Off-axis Holograms Research Articles

Off-axis metasurface hologram based on the principle of interference

Metasurface holograms based on flat optical devices have garnered increasing interest for their ability to miniaturize optical devices and systems. However, current off-axis metasurface holograms based on the Gerchberg-Saxton algorithm, superimpose additional phase in their design process, leading to holographic image of varying period in the reconstruction plane and an inability to create virtual images. We present an off-axis metasurface hologram created using the sparse Fourier transform method, which is based on interferometric holography theory. High-transmittance materials, such as SiO2 and Si3N4, are employed for the substrate and phase control units, respectively, operating at a wavelength of 635 nm. Numerical findings indicate that the unit cells designed achieve an average transmittance of 99.72%. Additionally, the overall transmittance of the constructed metasurface holograms reaches 80%. Furthermore, the design of the off-axis metasurface hologram effectively reproduces distinct holographic images. This study could provide an approach for designing off-axis metasurface holograms and broaden their range of applications.

Object image reconstruction: method for reconstructing images from digital off-axis holograms using a generative adversarial network

Object image reconstruction: method for reconstructing images from digital off-axis holograms using a generative adversarial network

A spatial phase-shifting method for real-space wave reconstruction of off-axis electron holograms

The Fourier transform with a side-band filter is the well-established method for reconstructing off-axis fringe-type holograms due to its ease of implementation and fast processing. However, this method works in reciprocal space and requires inversion of a side-band sub-region, which can degrade the spatial resolution of reconstructed wave compared to the original hologram. We present a new method, the spatial phase-shifting (SPS) method, for real-space wave reconstruction of off-axis electron holograms. We describe the working principles of the SPS method in analogy to the temporal phase-shifting method. We conducted both hologram simulations and experiments to evaluate its applicability and effectiveness. We compared the wave reconstruction results of the SPS and the conventional Fourier transform method, highlighting the advantages of the newly proposed SPS method. Our results demonstrate that the proposed SPS method is particularly effective for real-space wave reconstruction of small-sized hologram, providing an alternative approach to off-axis type holography wave reconstruction.

Off-axis digital lensless holographic microscopy based on spatially multiplexed interferometry.

Digital holographic microscopy (DHM) is a label-free microscopy technique that provides time-resolved quantitative phase imaging (QPI) by measuring the optical path delay of light induced by transparent biological samples. DHM has been utilized for various biomedical applications, such as cancer research and sperm cell assessment, as well as for in vitro drug or toxicity testing. Its lensless version, digital lensless holographic microscopy (DLHM), is an emerging technology that offers size-reduced, lightweight, and cost-effective imaging systems. These features make DLHM applicable, for example, in limited resource laboratories, remote areas, and point-of-care applications. In addition to the abovementioned advantages, in-line arrangements for DLHM also include the limitation of the twin-image presence, which can restrict accurate QPI. We therefore propose a compact lensless common-path interferometric off-axis approach that is capable of quantitative imaging of fast-moving biological specimens, such as living cells in flow. We suggest lensless spatially multiplexed interferometric microscopy (LESSMIM) as a lens-free variant of the previously reported spatially multiplexed interferometric microscopy (SMIM) concept. LESSMIM comprises a common-path interferometric architecture that is based on a single diffraction grating to achieve digital off-axis holography. From a series of single-shot off-axis holograms, twin-image free and time-resolved QPI is achieved by commonly used methods for Fourier filtering-based reconstruction, aberration compensation, and numerical propagation. Initially, the LESSMIM concept is experimentally demonstrated by results from a resolution test chart and investigations on temporal stability. Then, the accuracy of QPI and capabilities for imaging of living adherent cell cultures is characterized. Finally, utilizing a microfluidic channel, the cytometry of suspended cells in flow is evaluated. LESSMIM overcomes several limitations of in-line DLHM and provides fast time-resolved QPI in a compact optical arrangement. In summary, LESSMIM represents a promising technique with potential biomedical applications for fast imaging such as in imaging flow cytometry or sperm cell analysis.

Absolute testing of rotationally symmetric surfaces with computer-generated holograms

Extremely high accuracy is demanded for optics working at very short wavelength. Interferometric testing of optical aspheres or freeform surfaces requires null optics, typically computer-generated holograms (CGHs), to balance the wave aberrations. The measurement uncertainty is primarily limited by the accuracy of the test wavefront, which is predominantly influenced by the CGH and the interferometer optics. Absolute testing is fundamental to achieving accuracy much higher than that of the test wavefront through error separation. This paper presents a method for absolute testing of rotationally symmetric surfaces with CGH null optics. The basic assumption is that the off-axis hologram fabricated by raster scanning beam writing has negligible error of rotationally symmetric component due to pattern error of the CGH. Consequently, the wavefront error contributed by the CGH and the transmission flat can be completely separated from the absolute surface shape by combining the N-position method and the shift-rotation method. A theoretical model for absolute testing is proposed under the assumption. Experimental cross test is then presented to validate the method with sub-nanometer uncertainty. The assumption is further confirmed by characterizing the fabrication error of the hologram structures using a white light interferometer. Finally, the effect of noise, translation error, rotation error and eccentricity of rotation on the absolute testing is analyzed.

Fast and accurate phase processing in off-axis digital holography combining adaptive spatial filtering and an embedded GPU platform

Abstract Parallel-phase processing enables rapid phase extraction from off-axis digital holograms. To achieve fast and accurate results, the phase reconstruction processes were parallelized using improved filter algorithms and optimized programming strategies. First, an adaptive filtering method based on the Chan-Vese (CV) model which better suits parallelism was designed to extract the +1 term spectrum. We selected suitable computer unified device architecture (CUDA) libraries according to the characteristics of the key phase reconstruction steps. Acceleration technologies, such as virtual memory and shared memory, were used to improve the computational efficiency. Furthermore, we combined an improved 4f optical imaging system with an embedded graphic processing unit (GPU) platform to design a low-cost phase reconstruction system for off-axis digital holography. To verify the feasibility of our method, the reconstructed quality of the CV filtering method was estimated, and the run times of phase retrieval on the central processing unit (CPU) and embedded GPU were compared for off-axis holograms with different pixel sizes. Additionally, the dynamic fluctuation phase maps of water droplet evaporation were retrieved to demonstrate the real-time capability of the method.

Parallel two-step spatial carrier polarized phase-shifting common-path digital holography

A zero-order term causes bad effect on the phase reconstruction of off-axis holography, which can be solved by two-step carrier phase-shifting. Therefore, a common-path digital holography is proposed by using parallel two-step spatial carrier polarized phase-shifting in a 4f optical system for quantitative phase imaging. This holography is established based on a 4f optical system by inserting a 45° tilted cube polarized beamsplitter to split the horizontal and vertical polarization components in one beam. Via intentional polarization modulation, two off-axis holograms with π/2 phase-shift can be captured in one shot, so the subtraction between two holograms would cancel out the zero-order term. The phase distribution of a thin specimen can be retrieved with enhanced quality. There are two apertures at the input plane of the 4f optical system, one for object and the other for nothing, while only one polarized cube beamsplitter is inserted into a 4f optical system. Thus, this system is common-path with strong anti-noise ability and high stability, while it also has simple optical configuration and easy optical alignment. Several experimental results would be presented to demonstrate the validity of the proposed holography.

Single-shot dual-wavelength telecentric in-line-and-off-axis hybrid digital holography with non-prior reconstruction

Dual-wavelength in-line-and-off-axis hybrid digital holography (iohDH) can achieve high-resolution holographic dynamic imaging. However, it requires the prediction of the diffraction distance and the complex amplitude of the reference beam, which is time consuming and results in complications and accuracy limitations. While telecentric imaging technique can obtain nondiffractive images without predicting the diffraction distance, it also can even eliminate spherical aberration and astigmatic aberration. Therefore, a dual-wavelength telecentric iohDH is proposed to realize non-prior high-resolution reconstruction in a single shot. Employing the dual-wavelength telecentric iohDH, our approach acquires the focused in-line-and-off-axis hologram using a color camera in a single shot. In this case, we perform wavelength conversion on the phase and low-frequency information about the off-axis hologram as constraints for in-line iteration. Then, the in-line amplitude constraints are performed in the spatial and frequency domains until the algorithm converges. Compared to the state-of-the-art dual-wavelength iohDH, our approach can streamline the reconstructed processes without demanding a priori information of the diffraction distance and the complex amplitude of the reference beam. More importantly, our approach enables higher quality and efficient reconstruction under the telecentric system. We verified our approach using simulations and experiments, and the results indicate that our approach can allow the amplitude and phase reconstruction with high resolution in a single shot.

Accurate and fast autofocusing in off-axis digital holography based on step reduction search and particle swarm optimization

The accurate reconstruction distance is one of the important parameters in digital holography. Typical autofocusing methods have been proposed for digital holography to determine the focusing plane. In these methods, a series of holograms at fixed-step intervals always needed to be reconstructed and then locate the focal plane by using an evaluation function, a procedure that is very time-consuming. In this paper, an accurate and fast autofocusing method for off-axis digital holograms is proposed. The method first employs the step reduction search algorithm and the integral amplitude modulus (AMP) evaluation function with low computational effort to iteratively reduce the searching range of the focal plane. Then the particle swarm optimization (PSO) algorithm and a difference-in-amplitude (DIF) evaluation function with high sensitivity are used to accurately locate the focal plane. Numerical and experimental results show that the proposed method significantly improves the focusing plane detection accuracy and computational efficiency compared with the typical autofocusing methods.

Modal group refractive index measurement of few-mode fibers based on time-domain cross-correlation

We propose a measurement method based on the time-domain cross-correlation technique, combined with the cut-back method, enabling the measurement of group refractive indices (n g ) in few-mode fibers (FMF). A Mach–Zehnder interferometric system, equipped with high-precision and extensive range delay devices, is established. The system records off-axis holograms of spatial reference light at various delays interfering with the emitted light from the fiber under test. The interference energy is extracted from these holograms, and a time-domain mode energy curve is developed utilizing the principle of cross correlation. Optimal holograms at each of the curve peaks are used to reconstruct the modal field distribution, effectively separating and accurately identifying each mode within the FMF. By integrating the cut-back method, the n g corresponding to each mode is calculated based on the changes in group delay before and after fiber cutting. The n g of modes in the two-mode fibers was measured and the differential group delay calculated from the measurement agrees with the manufacturer’s specifications. The measured n g of a standard single-mode fiber aligns with the manufacturer’s specifications. Furthermore, the n g of the higher-order modes in four-mode fibers were measured by exciting them at different angles and validating the wave optics theory that the n g of the fiber modes is independent of the excitation angle. This method can simultaneously measure the n g of several modes in a fiber, providing support for the development and application of FMFs.

Reconstructing images of objects: method for reconstructing images from digital off-axis holograms based on a generative adversarial neural network

The reconstruction of object images that are located in 3D scene cross-sections using digital holography is described. The potential of generative adversarial networks for reconstructing cross-sections of 3D scenes composed of multiple layers of off-axis objects from holograms is investigated. Such scenes consist of a series of sections with objects that are not aligned with the camera’s axis. Digital holograms were used to reconstruct images of cross-sectional views of 3D scenes. It has been shown that the use of neural networks increases the speed and reconstruction quality, and reduces the image noise. A method for reconstructing images of objects using digital off-axis holograms and a generative adversarial neural network is proposed. The proposed method was tested on both numerically simulated and experimentally captured digital holograms. It was able to successfully reconstruct up to 8 cross-sections of a 3D scene from a single hologram. It was obtained that an average structural similarity index measure was equal to at least 0.73. Based on optically registered holograms, the method allowed us to reconstruct object image cross-sections of a 3D scene with a structural similarity index measure over cross-sections of a 3D scene of equal to 0.83. Therefore, the proposed technique provides the possibility for high-quality object image reconstruction and could be utilized in the analysis of micro- and macroobjects, including medical and biological applications, metrology, characterization of materials, surfaces, and volume media.

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

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

Dual-camera off-axis holographic particle tracking velocimetry: Development and application to air-blast swirl spray measurement

Quantifying the droplet field near the atomizer exit poses a challenge due to its three-dimensional (3D), multiscale and turbulent characteristics. An optical measurement method named dual-camera high-resolution holographic particle tracking velocimetry (DCHR-HPTV) is proposed. This method enables the extraction of near-field spatial Sauter mean diameter (SMD) distribution and three-dimensional two-component (3D-2C) velocity field, from off-axis hologram pairs with a frame interval of 6 μs, recorded using two synchronized industrial cameras and pulsed lasers. The system achieves a resolution of 9344 × 7000 pixels with an individual pixel size (dpix) of 3.2 μm. The droplet size measurement range is from 10 μm to above 500 μm with an absolute error within 3 μm. The velocity measurement range is adjustable and is set to be 0 to 38.4 m/s in this study, with errors of 0.23 m/s and 0.15 m/s for horizontal and axial components, respectively. The method is applied to investigate a spray region of 29 mm × 20 mm with a depth of 35 mm (equivalent to 20.3 cm3) at the exit of an air-blast atomizer. The spatial distribution of circumferentially integrated SMD along radial and axial directions is obtained. Statistical analysis is performed on both spatial and quantity distributions of droplet 3D-2C velocities. Concurrently acquired droplet size and velocity in the central toroidal recirculation zone (CTRZ) indicate that both the increasing air pressure and enlarged size range lead to a weakened droplet backflow motion. This method, distinguished by its large field of view and high resolution for particle velocimetry, is suited for dynamic analysis of near-nozzle droplet fields and can be employed in various testing scenarios involving 3D motion of micron-sized particles within multiscale flow fields.

A method for suppressing spectrum aliasing of off-axis digital holograms based on Kronecker interpolation and backpropagation

The research proposes a new method to solve the spectrum aliasing and improve the resolution of off-axis digital holograms based on Kronecker interpolation and backpropagation algorithms. The method suppresses the direct current (DC) image and increase the low-frequency information with Kronecker interpolation of the hologram. The size of the Fresnel reconstructed image can be controlled with the reconstruction distance, and this feature is used to select the appropriate reconstruction distance for the Fresnel amplitude reconstruction of interpolated holograms to separate the real and imaginary images. To obtain the complete first-order spectral information for the object, the amplitude of the desired image is obtained with spatial domain filtering and then inverted. Finally, the amplitude and phase of the object are reconstructed according to the angular spectrum reconstruction algorithm. The results show that the method can solve the spectrum aliasing problem of the holograms and thus improve the resolution of off-axis holograms. In addition, the background noise of the reconstructed phase is reduced because the influence of the zero-order spectrum can be completely avoided.

Carrier-frequency estimation for digital holograms of phase objects.

Accurate estimation of carrier fringe frequency is essential for the demodulation of off-axis digital holograms. The fringe frequency is often associated with the amplitude peak of the cross-term in the two-dimensional Fourier transform of a digital hologram. We point out that this definition of carrier frequency is not valid in general for holograms associated with phase objects. We examine the carrier-envelope representation for digital holograms from the viewpoint of Mandel's criterion [J. Opt. Soc. Am.57, 613 (1967)10.1364/JOSA.57.000613]. An appropriate definition of carrier frequency is observed to be the centroid of the power spectrum associated with the cross term. This definition is shown to apply uniformly to holograms associated with phase objects, is robust to noise, and leads to the smoothest (or least fluctuating) envelope representation for the demodulated object wave. The proposed definition is illustrated with simulated as well as experimentally recorded off-axis holograms.

Single-frame reconstruction by fractional Fourier-transform domain filtering in off-axis digital holographic microscopy

We propose a single-frame zero-order-eliminated reconstruction method by fractional Fourier transform filtering for an off-axis digital hologram. The filtering in the fractional Fourier transform domain of the hologram can effectively improve the reconstruction resolution, but it is required to remove its zero-order term. With the zero-order-term elimination of the Laplacian hologram, the higher reconstruction resolution of a single-frame hologram is achieved by zero-padding the hologram and choosing the optimal option of the fractional-order number. The results demonstrate that the resolutions of reconstructed amplitude and phase images are obviously improved. It will have a promising application in real-time imaging for biological cells and moving objects.

In-focus quantitative phase imaging from defocused off-axis holograms: synergistic reconstruction framework.

Digital holographic microscopy (DHM) enables the three-dimensional (3D) reconstruction of quantitative phase distributions from a defocused hologram. Traditional computational algorithms follow a sequential approach in which one first reconstructs the complex amplitude distribution and later applies focusing algorithms to provide an in-focus phase map. In this work, we have developed a synergistic computational framework to compensate for the linear tilt introduced in off-axis DHM systems and autofocus the defocused holograms by minimizing a cost function, providing in-focus reconstructed phase images without phase distortions. The proposed computational tool has been validated in defocused holograms of human red blood cells and three-dimensional images of dynamic sperm cells.

Simultaneous dual-wavelength digital holographic microscopy as a tool for the analysis of keratoacanthoma skin samples

A keratoacanthoma (KA) skin tumor is usually caused by sun exposure and may be an alert sign prior to the development of a more aggressive tumor or skin cancer. Studying the shape of the KA cells and their 3D rendering visualization are important parameters to prevent its evolution to higher stages of tumor cells or skin cancer. KA cells shape can be obtained through digital holographic microscopy; for that purpose, a setup with two illumination wavelengths (532 and 638 nm) is implemented to render a synthetic wavelength of 3.2 μm that avoids wrapping the optical phase of the processed holograms and increases measurement range. To recover the optical phase, two off-axis digital holograms are simultaneously recorded at each wavelength. From the processed hologram height variations, the shape and length of KA cells, as well as the stratum corneum epidermal layer, are obtained as phase images. The results achieved aid to discriminate healthy from malignant cells.

Single-shot experimental-numerical twin-image removal in lensless digital holographic microscopy

Lensless digital holographic microscopy (LDHM) offers very large field of view label-free imaging crucial, e.g., in high-throughput particle tracking and biomedical examination of cells and tissues. Compact layouts promote point-of-case and out-of-laboratory applications. The LDHM, based on the Gabor in-line holographic principle, is inherently spoiled by the twin-image effect, which complicates the quantitative analysis of reconstructed phase and amplitude maps. Popular family of solutions consists of numerical methods, which tend to minimize twin-image upon iterative process based on data redundancy. Additional hologram recordings are needed, and final results heavily depend on the algorithmic parameters, however. In this contribution we present a novel single-shot experimental-numerical twin-image removal technique for LDHM. It leverages two-source off-axis hologram recording deploying simple fiber splitter. Additionally, we introduce a novel phase retrieval numerical algorithm specifically tailored to the acquired holograms, that provides twin-image-free reconstruction without compromising the resolution. We quantitatively and qualitatively verify proposed method employing phase test target and cheek cells biosample. The results demonstrate that the proposed technique enables low-cost compact LDHM imaging with enhanced precision, achieved through the elimination of twin-image errors. This advancement opens new avenues for more accurate technical and biomedical imaging applications using LDHM, particularly in scenarios where cost-effective and portable imaging solutions are desired.

High-resolution reconstruction of spectrum-overlapped off-axis holography by deflecting reference beam of Gaussian symmetry

In digital holography, extracting the +1-order spectrum accurately and making full utilization of the spatial bandwidth of the CCD sensor are essential for high-resolution and artifacts-free quantitative phase imaging. In this paper, using the light intensity symmetry of the Gaussian laser beam, we delicately eliminate the zero-order spectrum by means of subtraction of two off-axis hologram spectra acquired by symmetrically deflecting the reference beam. Therefore, the +1-order spectrum can be extracted accurately even if it is completely overlapped with the zero-order spectrum. Compared with phase-shifting methods, such as pi-phase and random phase, which require accurate control or calculation of the phase-shifting amount, this proposed method does not need to precisely control the deflection angle of reference beam. Being achievable the maximum utilization of half-space bandwidth of the CCD sensor, the proposed method has realized high-resolution imaging demonstrated by the experimental results of three specimens. This method has general applications in digital holography, such as eliminating the zero-order spectrum and extracting the +1-order spectrum.