Object Wave Research Articles

Object wave retrieval using normalized holograms in three-step generalized phase-shifting digital holography.

Phase-shifting methods using interferogram normalization are often applied to smooth objects, for which the requirements for the normalization approach, including zero-order term elimination and the norm approximation condition, are easily achieved. Here we propose a three-step generalized phase-shifting method using the normalization approach for diffuse objects. In the proposed method, the zero-order terms are sufficiently suppressed by mutual subtraction of the phase-shifted holograms. The norm approximation condition is satisfied, and the complex field of the object wave can be estimated by the normalization approach when the hologram satisfies the phase randomness condition. We present an object wave retrieval algorithm using three phase-shifted holograms, in which estimation of phase-shift values is unnecessary. The proposed method is verified through simulations and optical experiments.

A tunable path-separated electron interferometer with an amplitude-dividing grating beamsplitter

We demonstrate a tunable path-separated electron interferometer using a single amplitude-dividing beamsplitter to prepare multiple spatially isolated, coherent electron probe beams. We place four electrostatic bi-prisms in the optical column of a scanning transmission electron microscope (STEM) to achieve path separations of up to 25 μm, the largest demonstrated within amplitude-division electron interferometers while maintaining fringe visibility of the directly observed interference fringes at the detector. We characterize the fringe visibility of this setup over a range of path separations and perform STEM holography to reconstruct the full object wave of a fabricated Si ramp test phase object. We report a quantitative object-wave measurement in this configuration and confirm with an independent off-axis electron holography measurement. This experimental design can potentially be applied to high-resolution phase imaging and fundamental physics experiments, such as an exploration of the electron wave packet coherence length and the Aharonov-Bohm effect.

Multiwavelength Multiplexing Hologram Designed Using Impedance Metasurfaces

We propose a method to generate microwave holograms using impedance metasurfaces for multiple simultaneous wavelengths. For recent impedance hologram designs in the microwave band, radiation from leaky waves can be controlled in the far field by creating holograms based on the interference of reference and object waves at a specific frequency. In our design, we vary only one physical dimension in the unit cell to simultaneously satisfy the requirement of impedance distribution for two frequencies in the same aperture. Two excitation ports are used to simultaneously generate the beams at 17 and 20 GHz. The simulation and measurement results show a very good agreement, confirming the validity of the proposed design method. The new low-profile holographic leaky-wave antenna has potential applications in designing multifrequency communication and radar systems.

Method for increasing the depth of field of images of flat transparencies reconstructed using synthesized holograms

The influence of the parameters used in synthesizing hologram projectors on the distribution of complex amplitude in the planes of hologram synthesis and the reconstructed image is considered. A method for increasing the depth of field of the reconstructed images is proposed and investigated. This method is based on the representation of the object wave in the synthesis of a hologram in the form of a superposition of object waves emanating from two identical objects, which are located at different distances from the plane of the hologram synthesis. The work involved mathematical modeling of the processes of synthesis and reconstruction of a hologram for the synthesis of the hologram projectors of two-dimensional binary objects for photolithography.

Wavelength-multiplexed digital holography for quantitative phase measurement using quantum dot film.

We propose an enhanced quantitative three-dimensional measurement system using wavelength-multiplexed digital holography. To simplify the configuration, a dual-peak quantum dot wavelength converter, combined with a blue LED, is adapted as a single low-coherence light source. Rather than a conventional dual-wavelength method, which records and reconstruct the object wave for each wavelength, the proposed system can capture the holograms of two wavelengths simultaneously with fewer acquisitions, simple setup, and low noise. To verify the system's performance, the measurements of the step height sample are presented.

Probing Light Atoms at Subnanometer Resolution: Realization of Scanning Transmission Electron Microscope Holography.

Atomic resolution imaging of light elements in electron-transparent materials has long been a challenge. Biomolecular materials, for example, are rapidly altered by incident electrons. We demonstrate a scanning transmission electron microscopy (STEM) technique, called STEM holography, capable of efficient structural analysis of beam-sensitive nanomaterials. STEM holography measures the absolute phase and amplitude of electrons passed through a specimen via interference with a vacuum reference wave. We use an amplitude-dividing nanofabricated grating to prepare multiple beams focused at the sample. We configure the postspecimen microscope imaging system to overlap the beams, forming an interference pattern. We record and analyze the pattern at each 2D-raster-scan-position, reconstructing the complex object wave. As a demonstration, we image gold nanoparticles on an amorphous carbon substrate at 2.4 Å resolution. STEM holography offers higher contrast of the carbon while maintaining gold atomic lattice resolution compared to high angle annular dark field STEM.

Characteristics of vibration frequency measurement based on sound field imaging by digital holography

We present the characteristics of indirect frequency measurement system based on off-axis digital holography (DH) for vibrating objects, which works on phase change characteristics of a medium where sound wave propagates. The sound field measurement method using off-axis DH already proposed by the author’s group is applied to the measurement of vibration frequency of arbitrary sound sources. In DH based sound imaging for frequency measurement, object wave passes near to vibrating object and the interference patterns are recorded in digital holograms as a function of time. After using inverse Fresnel calculation, acousto-optic data processing, and Fourier analysis, vibration frequency of an object of interest can be measured. In this paper, the measurement capability of vibration frequency for different objects and quantitative characteristics of the sound power are evaluated experimentally. The frequency range of the experimental results are from hundreds Hz to tens of kHz that covers audible range. The comparison with microphone recording and the analysis have also been carried out to check the strength and stability of the proposed scheme.

Generalized phase-shifting digital holography using normalized phase-shifted holograms

Abstract We propose a normalization method for the speckle-like holograms observed in digital holography. We show that the norm of phase-shifted holograms can be approximated by the same value, regardless of the phase shift, when the phase distribution of an object wave in a Fresnel diffraction field satisfies the randomness condition. We present an object-wave retrieval algorithm that uses normalized phase-shifted holograms to calculate the amplitude and phase of the object wave directly, without estimating phase-shift values. In addition, we develop a scheme to estimate a direct-current term by averaging several randomly phase-shifted holograms. The proposed method is verified through numerical simulations and optical experiments.

Twin-Image-Free Holography: A Compressive Sensing Approach.

Holographic reconstruction is troubled by the phase-conjugate wave front arising from Hermitian symmetry of the complex field. The so-called twin image obfuscates the reconstruction in solving the inverse problem. Here we quantitatively reveal how and how much the twin image affects the reconstruction and propose a compressive sensing (CS) approach to reconstruct a hologram completely free from the twin image. Using the canonical basis, the incoherence condition of CS is naturally satisfied by the Fourier transformation associated with wave propagation. With the propagation kernel function related to the distance, the object wave diffracts into a sharp pattern while the phase-conjugate wave diffracts into a diffuse pattern. An iterative algorithm using a total variation sparsity constraint could filter out the diffuse conjugated signal and overcome the inherent physical symmetry of holographic reconstruction. The feasibility is verified by simulation and experimental results, as well as a comparative study to an existing phase retrieval method.

Digital plasmonic holography

We demonstrate digital plasmonic holography for direct in-plane imaging with propagating surface-plasmon waves. Imaging with surface plasmons suffers from the lack of simple in-plane lenses and mirrors. Lens-less digital holography techniques, however, rely on digitally decoding an interference pattern between a reference wave and an object wave. With far-field diffractive optics, this decoding scheme provides a full recording, i.e., a hologram, of the amplitude and phase of the object wave, giving three-dimensional information from a two-dimensional recording. For plasmonics, only a one-dimensional recording is needed, and both the phase and amplitude of the propagating plasmons can be extracted for high-resolution in-plane imaging. Here, we demonstrate lens-less, point-source digital plasmonic holography using two methods to record the plasmonic holograms: a dual-probe near-field scanning optical microscope and lithographically defined circular fluorescent screens. The point-source geometry gives in-plane magnification, allowing for high-resolution imaging with relatively lower-resolution microscope objectives. These results pave the way for a new form of in-plane plasmonic imaging, gathering the full complex wave, without the need for plasmonic mirrors or lenses.

Autofocusing algorithm for a digital holographic imaging system using convolutional neural networks

Digital holographic imaging systems are promising three-dimensional imaging systems that acquire holograms via interference of a reference wave and an object wave. Using digital holography and the numerical diffraction theory, an image can be reconstructed at any distance from the hologram. However, accurate determination of the distance of the object from the hologram is required to focus the image. Various autofocusing algorithms have been studied. The conventional autofocusing algorithm creates the focused image by evaluating iteratively reconstructed images using focus metrics. Owing to the iterative image reconstruction process, the computational time is very long. In this paper, an autofocusing algorithm for a digital holographic imaging system using convolutional neural networks, similar to pattern recognition systems, is proposed. Using the proposed method, the distance of the object from the hologram is obtained more rapidly than using the conventional method.

Rough surface characterization using off-axis digital holographic microscopy compensated with self-hologram rotation

In this paper, an off-axis digital holographic microscopy compensated with self-hologram rotation is presented. The process is implemented via subtracting the unwrapped phase maps of the off-axis parabolic hologram and its rotation 180° to eliminate the tilt induced by the angle between the spherical object wave O and the plane reference wave R. Merit of the proposed method is that it can be done without prior knowledge of physical parameters and hence can reconstruct a parabolic hologram of 1024 × 768 pixels within tens of milliseconds since it doesn't require a digital reference wave. The method is applied to characterize rough gold bumps and the obtained results were compared with those extracted from the conventional reconstruction method. The comparison showed that the proposed method can characterize rough surfaces with excellent contrast and in real-time. Merit of the proposed method is that it can be used for monitoring smaller biological cells and micro-fluidic devices.

Quantitative phase imaging system with slightly-off-axis configuration and suitable for objects both larger and smaller than the size of the image sensor.

We propose a quantitative phase imaging system with exact slightly-off-axis configuration and suitable for objects both smaller and larger than the size of the effective recording region of the image sensors. In this system, the object is illuminated by a convergent spherical beam and a specially designed aperture filter is placed on the spatial frequency plane of the object wave; at the same time, a point source emitting from the edge of the aperture is taken as the reference beam, so that the optimal frequency condition for reconstruction of slightly-off-axis digital holograms can be always guaranteed for both large and small objects as well as different magnification (or the field of view) configurations. At the same time, a 1x2 single-mode optical fiber splitter is used for generating the reference and the illumination beams. Benefited from such fiber-based slightly-off-axis design, the proposed system provides a low-cost way to convert a regular microscope into a slightly-off-axis holographic one for microbiological specimens with a high spatial resolution.

Color Fourier orthoscopic holography with laser capture and an LED display

We present an end-to-end full color Fourier holographic imaging approach, which involves standard holographic recording with three wavelengths and an improved LED-driven display. It provides almost undistorted orthoscopic reconstruction of large objects in full color, which can be viewed with a naked eye. High quality reconstruction is preserved across large object depths, measured in meters, as shown theoretically and experimentally. Our imaging approach is based on capture, processing and display of the object wave fields without spherical phase factors. This efficient convention combined with a novel numerical propagator for confocal fields enables complete axial decoupling of both ends of the imaging chain, and consequently, free manipulation of axial position as well as size of the image without visible deformations and with minimal computation effort.

Comparing noniterative methods for phase-only Fresnel holograms, with speckle reduction, using a low-resolution spatial-light modulator in mostly phase mode

We analyze 10 cases of noniterative methods for speckle noise reduction in phase-only hologram generation. The analyzed methods are bidirectional error diffusion, random phase-free, double-phase, random displaced phase distribution (RDPD), and complex field encoding (CFE). The first three methods have been used before in the Fresnel hologram display, whereas the last two methods have been used in the area of holographic memory recording and generation of optical fields, respectively. We study the last two methods as alternatives to the generation of a Fresnel hologram without random phase (RP) and compare their results with the first three methods. We found that the RDPD also suffers a high degradation of low frequencies, so we introduce a modification for reducing the degradation effect. This method allows control of the spread angle of the object wave propagation. We also found that the CFE achieves a precise reconstruction of the object in different planes without the addition of any RP, with a very high signal-to-noise-ratio (SNR). We compare the results of 10 cases and discuss the advantages of each one. We include the peak signal-to-noise-ratio and SNR measurements of each case. We present simulated and experimental results.

Phase reconstruction using compressive two-step parallel phase-shifting digital holography

The linear relationship between the sample complex object wave and its approximated complex Fresnel field obtained using single shot parallel phase-shifting digital holograms (PPSDH) is used in compressive sensing framework and an accurate phase reconstruction is demonstrated. It is shown that the accuracy of phase reconstruction of this method is better than that of compressive sensing adapted single exposure inline holography (SEOL) method. It is derived that the measurement model of PPSDH method retains both the real and imaginary parts of the Fresnel field but with an approximation noise and the measurement model of SEOL retains only the real part exactly equal to the real part of the complex Fresnel field and its imaginary part is completely not available. Numerical simulation is performed for CS adapted PPSDH and CS adapted SEOL and it is demonstrated that the phase reconstruction is accurate for CS adapted PPSDH and can be used for single shot digital holographic reconstruction.

Automatic phase aberration compensation for digital holographic microscopy based on phase variation minimization.

We propose a numerical and totally automatic phase aberration compensation method in digital holographic microscopy. The phase aberrations are extracted in a nonlinear optimization procedure in which the phase variation of the reconstructed object wave is minimized. Not only phase curvature but also high-order aberrations could be corrected without extra devices. The correction is directly carried out with the wrapped phase map, which is not affected by phase unwrapping or fitting errors. Numerical simulation proves that the proposed method is more accurate than the conventional surface fitting method without selecting a cell-free background. Experimental results demonstrate the availability of the proposed method in real-time analysis of living cells.

Color quality improvement of reconstructed images in color digital holography using speckle method and spectral estimation

In this study, we report color quality improvement of reconstructed images in color digital holography using the speckle method and the spectral estimation. In this technique, an object is illuminated by a speckle field and then an object wave is produced, while a plane wave is used as a reference wave. For three wavelengths, the interference patterns of two coherent waves are recorded as digital holograms on an image sensor. Speckle fields are changed by moving a ground glass plate in an in-plane direction, and a number of holograms are acquired to average the reconstructed images. After the averaging process of images reconstructed from multiple holograms, we use the Wiener estimation method for obtaining spectral transmittance curves in reconstructed images. The color reproducibility in this method is demonstrated and evaluated using a Macbeth color chart film and staining cells of onion.

Single-shot Fourier ptychography based on diffractive beam splitting.

An optical setup and corresponding reconstruction algorithm are proposed to realize single-shot Fourier ptychography (FP). Multiple angle-varied object waves are generated by placing a Dammann grating at a certain distance behind the object, and the generated image array of low resolution corresponding to different diffraction orders formed on the detector plane is recorded simultaneously in a single exposure. The amplitude, as well as the phase information of the object, can be properly reconstructed with a common FP algorithm from the recorded image array. This method eliminates the requirement for the angular scanning of common FP, and the total acquisition time is dramatically reduced. The feasibility of this proposed method was demonstrated both numerically and experimentally. The proposed method has the advantages of fast data acquisition and corresponding high temporal resolution, making it very suitable for applications in which high imaging speed is required.

Four-wave mixing on thermal nonlinearity in a scheme with positive feedback

The influence of feedback for both signal and object waves on the amplitude reflection coefficient of a four-wave radiation converter on thermal nonlinearity has been considered. The dependences of the reflection coefficient of a four-wave converter on the parameters of a ring-type resonator, which provides the feedback, and the pump intensity have been obtained and analyzed. It was shown that the use of a ring-type resonator allows one to increase the reflection coefficient of a four-wave radiation converter on thermal nonlinearity by several times.