Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging

Three-dimensional ranging system based on Fresnel incoherent correlation holography

We proposed a three-dimensional (3D) ranging system based on Fresnel incoherent correlation holography (FINCH). Distinct from the displacement measurement based on coherent digital holography (DH), our system simultaneously achieves a 3D range measurement using incoherent illumination. The observation range is obtained by the holographic reconstruction, while the in-plane range is determined using the two-dimensional digital imaging correlation (2D-DIC) technique. Experimental results on the resolution target demonstrate precise 3D ranging determination and improved measurement accuracy.

Incoherent digital holography with two polarization-sensitive phase-only spatial light modulators and reduced number of exposures

I propose methods for reducing the number of exposures in incoherent digital holography with two polarization-sensitive phase-only spatial light modulators (IDH with TPP-SLMs). In IDH with TPP-SLMs, no polarization filters are required, and not only three-dimensional (3D), but polarization information is also obtained. However, seven exposures are required to conduct filter-free polarimetric incoherent holography. In this article, the optical designs and modified phase-shifting interferometry to reduce the number of recordings are described. IDH with TPP-SLMs has the potential for filter-free single-shot multidimensional incoherent holographic imaging.

General phase-difference imaging of incoherent digital holography

The hologram formed by incoherent holography based on self-interference should preserve the phase difference information of the object, such as the phase difference between the mutually orthogonal polarizations of anisotropic object. How to decode this phase difference from this incoherent hologram, i.e., phase-difference imaging, is of great significance for studying the properties of the measured object. However, there is no general phase-difference imaging theory due to both diverse incoherent holography systems and the complicated reconstruction process from holograms based on the diffraction theory. To realize phase-difference image in incoherent holography, the relationship between the phase difference of the object and the image reconstructed by holograms is derived using a general physical model of incoherent holographic systems, and then the additional phase that will distort this relationship in actual holographic systems is analyzed and eliminated. Finally, the phase-difference imaging that is suitable for the most incoherent holographic systems is realized and the general theory is experimentally verified. This technology can be applied to phase-difference imaging of anisotropic objects, and has potential applications in materials science, biomedicine, polarized optics and other fields.

Nonlinear edge enhancement imaging based on Laguerre-Gaussian superimposed vortex filters

Nonlinear reconstruction, which is based on the principle of cross correlation, is a commonly employed reconstruction technique in incoherent correlated digital holography systems. However, the modulation of phase masks in these systems is suppressed during the reconstruction process, resulting in an inability to express the characteristics of the phase masks. Consequently, achieving edge enhancement within these systems is constrained. We propose a nonlinear reconstruction method utilizing Laguerre-Gaussian superimposed vortex filters, which modulates the spectrum of the target during the reconstruction process. Experimental results demonstrate that this method performs well in reconstructing image edges for various phase-masked incoherent imaging systems and effectively suppresses noise. Additionally, this method enables directional edge enhancement.

Edge enhancement in three-dimensional vortex imaging based on FINCH by Bessel-like spiral phase modulation

Edge enhancement, as an important part of image processing, has played an essential role in amplitude-contrast and phase-contrast object imaging. The edge enhancement of three-dimensional (3D) vortex imaging has been successfully implemented by Fresnel incoherent correlation holography (FINCH), but the background noise and image contrast effects are still not satisfactory. To solve these issues, the edge enhancement of FINCH by employing Bessel-like spiral phase modulation is proposed and demonstrated. Compared with the conventional spiral phase modulated FINCH, the proposed technique can achieve high-quality edge enhancement 3D vortex imaging with lower background noise, higher contrast and resolution. The significantly improved imaging quality is mainly attributed to the effective sidelobes' suppression in the generated optical vortices with the Bessel-like modulation technique. Experimental results of the small circular aperture, resolution target, and the Drosophila melanogaster verify its excellent imaging performance. Moreover, we also proposed a new method for selective edge enhancement of 3D vortex imaging by breaking the symmetry of the spiral phase in the algorithmic model of isotropic edge enhancement. The reconstructed images of the circular aperture show that the proposed method is able to enhance the edges of the given objects selectively in any desired direction.

3D incoherent imaging using an ensemble of sparse self-rotating beams

Interferenceless coded aperture correlation holography (I-COACH) is one of the simplest incoherent holography techniques. In I-COACH, the light from an object is modulated by a coded mask, and the resulting intensity distribution is recorded. The 3D image of the object is reconstructed by processing the object intensity distribution with the pre-recorded 3D point spread intensity distributions. The first version of I-COACH was implemented using a scattering phase mask, which makes its implementation challenging in light-sensitive experiments. The I-COACH technique gradually evolved with the advancement in the engineering of coded phase masks that retain randomness but improve the concentration of light in smaller areas in the image sensor. In this direction, I-COACH was demonstrated using weakly scattered intensity patterns, dot patterns and recently using accelerating Airy patterns, and the case with accelerating Airy patterns exhibited the highest SNR. In this study, we propose and demonstrate I-COACH with an ensemble of self-rotating beams. Unlike accelerating Airy beams, self-rotating beams exhibit a better energy concentration. In the case of self-rotating beams, the uniqueness of the intensity distributions with depth is attributed to the rotation of the intensity pattern as opposed to the shifts of the Airy patterns, making the intensity distribution stable along depths. A significant improvement in SNR was observed in optical experiments.

Live Cell Light Sheet Imaging with Low- and High-Spatial-Coherence Detection Approaches Reveals Spatiotemporal Aspects of Neuronal Signaling

Light sheet microscopy in live cells requires minimal excitation intensity and resolves three-dimensional (3D) information rapidly. Lattice light sheet microscopy (LLSM) works similarly but uses a lattice configuration of Bessel beams to generate a flatter, diffraction-limited z-axis sheet suitable for investigating subcellular compartments, with better tissue penetration. We developed a LLSM method for investigating cellular properties of tissue in situ. Neural structures provide an important target. Neurons are complex 3D structures, and signaling between cells and subcellular structures requires high resolution imaging. We developed an LLSM configuration based on the Janelia Research Campus design or in situ recording that allows simultaneous electrophysiological recording. We give examples of using LLSM to assess synaptic function in situ. In presynapses, evoked Ca²⁺ entry causes vesicle fusion and neurotransmitter release. We demonstrate the use of LLSM to measure stimulus-evoked localized presynaptic Ca²⁺ entry and track synaptic vesicle recycling. We also demonstrate the resolution of postsynaptic Ca²⁺ signaling in single synapses. A challenge in 3D imaging is the need to move the emission objective to maintain focus. We have developed an incoherent holographic lattice light-sheet (IHLLS) technique to replace the LLS tube lens with a dual diffractive lens to obtain 3D images of spatially incoherent light diffracted from an object as incoherent holograms. The 3D structure is reproduced within the scanned volume without moving the emission objective. This eliminates mechanical artifacts and improves temporal resolution. We focus on LLS and IHLLS applications and data obtained in neuroscience and emphasize increases in temporal and spatial resolution using these approaches.

Deep learning-based incoherent holographic camera enabling acquisition of real-world holograms for holographic streaming system

While recent research has shown that holographic displays can represent photorealistic 3D holograms in real time, the difficulty in acquiring high-quality real-world holograms has limited the realization of holographic streaming systems. Incoherent holographic cameras, which record holograms under daylight conditions, are suitable candidates for real-world acquisition, as they prevent the safety issues associated with the use of lasers; however, these cameras are hindered by severe noise due to the optical imperfections of such systems. In this work, we develop a deep learning-based incoherent holographic camera system that can deliver visually enhanced holograms in real time. A neural network filters the noise in the captured holograms, maintaining a complex-valued hologram format throughout the whole process. Enabled by the computational efficiency of the proposed filtering strategy, we demonstrate a holographic streaming system integrating a holographic camera and holographic display, with the aim of developing the ultimate holographic ecosystem of the future.

3D single shot lensless incoherent optical imaging using coded phase aperture system with point response of scattered airy beams

Interferenceless coded aperture correlation holography (I-COACH) techniques have revolutionized the field of incoherent imaging, offering multidimensional imaging capabilities with a high temporal resolution in a simple optical configuration and at a low cost. The I-COACH method uses phase modulators (PMs) between the object and the image sensor, which encode the 3D location information of a point into a unique spatial intensity distribution. The system usually requires a one-time calibration procedure in which the point spread functions (PSFs) at different depths and/or wavelengths are recorded. When an object is recorded under identical conditions as the PSF, the multidimensional image of the object is reconstructed by processing the object intensity with the PSFs. In the previous versions of I-COACH, the PM mapped every object point to a scattered intensity distribution or random dot array pattern. The scattered intensity distribution results in a low SNR compared to a direct imaging system due to optical power dilution. Due to the limited focal depth, the dot pattern reduces the imaging resolution beyond the depth of focus if further multiplexing of phase masks is not performed. In this study, I-COACH has been realized using a PM that maps every object point into a sparse random array of Airy beams. Airy beams during propagation exhibit a relatively high focal depth with sharp intensity maxima that shift laterally following a curved path in 3D space. Therefore, sparse, randomly distributed diverse Airy beams exhibit random shifts with respect to one another during propagation, generating unique intensity distributions at different distances while retaining optical power concentrations in small areas on the detector. The phase-only mask displayed on the modulator was designed by random phase multiplexing of Airy beam generators. The simulation and experimental results obtained for the proposed method are significantly better in SNR than in the previous versions of I-COACH.

Expanded field of view frequency-selective incoherent holography by using a triple-beam setup

We propose a new, to the best of our knowledge, method of incoherent optical frequency selection called three-pack frequency-selective incoherent holography. Compressed holography is reconstructed using phase shift intercepts and spatial transfer function convolution in the form of separation without loss of magnification or resolution. The frequency-selective reconstruction process removes the conjugate and DC terms along with the interception of the object wave. This work attempts three-dimensional reconstruction and selected-frequency phase extraction of axial slices in submicron steps, and the experimental results show the potential of the proposed method in areas such as compressed holography, extended field of view, and slice tomography.

Computational adaptive holographic fluorescence microscopy based on the stochastic parallel gradient descent algorithm

Optical aberrations introduced by sample or system elements usually degrade the image quality of a microscopic imaging system. Computational adaptive optics has unique advantages for 3D biological imaging since neither bulky wavefront sensors nor complicated indirect wavefront sensing procedures are required. In this paper, a stochastic parallel gradient descent computational adaptive optics method is proposed for high-efficiency aberration correction in the fluorescent incoherent digital holographic microscope. The proposed algorithm possesses the advantage of parallelly estimating various aberrations with fast convergence during the iteration; thus, the wavefront aberration is corrected quickly, and the original object image is retrieved accurately. Owing to its high-efficiency adaptive optimization, the proposed method exhibits better performances for a 3D sample with complex and anisotropic optical aberration. The proposed method can be a powerful tool for the visualization of dynamic events that happen inside cells or thick tissues.

Nonlinear Reconstruction of Images from Patterns Generated by Deterministic or Random Optical Masks-Concepts and Review of Research

Indirect-imaging methods involve at least two steps, namely optical recording and computational reconstruction. The optical-recording process uses an optical modulator that transforms the light from the object into a typical intensity distribution. This distribution is numerically processed to reconstruct the object's image corresponding to different spatial and spectral dimensions. There have been numerous optical-modulation functions and reconstruction methods developed in the past few years for different applications. In most cases, a compatible pair of the optical-modulation function and reconstruction method gives optimal performance. A new reconstruction method, termed nonlinear reconstruction (NLR), was developed in 2017 to reconstruct the object image in the case of optical-scattering modulators. Over the years, it has been revealed that the NLR can reconstruct an object's image modulated by an axicons, bifocal lenses and even exotic spiral diffractive elements, which generate deterministic optical fields. Apparently, NLR seems to be a universal reconstruction method for indirect imaging. In this review, the performance of NLR isinvestigated for many deterministic and stochastic optical fields. Simulation and experimental results for different cases are presented and discussed.

Three-Dimensional Incoherent Imaging Using Spiral Rotating Point Spread Functions Created by Double-Helix Beams [Invited]

In recent years, there has been a significant transformation in the field of incoherent imaging with new possibilities of compressing three-dimensional (3D) information into a two-dimensional intensity distribution without two-beam interference (TBI). Most incoherent 3D imagers without TBI are based on scattering by a random phase mask exhibiting sharp autocorrelation and low cross-correlation along the depth axis. Consequently, during reconstruction, high lateral and axial resolutions are obtained. Scattering based-Imaging requires a wasteful photon budget and is therefore precluded in many power-sensitive applications. This study develops a proof-of-concept 3D incoherent imaging method using a rotating point spread function termed 3D Incoherent Imaging with Spiral Beams (3DI²SB). The rotation speed of the point spread function (PSF) with displacement and the orbital angular momentum has been theoretically analyzed. The imaging characteristics of 3DI²SB were compared with a direct imaging system using a diffractive lens, and the proposed system exhibited a higher focal depth than the direct imaging system. Different computational reconstruction methods such as the Lucy-Richardson algorithm (LRA), non-linear reconstruction (NLR), and the Lucy-Richardson-Rosen algorithm (LRRA) were compared. While LRRA performed better than both LRA and NLR for an ideal case, NLR performed better than both under real experimental conditions. Both single plane imaging, as well as synthetic 3D imaging, were demonstrated. We believe that the proposed approach might cause a paradigm shift in the current state-of-the-art incoherent imaging, fluorescence microscopy, and astronomical imaging.

Recent progress in digital holography with dynamic diffractive phase apertures [Invited]

Digital holography with diffractive phase apertures is a hologram recording technique in which at least one of the interfering waves is modulated by a phase mask. In this review, we survey several main milestones on digital holography with dynamic diffractive phase apertures. We begin with Fresnel incoherent correlation holography (FINCH), a hologram recorder with an aperture of a diffractive lens. FINCH has been used for many applications such as 3D imaging, fluorescence microscopy, superresolution, image processing, and imaging with sectioning ability. FINCH has played an important role by inspiring other digital holography systems based on diffractive phase aperture, such as Fourier incoherent single-channel holography and coded aperture correlation holography, which also are described in this review.

Historical development of FINCH from the beginning to single-shot 3D confocal imaging beyond optical resolution [Invited]

We chronicle a 15-year development effort of Fresnel incoherent correlation holography (FINCH) since its first description to its current 3D current microscopic wide-field or confocal imaging that doubles optical resolution beyond the Rayleigh limit to about 100 nm in a single snapshot. The path from the original demonstration of FINCH [Opt. Lett.32, 912 (2007) OPLEDP0146-959210.1364/OL.32.000912] to its current picture-perfect imaging of multicolor fluorescent biological specimens and reference test patterns by fluorescence or reflected light imaging is described.

Fast Image Reconstruction Technique for Parallel Phase-Shifting Digital Holography

For incoherent and coherent digital holography, the parallel phase-shifting technique has been used to reduce the number of exposures required for the phase-shifting technique which eliminates zero-order diffraction and conjugates image components. Although the parallel phase-shifting technique can decrease the hologram recording time, the image interpolations require additional calculation time. In this study, we propose a technique that reduces the calculation time for image interpolations; this technique is based on the convolution theorem. We experimentally verified the proposed technique and compared it with the conventional technique. The proposed technique is more effective for more precise interpolation algorithms because the calculation time does not depend on the size of interpolation kernels.

Roadmap on Recent Progress in FINCH Technology

Fresnel incoherent correlation holography (FINCH) was a milestone in incoherent holography. In this roadmap, two pathways, namely the development of FINCH and applications of FINCH explored by many prominent research groups, are discussed. The current state-of-the-art FINCH technology, challenges, and future perspectives of FINCH technology as recognized by a diverse group of researchers contributing to different facets of research in FINCH have been presented.

Investigation of the effective aperture: towards high-resolution Fresnel incoherent correlation holography

Fresnel incoherent correlation holography (FINCH) shows great advantages of coherent-light-source-free, high lateral resolution, no scanning, and easy integration, and has exhibited great potential in recording three-dimensional information of objects. Despite the rapid advances in the resolution of the FINCH system, little attention has been paid to the influence of the effective aperture of the system. Here, the effective aperture of the point spread function (PSF) has been investigated both theoretically and experimentally. It is found that the effective aperture is mainly restricted by the aperture of the charge-coupled device (CCD), the pixel size of the CCD, and the actual aperture of the PSF at different recording distances. It is also found that the optimal spatial resolution exists only for a small range of recording distance, while this range would become smaller as the imaging wavelength gets longer, leading to the result that the optimal spatial resolution is solely determined by the actual aperture of the PSF. By further combining the FINCH system with a microscopy system and optimizing the recording distance, a spatial resolution as high as 0.78 μm at the wavelength of 633 nm has been obtained, enabling a much higher quality imaging of unstained living biological cells compared to the commercial optical microscope. The results of this work may provide some helpful insights into the design of high-resolution FINCH systems and pave the way for their application in biomedical imaging.

Spatio-temporal performance in an incoherent holography lattice light-sheet microscope (IHLLS)

We propose an Incoherent holography detection technique for lattice light-sheet (IHLLS) systems for 3D imaging without moving either the sample stage or the detection microscope objective, providing intrinsic instrumental simplicity and high accuracy when compared to the original LLS schemes. The approach is based on a modified dual-lens Fresnel Incoherent Correlation Holography technique to produce a complex hologram and to provide the focal distance needed for the hologram reconstruction. We report such an IHLLS microscope, including characterization of the sensor performance, and demonstrate a significant contrast improvement on beads and neuronal structures within a biological test sample as well as quantitative phase imaging. The IHLLS has similar or better transverse performances when compared to the LLS technique. In addition, the IHLLS allows for volume reconstruction from fewer z-galvo displacements, thus facilitating faster volume acquisition.

Incoherent digital holography simulation based on scalar diffraction theory

Incoherent digital holography (IDH) enables passive 3D imaging through the self-interference of incoherent light. IDH imaging properties are dictated by the numerical aperture and optical layout in a complex manner [Opt. Express27, 33634 (2019)OPEXFF1094-408710.1364/OE.27.033634]. We develop an IDH simulation model to provide insight into its basic operation and imaging properties. The simulation is based on the scalar diffraction theory. Incoherent irradiance and self-interference holograms are numerically represented by the intensity-based summation of each propagation through finite aperture optics from independent point sources. By comparing numerical and experimental results, the applicability, accuracy, and limitation of the simulation are discussed. The developed simulation would be useful in optimizing the IDH setup.

Coherence aperture restricted spatial resolution for an arbitrary depth plane in incoherent digital holography

Incoherent digital holography (IDH) requires no spatial coherence; however, it requires high temporal coherence for a light source to capture holograms with high spatial resolution. Temporal coherence is often enhanced with a bandpass filter, reducing the light utilization efficiency. Thus, there is a trade-off between spatial resolution and light utilization efficiency. In this paper, we derive a relationship between spatial resolution and temporal coherence by including a conceptual aperture, determined by temporal coherence, in our previous theory of spatial resolution for arbitrary depth planes [Opt. Express27, 33634 (2019)OPEXFF1094-408710.1364/OE.27.033634]. Experimental evaluations verified the effectiveness of our theory, which is useful for the optimization of IDH setups and avoiding the trade-off.

Edge and Contrast Enhancement Using Spatially Incoherent Correlation Holography Techniques

Image enhancement techniques (such as edge and contrast enhancement) are essential for many imaging applications. In incoherent holography techniques such as Fresnel incoherent correlation holography (FINCH), the light from an object is split into two, each of which is modulated differently from one another by two different quadratic phase functions and coherently interfered to generate the hologram. The hologram can be reconstructed via a numerical backpropagation. The edge enhancement procedure in FINCH requires the modulation of one of the beams by a spiral phase element and, upon reconstruction, edge-enhanced images are obtained. An optical technique for edge enhancement in coded aperture imaging (CAI) techniques that does not involve two-beam interference has not been established yet. In this study, we propose and demonstrate an iterative algorithm that can yield from the experimentally recorded point spread function (PSF), a synthetic PSF that can generate edge-enhanced reconstructions when processed with the object hologram. The edge-enhanced reconstructions are subtracted from the original reconstructions to obtain contrast enhancement. The technique has been demonstrated on FINCH and CAI methods with different spectral conditions.

Phase-difference imaging based on FINCH

The diffraction theory was used to calculate the point spread function (PSF) of a typical Fresnel incoherent correlation holography (FINCH) system. It was found that the phase of the reconstructed image corresponds to the phase difference between the original points in two mutually perpendicular polarization directions. The experimental results show that the FINCH system with reasonable parameters can realize the phase-difference imaging of objects and measure the phase difference of cross-polarization directions in birefringent materials.

Single shot holographic super-resolution microscopy

An exceptionally simple and versatile advance in super-resolution microscopy has been created by adding a new birefringent FINCH holographic lens system including an inexpensive uncooled CMOS camera to a standard microscope. Resolution, after only a single image capture, is equivalent to or better than other more complex popular methods such as SIM, Airyscan and a number of image scanning microscopy methods that boost resolution about two-fold. This new FINCH implementation uniquely works for any objective power and NA and is solid state, fast, and calibration-free. In addition to being as easy to operate and maintain as a standard fluorescence microscope, it can uniquely create super-resolved images with any type or wavelength of light including fluorescence, bioluminescence or reflected light because its principle depends only on emitted light from objects and requires no prior training or knowledge about the sample being imaged. This microscope technique increases the utility and availability of super-resolution microscopy for any user in any research lab.

Comparative study on resolution enhancements in fluorescence-structured illumination Fresnel incoherent correlation holography

Fresnel incoherent correlation holography (FINCH) is a new approach for incoherent holography, which also has enhancement in the transverse resolution. Structured illumination microscopy (SIM) is another promising super-resolution technique. SI-FINCH, the combination of SIM and FINCH, has been demonstrated lately for scattering objects. In this study, we extended the application of SI-FINCH toward fluorescent microscopy. We have built a versatile multimodal microscopy system that can obtain images of four different imaging schemes: conventional fluorescence microscopy, FINCH, SIM, and SI-FINCH. Resolution enhancements were demonstrated by comparing the point spread functions (PSFs) of the four different imaging systems by using fluorescence beads of 1-μm diameter.

Interferenceless coded aperture correlation holography with synthetic point spread holograms

Lensless, interferenceless coded aperture correlation holography (LI-COACH) is an incoherent computational optical technique for three-dimensional (3D) imaging. In direct imaging, the image of the object is generated by a lens, whereas the LI-COACH is an indirect imaging technique that consists of two steps: one-time point spread hologram (PSH) training and then many times imaging of multiple-point objects. In the one-time training step, a point object moves in the object space along the optical axis. Light emitted from the point is modulated by a quasi-random phase mask, and the PSH library is recorded. In the imaging step, an object is mounted within the axial boundaries of the PSH library, and the object holograms are recorded using the same quasi-random phase masks. The 3D image of the object is reconstructed by the cross correlation of the object holograms with the PSH library. In this study, the entire PSH library is digitally synthesized from a single PSH, recorded at one plane only. The recorded PSH is scaled by magnification factors corresponding to the various axial planes. The reconstruction results from the synthetic PSH library are comparable with those from the recorded PSH library. The proposed approach can reduce the time of the training step in LI-COACH.

What about computational super-resolution in fluorescence Fourier light field microscopy?

Recently, Fourier light field microscopy was proposed to overcome the limitations in conventional light field microscopy by placing a micro-lens array at the aperture stop of the microscope objective instead of the image plane. In this way, a collection of orthographic views from different perspectives are directly captured. When inspecting fluorescent samples, the sensitivity and noise of the sensors are a major concern and large sensor pixels are required to cope with low-light conditions, which implies under-sampling issues. In this context, we analyze the sampling patterns in Fourier light field microscopy to understand to what extent computational super-resolution can be triggered during deconvolution in order to improve the resolution of the 3D reconstruction of the imaged data.

Randomly Multiplexed Diffractive Lens and Axicon for Spatial and Spectral Imaging

A new hybrid diffractive optical element (HDOE) was designed by randomly multiplexing an axicon and a Fresnel zone lens. The HDOE generates two mutually coherent waves, namely a conical wave and a spherical wave, for every on-axis point object in the object space. The resulting self-interference intensity distribution is recorded as the point spread function. A library of point spread functions are recorded in terms of the different locations and wavelengths of the on-axis point objects in the object space. A complicated object illuminated by a spatially incoherent multi-wavelength source generated an intensity pattern that was the sum of the shifted and scaled point spread intensity distributions corresponding to every spatially incoherent point and wavelength in the complicated object. The four-dimensional image of the object was reconstructed using computer processing of the object intensity distribution and the point spread function library.

Resolution-enhanced imaging using interferenceless coded aperture correlation holography with sparse point response

Interferenceless coded aperture correlation holography (I-COACH) is a non-scanning, motionless, incoherent digital holography technique. In this study we use a special type of I-COACH in which its point spread hologram (PSH) is ensemble of sparse dots. With this PSH an imaging resolution beyond the classic diffraction limit is demonstrated. This resolution improvement is achieved due to the position of the coded aperture between the object and the lens-based imaging system. The coded aperture scatters part of the light, that otherwise is blocked by the system aperture, into the optical system, and by doing that, extends the effective numerical aperture of the system. The use of sparse PSH increases the signal-to-noise ratio of the entire imaging system. A lateral resolution enhancement by a factor of about 1.6 was noted in the case of I-COACH compared to direct imaging.

Optimized reconstruction with noise suppression for interferenceless coded aperture correlation holography

A modified nonlinear reconstruction technique with a noise modulation parameter is proposed for interferenceless coded aperture correlation holography (I-COACH), and thus the signal-to-noise ratio of a reconstructed image is improved without sacrifice of the field of view and temporal resolution of the system. In order to obtain the optimal reconstructed image, no-reference structural sharpness (NRSS) is introduced as the evaluation metric of reconstructed image quality during nonlinear reconstruction. On the other hand, the noise modulation function is built in order to analyze the effect of phase on noise when the amplitude of the point spread hologram and object hologram is unity of 1. Both the NRSS and noise modulation functions are combined with nonlinear reconstruction in I-COACH for improving imaging performance. The validities of the proposed method under different experimental conditions have been demonstrated by experiments.

Analysis of three-dimensional mapping problems in incoherent digital holography

Self-interference digital holography (SIDH) and Fresnel incoherent correlation holography (FINCH) are recently introduced holographic imaging schemes to record and reconstruct three-dimensional (3-D) information of objects by using incoherent light. Unlike conventional holography, a reference wave in incoherent holography is not predetermined by an experimental setup, but changes with target objects in incoherent holography. This makes the relation between the 3-D position information of an object and those stored in a measured hologram quite complicated. In this paper, we provide simple analytic equations for an effective 3D mapping between object space and the image space in incoherent holography. We have validated our proposed method with numerical simulations and off-axis SIDH experiments.

Sampling requirements and adaptive spatial averaging for incoherent digital holography

Incoherent digital holography (IDH) enables passive 3D imaging under spatially incoherent light; however, the reconstructed images are seriously affected by detector noise. Herein, we derive theoretical sampling requirements for IDH to reduce this noise via simple postprocessing based on spatial averaging. The derived theory provides a significant insight that the sampling requirements vary depending on the recording geometry. By judiciously choosing the number of pixels used for spatial averaging based on the proposed theory, noise can be reduced without losing spatial resolution. We then experimentally verify the derived theory and show that the associated adaptive spatial averaging technique is a practical and powerful way of improving 3D image quality.

Common-path off-axis incoherent Fourier holography with a maximum overlapping interference area

In this Letter, we present a new method for recording spatially incoherent common-path off-axis Fourier holograms. This method records the three-dimensional (3D) information of an object into a Fourier hologram without the need of any mechanical scanning with incoherent illumination. The proposed setup consists of two gratings to form a common-path configuration, and two customized cells to create a rotational and radial shearing interferometer. While the first grating is placed on the first image plane, the second grating shifts axially from the second image plane to build off-axis geometry. A lens is used to combine two beams to generate the maximum overlapping area at the hologram plane. Proof-of-concept experiments confirm the ability of such a system to achieve the maximum overlapping interference area, stability of the system against the vibration of surrounding environment, numerical reconstruction using only one fast Fourier transform, and 3D capability to capture a 3D object illuminated by an LED light.

Pixel super-resolution for lens-free holographic microscopy using deep learning neural networks

Lens-free holographic microscopy (LFHM) provides a cost-effective tool for large field-of-view imaging in various biomedical applications. However, due to the unit optical magnification, its spatial resolution is limited by the pixel size of the imager. Pixel super-resolution (PSR) technique tackles this problem by using a series of sub-pixel shifted low-resolution (LR) lens-free holograms to form the high-resolution (HR) hologram. Conventional iterative PSR methods require a large number of measurements and a time-consuming reconstruction process, limiting the throughput of LFHM in practice. Here we report a deep learning-based PSR approach to enhance the resolution of LFHM. Compared with the existing PSR methods, our neural network-based approach outputs the HR hologram in an end-to-end fashion and maintains consistency in resolution improvement with a reduced number of LR holograms. Moreover, by exploiting the resolution degradation model in the imaging process, the network can be trained with a data set synthesized from the LR hologram itself without resorting to the HR ground truth. We validated the effectiveness and the robustness of our method by imaging various types of samples using a single network trained on an entirely different data set. This deep learning-based PSR approach can significantly accelerate both the data acquisition and the HR hologram reconstruction processes, therefore providing a practical solution to fast, lens-free, super-resolution imaging.

Superresolution beyond the diffraction limit using phase spatial light modulator between incoherently illuminated objects and the entrance of an imaging system

We present a superresolution technique for imaging objects beyond the diffraction limit imposed by the limited numerical aperture (NA) of a general optical system. A coded phase mask (CPM) displayed on a spatial light modulator is introduced between the object and the input aperture of an ordinary lens-based imaging system. Consequently, the effective NA is increased beyond the inherent NA of the optical imaging system. Unlike conventional systems, the imaging in our proposed method is not direct from an object to a sensor, and the system requires a one-time calibration. In the calibration mode, a point object is mounted in the object plane, and the point spread intensity pattern is recorded. Following the calibration, the system is ready for imaging an arbitrary number of 2D objects. The intensity pattern from any object placed at the same axial location of the point object, and modulated by the same CPM, is recorded once by a digital camera. The superresolved image of the object is reconstructed by a nonlinear cross-correlation between the abovementioned two intensity patterns. The effective NA and the new resolution limit can be tuned by changing the scattering degree of the CPM.

Bimodal Incoherent Digital Holography for Both Three-Dimensional Imaging and Quasi-Infinite-Depth-of-Field Imaging

Although three-dimensional (3D) imaging and extended depth-of-field (DOF) imaging are completely opposite techniques, both provide much more information about 3D scenes and objects than does traditional two-dimensional imaging. Therefore, these imaging techniques strongly influence a wide variety of applications, such as broadcasting, entertainment, metrology, security and biology. In the present work, we derive a generalised theory involving incoherent digital holography to describe both 3D imaging and quasi-infinite-DOF (QIDOF) imaging, which allows us to comprehensively discuss the functions of each imaging technique. On the basis of this theory, we propose and develop a bimodal incoherent digital holography system that allows both 3D imaging and QIDOF imaging. The proposed system allows imaging objects using spatially incoherent light and reconstructing 3D images or QIDOF images solely by changing the phase pattern of a spatial light modulator and without requiring mechanical adjustments or any other modifications to the setup. As a proof-of-principle experiment, we evaluate the DOF and record holograms of a reflective object with the proposed system. The experimental results show that the generalised theory is effective; our demonstration platform provides the function of 3D and QIDOF imaging.

Review of 3D Imaging by Coded Aperture Correlation Holography (COACH)

Coded aperture correlation holography (COACH) is a relatively new technique to record holograms of incoherently illuminated scenes. In this review, we survey the main milestones in the COACH topic from two main points of view. First, we review the prime architectures of optical hologram recorders in the family of COACH systems. Second, we discuss some of the key applications of these recorders in the field of imaging in general, and for 3D super-resolution imaging, partial aperture imaging, and seeing through scattering medium, in particular. We summarize this overview with a general perspective on this research topic and its prospective directions.

Resolution enhancement in nonlinear interferenceless COACH with point response of subdiffraction limit patterns

Interferenceless coded aperture correlation holography (I-COACH) is a non-scanning, motionless, incoherent digital holography technique for 3D imaging. The lateral and axial resolutions of I-COACH are equivalent to those of conventional direct imaging with the same numerical aperture. The main component of I-COACH is a coded phase mask (CPM) used as the system aperture. In this study, the CPM has been engineered using a modified Gerchberg-Saxton algorithm to generate a random distribution of subdiffraction spot arrays on the digital camera as a system response to a point source illumination. A library of point object holograms is created to calibrate the system for imaging different lateral sections of a 3D object. An object is placed within the calibrated 3D space and an object hologram is recorded with the same CPM. The various planes of the object are reconstructed by a non-linear cross-correlation between the object hologram and the point object hologram library. A lateral resolution enhancement of about 25% was noted in the case of I-COACH compared to direct imaging.

Subwavelength resolution Fourier ptychography with hemispherical digital condensers

Fourier ptychography (FP) is a promising computational imaging technique that overcomes the physical space-bandwidth product (SBP) limit of a conventional microscope by applying angular-varied illuminations. However, to date, the effective imaging numerical aperture (NA) achievable with a commercial LED board is still limited to the range of 0.3-0.7 with a 4 × /0.1NA objective due to the geometric constraint with the declined illumination intensities and attenuated signal-to-noise ratio (SNR). Thus the highest achievable half-pitch resolution is usually constrained between 500-1000 nm, which cannot meet the requirements of high-resolution biomedical imaging applications. Although it is possible to improve the resolution by using a high-NA objective lens, the FP approach is less appealing as the decrease of field-of-view (FOV) will far exceed the improvement of spatial resolution in this case. In this paper, we initially present a subwavelength resolution Fourier ptychography (SRFP) platform with a hemispherical digital condenser to provide high-angle programmable plane-wave illuminations of 0.95NA, attaining a 4 × /0.1NA objective with the final effective imaging performance of 1.05NA at a half-pitch resolution of 244 nm with the incident wavelength of 465 nm across a wide FOV of 14.60 mm², corresponding to a SBP of 245 megapixels. Our work provides an essential step of FP towards high-throughput imaging applications.

Non-linear adaptive three-dimensional imaging with interferenceless coded aperture correlation holography (I-COACH)

Interferenceless coded aperture correlation holography (I-COACH) is an incoherent digital holography technique for imaging 3D objects without two-wave interference. In I-COACH, the object beam is modulated by a pseudorandom coded phase mask (CPM) and propagates to the camera where its intensity pattern is recorded. The image of the object is reconstructed by a cross-correlation of the object intensity pattern with a point intensity response of the system, whereas the light from both the object and the point, are modulated by the same CPM. In order to recover the image of the object without bias level and background noise, multiple intensity recordings are necessary for both objects as well as the point object, which in turn significantly reduces the time resolution of imaging. In this study, a non-linear reconstruction technique is developed to reconstruct the image of the object with only a single camera shot. Furthermore, the proposed technique is adaptive to different experimental conditions in the sense of finding different optimal parameters for each experiment. The new method has been implemented on a regular I-COACH system in both transmission as well as reflection illumination modes.

Single-shot phase-shifting incoherent digital holography with multiplexed checkerboard phase gratings

Single-shot phase-shifting incoherent digital holography with multiplexed checkerboard phase gratings is proposed for acquiring holograms of moving objects. The gratings presented here play the following three roles: dividing the beams, modulating the curvature of spherical beams, and introducing different phase shifts. With the gratings of our proposed method, four individual holograms of a spatially incoherent light are formed on an image sensor. Therefore, it is possible to simultaneously capture four holograms and implement a phase-shifting technique. A proof-of-principle experiment was conducted to show the feasibility of the proposed method.

Extending the field of view by a scattering window in an I-COACH system

Interferenceless coded aperture correlation holography (I-COACH) is an incoherent digital holography technique developed to record and reconstruct 3D images of objects without two-wave interference. Herein, we introduce a novel technique to extend the field of view (FOV) of I-COACH beyond the limit imposed by the ratio between the finite area of the image sensor and the magnification of the optical system. Light diffracted from a point object located on the optical axis is modulated by a pseudorandom coded phase mask, and the central part of the point spread hologram (PSH) on the image sensor is recorded. The point object is shifted laterally to predetermined lateral locations in order to collect the exterior parts of the PSH. The recorded PSHs are stitched together to produce a synthetic PSH (SPSH) with an area nine times that of any individual PSH recorded by the image sensor. An object with a lateral extent beyond the FOV limit of the image sensor is placed at the same axial location as the point object, and the object hologram is recorded. The object is reconstructed by a cross-correlation between the zero-padded object hologram and the SPSH. Hence, the object parts beyond the FOV limit of the image sensor are recovered. An SPSH library is created for different axial planes, and the corresponding axial planes of the object are reconstructed.

Spatially incoherent common-path off-axis color digital holography

We describe a new method for recording spatially incoherent common-path off-axis color digital holograms. We present the theoretical and experimental evidence to demonstrate an incoherent common-path off-axis color digital holographic (ICOCH) system capable of capturing information from three-dimensional color objects under incoherent illumination, both in transmission and reflection modes. Fresnel incoherent correlation holography (FINCH), a common-path system, is a frequently used incoherent holography technique. Our proposed system is conceptually similar to an advanced form of FINCH; moreover, it has three advantages over this advanced form of FINCH. First, removal of the spatial light modulator makes our system simpler and more cost-effective. Second, removal of the polarizer or analyzer allows for greater light throughput. Third, the off-axis optical configuration enables separation of zero-order and twin images with only a single exposure per color rather than requiring three exposures per color for in-line holography FINCH. Therefore, we believe that this simple and cost-effective system with high light throughput can acquire incoherent holograms for different colors involving single exposure for each color, which makes the ICOCH system suitable for many applications.

Axial localization using time reversal multiple signal classification in optical scanning holography

This paper presents a method to identify the axial location of targets in an optical scanning holography (OSH) system. By combining time reversal (TR) technique with the multiple signal classification (MUSIC) method in OSH, axial location can be detected with high resolution. Both simulation and experimental work have been carried out to verify the feasibility of the proposed work.

Single camera shot interferenceless coded aperture correlation holography

We propose a new scheme for recording an incoherent digital hologram by a single camera shot. The method is based on a motionless, interferenceless, coded aperture correlation holography for 3D imaging. Two random-like coded phase masks (CPMs) are synthesized using the Gerchberg-Saxton algorithm with two different initial random phase profiles. The two CPMs are displayed side by side and used as the system aperture. Light from a pinhole is introduced into the system, and two impulse responses are recorded corresponding to the two CPMs. The two impulse responses are subtracted, and the resulting intensity profile is used as a reconstructing hologram. A library of reconstructing holograms is created corresponding to all possible axial locations. Following the above training stage, an object is placed within the axial limits of the library, and the intensity patterns of a single shot, corresponding to the same two CPMs, are recorded under identical conditions to generate the object hologram. The image of the object at any plane is reconstructed by a cross-correlation between the object hologram and the corresponding reconstructing hologram from the library.

Incoherent digital holograms acquired by interferenceless coded aperture correlation holography system without refractive lenses

We present a lensless, interferenceless incoherent digital holography technique based on the principle of coded aperture correlation holography. The acquired digital hologram by this technique contains a three-dimensional image of some observed scene. Light diffracted by a point object (pinhole) is modulated using a random-like coded phase mask (CPM) and the intensity pattern is recorded and composed as a point spread hologram (PSH). A library of PSHs is created using the same CPM by moving the pinhole to all possible axial locations. Intensity diffracted through the same CPM from an object placed within the axial limits of the PSH library is recorded by a digital camera. The recorded intensity this time is composed as the object hologram. The image of the object at any axial plane is reconstructed by cross-correlating the object hologram with the corresponding component of the PSH library. The reconstruction noise attached to the image is suppressed by various methods. The reconstruction results of multiplane and thick objects by this technique are compared with regular lens-based imaging.

Low photon count based digital holography for quadratic phase cryptography

Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.

Interferenceless coded aperture correlation holography-a new technique for recording incoherent digital holograms without two-wave interference

Recording digital holograms without wave interference simplifies the optical systems, increases their power efficiency and avoids complicated aligning procedures. We propose and demonstrate a new technique of digital hologram acquisition without two-wave interference. Incoherent light emitted from an object propagates through a random-like coded phase mask and recorded directly without interference by a digital camera. In the training stage of the system, a point spread hologram (PSH) is first recorded by modulating the light diffracted from a point object by the coded phase masks. At least two different masks should be used to record two different intensity distributions at all possible axial locations. The various recorded patterns at every axial location are superposed in the computer to obtain a complex valued PSH library cataloged to its axial location. Following the training stage, an object is placed within the axial boundaries of the PSH library and the light diffracted from the object is once again modulated by the same phase masks. The intensity patterns are recorded and superposed exactly as the PSH to yield a complex hologram of the object. The object information at any particular plane is reconstructed by a cross-correlation between the complex valued hologram and the appropriate element of the PSH library. The characteristics and the performance of the proposed system were compared with an equivalent regular imaging system.

Coded aperture correlation holography system with improved performance [Invited]

Coded aperture correlation holography (COACH) is a recently introduced technique for recording incoherent digital holograms of general three-dimensional scenes. In COACH, a random-like coded phase mask (CPM) is used as a coded aperture. Even though the CPM is optimized to reduce background noise, there is still a substantial amount of noise, mitigating the performance of COACH. In order to reduce the noise, we first modify the hologram reconstruction method. Instead of computing the correlation between a complex hologram of the entire object and a hologram of a source point, in this study the numerical correlation is performed with a phase-only filter. In other words, the phase function of the Fourier transform of the source point hologram is used as the spatial filter in the correlation process. Furthermore, we propose and demonstrate two additional methods for reducing the background noise in COACH. The first is based on the integration of a quadratic phase function, as used in Fresnel incoherent correlation holography (FINCH), with the CPM of COACH. This hybrid COACH-FINCH system enables a dynamic trade-off between the amount of background noise and the axial resolution of the system. The second method is employed by recording COACH holograms with multiple independent CPMs and averaging over the reconstructed images. The results of the above two techniques are compared with FINCH and with a regular imaging system.