On-axis Holograms Research Articles

Iterative technique for generating numerical on-axis holograms of an object on tilted planes using Rayleigh-Sommerfeld approximation

We present a new iterative technique based on successive field propagation using the Reyleigh-Sommerfeld (RS) approximation, to generate by computer the amplitude on-axis hologram of an object on a tilted plane. The technique was validated doing optical and computational reconstruction of the hologram.

Phase-Shifting Common-Path Polarization Self-Interferometry for Evaluating the Reconstruction of Holograms Displayed on a Phase-Only Display

In this work we apply a phase-shifting interferometry (PSI) to evaluate the reconstruction of complex-valued holograms displayed onto a phase-only spatial light modulator (SLM). The interferometer is vibration-free since it uses a common-path polarization arrangement based on the SLM itself, which is used simultaneously to display the hologram and to apply the phase-shifting values. The change from the hologram display configuration to the interferometer configuration involves only a rotation of a polarizer. The continuous phase modulation provided by the SLM allows using PSI with arbitrary phase bias values. Several examples are demonstrated by generating different combinations of modes with an efficient on-axis hologram encoding technique.

Two-pack frequency-selective incoherent holography by using a dual-beam setup

We proposed a new incoherent optical frequency selection method called two-pack frequency-selective (TPFS) incoherent holography, which compresses two on-axis holograms into a single multiplexed on-axis hologram without loss of magnification and resolution. The spectrum we want to reconstruct is intercepted by multiple confounding correlation terms in the spatial frequency domain. The background bias term and conjugate term can be effectively suppressed. This work is the first to attempt a multiplexed reconstruction in the field of incoherent light. Experiment results highlight the potential of the proposed method in several areas, such as compressed holography and extended field of view imaging.

Iterative technique for generating numerical on-axis holograms of an object on tilted planes using Rayleigh-Sommerfeld approximation

We present a new iterative technique based on successive field propagation using the Reyleigh-Sommerfeld (RS) approximation, to generate by computer the amplitude on-axis hologram of an object on a tilted plane. The technique was validated doing optical and computational reconstruction of the hologram.

Phase Retrieval of On-Axis Digital Holography With Modified Coherent Diffraction Imaging

In this paper, a phase retrieval method is proposed to reconstruct the high-quality image free from undesired terms in on-axis digital holography (DH) with modified coherent diffraction imaging (MCDI). A random phase plate (RPP) is applied to generate a modulated diffraction pattern which forms an on-axis digital hologram with a plane reference wave, and a proper iterative algorithm is designed to reconstruct high-quality object information from both on-axis digital hologram and modulated diffraction pattern. Numerical simulations and experiments prove that both modulus and phase distributions can be accurately reconstructed within 100 iterations while the undesired twin image and zero-order diffraction can be effectively removed, thus demonstrating the feasibility of the suggested method.

DarkFocus: numerical autofocusing in digital in-line holographic microscopy using variance of computational dark-field gradient

We report on a novel computational technique for automatic numerical refocusing in digital in-line holographic microscopy. It is based on the adaptive filtering of the recorded on-axis hologram to eliminate its background term and extract interference intensity-component connected with light scattered on the sample (interference fringes). Numerical propagation of such filtered hologram yields the computationally generated dark-field imaging coming from the amplitude part of the complex field. We propose a simple measure in the form of the variance of the dark-field gradient, which attains its maximum value in the focal planes for all types of objects (phase, amplitude and mixed phase-amplitude), as a robust indicator of overall sharpness and in-focus quality. Demonstrated novel autofocusing technique is positively validated using experimental data exhibiting significant variation of the magnification factor for both single and double focal plane scenarios. It compares favorably with other well-established automatic numerical refocusing techniques based on the high-pass filtered complex amplitude and edge sparsity, mainly in terms of higher axial resolution and better robustness to hologram low signal-to-noise ratio.

Phase Retrieval for Digital Holographic Microscopy With Defocused Holograms

A new phase retrieval technique in digital holographic microscopy (DHM) with three defocused holograms is proposed. Given the defocusing distance, the phase distributions of tested specimen can be reconstructed with a simple algebraic equation. We have deduced this equation in detail. To avoid the manual operation, the defocused holograms can be flexibly and precisely obtained by introducing an electronically tunable lens based 4f system. This method is suitable for an on-axis hologram as well as the off-axis one but avoids the requirements for not only the iterative process, complex spectrum selection in off-axis DHM or additional phase-shifting devices in on-axis DHM but also the assumption of tested specimen or previous knowledge of the system. A series of simulations and the experimental results of the microlens array and water drop demonstrate the feasibility and effectiveness of the proposed method.

Scattering of Poincaré beams: polarization speckles.

Polarization speckle is a fine granular light pattern having spatially varying random polarization profile. We generate these speckle patterns by using the scattering of Poincaré beams, a special class of vector vortex beams, through a ground glass plate. Here, the Poincaré beams are generated using a polarization sensitive spatial light modulator displaying an on-axis hologram corresponding to an optical vortex phase profile. The different inhomogeneities of the rough surface experience different polarizations, which control the ability for scattered waves to interfere at the detection plane and causes a spatially varying polarization profile. We experimentally determined the spatial variation of local degree of polarization and orientation of the polarization ellipse for these speckle patterns from the Stokes analysis. We also determined the size of scalar speckles using the auto-correlation function of Stokes parameter S0 and the size of polarization speckles using the sum of auto-correlation functions of remaining three Stokes parameters. We found that the change in scalar speckle size with the index of the vector beam is very small and of the order of 1 pixel size of the camera but the size of polarization speckles decreases with the increase in index of the vector beam.

Full-color, large area, transmissive holograms enabled by multi-level diffractive optics

We show that multi-level diffractive microstructures can enable broadband, on-axis transmissive holograms that can project complex full-color images, which are invariant to viewing angle. Compared to alternatives like metaholograms, diffractive holograms utilize much larger minimum features (>10 µm), much smaller aspect ratios (<0.2) and thereby, can be fabricated in a single lithography step over relatively large areas (>30 mm ×30 mm). We designed, fabricated and characterized holograms that encode various full-color images. Our devices demonstrate absolute transmission efficiencies of >86% across the visible spectrum from 405 nm to 633 nm (peak value of about 92%), and excellent color fidelity. Furthermore, these devices do not exhibit polarization dependence. Finally, we emphasize that our devices exhibit negligible absorption and are phase-only holograms with high diffraction efficiency.

Experiments on a Simple Setup for Two-Step Quadrature Phase-Shifting Holography

We report a simple setup for two-step quadrature phase-shifting holography that could be useful and suitable for industrial applications. Only two on-axis holograms are captured with the system and a complex hologram is formed from the two holograms. Autocorrelation is used to quantify the quality of all the reconstructed images from the holograms. We have tested a transparent sample as well as a reflective sample to validate this simple setup.

Compressive optical image encryption with two-step-only quadrature phase-shifting digital holography

An image encryption method which combines two-step-only quadrature phase-shifting digital holography with compressive sensing (CS) has been proposed in the fully optical domain. An object image is firstly encrypted to two on-axis quadrature-phase holograms using the two random phase masks in the Mach–Zehnder interferometer. Then, the two encrypted images are highly compressed to a one-dimensional signal using the single-pixel compressive holographic imaging in the optical domain. At the receiving terminal, the two compressive encrypted holograms are exactly reconstructed from much less than the Nyquist sampling number of observations by solving an optimization problem, and the original image can be decrypted with only two reconstructed holograms and the correct keys. This method largely decreases holograms data volume for the current optical image encryption system, and it is also suitable for some special optical imaging cases such as different wavelengths imaging and weak light imaging. Numerical simulation is performed to demonstrate the feasibility and validity of this novel image encryption method.

Laser and holographic stand for the alignment control of Cassegrain and Ritchey-Chretien telescopic systems

This paper presents some results of preliminary application studies of a system of two on-axis computer-generated holograms for controlling the alignment of two-mirror Cassegrain and Ritchey-Chretien telescopic systems using a test stand with a spherical primary mirror and a flat secondary mirror.

Classical sampling theorem in digital holography

It is proposed to change the present paradigm of the sampling theorem, accepted in papers on digital holography, from 'when recording digital hologram, Nyquist criterion should be fulfilled' to 'when recording on-axis digital hologram, low-pass sampling theorem should be fulfilled, and when recording off-axis one, band-pass sampling theorem should be fulfilled'. Experimental and theoretical basis for this proposal is presented.

Broadband suppression of the zero diffraction order of an SLM using its extended phase modulation range.

The diffraction efficiency of a hologram displayed on a phase-only spatial light modulator (SLM) is maximal, if the SLM modulates the phase of the diffracted beam in a range between 0 and 2π. However, if the readout wavelength changes, or a broadband beam is used, due to dispersion this ideal modulation range cannot be maintained, which leads to lower diffraction efficiency and to the appearance of an undesired intense zero diffraction order. Here we show how an SLM with an extended phase modulation range of 4π can be used to display on-axis holograms with a strong suppression of the zero diffraction order in a wide spectral range, extending over 200 nm. The basic idea is to transform the original on-axis hologram into an off-axis hologram by adding a blazed grating and performing a modulo 2π operation, and then transforming it back by adding the conjugate grating, but without performing a subsequent modulo operation. The final hologram then spans over a phase range of 4π. The total diffracted field corresponds to that of the original on-axis hologram, but now the zero-order Fourier component is diffracted away from the optical axis. The same principle can be used to entangle the on-axis hologram with other phase structures, e.g. a random phase mask or a second hologram structure, followed by a subsequent addition of the conjugate mask, which may also suppress higher diffraction orders. The reconstructed holograms show a strong contrast enhancement in a broad wavelength range.

Quantitative phase imaging with single shot digital holography

We demonstrate quantitative phase imaging using single shot digital holography for a calibrated spiral phase object. A single frame of near on-axis digital hologram of a spiral phase plate is recorded and the complex object field in the hologram plane is retrieved using a constrained optimization approach. Experimental results show the feasibility of a quantitative phase imaging technique which has superior performance to conventional Fourier filtering methods. Single shot capability suggests that this method is suitable for holographic imaging of dynamic objects such as live biological cells.

Three-dimensional optical holography using a plasmonic metasurface

Benefitting from the flexibility in engineering their optical response, metamaterials have been used to achieve control over the propagation of light to an unprecedented level, leading to highly unconventional and versatile optical functionalities compared with their natural counterparts. Recently, the emerging field of metasurfaces, which consist of a monolayer of photonic artificial atoms, has offered attractive functionalities for shaping wave fronts of light by introducing an abrupt interfacial phase discontinuity. Here we realize three-dimensional holography by using metasurfaces made of subwavelength metallic nanorods with spatially varying orientations. The phase discontinuity takes place when the helicity of incident circularly polarized light is reversed. As the phase can be continuously controlled in each subwavelength unit cell by the rod orientation, metasurfaces represent a new route towards high-resolution on-axis three-dimensional holograms with a wide field of view. In addition, the undesired effect of multiple diffraction orders usually accompanying holography is eliminated.

Complex Fresnel hologram display using a single SLM

We propose a novel optical method to display a complex Fresnel hologram using a single spatial light modulator (SLM). The method consists of a standard coherent image processing system with a sinusoidal grating at the Fourier plane. Two or three position-shifted amplitude holograms displayed at the input plane of the processing system can be coupled via the grating and will be precisely overlapped at the system's output plane. As a result, we can synthesize a complex hologram that is free of the twin image and the zero-order light using a single SLM. Because the twin image is not removed via filtering, the full bandwidth of the SLM can be utilized for displaying on-axis holograms. In addition, the degree of freedom of the synthesized complex hologram display can be extended by involving more than three amplitude holograms.

A Review of Incoherent Digital Fresnel Holography

We review three different methods of generating digital Fresnel holograms of 3-D real-existing objects illuminated by incoherent light. In the first method, a scanning hologram is generated by a unique scanning system in which Fresnel zone plates (FZP) are created by a homodyne rather than the common heterodyne interferometer. During the scanning, the FZP projected on the observed object is frozen rather than varied as previously. In each scanning period, the system produces an on-axis Fresnel hologram. The twin image problem is solved by a linear combination of at least three holograms taken with three FZPs with different phase values. The second hologram reviewed here is the digital incoherent modified Fresnel hologram. To calculate this hologram, multiple-viewpoint projections of the 3-D scene are acquired, and a Fresnel hologram of the 3-D scene is directly computed from these projections. This method enables to obtain digital holograms by using a simple digital camera, which operates under regular light conditions. The last digital hologram reviewed here is the Fresnel incoherent correlation hologram. In this motionless holographic technique, light is reflected from the 3-D scene, propagates through a diffractive optical element (DOE), and is recorded by a digital camera. Three holograms are recorded sequentially, each for a different phase factor of the DOE. The three holograms are superposed in the computer, such that the result is a complex-valued Fresnel hologram that does not contain a twin image.

Reconstruction of sectional images in holography using inverse imaging

This paper discusses the reconstruction of sectional images from a hologram generated by optical scanning holography. We present a mathematical model for the holographic image capture, which facilitates the use of inverse imaging techniques to recover individual sections. This framework is much more flexible than existing work, in the sense that it can handle objects with multiple sections, and possibly corrupted with white Gaussian noise. Simulation results show that the algorithm is capable of recovering a prescribed section while suppressing the other ones as defocus noise. The proposed algorithm is applicable to on-axis holograms acquired by conventional holography as well as phase-shifting holography.

Homodyne scanning holography

We have developed a modified version of a scanning holography microscope in which the Fresnel Zone Plates (FZP) are created by a homodyne rather than a heterodyne interferometer. Therefore, during the scanning the projected pattern on the specimen is frozen rather than varied as previously. In each scanning period the system produces an on-axis Fresnel hologram. The twin image problem is solved by a linear combination of at least three holograms taken with three FZPs with different phase values.