DeepOrientation: convolutional neural network for fringe pattern orientation map estimation.

Fringe pattern based measurement techniques are the state-of-the-art in full-field optical metrology. They are crucial both in macroscale, e.g., fringe projection profilometry, and microscale, e.g., label-free quantitative phase microscopy. Accurate estimation of the local fringe orientation map can significantly facilitate the measurement process in various ways, e.g., fringe filtering (denoising), fringe pattern boundary padding, fringe skeletoning (contouring/following/tracking), local fringe spatial frequency (fringe period) estimation, and fringe pattern phase demodulation. Considering all of that, the accurate, robust, and preferably automatic estimation of local fringe orientation map is of high importance. In this paper we propose a novel numerical solution for local fringe orientation map estimation based on convolutional neural network and deep learning called DeepOrientation. Numerical simulations and experimental results corroborate the effectiveness of the proposed DeepOrientation comparing it with a representative of the classical approach to orientation estimation called combined plane fitting/gradient method. The example proving the effectiveness of DeepOrientation in fringe pattern analysis, which we present in this paper, is the application of DeepOrientation for guiding the phase demodulation process in Hilbert spiral transform. In particular, living HeLa cells quantitative phase imaging outcomes verify the method as an important asset in label-free microscopy.

Hilbert phase microscopy based on pseudo thermal illumination in the Linnik configuration.

Quantitative phase microscopy (QPM) is often based on recording an object-reference interference pattern and its further phase demodulation. We propose pseudo Hilbert phase microscopy (PHPM) where we combine pseudo thermal light source illumination and Hilbert spiral transform (HST) phase demodulation to achieve hybrid hardware-software-driven noise robustness and an increase in resolution of single-shot coherent QPM. Those advantageous features stem from physically altering the laser spatial coherence and numerically restoring spectrally overlapped object spatial frequencies. The capabilities of PHPM are demonstrated by analyzing calibrated phase targets and live HeLa cells in comparison with laser illumination and phase demodulation via temporal phase shifting (TPS) and Fourier transform (FT) techniques. The performed studies verified the unique ability of PHPM to combine single-shot imaging, noise minimization, and preservation of phase details.

Common-path intrinsically achromatic optical diffraction tomography.

In this work we propose an open-top like common-path intrinsically achromatic optical diffraction tomography system. It operates as a total-shear interferometer and employs Ronchi-type amplitude diffraction grating, positioned in between the camera and the tube lens without an additional 4f system, generating three-beam interferograms with achromatic second harmonic. Such configuration makes the proposed system low cost, compact and immune to vibrations. We present the results of the measurements of 3D-printed cell phantom using laser diode (coherent) and superluminescent diode (partially coherent) light sources. Broadband light sources can be naturally employed without the need for any cumbersome compensation because of the intrinsic achromaticity of the interferometric recording (holograms generated by -1st and +1st conjugated diffraction orders are not affected by the illumination wavelength). The results show that the decreased coherence offers much reduced coherent noise and higher fidelity tomographic reconstruction especially when applied nonnegativity constraint regularization procedure.

Author Correction: Variational Hilbert Quantitative Phase Imaging.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Variational Hilbert Quantitative Phase Imaging.

Utilizing the refractive index as the endogenous contrast agent to noninvasively study transparent cells is a working principle of emerging quantitative phase imaging (QPI). In this contribution, we propose the Variational Hilbert Quantitative Phase Imaging (VHQPI)-end-to-end purely computational add-on module able to improve performance of a QPI-unit without hardware modifications. The VHQPI, deploying unique merger of tailored variational image decomposition and enhanced Hilbert spiral transform, adaptively provides high quality map of sample-induced phase delay, accepting particularly wide range of input single-shot interferograms (from off-axis to quasi on-axis configurations). It especially promotes high space-bandwidth-product QPI configurations alleviating the spectral overlapping problem. The VHQPI is tailored to deal with cumbersome interference patterns related to detailed locally varying biological objects with possibly high dynamic range of phase and relatively low carrier. In post-processing, the slowly varying phase-term associated with the instrumental optical aberrations is eliminated upon variational analysis to further boost the phase-imaging capabilities. The VHQPI is thoroughly studied employing numerical simulations and successfully validated using static and dynamic cells phase-analysis. It compares favorably with other single-shot phase reconstruction techniques based on the Fourier and Hilbert-Huang transforms, both in terms of visual inspection and quantitative evaluation, potentially opening up new possibilities in QPI.

Automatic fringe pattern enhancement using truly adaptive period-guided bidimensional empirical mode decomposition.

Fringe patterns encode the information about the result of a measurement performed via widely used optical full-field testing methods, e.g., interferometry, digital holographic microscopy, moiré techniques, structured illumination etc. Affected by the optical setup, changing environment and the sample itself fringe patterns are often corrupted with substantial noise, strong and uneven background illumination and exhibit low contrast. Fringe pattern enhancement, i.e., noise minimization and background term removal, at the pre-processing stage prior to the phase map calculation (for the measurement result decoding) is therefore essential to minimize the jeopardizing effect the mentioned error sources have on the optical measurement outcome. In this contribution we propose an automatic, robust and highly effective fringe pattern enhancement method based on the novel period-guided bidimensional empirical mode decomposition algorithm (PG-BEMD). The spatial distribution of the fringe period is estimated using the novel windowed approach and then serves as an indicator for the truly adaptive decomposition with the filter size locally adjusted to the fringe pattern density. In this way the fringe term is successfully extracted in a single (first) decomposition component alleviating the cumbersome mode mixing phenomenon and greatly simplifying the automatic signal reconstruction. Hence, the fringe term is dissected without the need for modes selection nor summation. The noise removal robustness is ensured employing the block matching 3D filtering of the fringe pattern prior to its decomposition. Performance validation against previously reported modified empirical mode decomposition techniques is provided using numerical simulations and experimental data verifying the versatility and effectiveness of the proposed approach.

Grating deployed total-shear 3-beam interference microscopy with reduced temporal coherence.

Interference microscopy is a powerful optical imaging technique providing quantitative phase distribution information to characterize various type technical and biomedical objects. Static and dynamic objects and processes can be investigated. In this paper we propose very compact, common-path and partially coherent diffraction grating-based interference microscopy system for studying small objects like single cells with low densities being sparsely distributed in the field of view. Simple binary amplitude diffraction grating is the only additional element to be introduced into a conventional microscope optical system. By placing it at a proper distance in front of the microscope image plane the total-shear operation mode is deployed resulting in interferograms of the object-reference beam type. Depending on the grating to image plane separation distance two or three-beam interferograms are generated. The latter ones are advantageous since they contain achromatic second harmonics in the interferogram intensity distributions. This feature enables to use reduced temporal coherence light sources for the microscope to reduce coherent noise and parasitic interference patterns. For this purpose we employ the laser diode with driving current below the threshold one. Results of conducted experiments including automatic computer processing of interferograms fully corroborate analytical description of the proposed method and illustrate its capabilities for studying static and dynamic phase objects.

Full-field vibration profilometry using time-averaged interference microscopy aided by variational analysis.

Full-field vibration testing is indispensable in characterization of micro-electro-mechanical components. Time-averaged interference (TAI) microscopy is a very capable and accurate vibration profilometry technique. It employs natural all-optical multiplexing of required information, i.e., recorded interferogram is amplitude-modulated by the Bessel pattern, which in turn encodes spatial distribution of vibration amplitude in its underlying phase function. We propose a complete end-to-end numerical scheme for efficient and robust vibration amplitude map demodulation based on the variational data-analysis paradigm. First, interferogram is variationally pre-filtered and complex analytic-interferogram is generated, exploiting the Hilbert spiral transform. The amplitude term of analytic-interferogram is accessed for Besselogram, i.e., TAI amplitude modulation distribution. Next, the Besselogram is variationally pre-filtered and complex analytic-Besselogram is calculated applying the Hilbert spiral transform. Finally, the phase term of the analytic-Besselogram is determined, unwrapped and post-filtered to achieve spatial distribution of vibration amplitude. Proposed approach is verified using simulated interferograms and corroborated upon experimental vibration testing. Reported method compares favorably with the reference Hilbert-Huang transform-based method. The improvement was gained by adding two new steps to the calculation path: (1) additional removal of the interferogram's residual background and noise and (2) variational based vibration amplitude map error correction method.

Automatized fringe pattern preprocessing using unsupervised variational image decomposition.

Successful single-frame fringe pattern preprocessing comprising high-frequency noise minimization and low-frequency background removal represents often the crucial step of the fringe pattern based full-field optical metrology (i.e., interferometry, moiré, structured light). It directly determines the measurement accuracy. Data-driven decomposition by means of the 2D empirical mode decomposition (EMD) serves the filtering purpose in adaptive and detail-preserving manner. The mode-mixing phenomenon resulting in troublesome automatic grouping of modes into three main fringe pattern components (background, information part and noise) is significantly limiting this process, however. In this paper we are introducing the unsupervised variational image decomposition (uVID) model especially tailored to overcome this preprocessing problem and assure successful sparse three-component fringe pattern decomposition. Comprehensive analysis and detailed studies of accomplished significant advancements ensuring automation, versatility and robustness of the proposed approach are provided. Main advancements include: (1) tailoring the VID calculation scheme to fringe pattern preprocessing purpose by focusing onto accurate fringe extraction with tolerance parameter and custom-made decomposition parameter values; (2) fringe pattern tailored BM3D denoising algorithm with fixed parameter values. Numerical and experimental investigations corroborate that the demonstrated uVID method compares favorably with the reference 2D EMD algorithm and classical VID model. Remarkable range of acceptable local variations of the fringe pattern orientation, period, noise, contrast and background terms is to be highlighted.

Single-shot two-frame π-shifted spatially multiplexed interference phase microscopy.

Single-shot, two-frame, π-shifted spatially multiplexed interference microscopy (π-SMIM) is presented as an improvement to previous SMIM implementations, introducing a versatile, robust, fast, and accurate method for cumbersome, noisy, and low-contrast phase object analysis. The proposed π-SMIM equips a commercially available nonholographic microscope with a high-speed (video frame rate) enhanced quantitative phase imaging (QPI) capability by properly placing a beam-splitter in the microscope embodiment to simultaneously (in a single shot) record two holograms mutually phase shifted by π radians at the expense of reducing the field of view. Upon subsequent subtractive superimposition of holograms, a π-hologram is generated with reduced background and improved modulation of interference fringes. These features determine superior phase retrieval quality, obtained by employing the Hilbert spiral transform on the π-hologram, as compared with a single low-quality (low signal-to-noise ratio) hologram analysis. In addition, π-SMIM enables accurate in-vivo analysis of high dynamic range phase objects, otherwise measurable only in static regime using time-consuming phase-shifting. The technique has been validated utilizing a 20 × / 0.46 NA objective in a regular Olympus BX-60 upright microscope for QPI of different lines of prostate cancer cells and flowing microbeads.

Three-level transmittance 2D grating with reduced spectrum and its self-imaging.

A simple method for generating 2D binary amplitude structure with additive superimposition of mutually orthogonal 1D amplitude gratings is proposed. Its implementation requires software generated three binary amplitude gratings, i.e., the crossed Ronchi, checker board and 1D Ronchi gratings with aspect ratio equal to 0.5. Their computer processing involves only two steps. First the checker grating is multiplied by a high frequency 1D grating. Next the product is added to the crossed grating. In result 3-level transmittance (0, 0.5, 1) hybrid diffraction structure is obtained. The intermediate level results from the use of a dense 1D grating. The zero diffraction order, well separated from the rest of the spectrum, consists of crossed spectra of additively superimposed 1D Ronchi gratings. Detailed heuristic explanation of the process aided by spectrum domain analyses is presented. Additionally, simulations and experiments conducted in the Fresnel diffraction field exemplify the invented structure properties in comparison with the multiplicative superimposition crossed Ronchi grating. Up to authors' best knowledge the Fresnel field (self-imaging phenomenon or Talbot effect) properties of 2D periodic structure with additive superimposition of component 1D gratings have not been published in the literature.

5-beam grating interferometry for extended phase gradient sensing.

A novel, single-shot, low-cost, multidirectional lateral shear interferometer for extended range wave front phase gradient sensing has been developed. It exploits the Fresnel diffraction field, which is formed by the five lowest diffraction orders of a simple binary amplitude checker grating. The Fresnel intensity pattern encodes information on four directional partial derivatives of the wave front under test. It has been theoretically, numerically, and experimentally shown that for larger gradient phase objects or shear amounts only the diagonal derivative information is easily accessible. The horizontal and vertical direction gradient maps are strongly amplitude modulated. Therefore, their demodulation becomes a challenging task. The same feature has been found in widely used quadriwave interferometer, which was developed at ONERA, France. The results of analytical and numerical studies and experimental works, including fringe pattern processing and phase demodulation, are presented.

Hilbert-Huang single-shot spatially multiplexed interferometric microscopy.

Hilbert-Huang single-shot spatially multiplexed interferometric microscopy (H2S2MIM) is presented as the implementation of a robust, fast, and accurate single-shot phase estimation algorithm with an extremely simple, low-cost, and highly stable way to convert a bright field microscope into a holographic one using partially coherent illumination. Altogether, H2S2MIM adds high-speed (video frame rate) quantitative phase imaging capability to a commercially available nonholographic microscope with improved phase reconstruction (coherence noise reduction). The technique has been validated using a 20×/0.46 NA objective in a regular Olympus BX-60 upright microscope for static, as well as dynamic, samples showing perfect agreement with the results retrieved from a temporal phase-shifting algorithm.

Evaluation of adaptively enhanced two-shot fringe pattern phase and amplitude demodulation methods.

Phase-shifting interferometry is a standard tool in optical metrology. Most frequently, it needs three or more interferograms to solve the system of fringe equations for phase or amplitude retrieval, which limits its time resolution. Recently, the topic of two-shot, arbitrary-phase-step fringe pattern phase and amplitude demodulation has been flourishing and attracting attention with several novel and interesting methods being proposed. In this work, we evaluate six up-to-date two-shot phase-shifting methods analyzing their main error sources and proposing efficient ways to minimize their influence by adaptive filtering using the Hilbert-Huang transform.

Generation of phase edge singularities by coplanar three-beam interference and their detection.

In recent years singular optics has gained considerable attention in science and technology. Up to now optical vortices (phase point dislocations) have been of main interest. This paper presents the first general analysis of formation of phase edge singularities by coplanar three-beam interference. They can be generated, for example, by three-slit interference or self-imaging in the Fresnel diffraction field of a sinusoidal grating. We derive a general condition for the ratio of amplitudes of interfering beams resulting in phase edge dislocations, lateral separation of dislocations depends on this ratio as well. Analytically derived properties are corroborated by numerical and experimental studies. We develop a simple, robust, common path optical self-imaging configuration aided by a coherent tilted reference wave and spatial filtering. Finally, we propose an automatic fringe pattern analysis technique for detecting phase edge dislocations, based on the continuous wavelet transform. Presented studies open new possibilities for developing grating based sensing techniques for precision metrology of very small phase differences.

Quantitative phase imaging by single-shot Hilbert-Huang phase microscopy.

We propose a novel single-shot Hilbert-Huang transform-based algorithm applied to digital holographic microscopy (DHM) for robust, fast, and accurate single-shot quantitative phase imaging in on-axis and off-axis configurations. Fringe pattern with possible defects and closed fringes are adaptively filtered and accurately phase demodulated using local fringe direction estimation. Experimental validation of the proposed techniques is presented as the DHM study of microbeads and red blood cells phase samples. Obtained results compare very favorably with the Fourier approach (off-axis) and temporal phase shifting (on-axis).

Single-shot 3 × 3 beam grating interferometry for self-imaging free extended range wave front sensing.

Crossed grating 3×3 beam lateral shear interferometry for extended range wave front sensing is presented. A Fresnel diffraction pattern of two multiplicatively superimposed linear diffraction gratings each generating three diffraction orders is recorded. A simple solution employs a common crossed binary amplitude Ronchi grating with spatial filtering. Digital processing of a single-shot pattern includes separating multidirectional pairs of orthogonal lateral shear interferograms, retrieving second harmonics of their intensity distribution, and calculating shearing phases. Single-frame automatic fringe pattern processing based on the Hilbert-Huang transform is used for this purpose. Using second harmonics extends the aberration measurement range since they encode self-imaging free two-beam interferograms without contrast modulations. Experimental works corroborate the principle and capabilities of the proposed approach.

Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis.

Hybrid single shot algorithm for accurate phase demodulation of complex fringe patterns is proposed. It employs empirical mode decomposition based adaptive fringe pattern enhancement (i.e., denoising, background removal and amplitude normalization) and subsequent boosted phase demodulation using 2D Hilbert spiral transform aided by the Principal Component Analysis method for novel, correct and accurate local fringe direction map calculation. Robustness to fringe pattern significant noise, uneven background and amplitude modulation as well as local fringe period and shape variations is corroborated by numerical simulations and experiments. Proposed automatic, adaptive, fast and comprehensive fringe analysis solution compares favorably with other previously reported techniques.

Subtractive two-frame three-beam phase-stepping interferometry for testing surface shape of quasi-parallel plates.

We present an effective method of testing the surface shape of quasi-parallel plates which requires only two phase-shifted three-beam interferograms. We derive a general formula for difference of two three-beam interferograms as a function of the phase shift value. The phase shift does not have to be precisely determined and uniform in the image domain. We show and compare results of extracting the fringe set and corresponding phase distribution related to the plate front surface shape using the two dimensional continuous wavelet transform, Hilbert-Huang transform and Fourier transform methods. Simulated and experimental data is used to verify the algorithm performance and robustness.

Two-frame tilt-shift error estimation and phase demodulation algorithm.

We present an algorithm capable of performing fringe pattern phase demodulation from two frames with unknown, linearly nonuniform phase shift, i.e., under presence of the tilt-shift error. The method consists of intensity-based filtration of the tilt-shift component and subsequent two steps of a nonlinear error functional minimization. We verify the algorithm performance and robustness using both simulated and experimental data, indicating high accuracy of the presented method and its good numerical properties. Both small and large tilts can be treated. The Letter is complemented by numerical codes available online in Wielgus, "Two-frame tilt-shift error estimation and phase demodulation algorithm" (2015).