R1. New methods of grating microscopy and interference tomography of the common path for measuring the phase and amplitude of micro-objects (with moderate packing) in 2D and 3D – papers [2, 10]. Main advantages with respect to state-of-the-art: achromatic generation of second harmonic striations at zero achromatic generation of second-harmonic bars with zero difference of optical paths of coupled orders in a common path system, which promotes sources with wide bandwidth to reduce coherence artifacts and improve phase imaging accuracy; reduction of system aberrations system aberrations by initial reference measurement; ability to accurately study non-invasive dynamic 2D biological processes; simple registration of tomographic sequences by changing the angle of sample illumination (which does not affect the unique achromaticity of the system) and accurate 3D reconstruction.  

R2. A new algorithmic method that universally solves the problem of limited bandwidth phase information in single-image quantitative phase imaging methods – work [6]. Main advantages over state-of-the-art: novel ability to recover detailed phase information of complex biological objects in the case of overlapping spectral members of holograms, which Until now strongly limited coherent microscopy with quantitative phase contrast performed with computational Fourier transform technique and Kramers-Kronig analyticity; in other words the proposed method allows for numerical phase super-resolution.  

R3. Proposing noise reduction in non-coherent STED-type nanoscopy using the algorithm BM3D digital image analysis algorithm – work [13], increasing the measurement volume of STED nanoscopy – work [22]. The main advantages over state-of-the-art: numerically increased effective resolution of STED nanoscopy (so far completely “optical” imaging method) by algorithmic improvement of signal to noise ratio of registered fluorophore images; completely optically increased measurement volume through use of dualized adaptive optics to control the wavefront of the quenching beam.  

R4. A new grating interference common path microscope system (with a specialized method for phase demodulation of spatially multiplexed interferograms) using a light cube and simple commercial biological microscope – works [15,18]. Main advantages over state-of-the-art: simplicity of implementation in the body of a basic commercial body of a basic commercial biological microscope [15] or as an overlay [18]; possibility of analysis of dynamic phenomena and objects (single-frame method); unprecedented noise immunity and low contrast of holograms (simultaneous simultaneous registration of two phase-shifted holograms allows to improve signal-to-noise ratio by their subtraction); increased information throughput in comparison to existing solutions (possibility of analyzing more complex phase objects and transferring high object spatial frequencies).  

R5. New application enabling to design, perform measurements and reconstruct results with Fourier transform ptychographic microscopy method – work [4]. Main advantages with respect to state-of-the-art: it is the first such application in the world, it enables accurate numerical design of the experiment, facilitates its execution and allows for high quality iterative image reconstruction of amplitude and phase with increased resolution using three proprietary enhancements (automation, calibration error reduction, and noise correction).  

R6. A new numerical method to automatically determine the plane of focus in axial lensless holographic microscopy (Gabor microscopy) – work [8], a new experimental method allowing smooth change of magnification and field of view in Gabor microscopy – paper [14]. Main advantages relative to state-of-the-art: uniquely high axial resolution, large field of view, robustness to noise, low contrast of holograms, variable confluence of objects in the measurement volume and amplitude-phase nature of the studied samples; possibility of smooth change of magnification and field of view.  

R7. A new method for automatic preprocessing of stripe images based on unsupervised variational image decomposition – works [16,17]. Main advantages over state-of-the-art: efficient, unsupervised, automatic, adaptive filtering of strongly noisy interferograms with low contrast and high local variability of period and orientation striations; long computation time is the object of current research oriented towards numerical acceleration.  

R8. A new method for determining the local density map (spatial frequency) of a stripe image using using author’s DeepDensity neural network – work [1]. Main advantages over state-of-the-art: use of a small, fully numerically simulated learning set The main advantages compared to the state-of-the-art: the use of a small, fully numerically simulated learning set, independence of the analysis from the background and noise of the stripe image pre-experimental interferograms; high accuracy and versatility of the developed network.  

R9. A new algorithm for empirical modal decomposition matching the stripe shape – work [9]. Main advantages compared to the state-of-the-art: elimination of the unfavorable phenomenon of modal mixing, extraction complete stripe segment (without influence of noise and background) in the first decomposition mode, quantitatively confirmed uniquely high accuracy of bandpass filtering with a very large range of local variation of period and orientation.  

R10. Two algorithmic solutions based on variational and empirical image decomposition aided Hilbert transform for the generation and analysis of Bessel stripes in interference microscopy with time averaging time averaging interference microscopy applied to vibration studies of reflective micro-objects – works [11, 23]. Main advantages over state-of-the-art: minimal requirements on the number of component interferograms (2) while simultaneous maximization of accuracy of demodulation of the final distribution of vibration amplitude from a single besselogram (no need to implement a costly experimental heterodyning method to shift the to shift the phase of the besselogram); the use of very effective preprocessing of interferograms and besselograms by variational [11] and empirical [23] decomposition methods.  

R11. Grid interference microscopy of the common path based on phase demodulation by the transform method Hilbert-Huang work [25], and multibeam interference gradient method for wavefront measurements wavefront measurements using a cross diffraction grating [24]. Main advantages over state-of-the-art: algorithmically realized ability to use the detector bandwidth to a degree similar to multi-arm methods, with a great advantage in the field of time resolution (operation on a single interferogram), noteworthy is the original combination of variational and empirical decomposition in preprocessing of a single interferogram [25]; measurements of strong aberrations [24].  

R12. Two review articles: (1) on high-speed high-throughput holographic imaging published in the prestigious journal Advances of Optics and Photonics IF>20 – paper [7], (2) on interference microscopy with spatial multiplexing – paper [3].  

R13. New methods for designing binary diffraction gratings with reduced spectrum – papers [5, 21].  

R14. Non-coherent imaging in (1) microscale using phase contrast method – work [12], (2) macroscale using the fringe projection method – reference [19,20].