Quantitative phase imaging is the representative of state-of-the-art marker-free full-field optical metrology techniques. The inPhaseNet is a phase demodulation algorithmic solution, where convolutional neural network was used for the quadrature function (input fringe pattern shifted in phase by π/2) retrieval. Having both neural network input and output data phase function is calculated via arctangent function. Since phase demodulation consists a very important part in a measurement process its algorithm imposes one of the main limitations of the entire QPI unit. Phase decoding results are favorably compared with reference algorithms, i.e., classical Variational Hilbert Quantitative Phase Imaging, the Hilbert-Huang and Fourier transforms.
Quantitative phase imaging is the representative of state-of-the-art marker-free full-field optical metrology techniques based on principles of interferometry, holography, microscopy and numerical processing. The measurand is encoded in the phase distribution (optical path delay) of the recorded fringe pattern. To retrieve the measured information the phase demodulation process needs to be performed. Considering the analysis of biomedical samples, the development of very accurate single-frame interferogram/hologram demodulation method is especially important because of the changing nature of the studied phenomenon. In that case the whole process of information recovery can be divided into two steps: (1) interferogram/hologram preprocessing and (2) phase demodulation. We are proposing the “black-box” algorithmic solution called Deep Variational Hilbert Quantitative Phase Imaging (Deep-VHQPI), where convolutional neural networks were used for automation, facilitation and acceleration of the previously complicated and arduous multi-step fringe pattern filtration and orientation estimation processes. It is worth to mention that convolutional neural networks in this work were used for the support of mathematically rigorous quantitative phase imaging algorithm (Hilbert transformation), not with aim to supersede it. For the sake of metrological figure of merit deep learning based solutions were employed to accelerate powerful and well-established VHQPI approach, not to bypass it completely. Deep-VHQPI algorithm enables analysis of variety of biological samples and constitutes an important step towards simplifying optical measurement of complicated and fragile biological samples. Phase decoding results are compared with reference algorithms, i.e., classical VHQPI, the Hilbert-Huang and Fourier transforms. Versatility of the proposed method and its potentially ubiquitous applications in full-field optical metrology are highlighted.
Quantitative phase imaging, employing the refractive index as endogenous contrast agent, opens wide possibilities to perform high-contrast cell measurements enabling reliable diagnostics and assessable examination. This capability can be rather easily obtained in a common-path total-shear regime after introducing a grating or beam-splitter into a regular microscope layout with a (partially-)coherent light source. Although these solutions are attractive due to straightforward implementation, overall good stability (thanks to common-path configuration) and high contrast, they are limited in timespace- bandwidth product (TSBP) as multi-frame phase reconstruction is needed to ensure sufficient accuracy and robustness. Alternative single-shot Fourier transform based approaches do allow for dynamic imaging; however they need off-axis recording and thus limit detector bandwidth and can severely truncate object spectrum (phase lateral resolution), which stays virtually intact in the multi-frame approach. Additionally, low signal-to-noise ratio of recorded fringe pattern significantly adds to the error budget via low contrast, high noise and strong incoherent background. In this contribution we study an interesting way to bypass mentioned shortcomings by recording two out-of-phase interferograms simultaneously to subtract them and thus experimentally increase the signal-to-noise ratio of otherwise low-quality dimmed fringe patterns. Ideal subtraction should yield background-rejected and modulation-doubled π- hologram, however in reality additional processing is needed. We will investigate three algorithms for such processing. Filtered interferogram is then analyzed employing Hilbert spiral transform, which is not sensitive to the carrier frequency like the Fourier transform and preserves object spectrum also in quasi on-axis configurations. Finally, sacrificing the field of view to record two interferograms at once, we gain unique feature of significantly increased TSBP enabling realtime investigation of broad-spectrum (highly detailed) transparent objects with enhanced phase resolution and signal-tonoise ratio. We corroborate the claims successfully analyzing prostate cancer cells and flowing microbeads otherwise measurable only in static regime using time-consuming phase-shifting. The technique has been validated utilizing 20x/0.46NA objective in a regular Olympus BX-60 upright microscope.
Proposed convolutional neural network based, fast and accurate local fringe density map estimation by DeepDensity was developed to significantly enhance full-field optical measurement techniques, e.g., interferometry, holographic microscopy, fringe projection or moiré techniques. The use of neural networks to determine the final result of the optical measurement may raise legitimate metrological concerns and therefore for the sake of versatility and independence from measurement technique we still recommend the use of fully mathematically sound solutions for both fringe pattern prefiltration and phase retrieval. It is worth to acknowledge that proposed DeepDensity network does not supersede mathematically rigorous phase extraction algorithmic solutions, but it only supports them. For that reason during the neural network learning process it was assumed that the data fed to neural network will be prefiltered so background and amplitude modulation should be successfully minimized. Nevertheless, it is still interesting how sensitive to the prefiltration accuracy is proposed DeepDensity. In this contribution we present a thorough analysis of the DeepDensity numerical capabilities in the case of insufficient fringe pattern (interferogram, hologram, moiregram) background and/or amplitude filtration. The analysis was performed with the use of simulated data and then verified using experimentally recorded fringe pattern.
The unsupervised variational image decomposition (uVID) algorithm developed in our group allows for automatic, accurate and robust preprocessing of diverse fringe patterns. Classical VID was initially used for image denoising. Its tailoring for fringe pattern preprocessing was justified by clear advantage over other methods (e.g. Wiener or Gauss filters) in maintaining sharp edges and details of the image. Historically first fringe pattern dedicated three-component variational image decomposition model assumed the use of the shearlet algorithm to separate the information component (fringes) and noise and the Chambolle projection algorithm to separate the fringes and background. We noticed that this model is computationally complicated and the result strongly depends on the values of the algorithm’s internal parameters, to be set manually. The uVID automatically introduces the parameters and stopping criterion for Chambolle’s iterative projection algorithm. Nevertheless, determining the stopping criterion in each iteration is a severely time-consuming process, which is particularly important given the fact that in many cases thousands of iterations have to be calculated in order to obtain a satisfactory fringe pattern decomposition result. Therefore, the idea of using machine learning algorithms to classify fringe patterns according to the required number of Chambolle projection iterations has emerged. Thus, it is no longer required to determine the value of the stopping criterion in every iteration, but only in the area of the predetermined number of iterations. We showed that the calculation time is reduced on average by half by employing the machine-learning based acceleration. This way we made a progress in developing uVID algorithm features for real-time studies of dynamic phenomena, i.e., biological cell development investigated by fringe-based bio-interferometry methods.
Quantitative phase imaging (QPI) measurement is achieved by interference, e.g., in digital holographic microscopy and interference microscopy, where the fringe pattern (hologram/interferogram) phase distribution stores information about the refractive index structure of studied transparent biological samples. In this contribution we report the base for new endto- end QPI computational technique named the Variational Hilbert Imaging (VHI). It can be divided into two steps: hologram filtration using modified variational image decomposition (mVID) approach and phase map (sample-induced optical path delay) extraction using the Hilbert spiral transform (HST). The mVID employs new denoising approach and reliable criterion for determination of the end of calculations with careful investigation of proper parameter values. Quality of obtained results is therefore significantly increased ensuring acceleration and automation of calculations combined with remarkable robustness to different strongly varying hologram characteristics, i.e., local fringe period and orientation, background intensity, contrast deteriorations and noise. Additionally the HST makes it possible to retrieve phase from single hologram, even in case of closed fringes, providing efficient means for biological events characterization in dynamic regime. The VHI algorithm enables analysis of variety of biological samples without user’s meddling and loss of the accuracy. It is an important step to simplify optical measurement of complicated and fragile biological samples. Investigated VHI algorithm is tested on simulated and experimental data (i.e., swine spermatozoon). Phase decoding results are compared with reference algorithms, i.e., the Hilbert-Huang and Fourier transforms. Versatility of the proposed method and its potentially ubiquitous applications in full-field optical metrology are highlighted.
Analysis of fringe patterns with greatly variable density is a huge challenge for the single-frame fringe pattern analysis algorithms. The broad range of spatial frequencies contained in the image widens the Fourier spectrum and makes the separation of the information difficult or even impossible. The background and information differentiation is also a challenging task in the case of fringe pattern preprocessing. On the other hand single-frame fringe pattern analysis algorithms need to be taken into the consideration and developed because of their ability to analyze transient events. One of the newest phase demodulation method is the Hilbert spiral transform (HST). At the output of the HST the fringesignal which is in quadrature with the input fringe pattern is obtained. Both fringe-signals form the 2D analytic signal with phase and amplitude clearly defined by angle and modulus of this complex valued analytic fringe pattern. Nevertheless, HST input signal has to fulfill a few requirements: zero mean value (which can be obtained by successful background removal), low-pass amplitude modulation function (according to Bedrosian’s theorem) and successful noise removal. In this work the new approach to the preprocessing of images containing wide range of spatial frequencies will be introduced using modified variational image decomposition. By modifications we mean acceleration and improved background and fringes differentiation. It will be also proven that quality of the preprocessing plays a key role in the phase demodulation process. Received results will be compared with the ones provided by already well-established and versatile 2D Hilbert-Huang Transform technique.
The emerge of super-resolution (SR) microscopy enabled imaging below the diffraction barrier. One of the SR techniques, Stimulated Emission Depletion (STED) microscopy, has shown promise in super-resolution imaging of thick specimen. Imaging such structures is a non-trivial task due to the increased aberrations introduced by the sample. Adaptive optics provides the solution to this problem. AO can correct the aberrations by modulation of the phase. Although STED microscopy is theoretically a diffraction unlimited technique, the resolution limiting factor is noise. Modern filtering techniques, such as block matching and 3D filtering (BM3D), can increase the signal-to-noise ratio of the STED images. This work presents an AO 3D STED microscope with aberration correction and background noise filtering using BM3D algorithm. We show the super-resolution images of thick samples and emphasize the importance of image processing for recovering of object high spatial frequencies.
The process of information recovering from fringe pattern can be divided into two main parts: filtration (fringe pattern background and noise removal) and phase (or amplitude) demodulation. In recent years the 2D Hilbert spiral transform (HST) has become one of the most popular phase demodulation techniques. Together with empirical mode decomposition used for fringe pattern preprocessing forms a strong fringe pattern analysis algorithm called 2D HilbertHuang transform (HHT). Variational image decomposition was recently adapted for fringe pattern filtration. In combination with the 2D Hilbert spiral transform and after some modifications it might become an excellent tool for fringe pattern analysis purpose and can compete with well-developed HHT. Proposed modification is the first attempt to automate the variational image decomposition in terms of fringe pattern filtration. Received results show that VID-HST can compete with HHT and may become an excellent alternative for fringe pattern evaluation. Another fact encouraging the development of VID is a wide range of applications that have been proposed up to now, i.e., image denoising, fringe pattern filtration and phase filtration.
Interference microscopy for biospecimen characterization based on the moiré phenomena is described. Two scenarios of incoherent multiplicative superimposition are employed: (1) object information carrying interferogram is superimposed with reference one or (2) two object interferograms are superimposed (with equal or opposite phase signs). Second strategy provides additional doubling of underlying phase function of interest. Superimposition can be performed using two experimental interferograms or single real interferogram and numerically designed reference structure in so-called digital moiré regime. Multiplicative superimposition of two periodic intensity distribution yields moiré pattern containing low spatial frequency difference beat term (moiré fringes – macrostructure) and high spatial frequency sum beat term (microstructure). The macrostructure was studied in great majority of previously reported moiré techniques. In this contribution we point attention onto the sum beat spatial frequency component and report efficient means for its recovery using numerically advanced digital filtering (variational/empirical decomposition approaches). Its single-frame (single-pattern) phase demodulation by 2D Hilbert spiral transform with enhanced accuracy follows - this feature comes from the fact that sum beat moiré term has high spatial frequency which is generally beneficial in single-frame fringe analysis and its phase function is be doubled. In particular spatial phase change is better sampled by fringes for denser interferogram and more importantly numerical filtering of fringe term of interest from background intensity is easier. We propose and preliminarily evaluate experimental proof-of-concept strategy where two interferograms with slight difference in spatial frequency are simultaneously recorded in two halves of CCD camera and superimposed multiplicatively. Proposed moiré technique opens up new possibilities in interference microscopy based bio-phase imaging mainly due to its data-driven enhanced phase sensitivity (fringe doubling effect) and real-time operation. Evaluation employing numerical simulations and validation using experimental recordings of phase bio-samples, i.e., prostate cancer cells are enclosed.
In this contribution we present a novel one-stop-shop solution providing comprehensive, robust and automatic singleframe fringe pattern analysis for quantitative phase imaging. It is based on the modified variational image decomposition (mVID) algorithm and the Hilbert spiral transform. The VID concept is applied to tailor input data for efficient Hilbert spiral transform (HST). It returns the fringe-signal which is in quadrature to the input VID-filtered zero-mean-value fringe pattern. Both fringe-signals form the 2D complex analytic fringe pattern with phase and amplitude clearly defined by angle and modulus. Additional means for mVID-based compensation of characteristic phase errors are to be provided. The performance of the proposed novel mVID-HST technique is tested on simulated and experimental data. Its versatility and data-driven nature is emphasized processing off-axis, slightly off-axis and on-axis holograms.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.