Phase imaging is a solution for the reconstruction of phase information from intensity observations. To make phase imaging possible, sophisticated extra systems are embedded into the existing imaging systems. Contrary, we propose a phase problem solution by DCNN-based framework, which is simple in terms of an optical system. We propose to replace optical lenses with computational algorithms such as CNN phase reconstruction and wavefront propagation. The framework is tested in simulation and real-life experimental phase imaging. To have real experiments with objects close to real-life biological cells, we simulated experimental training datasets on a phase-only spatial light modulator, where phase objects are modeled with corresponding phase distribution to biological cells.
A hybrid imaging system is a simultaneous physical arrangement of a refractive lens and a multilevel phase mask (MPM) as a diffractive optical element (DOE). The favorable properties of the hybrid setup are improved extended-depth-of-field (EDoF) imaging and low chromatic aberrations. We built a fully differentiable image formation model in order to use neural network techniques to optimize imaging. At the first stage, the design framework relies on the model-based approach with numerical simulation and end-to-end joint optimization of both MPM and imaging algorithms. In the second stage, MPM is fixed as found at the first stage, and the image processing is optimized experimentally using the CNN learning-based approach with MPM implemented by a spatial light modulator. The paper is concentrated on a comparative analysis of imaging accuracy and quality for design with various basic optical parameters: aperture size, lens focal length, and distance between MPM and sensor. We point out that the varying aperture size, lens focal length, and distance between MPM and sensor are for the first time considered for end-to-end optimization of EDoF. We numerically and experimentally compare the designs for visible wavelength interval [400-700]~nm and the following EDoF ranges: [0.5-100]~m for simulations and [0.5-1.9]~m for experimental tests. This study concerns an application of hybrid optics for compact cameras with aperture [5-9] mm and distance between MPM and sensor [3-10] mm.
In this paper, we employ a deep convolutional neural network for the solution of the phase retrieval problem in a lensless optical system from a single observation. We utilize U-net structured DCNN to reconstruct phase from the amplitude images at the sensor plane, and after applying computational backpropagation, complex objects' amplitude is reconstructed at the object plane. Results are demonstrated by simulation experiments.
Hyperspectral (HS) imaging retrieves information from data obtained across broadband spectral channels. Information to retrieve is a 3D cube, where two coordinates are spatial and the third one is spectral. This cube is complex-valued with varying amplitude and phase. We consider shearography optical setup, in which two phase-shifted broadband copies of the object projections are interfering at a sensor. Registered observations are intensities summarized over spectral channels. For phase reconstruction, the variational setting of the phase retrieval problem is used to derive the iterative algorithm, which includes the original proximity spectral analysis operator and the sparsity modeling of the complex-valued object 3D cube. We resolve the HS phase retrieval problem without random phase coding of wavefronts typical for the most conventional phase retrieval techniques. We show the performance of the algorithm for object phase and thickness imaging in simulation and experimental tests.
Hyperspectral (HS) imaging retrieves information from data obtained across a broad spectral range of spectral channels. The object to reconstruct is a 3D cube, where the two coordinates are spatial and the third one is spectral. We assume that this cube is complex-valued, i.e. characterized spatially-frequency varying amplitude and phase. The observations are squared magnitudes measured as intensities summarized over spectra. HS phase retrieval is formulated as a reconstruction of an HS complex-valued object cube from Gaussian noisy intensity observations. The considered observation model, projections of the object on the sensor plane, includes varying delay operators such that identical but mutually phase-shifted broadband copies of the object are interfering at the sensor plane. The derived iterative algorithm includes an original proximity spectral analysis operator and sparsity modeling for complex-valued 3D cubes. It is demonstrated that the HS phase retrieval problem can be resolved without random phase coding of wavefronts typical for the conventional phase retrieval techniques. The performance of the new algorithm for phase imaging is demonstrated in simulation tests and in the processing of experimental data.
Lensless phase-retrieval system with phase modulation of free propagation wavefront is proposed. Contrary to the traditional super-resolution phase-retrieval, the method in this paper requires a single observation only and uses advanced SR-SPAR iterative technique. Successful object imaging relies on modulation of the object wavefront with a random phase-mask, which generates enlarged intensity patterns, allowing us to extract more information than it is possible without such a mask. The achieved high-quality super-resolution phase-imaging is demonstrated by simulation-tests produced with the parameters corresponding to the physical prototype of the considered optical system.
Off-axis lensless holography is considered with a sinusoidal phase modulation at the object plane. The variational algorithm for phase and amplitude reconstruction is based on the algorithm proposed in the paper 1[V. Katkovnik, I. A. Shevkunov, N. V. Petrov, and K. Egiazarian, “Wavefront reconstruction in digital off-axis holography via sparse coding of amplitude and absolute phase”, Opt. Lett. 40, 2417-2420 (2015)]. The forward wavefront propagation is modelled using the Fourier transform with the angular spectrum transfer function. The multiple intensities (holograms) recorded by the sensor vary in dependence to the angle of the phase diffraction grating. The i.i.d. Gaussian noise is added to observations to make them closer to real experimental conditions. The root mean square error (RMSE) values of the phase reconstructions were compared in two scenarios: with and without the diffraction grating. Computational experiments showed that with sinusoidal phase modulation RMSE values are decreased about 20%. These results support the conclusion on advantage of the proposed phase modulation gratings in off-axis lensless digital holography.
We propose an algorithm for absolute phase retrieval from multiwavelength noisy phase coded diffraction patterns. A lensless optical system is considered with a set of successive single wavelength experiments (wavelength-division setup). The phase masks are applied for modulation of the multiwavelength object wavefronts. The algorithm uses the forward/backward propagation for coherent light beams and sparsely encoding wavefronts, which leads to the complex-domain block-matching three-dimensional filtering. The key-element of the algorithm is an original aggregation of the multiwavelength object wavefronts for high-dynamic-range absolute phase reconstruction. Simulation tests demonstrate that the developed approach leads to the effective solutions explicitly using the sparsity for noise suppression and high-accuracy object absolute phase reconstruction from noisy data.
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.
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.
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.
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.
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.
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