Single-shot self-interference incoherent digital holography using off-axis configuration

Roadmap on computational methods in optical imaging and holography [invited]

Computational methods have been established as cornerstones in optical imaging and holography in recent years. Every year, the dependence of optical imaging and holography on computational methods is increasing significantly to the extent that optical methods and components are being completely and efficiently replaced with computational methods at low cost. This roadmap reviews the current scenario in four major areas namely incoherent digital holography, quantitative phase imaging, imaging through scattering layers, and super-resolution imaging. In addition to registering the perspectives of the modern-day architects of the above research areas, the roadmap also reports some of the latest studies on the topic. Computational codes and pseudocodes are presented for computational methods in a plug-and-play fashion for readers to not only read and understand but also practice the latest algorithms with their data. We believe that this roadmap will be a valuable tool for analyzing the current trends in computational methods to predict and prepare the future of computational methods in optical imaging and holography.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00340-024-08280-3.

Fresnel incoherent compressive holography toward 3D videography via dual-channel simultaneous phase-shifting interferometry

Fresnel incoherent correlation holography (FINCH) enables high-resolution 3D imaging of objects from several 2D holograms under incoherent light and has many attractive applications in motionless 3D fluorescence imaging. However, FINCH has difficulty implementing 3D imaging of dynamic scenes since multiple phase-shifting holograms need to be recorded for removing the bias term and twin image in the reconstructed scene, which requires the object to remain static during this progress. Here, we propose a dual-channel Fresnel noncoherent compressive holography method. First, a pair of holograms with π phase shifts obtained in a single shot are used for removing the bias term noise. Then, a physic-driven compressive sensing (CS) algorithm is used to achieve twin-image-free reconstruction. In addition, we analyze the reconstruction effect and suitability of the CS algorithm and two-step phase-shift filtering algorithm for objects with different complexities. The experimental results show that the proposed method can record hologram videos of 3D dynamic objects and scenes without sacrificing the imaging field of view or resolution. Moreover, the system refocuses images at arbitrary depth positions via computation, hence providing a new method for fast high-throughput incoherent 3D imaging.

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.

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.

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.

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.

Two-step phase-shifting interferometry for self-interference digital holography

We propose a phase-shifting interferometry technique using only two in-line phase-shifted self-interference holograms. There is no requirement for additional recording or estimation in the measurement. The proposed technique adopts a mathematical model for self-interference digital holography. The effectiveness of the proposed technique is demonstrated by experiments on incoherent digital holographic microscopy and color-multiplexed fluorescence digital holography with computational coherent superposition. Two-color-multiplexed four-step phase-shifting incoherent digital holography is realized for the first time, to the best of our knowledge, using the proposed technique.

Depth-of-field engineering in coded aperture imaging

Extending the depth-of-field (DOF) of an optical imaging system without effecting the other imaging properties has been an important topic of research for a long time. In this work, we propose a new general technique of engineering the DOF of an imaging system beyond just a simple extension of the DOF. Engineering the DOF means in this study that the inherent DOF can be extended to one, or to several, separated different intervals of DOF, with controlled start and end points. Practically, because of the DOF engineering, entire objects in certain separated different input subvolumes are imaged with the same sharpness as if these objects are all in focus. Furthermore, the images from different subvolumes can be laterally shifted, each subvolume in a different shift, relative to their positions in the object space. By doing so, mutual hiding of images can be avoided. The proposed technique is introduced into a system of coded aperture imaging. In other words, the light from the object space is modulated by a coded aperture and recorded into the computer in which the desired image is reconstructed from the recorded pattern. The DOF engineering is done by designing the coded aperture composed of three diffractive elements. One element is a quadratic phase function dictating the start point of the in-focus axial interval and the second element is a quartic phase function which dictates the end point of this interval. Quasi-random coded phase mask is the third element, which enables the digital reconstruction. Multiplexing several sets of diffractive elements, each with different set of phase coefficients, can yield various axial reconstruction curves. The entire diffractive elements are displayed on a spatial light modulator such that real-time DOF engineering is enabled according to the user needs in the course of the observation. Experimental verifications of the proposed system with several examples of DOF engineering are presented, where the entire imaging of the observed scene is done by single camera shot.

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.

Single-shot in-line Fresnel incoherent holography using a dual-focus checkerboard lens

Fresnel incoherent correlation holography (FINCH) is a technology that can acquire three-dimensional information of incoherent objects such as fluorescence with an in-line optical system. However, it is difficult to apply FINCH to dynamic phenomena, since FINCH has to detect phase-shifted holograms sequentially to eliminate twin and zero-order images. In this paper, a method in which the phase-shifted holograms can be obtained simultaneously with an in-line setup by using an optimized simulated diffraction optical element (sDOE), realized by a phase-only spatial light modulator, is proposed. The optimized sDOE is an optical device with a dual-focus lens, 2D grating, and spatial phase shifter. Therefore, the sDOE is called a dual-focus checkerboard lens. The optical experiment confirms the feasibility of the proposed method.

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.

Michelson-interferometric-configuration-based incoherent digital holography with a geometric phase shifter

The phase-shifting method is a simple and efficient approach to extract complex hologram information free of bias and twin-image noise. In this study, the geometric phase-shifting method is utilized for a self-interference incoherent digital holographic recording system based on the Michelson-type interferometer. The phase-shifting module consists of a horizontal polarizer, and two achromatic quarter-wave plates are employed inside the interferometer, replacing conventional phase-shifting devices, such as the piezo-actuated mirror. Since the phase-shifting amount of the introduced method herein is theoretical, regardless of the input wavelength, the simultaneous recording of step-wise phase-shifted interferograms for different color channels is available. Therefore, the multi-color hologram recording is achieved with fewer numbers of exposures. The demonstration of multi-color hologram recording and reconstruction are presented to validate the proposed idea.

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.

Single-shot phase-shifting image-plane digital holography with tri-focal Fibonacci-Billet split lens

Phase-shifting holography has been widely applied in the field of non-destructive testing and interference imaging. Compared to the previous single-shot phase-shifting holography, here tri-focal Fibonacci-Billet split lens was introduced into Mach-Zehnder interferometer, in which the upper half of the Fibonacci-Billet split lens can realize three phase-locking copies of the planar reference wave and the lower half is used to generate three identical copies of object. The interference pattern is recorded by a detector in one single exposure. The test object can be reconstructed by three-step phase-shifting interferometry. The corresponding experiment is carried out to verify the effectiveness of this method. With advantages of real-time reconstruction and amplitude-only diffraction lens, it is very useful for fast imaging and optical element detection.

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.

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.

Compact self-interference incoherent digital holographic camera system with real-time operation

The video recording-capable compact incoherent digital holographic camera system is proposed. The system consists of the linear polarizer, convex lens, geometric phase lens, and the polarized image sensor. The Fresnel hologram is recorded by this simple configuration in real time. The system parameters are analyzed and evaluated to record a better-quality hologram in a compact form-factor. The real-time holographic recording and its digitally reconstructed video playback are demonstrated with the proposed system.

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.

Microparticle Manipulation and Imaging through a Self-Calibrated Liquid Crystal on Silicon Display

We present in this paper a revision of three different methods we conceived in the framework of liquid crystal on silicon (LCoS) display optimization and application. We preliminarily demonstrate an LCoS self-calibration technique, from which we can perform a complete LCoS characterization. In particular, two important characteristics of LCoS displays are retrieved by using self-addressed digital holograms. On the one hand, we determine its phase-voltage curve by using the interference pattern generated by a digital two-sectorial split-lens configuration. On the other hand, the LCoS surface profile is also determined by using a self-addressed dynamic micro-lens array pattern. Second, the implementation of microparticle manipulation through optical traps created by an LCoS display is demonstrated. Finally, an LCoS display based inline (IL) holographic imaging system is described. By using the LCoS display to implement a double-sideband filter configuration, this inline architecture demonstrates the advantage of obtaining dynamic holographic imaging of microparticles independently of their spatial positions by avoiding the non-desired conjugate images.

Three-dimensional stimulation and imaging-based functional optical microscopy of biological cells

A new type of functional optical microscope system called three-dimensional (3D) stimulation and imaging-based functional optical microscopy (SIFOM) is proposed, to the best of our knowledge. SIFOM can precisely stimulate user-defined targeted biological cells and can simultaneously record the volumetric fluorescence distribution in a single acquisition. Precise and simultaneous stimulation of fluorescent-labeled biological cells is achieved by multiple 3D spots generated by digital holograms displayed on a phase-mode spatial light modulator. Single-shot 3D acquisition of the fluorescence distribution is accomplished by common-path off-axis incoherent digital holographic microscopy in which a diffraction grating with a focusing lens is displayed on another phase-mode spatial light modulator. The effectiveness of the proposed functional microscope system was verified in experiments using fluorescent microbeads and human lung cancer cells located at various defocused positions. The system can be used for manipulating the states of cells in optogenetics.

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.

Achromatic phase shifting self-interference incoherent digital holography using linear polarizer and geometric phase lens

A simple Fresnel-type self-interference incoherent digital holographic recording system is proposed. The main part of the system consists of the two linear polarizers and geometric phase lens. The geometric phase lens is employed as a polarization selective common-path interferometer. One of the polarizers is rotated by the motor and serves as a phase-shifter with the geometric phase lens, to eliminate the bias and twin image noise. A topological phase is obtained by the relative angle between the polarizer and geometric phase lens. Since this phase shifting method does not depend on the change of the optical path length, the phase shifting performance is almost constant in the broad spectral range. Using the proposed achromatic phase shifting method, a simultaneous three-color phase shifting digital hologram recording under the incoherent light source is demonstrated.

Off-axis digital holography with multiplexed volume Bragg gratings

We report on an optical imaging design based on common-path off-axis digital holography, using a multiplexed volume Bragg grating. In the reported method, a reference optical wave is made by deflection and spatial filtering through a volume Bragg grating. This design has several advantages, including simplicity, stability, and robustness against misalignment.

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.

Digital holography and its multidimensional imaging applications: a review

In this review, we introduce digital holographic techniques and recent progress in multidimensional sensing by using digital holography. Digital holography is an interferometric imaging technique that does not require an imaging lens and can be used to perform simultaneous imaging of multidimensional information, such as three-dimensional structure, dynamics, quantitative phase, multiple wavelengths and polarization state of light. The technique can also obtain a holographic image of nonlinear light and a three-dimensional image of incoherent light with a single-shot exposure. The holographic recording ability of this technique has enabled a variety of applications.

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.

Self-interference digital holography with a geometric-phase hologram lens

Self-interference digital holography (SIDH) is actively studied because the hologram acquisition under the incoherent illumination condition is available. The key component in this system is wavefront modulating optics, which modulates an incoming object wave into two different wavefront curvatures. In this Letter, the geometric-phase hologram lens is introduced in the SIDH system to perform as a polarization-sensitive wavefront modulator and a single-path beam splitter. This special optics has several features, such as high transparency, a modulation efficiency up to 99%, a thinness of a few millimeters, and a flat structure. The demonstration system is devised, and the numerical reconstruction results from an acquired complex hologram are presented.

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.

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.

Self-interference compressive digital holography with improved axial resolution and signal-to-noise ratio

Fresnel incoherent correlation holography (FINCH) was proposed to break the barrier of spatial incoherent digital holographic imaging and show the potential of super-resolution imaging preferences. We developed FINCH as a compressive sensing modality and reconstruction procedure as an inverse problem in order to realize 3D tomographic imaging. Improved axial resolution is obtained via compressive reconstruction. Reconstruction guarantees and accuracy of the proposed method are discussed. Compared with the real-valued signal operation, the signal-to-noise ratio of the results is increased when reconstructing from the complex-valued hologram obtained from the FINCH system.

Optical defocus noise suppressing by using a pinhole-polarizer in Fresnel incoherent correlation holography

We propose the method that suppresses the defocus noise optically in the Fresnel incoherent correlation holographic system using a pinhole-polarizer (PP), which is made by punching a pinhole on the linear polarizer. The system configuration of this suggestion is based on the original system with optical-sectioning capability, which is realized by presenting the phase-pinhole on the phase-only spatial light modulator. In our system, the phase-pinhole is replaced with a PP. The replaced component is no longer programmable yet provides an affordable, simple, and light-efficient system configuration. The feasibility of the system with the PP is analyzed and demonstrated.

Image recovery from defocused 2D fluorescent images in multimodal digital holographic microscopy

A technique of three-dimensional (3D) intensity retrieval from defocused, two-dimensional (2D) fluorescent images in the multimodal digital holographic microscopy (DHM) is proposed. In the multimodal DHM, 3D phase and 2D fluorescence distributions are obtained simultaneously by an integrated system of an off-axis DHM and a conventional epifluorescence microscopy, respectively. This gives us more information of the target; however, defocused fluorescent images are observed due to the short depth of field. In this Letter, we propose a method to recover the defocused images based on the phase compensation and backpropagation from the defocused plane to the focused plane using the distance information that is obtained from a 3D phase distribution. By applying Zernike polynomial phase correction, we brought back the fluorescence intensity to the focused imaging planes. The experimental demonstration using fluorescent beads is presented, and the expected applications are suggested.

Single-shot incoherent digital holography using a dual-focusing lens with diffraction gratings

A new optical configuration of incoherent digital holography is presented to improve the quality of reconstructed images when the random polarization state of incoherent light is used. The proposed system improves the signal-to-noise ratio of the holograms by suppressing the unmodulated terms of a spatial light modulator. To generate the self-interference of a quasi-incoherent point-like source, we use a dual-focusing lens with diffraction gratings. The preliminary experimental results confirm the validity of the proposed method by reconstructing two point-like sources generated by a LED light source. When the pixel pitch of the phase-mode SLM is small enough, the off-axis hologram can be generated. The single-shot recording of the incoherent digital holography is expected.

Spatially incoherent off-axis Fourier holography without using spatial light modulator (SLM)

We present a spatially incoherent dual path Fourier holographic system. Conceptually it is similar to Fourier incoherent single channel holography (FISCH). Although our incoherent off-axis Fourier holographic (IOFH) system does not have the robustness of a single channel system, it has three advantages over FISCH, with two being quite obvious from setup. First, no SLM is required, thus making the system simple and cost-effective. Second, it is capable of high light throughput because in FISCH, the use of SLM reduces light intensity in half by splitting one beam into two; furthermore, an analyzer is required to create interference which also reduces light intensity. The third advantage, which makes this IOFH system applicable even for on-axis samples (as opposed to samples in a half plane as is necessary for FISCH), is achieved by tilting one mirror. Here we demonstrate our system with a sample in half plane as in FISCH for different axial positions, and then by placing the object on an optical axis and tilting one mirror. The reconstructed images demonstrate holographic capabilities of our IOFH system for both on-axis and half plane sample locations.

Dual-wavelength digital holography with a single low-coherence light source

We propose a measurement system using dual-wavelength digital holography and low-coherence interferometry to measure micro- and nanostructure surface heights. To achieve an extended axial step-measurement range and better image quality, a single light-emitting diode generates two distinct light sources by filtering different center wavelengths and narrower bandwidths. The system can measure surface profile with higher step heights and lower speckle noise in a large field-of-view. Using single-source lighting and a simple configuration, the method supports compactly configured and lower-cost surface-topography measurement systems applicable in various fields. Experimental results for a standard step sample verify the system's performance.

Automated Fourier space region-recognition filtering for off-axis digital holographic microscopy

Automated label-free quantitative imaging of biological samples can greatly benefit high throughput diseases diagnosis. Digital holographic microscopy (DHM) is a powerful quantitative label-free imaging tool that retrieves structural details of cellular samples non-invasively. In off-axis DHM, a proper spatial filtering window in Fourier space is crucial to the quality of reconstructed phase image. Here we describe a region-recognition approach that combines shape recognition with an iterative thresholding method to extracts the optimal shape of frequency components. The region recognition technique offers fully automated adaptive filtering that can operate with a variety of samples and imaging conditions. When imaging through optically scattering biological hydrogel matrix, the technique surpasses previous histogram thresholding techniques without requiring any manual intervention. Finally, we automate the extraction of the statistical difference of optical height between malaria parasite infected and uninfected red blood cells. The method described here paves way to greater autonomy in automated DHM imaging for imaging live cell in thick cell cultures.

Three-dimensional mapping of fluorescent nanoparticles using incoherent digital holography

Three-dimensional mapping of fluorescent nanoparticles was performed by using incoherent digital holography. The positions of the nanoparticles were quantitatively determined by using Gaussian fitting of the axial- and lateral-diffraction distributions through position calibration from the observation space to the sample space. It was found that the axial magnification was constant whereas the lateral magnification linearly depended on the axial position of the fluorescent nanoparticles. The mapping of multiple fluorescent nanoparticles fixed in gelatin and a single fluorescent nanoparticle manipulated with optical tweezers in water were demonstrated.

Recording spatially incoherent Fourier hologram using dual channel rotational shearing interferometer

The method to record an incoherent Fourier hologram is proposed. The interference patterns in the dual channel rotational shearing interferometer are obtained as the figure of the cosine and the sine transformation in the vertical and the horizontal polarization, respectively. The proposed optical system is simple without spatial light modulators or mechanical phase shifting devices. The experiment, in which the letter "A" displayed on a liquid crystal display with a blue LED backlight was used as an object, confirms the proposed method to obtain an incoherent Fourier hologram.

Phase derivative method for reconstruction of slightly off-axis digital holograms

A phase derivative (PD) method is proposed for reconstruction of off-axis holograms. In this method, a phase distribution of the tested object wave constrained within 0 to pi radian is firstly worked out by a simple analytical formula; then it is corrected to its right range from -pi to pi according to the sign characteristics of its first-order derivative. A theoretical analysis indicates that this PD method is particularly suitable for reconstruction of slightly off-axis holograms because it only requires the spatial frequency of the reference beam larger than spatial frequency of the tested object wave in principle. In addition, because the PD method belongs to a pure local method with no need of any integral operation or phase shifting algorithm in process of the phase retrieval, it could have some advantages in reducing computer load and memory requirements to the image processing system. Some experimental results are given to demonstrate the feasibility of the method.

Fast reconstruction of off-axis digital holograms based on digital spatial multiplexing

A method for fast reconstruction of off-axis digital holograms based on digital multiplexing algorithm is proposed. Instead of the existed angular multiplexing (AM), the new method utilizes a spatial multiplexing (SM) algorithm, in which four off-axis holograms recorded in sequence are synthesized into one SM function through multiplying each hologram with a tilted plane wave and then adding them up. In comparison with the conventional methods, the SM algorithm simplifies two-dimensional (2-D) Fourier transforms (FTs) of four N*N arrays into a 1.25-D FTs of one N*N arrays. Experimental results demonstrate that, using the SM algorithm, the computational efficiency can be improved and the reconstructed wavefronts keep the same quality as those retrieved based on the existed AM method. This algorithm may be useful in design of a fast preview system of dynamic wavefront imaging in digital holography.