Phase-shifting digital holography

Fourier-inspired single-pixel holography

Fourier-inspired single-pixel holography (FISH) is an effective digital holography (DH) approach that utilizes a single-pixel detector instead of a conventional camera to capture light field information. FISH combines the Fourier single-pixel imaging and off-axis holography technique, allowing one to acquire useful information directly, rather than recording the hologram in the spatial domain and filtering unwanted terms in the Fourier domain. Furthermore, we employ a deep learning technique to jointly optimize the sampling mask and the imaging enhancement model, to achieve high-quality results at a low sampling ratio. Both simulations and experimental results demonstrate the effectiveness of FISH in single-pixel phase imaging. FISH combines the strengths of single-pixel imaging (SPI) and DH, potentially expanding DH's applications to specialized spectral bands and low-light environments while equipping SPI with capabilities for phase detection and coherent gating.

Wide-field quantitative ghost phase imaging with phase-shifting holographic ghost diffraction

Ghost holography has attracted notable applied interest in the modern quantitative imaging applications with the futuristic features of complex field recovery in the diversified imaging scenarios. However, the utilization of digital holography in ghost frame works introduces space bandwidth or time bandwidth restrictions in the implementation of the technique in applied domains. Here, we propose and demonstrate a quantitative ghost phase imaging approach with holographic ghost diffraction scheme in combination with the phase-shifting technique. The approach makes use of an off-axis holography system by superposing the ghost diffraction fields with a reference random field generated from an independent diffuser. In addition, the technique utilizes the high-speed response of a spatial light modulator to introduce a fast temporal phase shifting to one of the ghost-diffraction fields that views the object, which practically results in the enhancement of the effective bandwidth in the frequency domain by suppressing redundant terms. The applicability of the technique is experimentally validated by demonstrating the quantitative phase imaging of various abrupt and continuous phase samples.

Phase recovery from Fresnel incoherent correlation holography using differential Zernike fitting

Fresnel incoherent correlation holography (FINCH) was created to improve imaging resolution and 3D imaging capabilities using spatially incoherent illumination. The optical setup of a FINCH-based interferometer is closely related to a radial shearing interferometer, which measures the radial phase difference of an input wavefront. By using phase retrieval methodologies from lateral shearing interferometry, namely, differential Zernike fitting (DZF), we show that FINCH-based and radial shearing interferometry can be used for phase retrieval and adaptive optics (AO). In this paper, we describe the phase retrieval algorithm using least squares-based DZF and demonstrate a simple adaptive optics loop with an aberrated point spread function using wave optics simulation. We find that FINCH-based phase retrieval has the advantages of fast phase retrieval measurements, thanks to well-studied least squares-based phase reconstruction methods, improved resolution compared to the Shack-Hartmann-based wavefront sensing, and the simplified optical setup of radial shearing interferometry.

Rapid terahertz beam profiling and antenna characterization with phase-shifting holography

In this paper we investigate the application of phase-shifting digital holography for the real-time characterization of electromagnetic sources in the THz frequency range. We use an off-the-shelf terahertz detector array composed of 64 × 64 power-sensitive pixels, over an area of 96 mm × 96 mm , to record intensity interferograms cast between the coherent radiation emitted from a reference source and an unknown antenna under test. This approach parallelizes the acquisition process with respect to conventional near-field point scanning methods, reducing the measurement time by orders of magnitude. In our system, the measurement time is limited only by the refresh rate of the detector array and the speed of a delay line stage that is used to phase-shift the reference wave. As a proof-of-principle demonstration, we map the 2D near-field distribution and estimate the far-field radiation pattern emitted by a plano-convex PTFE spherical lens antenna illuminated by a diagonal horn at 290 GHz frequency with ∼ 1 Hz refresh rate.

Interframe-tunable ultrafast differential-displacement holography

We describe the details of a digital holographic microscopy diagnostic capable of quantifying both the topography and velocity of a km/s object with adjustable temporal sensitivity. This technique involves spatially multiplexing a double pulse reflected from a target with reference beams of precisely known temporal separation.

Single-shot spatial light interference microscopy for dynamic monitoring of membrane fluctuations

Single-shot spatial light interference microscopy (SS-SLIM) with a pair of non-polarizing beam splitters is proposed for substantially enhancing the speed and efficiency of conventional SLIM systems. Traditional methods are limited by the need for multiple-frame serial modulation and acquisition by spatial light modulators and detectors. Our approach integrates non-polarizing beam splitters to simultaneously capture four phase-shifted intensity images, increasing the imaging speed by at least fourfold while maintaining high quality. This capability is crucial for effectively monitoring the dynamic fluctuations of red blood cell membranes. Furthermore, the potential applications of the SS-SLIM system in biomedical research are demonstrated, particularly in scenarios requiring high temporal resolution and label-free imaging.

Hiding Images in Quantum Correlations

Photon-pair correlations in spontaneous parametric down-conversion are ubiquitous in quantum photonics. The ability to engineer their properties for optimizing a specific task is essential, but often challenging in practice. We demonstrate the shaping of spatial correlations between entangled photons in the form of arbitrary amplitude and phase objects. By doing this, we encode image information within the pair correlations, making it undetectable by conventional intensity measurements. It enables the transmission of complex, high-dimensional information using quantum correlations of photons, which can be useful for developing quantum communication and imaging protocols.

Self-Heterodyne Diffractive Imaging of Ultrafast Electron Dynamics Monitored by Single-Electron Pulses

The direct imaging of time-evolving molecular charge densities on atomistic scale and at femtosecond resolution has long been an elusive task. In this theoretical study, we propose a self-heterodyne electron diffraction technique based on single electron pulses. The electron is split into two beams, one passes through the sample and its interference with the second beam produces a heterodyne diffraction signal that images the charge density. Application to probing the ultrafast electronic dynamics in Mg-phthalocyanine demonstrates its potential for imaging chemical dynamics.

Characterizing Biphoton Spatial Wave Function Dynamics with Quantum Wavefront Sensing

With an extremely high dimensionality, the spatial degree of freedom of entangled photons is a key tool for quantum foundation and applied quantum techniques. To fully utilize the feature, the essential task is to experimentally characterize the multiphoton spatial wave function including the entangled amplitude and phase information at different evolutionary stages. However, there is no effective method to measure it. Quantum state tomography is costly, and quantum holography requires additional references. Here, we introduce quantum Shack-Hartmann wavefront sensing to perform efficient and reference-free measurement of the biphoton spatial wave function. The joint probability distribution of photon pairs at the back focal plane of a microlens array is measured and used for amplitude extraction and phase reconstruction. In the experiment, we observe that the biphoton amplitude correlation becomes weak while phase correlation shows up during free-space propagation. Our work is a crucial step in quantum physical and adaptive optics and paves the way for characterizing quantum optical fields with high-order correlations or topological patterns.

Quantitative phase imaging based on holography: trends and new perspectives

In 1948, Dennis Gabor proposed the concept of holography, providing a pioneering solution to a quantitative description of the optical wavefront. After 75 years of development, holographic imaging has become a powerful tool for optical wavefront measurement and quantitative phase imaging. The emergence of this technology has given fresh energy to physics, biology, and materials science. Digital holography (DH) possesses the quantitative advantages of wide-field, non-contact, precise, and dynamic measurement capability for complex-waves. DH has unique capabilities for the propagation of optical fields by measuring light scattering with phase information. It offers quantitative visualization of the refractive index and thickness distribution of weak absorption samples, which plays a vital role in the pathophysiology of various diseases and the characterization of various materials. It provides a possibility to bridge the gap between the imaging and scattering disciplines. The propagation of wavefront is described by the complex amplitude. The complex-value in the complex-domain is reconstructed from the intensity-value measurement by camera in the real-domain. Here, we regard the process of holographic recording and reconstruction as a transformation between complex-domain and real-domain, and discuss the mathematics and physical principles of reconstruction. We review the DH in underlying principles, technical approaches, and the breadth of applications. We conclude with emerging challenges and opportunities based on combining holographic imaging with other methodologies that expand the scope and utility of holographic imaging even further. The multidisciplinary nature brings technology and application experts together in label-free cell biology, analytical chemistry, clinical sciences, wavefront sensing, and semiconductor production.

Analytical solution for single-pixel ptychography through linear modeling

Amplitude-modulated single-pixel ptychography (SPP) enables non-interferometric complex-field imaging of objects. However, the conventional iterative and nondeterministic reconstruction methods, based on the ptychography algorithm, pose challenges in fully understanding the role of critical optical parameters. In response, this paper introduces an innovative analytical approach that establishes a theoretical foundation for the uniqueness of SPP reconstruction results. The proposed method conceptualizes SPP as a system of linear equations in the frequency domain, involving both object and modulated illumination. Solving this equation system reveals a determined solution for the complex object, providing an alternative to iterative and nondeterministic techniques. Through a series of simulations, this approach not only validates the uniqueness of SPP reconstruction, but also explores key properties influencing accuracy.

Double-slit holography-a single-shot lensless imaging technique

In this study, we propose a new method for single-shot, high-resolution lensless imaging called double-slit holography. This technique combines the properties of in-line and off-axis holography in one single-shot measurement using the simplest double-slit device: a plate with two apertures. In double-slit holography, a plane wave illuminates the two apertures giving rise to two spherical waves. While diffraction of one spherical wave from a sample positioned behind the first aperture (the object aperture) provides the object wave, the other spherical wave diffracted from the second (reference) aperture provides the reference wave. The resulting interference pattern in the far-field (hologram) combines the properties of an in-line (or Gabor-type) hologram and an off-axis hologram due to the added reference wave from the second aperture. Both the object and reference waves have the same intensity, which ensures high contrast of the hologram. Due to the off-axis scheme, the amplitude and phase distributions of the sample can be directly reconstructed from the hologram, and the twin image can be easily separated. Due to the object wave being the same as in-line holography with a spherical wave, imaging at different magnifications is similarly done by simply adjusting the aperture-to-sample distance. The resolution of the reconstructed object is given by the numerical aperture of the optical setup and the diameter of the reference aperture. It is shown both by theory and simulations that the resolution of the reconstructed object depends on the diameter of the reference wave aperture but does not depend on the diameter of the object aperture. Light optical proof-of-concept experiments are provided. The proposed method can be particularly practical for X-rays, where optical elements such as beam splitters are not available and conventional off-axis holography schemes cannot be realised.

Multispectral Holographic Intensity and Phase Imaging of Semitransparent Ultrathin Films

In this paper, we demonstrate a novel optical characterization method for ultrathin semitransparent and absorbing materials through multispectral intensity and phase imaging. The method is based on a lateral-shearing interferometric microscopy (LIM) technique, where phase-shifting allows extraction of both the intensity and the phase of transmitted optical fields. To demonstrate the performance in characterizing semitransparent thin films, we fabricated and measured cupric oxide (CuO) seeded gold ultrathin metal films (UTMFs) with mass-equivalent thicknesses from 2 to 27 nm on fused silica substrates. The optical properties were modeled using multilayer thin film interference and a parametric model of their complex refractive indices. The UTMF samples were imaged in the spectral range from 475 to 750 nm using the proposed LIM technique, and the model parameters were fitted to the measured data in order to determine the respective complex refractive indices for varying thicknesses. Overall, by using the combined intensity and phase not only for imaging and quality control but also for determining the material properties, such as complex refractive indices, this technique demonstrates a high potential for the characterization of the optical properties, of (semi-) transparent thin films.

Technology Selection for Inline Topography Measurement with Rover-Borne Laser Spectrometers

This work studies enhancing the capabilities of compact laser spectroscopes integrated into space-exploration rovers by adding 3D topography measurement techniques. Laser spectroscopy enables the in situ analysis of sample composition, aiding in the understanding of the geological history of extraterrestrial bodies. To complement spectroscopic data, the inclusion of 3D imaging is proposed to provide unprecedented contextual information. The morphological information aids material characterization and hence the constraining of rock and mineral histories. Assigning height information to lateral pixels creates topographies, which offer a more complete spatial dataset than contextual 2D imaging. To aid the integration of 3D measurement into future proposals for rover-based laser spectrometers, the relevant scientific, rover, and sample constraints are outlined. The candidate 3D technologies are discussed, and estimates of performance, weight, and power consumptions guide the down-selection process in three application examples. Technology choice is discussed from different perspectives. Inline microscopic fringe-projection profilometry, incoherent digital holography, and multiwavelength digital holography are found to be promising candidates for further development.

Recent Advances and Current Trends in Transmission Tomographic Diffraction Microscopy

Optical microscopy techniques are among the most used methods in biomedical sample characterization. In their more advanced realization, optical microscopes demonstrate resolution down to the nanometric scale. These methods rely on the use of fluorescent sample labeling in order to break the diffraction limit. However, fluorescent molecules' phototoxicity or photobleaching is not always compatible with the investigated samples. To overcome this limitation, quantitative phase imaging techniques have been proposed. Among these, holographic imaging has demonstrated its ability to image living microscopic samples without staining. However, for a 3D assessment of samples, tomographic acquisitions are needed. Tomographic Diffraction Microscopy (TDM) combines holographic acquisitions with tomographic reconstructions. Relying on a 3D synthetic aperture process, TDM allows for 3D quantitative measurements of the complex refractive index of the investigated sample. Since its initial proposition by Emil Wolf in 1969, the concept of TDM has found a lot of applications and has become one of the hot topics in biomedical imaging. This review focuses on recent achievements in TDM development. Current trends and perspectives of the technique are also discussed.

Real-time millimeter wave holography with an arrayed detector

Millimeter and terahertz wave imaging has emerged as a powerful tool for applications such as security screening, biomedical imaging, and material analysis. However, intensity images alone are often insufficient for detecting variations in the dielectric constant of a sample, and extraction of material properties without additional phase information requires extensive prior knowledge of the sample. Digital holography provides a means for intensity-only detectors to reconstruct both amplitude and phase images. Here we utilize a commercially available source and detector array, both operating at room temperature, to perform digital holography in real-time for the first time in the mm-wave band (at 290 GHz). We compare the off-axis and phase-shifting approaches to digital holography and discuss their trade-offs and practical challenges in this regime. Owing to the low pixel count, we find phase-shifting holography to be the most practical and high fidelity approach for such commercial mm-wave cameras even under real-time operational requirements.

Comparative oncology chemosensitivity assay for personalized medicine using low-coherence digital holography of dynamic light scattering from cancer biopsies

Nearly half of cancer patients who receive standard-of-care treatments fail to respond to their first-line chemotherapy, demonstrating the pressing need for improved methods to select personalized cancer therapies. Low-coherence digital holography has the potential to fill this need by performing dynamic contrast OCT on living cancer biopsies treated ex vivo with anti-cancer therapeutics. Fluctuation spectroscopy of dynamic light scattering under conditions of holographic phase stability captures ultra-low Doppler frequency shifts down to 10 mHz caused by light scattering from intracellular motions. In the comparative preclinical/clinical trials presented here, a two-species (human and canine) and two-cancer (esophageal carcinoma and B-cell lymphoma) analysis of spectral phenotypes identifies a set of drug response characteristics that span species and cancer type. Spatial heterogeneity across a centimeter-scale patient biopsy sample is assessed by measuring multiple millimeter-scale sub-samples. Improved predictive performance is achieved for chemoresistance profiling by identifying red-shifted sub-samples that may indicate impaired metabolism and removing them from the prediction analysis. These results show potential for using biodynamic imaging for personalized selection of cancer therapy.

On the use of deep learning for phase recovery

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and provide an outlook on how to better use DL to improve the reliability and efficiency of PR. Furthermore, we present a live-updating resource ( https://github.com/kqwang/phase-recovery ) for readers to learn more about PR.

Intensity correlation holography for remote phase sensing and 3D imaging

Holography is an established technique for measuring the wavefront of optical signals through interferometric combination with a reference wave. Conventionally the integration time of a hologram is limited by the interferometer coherence time, thus making it challenging to prepare holograms of remote objects, especially using weak illumination. Here, we circumvent this limitation by using intensity correlation interferometry. Although the exposure time of individual holograms must be shorter than the interferometer coherence time, we show that any number of randomly phase-shifted holograms can be combined into a single intensity-correlation hologram. In a proof-of-principle experiment, we use this technique to perform phase imaging and 3D reconstruction of an object at a ∼3 m distance using weak illumination and without active phase stabilization.

Roadmap on Label-Free Super-Resolution Imaging

Label-free super-resolution (LFSR) imaging relies on light-scattering processes in nanoscale objects without a need for fluorescent (FL) staining required in super-resolved FL microscopy. The objectives of this Roadmap are to present a comprehensive vision of the developments, the state-of-the-art in this field, and to discuss the resolution boundaries and hurdles which need to be overcome to break the classical diffraction limit of the LFSR imaging. The scope of this Roadmap spans from the advanced interference detection techniques, where the diffraction-limited lateral resolution is combined with unsurpassed axial and temporal resolution, to techniques with true lateral super-resolution capability which are based on understanding resolution as an information science problem, on using novel structured illumination, near-field scanning, and nonlinear optics approaches, and on designing superlenses based on nanoplasmonics, metamaterials, transformation optics, and microsphere-assisted approaches. To this end, this Roadmap brings under the same umbrella researchers from the physics and biomedical optics communities in which such studies have often been developing separately. The ultimate intent of this paper is to create a vision for the current and future developments of LFSR imaging based on its physical mechanisms and to create a great opening for the series of articles in this field.

Six-pack holography for dynamic profiling of thick and extended objects by simultaneous three-wavelength phase unwrapping with doubled field of view

Dynamic holographic profiling of thick samples is limited due to the reduced field of view (FOV) of off-axis holography. We present an improved six-pack holography system for the simultaneous acquisition of six complex wavefronts in a single camera exposure from two fields of view (FOVs) and three wavelengths, for quantitative phase unwrapping of thick and extended transparent objects. By dynamically generating three synthetic wavelength quantitative phase maps for each of the two FOVs, with the longest wavelength being 6207 nm, hierarchical phase unwrapping can be used to reduce noise while maintaining the improvements in the 2π phase ambiguity due to the longer synthetic wavelength. The system was tested on a 7 μm tall PDMS microchannel and is shown to produce quantitative phase maps with 96% accuracy, while the hierarchical unwrapping reduces noise by 93%. A monolayer of live onion epidermal tissue was also successfully scanned, demonstrating the potential of the system to dynamically decrease scanning time of optically thick and extended samples.

Holographic imaging platform for particle discrimination based on simultaneous mass density and refractive index measurements

Real-time detection, classification and identification of aerosol particles is crucial in various industries and public health areas. In order to circumvent the limitations of existing particle analysis methods for efficient discrimination, we demonstrate a compact digital in-line holographic microscopy platform with an inertial spectrometer for simultaneous measurement of two independent fingerprint parameters at single species level. In particular, by interrogating the particle location and size captured with the platform, particle mass density can be estimated. Furthermore, by employing Monte Carlo fitting to the Lorenz-Mie theory, the refractive index of each particle can also be extracted from the interference patterns. It is demonstrated that the combination of mass density and optical density characterization unambiguously enhances the discriminatory power of the system, especially when dealing with particles that exhibit similar mass densities but distinctive refractive indices or vice versa. This innovative approach represents a significant advancement in particle characterization and composition identification, with potential applications in various industrial, scientific, and research domains. An iOS-based app interface is then customized for wireless controlling of the CMOS imager, image acquisition, reconstruction, and data analysis. The imaging platform proposed in this work has prominent advantages including compactness, accuracy, efficiency, high throughput, and remote sensing capability, which is especially relevant for applications where on-site/remote metrology and identification of particles is required.

Artificial intelligence-enabled quantitative phase imaging methods for life sciences

Quantitative phase imaging, integrated with artificial intelligence, allows for the rapid and label-free investigation of the physiology and pathology of biological systems. This review presents the principles of various two-dimensional and three-dimensional label-free phase imaging techniques that exploit refractive index as an intrinsic optical imaging contrast. In particular, we discuss artificial intelligence-based analysis methodologies for biomedical studies including image enhancement, segmentation of cellular or subcellular structures, classification of types of biological samples and image translation to furnish subcellular and histochemical information from label-free phase images. We also discuss the advantages and challenges of artificial intelligence-enabled quantitative phase imaging analyses, summarize recent notable applications in the life sciences, and cover the potential of this field for basic and industrial research in the life sciences.

Referenceless characterization of complex media using physics-informed neural networks

In this work, we present a method to characterize the transmission matrices of complex scattering media using a physics-informed, multi-plane neural network (MPNN) without the requirement of a known optical reference field. We use this method to accurately measure the transmission matrix of a commercial multi-mode fiber without the problems of output-phase ambiguity and dark spots, leading to up to 58% improvement in focusing efficiency compared with phase-stepping holography. We demonstrate how our method is significantly more noise-robust than phase-stepping holography and show how it can be generalized to characterize a cascade of transmission matrices, allowing one to control the propagation of light between independent scattering media. This work presents an essential tool for accurate light control through complex media, with applications ranging from classical optical networks, biomedical imaging, to quantum information processing.

Multiplexed digital holography for fluid surface profilometry

Digital holography (DH) has been widely used for imaging and characterization of microstructures and nanostructures in materials science and biology and also has the potential to provide high-resolution, nondestructive measurement of fluid surfaces. DH setups capture the complex wavefronts of light scattered by an object or reflected from a surface, allowing the quantitative measurements of their shape and deformation. However, their use in fluid profilometry is scarce and has not been explored in much depth to the best of our knowledge. We present an alternative use for a DH setup that can measure and monitor the surface of fluid samples. Based on DH reflectometry, our modeling shows that multiple reflections from the sample and the reference interfere and generate multiple holograms of the sample, resulting in a multiplexed image of the wavefront. The individual interferograms can be isolated in the spatial frequency domain, and the fluid surface can be digitally reconstructed from them. We further show that this setup can be used to track changes in the surface of a fluid over time, such as during the formation and propagation of waves or the evaporation of surface layers.

Linear optical random projections without holography

We introduce what we believe to be a novel method to perform linear optical random projections without the need for holography. Our method consists of a computationally trivial combination of multiple intensity measurements to mitigate the information loss usually associated with the absolute-square non-linearity imposed by optical intensity measurements. Both experimental and numerical findings demonstrate that the resulting matrix consists of real-valued, independent, and identically distributed (i.i.d.) Gaussian random entries. Our optical setup is simple and robust, as it does not require interference between two beams. We demonstrate the practical applicability of our method by performing dimensionality reduction on high-dimensional data, a common task in randomized numerical linear algebra with relevant applications in machine learning.

Intensity interferometry for holography with quantum and classical light

As first demonstrated by Hanbury Brown and Twiss, it is possible to observe interference between independent light sources by measuring correlations in their intensities rather than their amplitudes. In this work, we apply this concept of intensity interferometry to holography. We combine a signal beam with a reference and measure their intensity cross-correlations using a time-tagging single-photon camera. These correlations reveal an interference pattern from which we reconstruct the signal wavefront in both intensity and phase. We demonstrate the principle with classical and quantum light, including a single photon. Since the signal and reference do not need to be phase-stable nor from the same light source, this technique can be used to generate holograms of self-luminous or remote objects using a local reference, thus opening the door to new holography applications.

Randomness assisted in-line holography with deep learning

We propose and demonstrate a holographic imaging scheme exploiting random illuminations for recording hologram and then applying numerical reconstruction and twin image removal. We use an in-line holographic geometry to record the hologram in terms of the second-order correlation and apply the numerical approach to reconstruct the recorded hologram. This strategy helps to reconstruct high-quality quantitative images in comparison to the conventional holography where the hologram is recorded in the intensity rather than the second-order intensity correlation. The twin image issue of the in-line holographic scheme is resolved by an unsupervised deep learning based method using an auto-encoder scheme. Proposed learning technique leverages the main characteristic of autoencoders to perform blind single-shot hologram reconstruction, and this does not require a dataset of samples with available ground truth for training and can reconstruct the hologram solely from the captured sample. Experimental results are presented for two objects, and a comparison of the reconstruction quality is given between the conventional inline holography and the one obtained with the proposed technique.

Femtosecond-laser-based full-field three-dimensional imaging with phase compensation

Coherence scanning interferometer (CSI) enables 3D imaging with nanoscale precision. However, the efficiency of such a system is limited because of the restriction imposed by the acquisition system. Herein, we propose a phase compensation method that reduces the interferometric fringe period of femtosecond-laser-based CSI, resulting in larger sampling intervals. We realize this method by synchronizing the heterodyne frequency with the repetition frequency of the femtosecond laser. The experimental results show that our method can keep the root-mean-square axial error down to 2 nm at a high scanning speed of 6.44 µm per frame, which enables fast nanoscale profilometry over a wide area.

Far-field mid-infrared microscopy via spatial frequency shifting of evanescent waves in photorefractive nematic liquid crystal

Mid-infrared wavelength has unique advantages in revealing the nanostructures and molecular vibrational signatures. However, the mid-infrared subwavelength imaging is also limited by diffraction. Here, we propose a scheme for breaking the limitation in mid-infrared imaging. With the assistance of orientational photorefractive grating established in nematic liquid crystal, evanescent waves are efficiently shifted back into the observation window. The visualized propagation of power spectra in k-space also proves this point. The resolution has an improvement about 3.2 times higher than the linear case, showing potentials in various imaging areas, such as biological tissues imaging and label-free chemical sensing.

Nanometer-precision surface metrology of millimeter-sized stepped objects using full-cascade-linked synthetic-wavelength digital holography using a line-by-line full-mode-extracted optical frequency comb

Digital holography (DH) is a powerful tool for the surface profilometry of objects with sub-wavelength precision. In this article, we demonstrate full-cascade-linked synthetic-wavelength DH for nanometer-precision surface metrology of millimeter-sized stepped objects. 300 modes of optical frequency comb (OFC) with different wavelengths are sequentially extracted at a step of mode spacing from a 10GHz-spacing, 3.72THz-spanning electro-optic modulator OFC. The resulting 299 synthetic wavelengths and a single optical wavelength are used to generate a fine-step wide-range cascade link covering within a wavelength range of 1.54 µm to 29.7 mm. We determine the sub-millimeter and millimeter step differences with axial uncertainty of 6.1 nm within the maximum axial range of 14.85 mm.

Wave-optics-based image synthesis for super resolution reconstruction of a FZA lensless camera

A Fresnel Zone Aperture (FZA) mask for a lensless camera, an ultra-thin and functional computational imaging system, is beneficial because the FZA pattern makes it easy to model the imaging process and reconstruct captured images through a simple and fast deconvolution. However, diffraction causes a mismatch between the forward model used in the reconstruction and the actual imaging process, which affects the recovered image's resolution. This work theoretically analyzes the wave-optics imaging model of an FZA lensless camera and focuses on the zero points caused by diffraction in the frequency response. We propose a novel idea of image synthesis to compensate for the zero points through two different realizations based on the linear least-mean-square-error (LMSE) estimation. Results from computer simulation and optical experiments verify a nearly two-fold improvement in spatial resolution from the proposed methods compared with the conventional geometrical-optics-based method.

Range selective phase-shifting frequency-modulated digital holography with temporal-heterodyning

We demonstrate that a time of flight (TOF) camera can be used to perform range selective temporal-heterodyne frequency-modulated continuous wave digital holography (TH FMCW DH). The modulated arrayed detection of a TOF camera allows efficient integration of holograms at a selected range with range resolutions significantly less than the optical system's depth of field. TH FMCW DH also allows for on-axis geometries to be achieved, where background light not at the internal modulation frequency of the camera is filtered out. Range selective TH FMCW DH imaging was achieved for both image holograms and Fresnel holograms using on-axis DH geometries. A 2.39 GHz FMCW chirp bandwidth resulted in a DH range resolution of 6.3 cm.

Decorrelation and anti-correlation from defocus in digital holographic interferometry

This paper presents a theoretical modeling of the speckle noise decorrelation in digital Fresnel holographic interferometry in out-of-focus reconstructed images. The complex coherence factor is derived by taking into account the focus mismatch, which depends on both the sensor-to-object distance and the reconstruction distance. The theory is confirmed by both simulated data and experimental results. The very good agreement between data demonstrates the high relevance of the proposed modeling. The particular phenomenon of anti-correlation in phase data from holographic interferometry is highlighted and discussed.

Fractional Fourier-transform filtering and reconstruction in off-axis digital holographic imaging

An off-axis digital holographic reconstruction method with fractional Fourier transform domain filtering is proposed. The theoretical expression and analysis of the characteristics of fractional-transform-domain filtering are given. It is proven that the filtering in a lower fractional-order transform domain can utilize more high-frequency components than that in a conventional Fourier transform domain under the same size of filtering regions. In simulation and experiment, the results demonstrate that the reconstruction imaging resolution can be improved by filtering in the fractional Fourier transform domain. The presented fractional Fourier transform filtering reconstruction provides a novel (to our knowlede) optional way for off-axis holographic imaging.

Complex wave and phase retrieval from a single off-axis interferogram

Single-frame off-axis holographic reconstruction is promising for quantitative phase imaging. However, reconstruction accuracy and contrast are degraded by noise, frequency spectrum overlap of the interferogram, severe phase distortion, etc. In this work, we propose an iterative single-frame complex wave retrieval based on an explicit model of object and reference waves. We also develop a phase restoration algorithm that does not resort to phase unwrapping. Both simulation and real experiments demonstrate higher accuracy and robustness compared to state-of-the-art methods, for both complex wave estimation and phase reconstruction. Importantly, the allowed bandwidth for the object wave is significantly improved in realistic experimental conditions (similar amplitudes for object and reference waves), which makes it attractive for large field-of-view and high-resolution imaging applications.

Multimodal image reconstruction from tomographic diffraction microscopy data

Tomographic diffraction microscopy (TDM) is a tool of choice for high-resolution, marker-less 3D imaging of biological samples. Based on a generalization of digital holographic microscopy with full control of the sample's illumination, TDM measures, from many illumination directions, the diffracted fields in both phase and amplitude. Photon budget associated to TDM imaging is low. Therefore, TDM is not limited by phototoxicity issues. The recorded information makes it possible to reconstruct 3D refractive index distribution (with both refraction and absorption contributions) of the object under scrutiny, without any staining. In this contribution, we show an alternate use of this information. A tutorial for multimodal image reconstruction is proposed. Both intensity contrasts and phase contrasts are proposed, from the image formation model to the final reconstruction with both 2D and 3D rendering, turning TDM into a kind of 'universal' digital microscope.

Phase retrieval algorithm using edge point referencing

In the past few decades, extensive research and efforts have been made for developing a phase retrieval iterative algorithm (PRA) for reconstructing a complex object from far-field intensity equivalently from the object autocorrelation. Since most of the existing PRA techniques employ a random initial guess, the reconstruction output sometimes changes in different trials leading to a non-deterministic output. Additionally, the output of such algorithm occasionally either shows non-convergence, needs a longer time to converge, or shows the twin-image problem. Due to these problems, PRA methods are unsuitable for cases where consecutive reconstructed outputs need to be compared. In this Letter, a novel, to the best of our knowledge, method is developed and discussed using edge point referencing (EPR). In the EPR scheme, in addition to illuminating a region of interest (ROI) of the complex object, a small area near the periphery of the complex object within the ROI is illuminated with an additional beam. Such illumination creates an imbalance in the autocorrelation that can be used to improve the initial guess for achieving unique deterministic output free from the aforementioned problems. Furthermore, by introducing the EPR, one can also achieve faster convergence. To support our theory, derivation, simulations, and experiment are performed and presented.

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.

The Phase Modulating Micro-Mover Based on the MHD/MET System in the Reference Arm of the Scanning Interferometer

The possibility of using a magnetohydrodynamic drive (MHD) and amolecular-electronic transfer (MET) sensor as a single device for moving and precise control of the displacement of a movable mirror, which is part of a scanning interferometer, is considered. A prototype of such a device was developed and experimentally studied. A digital holographic image of the test object was obtained using an optical scheme containing a scanning interferometer with an MHD drive. The important advantages of the MHD drive in the problems of digital recording of hyperspectral holographic images have been discussed.

Wave-front reconstruction via single-pixel homodyne imaging

We combine single-pixel imaging and homodyne detection to perform full object recovery (phase and amplitude). Our method does not require any prior information about the object or the illuminating fields. As a demonstration, we reconstruct the optical properties of several semi-transparent objects and find that the reconstructed complex transmission has a phase precision of 0.02 radians and a relative amplitude precision of 0.01.

Three-dimensional dynamic measurement of unstable temperature fields by multi-view single-shot phase-shifting digital holography

A multi-view phase measurement system based on single-shot phase-shifting digital holography is proposed to dynamically obtain three-dimensional (3-D) information of an unstable temperature field. The proposed system consists of a laser, three polarization imaging cameras, and the corresponding optical components. The laser beam emitted from the laser is separated by the fibers into three pairs that contain three object beams and three reference beams. The object beams pass through the object in three different directions and interfere with the reference beams at the image sensor plane respectively. The recording of the three cameras is triggered simultaneously, which enables the phase measurement of dynamic objects from different viewpoints. We successfully measured the 3-D distributions of an unstable temperature field in the experiments with the proposed system.

Spatial tomography of light resolved in time, spectrum, and polarisation

Measuring polarisation, spectrum, temporal dynamics, and spatial complex amplitude of optical beams is essential to studying phenomena in laser dynamics, telecommunications and nonlinear optics. Current characterisation techniques apply in limited contexts. Non-interferometric methods struggle to distinguish spatial phase, while phase-sensitive approaches necessitate either an auxiliary reference source or a self-reference, neither of which is universally available. Deciphering complex wavefronts of multiple co-propagating incoherent fields remains particularly challenging. We harness principles of spatial state tomography to circumvent these limitations and measure a complete description of an unknown beam as a set of spectrally, temporally, and polarisation resolved spatial state density matrices. Each density matrix slice resolves the spatial complex amplitude of multiple mutually incoherent fields, which over several slices reveals the spectral or temporal evolution of these fields even when fields spectrally or temporally overlap. We demonstrate these features by characterising the spatiotemporal and spatiospectral output of a vertical-cavity surface-emitting laser.

The work harnesses principles of spatial state tomography to fully characterise an optical beam in space, time, spectrum, and polarisation. Analysis of the output of a vertical-cavity surface-emitting laser illustrates the technique’s capabilities.

Grating-based in-line geometric-phase-shifting incoherent digital holographic system toward 3D videography

Incoherent digital holography (IDH) with a sequential phase-shifting method enables high-definition 3D imaging under incoherent lights. However, sequential recording of multiple holograms renders IDH impractical for 3D videography. In this study, we propose grating-based in-line geometric-phase-shifting IDH. Our method divides orthogonal circularly polarized lights into four copies with a fabricated phase grating and subsequently creates self-interference holograms with geometric phases introduced by a segmented linear polarizer. This enables single-shot recording of holograms without the need for a specially designed image sensor, such as a polarization-sensitive sensor. Moreover, the achievable spatial resolution is higher than that of off-axis methods. As a proof-of-principle experiment, we demonstrated snapshot and video recording of 3D reflective objects using our IDH method. The results confirmed the feasibility of the proposed method.

Label-free single-shot imaging with on-axis phase-shifting holographic reflectance quantitative phase microscopy

Quantitative phase microscopy (QPM) has been emerged as an indispensable diagnostic and characterization tool in biomedical imaging with its characteristic nature of label-free, noninvasive, and real time imaging modality. The integration of holography to the conventional microscopy opens new advancements in QPM featuring high-resolution and quantitative three-dimensional image reconstruction. However, the holography schemes suffer in space-bandwidth and time-bandwidth issues in the off-axis and phase-shifting configuration, respectively. Here, we introduce an on-axis phase-shifting holography based QPM system with single-shot imaging capability. The technique utilizes the Fizeau interferometry scheme in combination with polarization phase-shifting and space-division multiplexing to achieve the single-shot recording of the multiple phase-shifted holograms. Moreover, the high-speed imaging capability with instantaneous recording of spatially phase shifted holograms offers the flexible utilization of the approach in dynamic quantitative phase imaging with robust phase stability. We experimentally demonstrated the validity of the approach by quantitative phase imaging and depth-resolved imaging of paramecium cells. Furthermore, the technique is applied to the phase imaging and quantitative parameter estimation of red blood cells. This integration of a Fizeau-based phase-shifting scheme to the optical microscopy enables a simple and robust tool for the investigations of engineered and biological specimen with real-time quantitative analysis.

Pixel Resolution Imaging in Parallel Phase-Shifting Digital Holography

Parallel phase-shifting digital holography (PPSDH) employing a polarization image sensor can suppress zero-order and twin-image noise through a single exposure, achieve instantaneous measurement of complex-valued dynamic objects, and have broad applications in the areas of biomedicine, etc. To improve the imaging resolution of PPSDH, we propose an oversampled super-pixel image reconstruction method, which can be expressed as the implementation of nearest-neighbor interpolation to replace blank pixels in sparse sub-phase-shift holograms. We found experimentally that the maximum spatial lateral resolution of the reconstructed image based on the existing super-pixel method, B-spline, bicubic, bilinear, and the proposed nearest-neighbor interpolation was 12.4 µm, 11.4 µm, 9.8 µm, 8.8 µm, and 7.8 µm, respectively. The main reason for not reaching the ideal value of 6.9 µm was the inherent residual zero-order and twin-image noise, which needs to be removed in the future.

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.

Fast and pure phase-shifting off-axis holographic microscopy with a digital micromirror device

We present a phase-shifting digital holographic microscopy technique, where a digital micromirror device enables to perform a precise phase-only shift of the reference wave. By coupling the beam into a monomode fiber, we obtain a laser mode with a constant phase shift, equally acting on all pixels of the hologram. This method has the advantage of being relatively simple and compatible with high frame rate cameras, which makes it of great interest for the observation of fast phenomena. We demonstrate the validity of the technique in an off-axis configuration by imaging living paramecia caudata.

Accurate EOM-based phase-shifting digital holography with a monitoring interferometer

Phase-shifting digital holography (PSDH) can effectively remove the zero-order term and twin image in on-axis holography, but the phase-shifting error deteriorates the quality of reconstructed object images. In this paper, accurate PSDH with an electro-optic modulator (EOM) is proposed. The EOM is used to generate the required phase shift of on-axis digital holography, and the required phase shift is precisely measured with orthogonal detection of a homodyne interferometer and controlled with proportional-integral-derivative feedback in real time. The merits of our method are that it can achieve fast and accurate phase shifting without mechanical motion or sacrificing the resolution and field of view. The optical configuration was designed, an experimental setup was constructed, and real-time phase shifting was realized. Experiments of the phase-shifting accuracy evaluation, suppression effectiveness of the zero-order and twin image terms, and the specimen measurement demonstrate that the proposed method has significant application for precision topography measurement.

Zero-order-term elimination by using two hologram subtraction based on reference wave polarization adjustment in off-axis digital holography

We propose a method for the removal of the zero-order term by the subtraction of two off-axis holograms based on a reference wave polarization adjustment. The zero-order elimination hologram is generated by the subtraction of two off-axis holograms that are formed by the interference of two reference waves of different linear-polarization orientations with the same s-polarization object wave. The expression about the zero-order elimination hologram is derived according to the essential formula of holographic recording, which proves the validity of this method in principle. The experimental results show that imaging reconstruction from the zero-order elimination hologram can achieve a higher resolution than conventional reconstruction.