We present both numerical predictions and experimental results for the proposed methods, estimate the achievable spatial and other limits of the techniques and compare them to the others used in different spectral ranges.

Wavefront reconstruction in digital off-axis holography via sparse coding of amplitude and absolute phase

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.

Phase retrieval of THz radiation using set of 2D spatial intensity measurements with different wavelengths

Using the infrared matrix of pyroelectric or other photodetectors along with THz band pass filters with pulsed or CW sources one can record the 2D intensity distribution of THz radiation with a high degree of monochromatization. This allows one to use various approaches to solving the phase problem which were developed for the visible frequencies. In this contribution we present the results of the numerical investigation of the wavefront reconstruction using THz radiation at several wavelengths and taking the intensity distribution at various distances.

Computational super-resolution phase retrieval from multiple phase-coded diffraction patterns: simulation study and experiments

In this paper, we consider computational super-resolution inverse diffraction phase retrieval. The optical setup is lensless, with a spatial light modulator for aperture phase coding. The paper is focused on experimental tests of the super-resolution sparse phase amplitude retrieval algorithm. We start from simulations and proceed to physical experiments. Both simulation tests and experiments demonstrate good-quality imaging for super-resolution with a factor of 4 and a serious advantage over diffraction-limited resolution as defined by Abbe’s criterion.

Nondestructive monitoring of aircraft composites using terahertz radiation

In this paper we consider using the terahertz (THz) time domain spectroscopy (TDS) for non destructive testing and determining the chemical composition of the vanes and rotor-blade spars. A versatile terahertz spectrometer for reflection and transmission has been used for experiments. We consider the features of measured terahertz signal in temporal and spectral domains during propagation through and reflecting from various defects in investigated objects, such as voids and foliation. We discuss requirements are applicable to the setup and are necessary to produce an image of these defects, such as signal-to-noise ratio and a method for registration THz radiation. Obtained results indicated the prospects of the THz TDS method for the inspection of defects and determination of the particularities of chemical composition of aircraft parts.

Characterization of particles suspended in a volume of optical medium at high concentrations by coherent image processing

Abstract. We give a broad discussion of existing typical works devoted to particle image processing. We propose the approach based on the postprocessing of coherent images of the particles at various planes of the volume. These images can be obtained both by reconstruction of inline digital hologram and by means of defocussing of the lens with high numerical aperture. Processing of the reconstructed holograms or recorded images is carried out using the proposed image analysis approach based on the edge-point linking and thresholding technique, which is considered to be simple to implement and reliable. After the review of existing methods and approaches, we noted that, in general, only cases of low concentrations are considered and, therefore, we investigated the performance of our proposed approach for characterization of particles of high density in a volume of optical medium. In this study of the method, we increase the concentration of particles until we ensure that every volume element comprises many particle images, yet these images do not create a speckle pattern, and look for the concentrations at which normalized density distributions of the particles can be constructed with an acceptable error for us. It is shown that the proposed approach exhibits good results of recognition and allows investigation of high concentrations.

Sparse approximations of phase and amplitude for wave field reconstruction from noisy data

The topic of sparse representations (SR) of images has attracted tremendous interest from the research community in the last ten years. This interest stems from the fundamental role that the low dimensional models play in many signal and image processing areas, i.e., real world images can be well approximated by a linear combination of a small number of atoms (i.e., patches of images) taken from a large frame, often termed dictionary. The principal point is that these large dictionaries as well as the elements of these dictionaries taken for approximation are not known in advance and should be taken from given noisy observations. The sparse phase and amplitude reconstruction (SPAR) algorithm has been developed for monochromatic coherent wave field reconstruction, for phase-shifting interferometry and holography. In this paper the SPAR technique is extended to off-axis holography. Pragmatically, SPAR representations are result in design of efficient data-adaptive filters. We develop and study the algorithm where these filters are applied for denoising of phase and amplitude in object and sensor planes. This algorithm is iterative and developed as a maximum likelihood optimal solution provided that the noise in intensity measurements is Gaussian. The multiple simulation and real data experiments demonstrate the advance performance of the new technique.

Comparison of digital holography and iterative phase retrieval methods for wavefront reconstruction

An experimental comparison of four methods of wavefront reconstruction is presented. We considered two iterative and two holographic methods with differences in mathematical models and reconstruction algorithms. The first two of these methods do not use the reference wave in the recording scheme that reduces the need of setup stability. A set of spatial intensity measurements of a volume scattered field plays the main role in phase retrieval in such methods. The obtained data are sequentially used for iterative wavefront reconstruction. Iterative approach involves numerical wavefront propagation between various planes of the volume scattered fiels. Throughout this procedure the phase information of the wavefront is retained while the calculated amplitudes is replaced by the square root of the intensity distributions measured in corresponding planes. In the first compared phase retrieval method (FRIM), a two-dimensional Fresnel transform and iterative calculation in the object plane are used as a mathematical model. In the second method (SBMIR), the angular spectrum is used for numerical wavefront propagation, and iterative calculation is made only between closely spaced planes for data registration. Two methods of digital holography, which we compared, differ from each other in algorithm of a waverfont reconstruction. The first holographic method (CWR-DH) uses the conception of spatial phase steps for complex wave retrieval, and the second method (FT-DH) is a widespread Fourier transformation method. All methods provide satisfactory capacity for image reconstruction. The results of the comparison showed that FRIM produces better quality of reconstruction, but a diffraction artifacts takes place at the boundaries of the reconstructed image. Taking this into account we can conclude that the CWR-DH method is the best among considered.

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.

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.