Variational Hilbert Quantitative Phase Imaging

One step accurate phase demodulation from a closed fringe pattern with the convolutional neural network HRUnet

Retrieving a phase map from a single closed fringe pattern is a challenging task in optical interferometry. In this paper, a convolutional neural network (CNN), HRUnet, is proposed to demodulate phase from a closed fringe pattern. The HRUnet, derived from the Unet model, adopts a high resolution network (HRnet) module to extract high resolution feature maps of the data and employs residual blocks to erase the gradient vanishing in the network. With the trained network, the unwrapped phase map can be directly obtained by feeding a scaled fringe pattern. The high accuracy of the phase map obtained from HRUnet is demonstrated by demodulation of both simulated data and actual fringe patterns. Compared results between HRUnet and two other CNNS are also provided, and the results proved that the performance of HRUnet in accuracy is superior to the two other counterparts.

Polarization differential interference contrast microscopy with physics-inspired plug-and-play denoiser for single-shot high-performance quantitative phase imaging

We present single-shot high-performance quantitative phase imaging with a physics-inspired plug-and-play denoiser for polarization differential interference contrast (PDIC) microscopy. The quantitative phase is recovered by the alternating direction method of multipliers (ADMM), balancing total variance regularization and a pre-trained dense residual U-net (DRUNet) denoiser. The custom DRUNet uses the Tanh activation function to guarantee the symmetry requirement for phase retrieval. In addition, we introduce an adaptive strategy accelerating convergence and explicitly incorporating measurement noise. After validating this deep denoiser-enhanced PDIC microscopy on simulated data and phantom experiments, we demonstrated high-performance phase imaging of histological tissue sections. The phase retrieval by the denoiser-enhanced PDIC microscopy achieves significantly higher quality and accuracy than the solution based on Fourier transforms or the iterative solution with total variance regularization alone.

Single-shot wavelength-multiplexed phase microscopy under Gabor regime in a regular microscope embodiment

Phase imaging microscopy under Gabor regime has been recently reported as an extremely simple, low cost and compact way to update a standard bright-field microscope with coherent sensing capabilities. By inserting coherent illumination in the microscope embodiment and producing a small defocus distance of the sample at the input plane, the digital sensor records an in-line Gabor hologram of the target sample, which is then numerically post-processed to finally achieve the sample's quantitative phase information. However, the retrieved phase distribution is affected by the two well-known drawbacks when dealing with Gabor's regime, that is, coherent noise and twin image disturbances. Here, we present a single-shot technique based on wavelength multiplexing for mitigating these two effects. A multi-illumination laser source (including 3 diode lasers) illuminates the sample and a color digital sensor (conventional RGB color camera) is used to record the wavelength-multiplexed Gabor hologram in a single exposure. The technique is completed by presenting a novel algorithm based on a modified Gerchberg-Saxton kernel to finally retrieve an enhanced quantitative phase image of the sample, enhanced in terms of coherent noise removal and twin image minimization. Experimental validations are performed in a regular Olympus BX-60 upright microscope using a 20X 0.46NA objective lens and considering static (resolution test targets) and dynamic (living spermatozoa) phase samples.

Fluholoscopy-Compact and Simple Platform Combining Fluorescence and Holographic Microscopy

The combination of different imaging modalities into single imaging platforms has a strong potential in biomedical sciences as it permits the analysis of complementary properties of the target sample. Here, we report on an extremely simple, cost-effective, and compact microscope platform for achieving simultaneous fluorescence and quantitative phase imaging modes with the capability of working in a single snapshot. It is based on the use of a single illumination wavelength to both excite the sample's fluorescence and provide coherent illumination for phase imaging. After passing the microscope layout, the two imaging paths are separated using a bandpass filter, and the two imaging modes are simultaneously obtained using two digital cameras. We first present calibration and analysis of both fluorescence and phase imaging modalities working independently and, later on, experimental validation for the proposed common-path dual-mode imaging platform considering static (resolution test targets, fluorescent micro-beads, and water-suspended lab-made cultures) as well as dynamic (flowing fluorescent beads, human sperm cells, and live specimens from lab-made cultures) samples.

Experimental optimization of lensless digital holographic microscopy with rotating diffuser-based coherent noise reduction

Laser-based lensless digital holographic microscopy (LDHM) is often spoiled by considerable coherent noise factor. We propose a novel LDHM method with significantly limited coherent artifacts, e.g., speckle noise and parasitic interference fringes. It is achieved by incorporating a rotating diffuser, which introduces partial spatial coherence and preserves high temporal coherence of laser light, crucial for credible in-line hologram reconstruction. We present the first implementation of the classical rotating diffuser concept in LDHM, significantly increasing the signal-to-noise ratio while preserving the straightforwardness and compactness of the LDHM imaging device. Prior to the introduction of the rotating diffusor, we performed LDHM experimental hardware optimization employing 4 light sources, 4 cameras, and 3 different optical magnifications (camera-sample distances). It was guided by the quantitative assessment of numerical amplitude/phase reconstruction of test targets, conducted upon standard deviation calculation (noise factor quantification), and resolution evaluation (information throughput quantification). Optimized rotating diffuser LDHM (RD-LDHM) method was successfully corroborated in technical test target imaging and examination of challenging biomedical sample (60 µm thick mouse brain tissue slice). Physical minimization of coherent noise (up to 50%) was positively verified, while preserving optimal spatial resolution of phase and amplitude imaging. Coherent noise removal, ensured by proposed RD-LDHM method, is especially important in biomedical inference, as speckles can falsely imitate valid biological features. Combining this favorable outcome with large field-of-view imaging can promote the use of reported RD-LDHM technique in high-throughput stain-free biomedical screening.

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.

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.

Low-intensity illumination for lensless digital holographic microscopy with minimized sample interaction

Exposure to laser light alters cell culture examination via optical microscopic imaging techniques based on label-free coherent digital holography. To mitigate this detrimental feature, researchers tend to use a broader spectrum and lower intensity of illumination, which can decrease the quality of holographic imaging due to lower resolution and higher noise. We study the lensless digital holographic microscopy (LDHM) ability to operate in the low photon budget (LPB) regime to enable imaging of unimpaired live cells with minimized sample interaction. Low-cost off-the-shelf components are used, promoting the usability of such a straightforward approach. We show that recording data in the LPB regime (down to 7 µW of illumination power) does not limit the contrast or resolution of the hologram phase and amplitude reconstruction compared to regular illumination. The LPB generates hardware camera shot noise, however, to be effectively minimized via numerical denoising. The ability to obtain high-quality, high-resolution optical complex field reconstruction was confirmed using the USAF 1951 amplitude sample, phase resolution test target, and finally, live glial restricted progenitor cells (as a challenging strongly absorbing and scattering biomedical sample). The proposed approach based on severely limiting the photon budget in lensless holographic microscopy method can open new avenues in high-throughout (optimal resolution, large field-of-view, and high signal-to-noise-ratio single-hologram reconstruction) cell culture imaging with minimized sample interaction.

Common-path off-axis single-pixel holographic imaging

Common-path off-axis single-pixel holographic imaging (COSHI) is proposed to obtain complex amplitude information using an in-line interferometer and a single-pixel (point-like) detector. COSHI is more robust to disturbances such as vibration than the conventional single-pixel digital holography technique because of its common-path configuration. In addition, the number of measurements can be reduced due to COSHI's reconstruction process based on the Fourier fringe analysis. In COSHI, an off-axis digital hologram can be obtained using the structured patterns composed of Hadamard basis patterns and stationary tilted phase distribution. Interestingly, COSHI's space bandwidth is larger than of the conventional off-axis digital holography because COSHI does not reconstruct the self-correlation term of an object. The proposed method is theoretically confirmed and numerical and experimental results show its feasibility.

Video-Rate Quantitative Phase Imaging Using a Digital Holographic Microscope and a Generative Adversarial Network

The conventional reconstruction method of off-axis digital holographic microscopy (DHM) relies on computational processing that involves spatial filtering of the sample spectrum and tilt compensation between the interfering waves to accurately reconstruct the phase of a biological sample. Additional computational procedures such as numerical focusing may be needed to reconstruct free-of-distortion quantitative phase images based on the optical configuration of the DHM system. Regardless of the implementation, any DHM computational processing leads to long processing times, hampering the use of DHM for video-rate renderings of dynamic biological processes. In this study, we report on a conditional generative adversarial network (cGAN) for robust and fast quantitative phase imaging in DHM. The reconstructed phase images provided by the GAN model present stable background levels, enhancing the visualization of the specimens for different experimental conditions in which the conventional approach often fails. The proposed learning-based method was trained and validated using human red blood cells recorded on an off-axis Mach–Zehnder DHM system. After proper training, the proposed GAN yields a computationally efficient method, reconstructing DHM images seven times faster than conventional computational approaches.

Transform-based phase retrieval techniques from a single off-axis interferogram

Optical phase retrieval (OPR) methods are important because they are used to obtain the transverse phase profile information of a beam. Interference methods are extensively used to convert the phase information into an intensity pattern, which can then be processed further to retrieve the unknown phase. The most widely used interference method involves the interference of the unknown object beam and a known reference beam with an angle between them. There are several algorithms that retrieve the phase information from such a single off-axis interference pattern. For a particular application, the choice of an algorithm for OPR is very important. Therefore, it is necessary to choose between them, depending on the requirements. Three entirely different noniterative, transform-based algorithms, namely the Fourier transform (FT) method, the continuous wavelet transform (CWT) method, and the Hilbert transform (CWT) method, are explained in detail. A quantitative comparison is made using a combination of rms error and standard structural similarity measure. The advantages of using a standard unwrapping algorithm are also validated using the same combination of comparison metrics. We show that the HT method has a better response with object beam with higher spatial frequency content, but with the penalty of affected noise. The FT method and CWT method have better noise immunity, but have the limitation of the spatial frequency range of the object beam. The different constraints, advantages, and some practical limitations of the methods are discussed with the help of a quantitative phase imaging experiment of monodispersed polymethyl methacrylate beads.

Further improvements to iterative off-axis digital holography

In order to break through the limitation of off-axis holography in the field of measuring rough or strong scattering objects, a new iterative algorithm based on the concept of wavefront-coding was proposed. The reference wave is regarded as a wave modulator and it starts with random guess freed from the result of traditional off-axis holography. The full frequency spectrum could be retrieved iteratively after taking full advantage of the space-bandwidth production of the detector. As one form of coherent diffractive imaging, the theoretical resolution is diffraction limitation. According to the simulations and experiments with random phase plate, when the object fails to be reconstructed by traditional off-axis holography and other iterative off-axis holography algorithm due to the frequency spectrum of object is too wide, the proposed algorithm works well. It could be a general algorithm to prominently improve the capability of off-axis holography to measure rough or strong scattering objects.

Fringe analysis: single-shot or two-frames? Quantitative phase imaging answers

Conditions of the digital recording of the fringe pattern determine the phase reconstruction procedure, which in turn directly shapes the final accuracy and throughput of the full-field (non-scanning) optical measurement technique and defines the system capabilities. In this way, the fringe pattern analysis plays a crucial role in the ubiquitous optical measurements and thus is under constant development focused on high temporal/spatial resolution. It is especially valuable in the quantitative phase imaging technology, which emerged in the high-contrast label-free biomedical microscopy. In this paper, I apply recently blossomed two-frame phase-shifting techniques to the QPI and merge them with advanced adaptive interferogram pre-filtering algorithms. Next, I comprehensively test such frameworks against classical and adaptive single-shot methods applied for phase reconstruction in dynamic QPI enabling highest phase time-space-bandwidth product. The presented study systematically tackles important question: what is the gain, if any, in QPI realized by recording two phase-shifted interferograms? Counterintuitively, the results show that single-shot demodulation exhibited higher phase reconstruction accuracy than two-frame phase-shifting methods in low and medium interferogram signal-to-noise ratio regimes. Thus, the single-shot approach is promoted due to not only high temporal resolution but also larger phase-information throughput. Additionally, in the majority of scenarios, the best option is to shift the paradigm and employ two-frame pre-filtering rather than two-frame phase retrieval. Experimental fringe analysis in QPI of LSEC/RWPE cell lines successfully corroborated all novel numerical findings. Hence, the presented numerical-experimental research advances the important field of fringe analysis solutions for optical full-field measurement methods with widespread bio-engineering applications.