Phase retrieval with resolution enhancement by using structured illumination

Structured illumination contrast transfer function for high resolution quantitative phase imaging

We report a sub-diffraction resolution imaging of non-fluorescent samples through quantitative phase imaging. This is achieved through a novel application of structured illumination microscopy (SIM), a super-resolution imaging technique established primarily for fluorescence microscopy. Utilizing our contrast transfer function formalism with SIM, we extract the high spatial frequency components of the phase profile from the defocused intensity images, enabling the reconstruction of a quantitative phase image with a frequency spectrum that surpasses the diffraction limit imposed by the imaging system. Our approach offers several advantages including a deterministic, phase-unwrapping-free algorithm and an easily implementable, non-interferometric setup. We validate the proposed technique for high-resolution phase imaging through both simulation and experimental results, demonstrating a two-fold enhancement in resolution. A lateral resolution of 0.814 µm is achieved for the phase imaging of human cheek cells using a 0.42 NA objective lens and an illumination wavelength of 660 nm, highlighting the efficacy of our approach for high-resolution quantitative phase imaging.

Decision-free downsampling method assisted via channel-transfer information to improve the reliability of holographic data storage systems

A decision-free downsampling method (DFDS) assisted by channel-transfer information for phase-modulated holographic data storage is proposed. DFDS is used to address the issue of the accumulation of decision errors induced by traditional downsampling. The issue degrades the downsampling accuracy. DFDS comprises two functional segments: acquiring the channel-transfer information offline and performing decision-free downsampling online. With the assistance of the channel-transfer information, DFDS uses Bayesian posterior probabilities instead of traditional decision results to avoid the accumulation of decision errors and achieve more accurate downsampling. The simulation and experimental results show that DFDS reduces the phase error rate, thereby improving the reliability of the holographic data storage system.

Improving the data reliability of phase modulated holographic storage using a reliable bit aware low-density parity-check code

Phase modulated holographic storage offers superior storage capacity and a longer life span compared with other storage technologies. However, its application is limited by its high raw bit error rate. We aimed to introduce low-density parity-check (LDPC) codes for data protection in phase modulated holographic storage systems. However, traditional LDPC codes can not fully exploit data error characteristics, causing inaccurate initial log-likelihood ratio (LLR) information, which degrades decoding performance, thus limiting the improvement degree of data reliability in phase modulated holographic storage. Therefore, we propose a reliable bit aware LDPC optimization method (RaLDPC) that analyzes and employs phase demodulation characteristics to obtain reliable bits. More accurate initial LLR weights are assigned to these reliable bits. Hence, the optimized initial LLR can reflect the reliability of the demodulated data more accurately. Experimental results show that RaLDPC can reduce the bit error rate by an average of 38.89% compared with the traditional LDPC code, improving the data reliability of phase modulated holographic storage.

Phase-distribution-aware adaptive decision scheme to improve the reliability of holographic data storage

Owing to their high storage density and long storage life, holographic data storage (HDS) technologies are viable options for mass cold data storage in the era of big data. Phase-modulated holographic data storage (PHDS) is a promising implementation of HDS. However, because of complex noise in the storage channel, many errors remain after phase demodulation. This study investigates the phase decision in the data-reading stage of PHDS. We propose a phase-distribution-aware adaptive (PDAA) decision scheme to address the inaccurate thresholds in traditional phase decision schemes. The PDAA decision scheme can determine more accurate decision thresholds based on the phase distribution characteristics of each reconstructed phase data page and adaptively match different decision thresholds to each phase data page. The experimental results show that when compared to the traditional decision scheme, the PDAA decision scheme can significantly reduce the phase error of data pages, improving the data reliability of holographic storage.

Reflectional quantitative phase-contrast microscopy (RQPCM) with annular epi-illumination

Quantitative phase microscopy (QPM) is a label-free microscopic technique that exploits the phase of a wave passing through a sample; hence, it has been applied to many fields, including biomedical research and industrial inspection. However, the high spatiotemporal resolution imaging of reflective samples still challenges conventional transmission QPM. In this paper, we propose reflectional quantitative phase-contrast microscopy based on annular epi-illumination of light-emitting diodes. The unscattered wave from the sample is successively phase-retarded by 0, π/2, π, and 3π/2 through a spatial light modulator, and high-resolution phase-contrast images are obtained, revealing the finer structure or three-dimensional tomography of reflective samples. With this system, we have quantitatively obtained the contour of tissue slices and silicon semiconductor wafers. We believe that the proposed system will be very helpful for the high-resolution imaging of industrial devices and biomedical dynamics.

Structured illumination microscopy with partially coherent illumination for phase and fluorescent imaging

This study presents a partially coherent illumination based (PCI-based) SIM apparatus for dual-modality (phase and fluorescent) microscopic imaging. The partially coherent illumination (PCI) is generated by placing a rotating diffuser on a monochromatic laser beam, which suppresses speckle noise in the dual-modality images and endows the apparatus with sound sectioning capability. With this system, label-free quantitative phase and super-resolved/sectioned fluorescent images can be obtained for the same sample. We have demonstrated the superiority of the system in phase imaging of transparent cells with high endogenous contrast and in a quantitative manner. In the meantime, we have also demonstrated fluorescent imaging of fluorescent beads, rat tail crosscut, wheat anther, and hibiscus pollen with super-resolution and optical sectioning. We envisage that the proposed method can be applied to many fields, including but not limited to biomedical, industrial, chemistry fields.

Cross-iteration multi-step optimization strategy for three-dimensional intensity position correction in phase diverse phase retrieval

Parameters mismatching between the real optical system and phase retrieval model undermines wavefront reconstruction accuracy. The three-dimensional intensity position is corrected in phase retrieval, which is traditionally separated from lateral position correction and axial position correction. In this paper, we propose a three-dimensional intensity position correction method for phase diverse phase retrieval with the cross-iteration nonlinear optimization strategy. The intensity position is optimized via the coarse optimization method at first, then the intensity position is cross-optimized in the iterative wavefront reconstruction process with the exact optimization method. The analytic gradients about the three-dimensional intensity position are derived. The cross-iteration optimization strategy avoids the interference between the incomplete position correction and wavefront reconstruction during the iterative process. The accuracy and robustness of the proposed method are verified both numerically and experimentally. The proposed method achieves robust and accurate intensity position correction and wavefront reconstruction, which is available for wavefront measurement and phase imaging.

High-resolution and large field-of-view Fourier ptychographic microscopy and its applications in biomedicine

Fourier ptychographic microscopy (FPM) is a promising and fast-growing computational imaging technique with high resolution, wide field-of-view (FOV) and quantitative phase recovery, which effectively tackles the problems of phase loss, aberration-introduced artifacts, narrow depth-of-field and the trade-off between resolution and FOV in conventional microscopy simultaneously. In this review, we provide a comprehensive roadmap of microscopy, the fundamental principles, advantages, and drawbacks of existing imaging techniques, and the significant roles that FPM plays in the development of science. Since FPM is an optimization problem in nature, we discuss the framework and related work. We also reveal the connection of Euler's formula between FPM and structured illumination microscopy. We review recent advances in FPM, including the implementation of high-precision quantitative phase imaging, high-throughput imaging, high-speed imaging, three-dimensional imaging, mixed-state decoupling, and introduce the prosperous biomedical applications. We conclude by discussing the challenging problems and future applications. FPM can be extended to a kind of framework to tackle the phase loss and system limits in the imaging system. This insight can be used easily in speckle imaging, incoherent imaging for retina imaging, large-FOV fluorescence imaging, etc.

High-resolution quantitative phase imaging based on a spatial light modulator and incremental binary random sampling

We propose a single-beam high-resolution quantitative phase imaging method based on a spatial light modulator (SLM) and an incremental binary random sampling (IBRS) algorithm. In this method, the image of the test object presents on the image sensor through an optical microscopy system composed of an objective lens and a collimating lens. A transmittance SLM displaying a group of well-designed IBRS patterns is inserted in the optical microscopy system to modulate the object wavefront. The phase information of the object image can be quantitatively retrieved from the recorded intensities using the IBRS algorithm and the amplitude obtained directly from the diffraction intensity. The IBRS algorithm employed in our method has higher accuracy for phase retrieval compared with our previously proposed complementary random sampling algorithm, which is confirmed by simulations. Further, we demonstrate experimentally the feasibility of our method through several examples: phase imaging of immersion oil droplets with a diffraction-limited lateral resolution of 1.54 µm and a few microbiological specimens with 0.70 µm. Experimental results reveal that our proposed method provides a feasible single-beam technique for quantitative phase imaging with a high spatial resolution.

3D Imaging Based on Depth Measurement Technologies

Three-dimensional (3D) imaging has attracted more and more interest because of its widespread applications, especially in information and life science. These techniques can be broadly divided into two types: ray-based and wavefront-based 3D imaging. Issues such as imaging quality and system complexity of these techniques limit the applications significantly, and therefore many investigations have focused on 3D imaging from depth measurements. This paper presents an overview of 3D imaging from depth measurements, and provides a summary of the connection between the ray-based and wavefront-based 3D imaging techniques.

Fast non-interferometric iterative phase retrieval for holographic data storage

Fast non-interferometric phase retrieval is a very important technique for phase-encoded holographic data storage and other phase based applications due to its advantage of easy implementation, simple system setup, and robust noise tolerance. Here we present an iterative non-interferometric phase retrieval for 4-level phase encoded holographic data storage based on an iterative Fourier transform algorithm and known portion of the encoded data, which increases the storage code rate to two-times that of an amplitude based method. Only a single image at the Fourier plane of the beam is captured for the iterative reconstruction. Since beam intensity at the Fourier plane of the reconstructed beam is more concentrated than the reconstructed beam itself, the requirement of diffractive efficiency of the recording media is reduced, which will improve the dynamic range of recording media significantly. The phase retrieval only requires 10 iterations to achieve a less than 5% phase data error rate, which is successfully demonstrated by recording and reconstructing a test image data experimentally. We believe our method will further advance the holographic data storage technique in the era of big data.

Determination of the complex refractive index segments of turbid sample with multispectral spatially modulated structured light and models approximation

Spectral data enabling the derivation of a biological tissue sample's complex refractive index (CRI) can provide a range of valuable information in the clinical and research contexts. Specifically, changes in the CRI reflect alterations in tissue morphology and chemical composition, enabling its use as an optical marker during diagnosis and treatment. In the present work, we report a method for estimating the real and imaginary parts of the CRI of a biological sample using Kramers-Kronig (KK) relations in the spatial frequency domain. In this method, phase-shifted sinusoidal patterns at single high spatial frequency are serially projected onto the sample surface at different near-infrared wavelengths while a camera mounted normal to the sample surface acquires the reflected diffuse light. In the offline analysis pipeline, recorded images at each wavelength are converted to spatial phase maps using KK analysis and are then calibrated against phase-models derived from diffusion approximation. The amplitude of the reflected light, together with phase data, is then introduced into Fresnel equations to resolve both real and imaginary segments of the CRI at each wavelength. The technique was validated in tissue-mimicking phantoms with known optical parameters and in mouse models of ischemic injury and heat stress. Experimental data obtained indicate variations in the CRI among brain tissue suffering from injury. CRI fluctuations correlated with alterations in the scattering and absorption coefficients of the injured tissue are demonstrated. This technique for deriving dynamic changes in the CRI of tissue may be further developed as a clinical diagnostic tool and for biomedical research applications. To the best of our knowledge, this is the first report of the estimation of the spectral CRI of a mouse head following injury obtained in the spatial frequency domain.

Synthetic aperture microscopy based on referenceless phase retrieval with an electrically tunable lens

Phase imaging microscopy, based either on holography or nonholographic methods such as phase retrieval, has seen considerable attention recently. Phase retrieval offers the advantage of being free of a reference arm and enables a more stable and compact setup. We present an optical setup that provides enhanced resolution by implementing synthetic aperture imaging based on phase retrieval using an electrically tunable lens (ETL). The ETL is a more compact and less expensive alternative to computerized translation stages and spatial light modulators. Before applying phase retrieval, we discuss a general calibration algorithm, which performs image registration, corrects for magnifications, and determines the axial locations of image planes. Finally, we obtain resolution-enhanced images of a phase grating and of cells to demonstrate the practical application of our technique.

Vibrational phase imaging in wide-field CARS for nonresonant background suppression

Coherent Anti-Stokes Raman Scattering (CARS) microscopy is a valuable tool for label-free imaging of biological samples. As a major drawback quantification based on CARS images is compromised by the appearance of a nonresonant background. In this paper we propose and demonstrate a wide-field CARS vibrational phase imaging scheme that allows for nonresonant background suppression. Several CARS images at a few consecutive planes perpendicular to the propagation direction were recorded to reconstruct a phase map utilizing the iteration phase retrieval method. Experimental results verify that the CARS background is efficiently suppressed by the phase imaging approach, as compared to traditional CARS imaging without background correction. The proposed background correction method is robust against environmental disturbance, since the experimental implementation of the suggested detection scheme requires no reference beam.

Overlapped Fourier coding for optical aberration removal

We present an imaging procedure that simultaneously optimizes a camera's resolution and retrieves a sample's phase over a sequence of snapshots. The technique, termed overlapped Fourier coding (OFC), first digitally pans a small aperture across a camera's pupil plane with a spatial light modulator. At each aperture location, a unique image is acquired. The OFC algorithm then fuses these low-resolution images into a full-resolution estimate of the complex optical field incident upon the detector. Simultaneously, the algorithm utilizes redundancies within the acquired dataset to computationally estimate and remove unknown optical aberrations and system misalignments via simulated annealing. The result is an imaging system that can computationally overcome its optical imperfections to offer enhanced resolution, at the expense of taking multiple snapshots over time.

Recent advances in digital holography [invited]

This article presents an overview of recent advances in the field of digital holography, ranging from holographic techniques designed to increase the resolution of microscopic images, holographic imaging using incoherent illumination, phase retrieval with incoherent illumination, imaging of occluded objects, and the holographic recording of depth-extended objects using a frequency-comb laser, to the design of an infrastructure for remote laboratories for digital-holographic microscopy and metrology. The paper refers to current trends in digital holography and explains them using new results that were recently achieved at the Institute for Applied Optics of the University Stuttgart.

Phase retrieval using spatially modulated illumination

In this Letter, we propose a method for retrieving the phase of a wavefront from the diffraction patterns recorded when the object is sequentially illuminated by spatially modulated light. For wavefronts having a smooth phase, the retrieval is achieved by using a deterministic method. When the phase has discontinuities, an iterative process is used for the retrieval and enhancement of the spatial resolution. Both the deterministic and iterative phase reconstructions are demonstrated by experiments.