Igor Shevkunov

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.

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.

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.

Surface relief and refractive index gratings patterned in chalcogenide glasses and studied by off-axis digital holography

Surface relief gratings and refractive index gratings are formed by direct holographic recording in amorphous chalcogenide nanomultilayer structures As2S3-Se and thin films As2S3. 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.

Computational wavelength resolution for in-line lensless holography: phase-coded diffraction patterns and wavefront group-sparsity

In-line lensless holography is considered with a random phase modulation at the object plane. The forward wavefront propagation is modelled using the Fourier transform with the angular spectrum transfer function. The multiple intensities (holograms) recorded by the sensor are random due to the random phase modulation and noisy with Poissonian noise distribution. It is shown by computational experiments that high-accuracy reconstructions can be achieved with resolution going up to the two thirds of the wavelength. With respect to the sensor pixel size it is a super-resolution with a factor of 32. The algorithm designed for optimal superresolution phase/amplitude reconstruction from Poissonian data is based on the general methodology developed for phase retrieval with a pixel-wise resolution in V. Katkovnik, ”Phase retrieval from noisy data based on sparse approximation of object phase and amplitude”, http://www.cs.tut.fi/~lasip/DDT/index3.html.

Multiwavelength surface contouring from phase-coded diffraction patterns

We propose a new algorithm for absolute phase retrieval from multiwavelength noisy phase coded diffraction patterns in the task of surface contouring. A lensless optical setup is considered with a set of successive single wavelength experiments. The phase masks are applied for modulation of the multiwavelength object wavefronts. The algorithm uses the forward and backward propagation for coherent light beams and sparsely encoding wavefronts which leads to the complex-domain block-matching 3D filtering. The key-element of the algorithm is an original aggregation of the multiwavelength object wavefronts for high-dynamic-range profile measurement. Numerical experiments demonstrate that the developed approach leads to the effective solutions explicitly using the sparsity for noise suppression and high-accuracy object profile reconstruction.

Features of surface contouring by digital holographic interferometry with tilt of the object illumination

One of the problems of interferometric methods is the difficulty of measuring surface shape with sharp boundaries due to the wavelength-limited dynamic range of the measurement. To circumvent this limitation multiwavelength methods or techniques based on hologram capturing at the different tilt of the illumination beam are applied. In this work we examine the performance of the digital holographic interferometry with multi-inclination illumi- nation in the numerical and real experiments. Lensless implementation of the technique implies the wavefront propagation by numerical algorithms. In this regard the speckle scattering in the Fresnel diffraction area caused by surface roughness and the impact of distance from the object to the registration plane are analyzed. Since shape measurement is based on the calculation of phase difference for the wavefronts recorded with tilt of the object illuminating beam, the requirements to preciseness of measurements of the angle of incidence of this beam are considered. The algorithm of the inclination angle determination are developed. The performance of noise suppression techniques, namely sine-cosine and BM3D methods are considered for high noisy conditions, when the phase distributions are formed by reflecting object with a great roughness and height differences.

Time-Resolved Inline Digital Holography for Investigation of Noncollinear Pump Pulse-Induced Phase Variation

Time-resolved inline digital holography technique for investigation of optical nonlinear interaction of high-energy pump with probe pulse in transparent samples is presented. The observed inline hologram in the Fresnel diffraction zone depends on variation of refractive index and allows one to analyze some properties of the nonlinear media.