Pixel resolution control in numerical reconstruction of digital holography

Wavefront sensing based on a spatial light modulator and incremental binary random sampling

A wavefront sensing method based on a spatial light modulator (SLM) and an incremental binary random sampling (IBRS) algorithm is proposed. In this method, the recording setup is built just by a transmittance SLM and an image sensor. The tested wavefront incident to the SLM plane can be quantitatively retrieved from the diffraction intensities of the wavefront passed through the SLM displaying a IBRS pattern. Because only two modulation states (opaque and transparent) of the SLM are used, the method does not need to know the concrete modulation function of the SLM in advance. In addition by introducing the concept of the incremental random sampling into wavefront sensing, the adaptability of phase retrieving based on the diffraction intensities is significantly improved. To the best of our knowledge, no previous study has used this concept for the same purpose. Some experimental results are given for demonstrating the feasibility of our method.

Analysis and adaptation of convolution algorithms to reconstruct extended objects in digital holography

This paper discusses convolution algorithms to reconstruct off-axis digital holograms. The problem of convolution is addressed by considering the spatial spectral properties of digital holograms, especially the unusual localization property of the Fourier spectrum of the hologram, in regard to the physical object space. After deriving the sampling requirements for the transfer functions, three approaches are considered with the concept of spatial bandwidth extension: zero padding, spectrum scanning, and adjustable magnification. The theoretical discussion is completed by experimental illustrations that enable the algorithms to be objectively compared.

Digital focusing of OCT images based on scalar diffraction theory and information entropy

This paper describes a digital method that is capable of automatically focusing optical coherence tomography (OCT) en face images without prior knowledge of the point spread function of the imaging system. The method utilizes a scalar diffraction model to simulate wave propagation from out-of-focus scatter to the focal plane, from which the propagation distance between the out-of-focus plane and the focal plane is determined automatically via an image-definition-evaluation criterion based on information entropy theory. By use of the proposed approach, we demonstrate that the lateral resolution close to that at the focal plane can be recovered from the imaging planes outside the depth of field region with minimal loss of resolution. Fresh onion tissues and mouse fat tissues are used in the experiments to show the performance of the proposed method.

Multi-wavelengths digital holography: reconstruction, synthesis and display of holograms using adaptive transformation

A method based on spatial transformations of multiwavelength digital holograms and the correlation matching of their numerical reconstructions is proposed, with the aim to improve superimposition of different color reconstructed images. This method is based on an adaptive affine transform of the hologram that permits management of the physical parameters of numerical reconstruction. In addition, we present a procedure to synthesize a single digital hologram in which three different colors are multiplexed. The optical reconstruction of the synthetic hologram by a spatial light modulator at one wavelength allows us to display all color features of the object, avoiding loss of details.

Using an aliasing operator and a single discrete Fourier transform to down-sample the Fresnel transform

In Digital Holography there are applications where computing a few samples of a wavefield is sufficient to retrieve an image of the region of interest. In such cases, the sampling rate achieved by the direct and the spectral methods of the discrete Fresnel transform could be excessive. A few algorithmic methods have been proposed to numerically compute samples of propagated wavefields while allowing down-sampling control. Nevertheless, all of them require the computation of at least two 2D discrete Fourier transforms which increases the computational load. Here, we propose the use of an aliasing operator and a single discrete Fourier transform to achieve an efficient method to down-sample the wavefields obtained by the Fresnel transform.

Detail displaying difference of the digital holographic reconstructed image between the convolution algorithm and Fresnel algorithm

To reach the limiting resolution of a digital holographic system and improve the displaying quality of the reconstructed image, the subdivision convolution algorithm and the subdivision Fresnel algorithm are presented, respectively. The obtained results show that the lateral size of the reconstructed image obtained by two kinds of subdivision algorithms is the same in the central region of the reconstructed image-plane; moreover, the size of the central region is in proportional to the recording distance. Importantly, in the central region of the reconstructed image-plane, the reconstruction can be performed by the subdivision Fresnel algorithm instead of the subdivision convolution algorithm effectively, and, based on these subdivision approaches, both the displaying quality and the resolution of the reconstructed image can be improved significantly. Furthermore, in the reconstruction of the digital hologram with the large numerical aperture, the computer's memory consumed and the calculating time resulting from the subdivision Fresnel algorithm is significantly less than those from the subdivision convolution algorithm.

Estimation of wavelength difference using scale adjustment in two-wavelength digital holographic interferometry

We propose a method for an estimation of wavelength difference using scale adjustment in two-wavelength digital holographic interferometry. To estimate wavelength difference, two holograms recorded with different wavelengths are reconstructed on the basis of the Fresnel diffraction integral, and pixel sizes in the reconstruction plane, which depend on the wavelength in recording hologram, are analyzed. In the analysis, a zero-padding method and an intensity correlation function are used to adjust pixel sizes in the reconstruction plane and then obtain a wavelength difference given by a difference between the pixel sizes. Theoretical predictions and experimental results are shown to indicate the usefulness of the proposed method in this paper.

Magnified reconstruction of digitally recorded holograms by Fresnel-Bluestein transform

A method for numerical reconstruction of digitally recorded holograms with variable magnification is presented. The proposed strategy allows for smaller, equal, or larger magnification than that achieved with Fresnel transform by introducing the Bluestein substitution into the Fresnel kernel. The magnification is obtained independent of distance, wavelength, and number of pixels, which enables the method to be applied in color digital holography and metrological applications. The approach is supported by experimental and simulation results in digital holography of objects of comparable dimensions with the recording device and in the reconstruction of holograms from digital in-line holographic microscopy.

Shifted angular spectrum method for off-axis numerical propagation

A novel method is proposed for simulating free-space propagation from an input source field to a destination sampling window laterally shifted from that in the source field. This off-axis type numerical propagation is realized using the shifted-Fresnel method (Shift-FR) and is very useful for calculating non-paraxial and large-scale fields. However, the Shift-FR is prone to a serious problem, in that it causes strong aliasing errors in short distance propagation. The proposed method, based on the angular spectrum method, resolves this problem. Numerical examples as well as the formulation are presented.

Method of digital holographic recording and reconstruction using a stacked color image sensor

We discuss a method to record and reconstruct color holograms by using a stack of photodiode sensors associated to a one-way reference beam. The reconstruction algorithm follows a convolution strategy in which a transverse magnification leads to the full reconstruction of the object in the reconstructed horizon. The transverse magnification of the object depends on the curvature of the reference wave. Analysis of the spatial resolution indicates that it is linked to the transversal magnification but that no extra information is gained or lost in the process. Experimental results confirm the validity of the proposed approach for two-color digital holography. The error due to spectral mixing is investigated and found to be quite irrelevant compared to the range of the phase measurement.

Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields

A novel method is proposed for simulating free-space propagation. This method is an improvement of the angular spectrum method (AS). The AS does not include any approximation of the propagation distance, because the formula thereof is derived directly from the Rayleigh-Sommerfeld equation. However, the AS is not an all-round method, because it produces severe numerical errors due to a sampling problem of the transfer function even in Fresnel regions. The proposed method resolves this problem by limiting the bandwidth of the propagation field and also expands the region in which exact fields can be calculated by the AS. A discussion on the validity of limiting the bandwidth is also presented.

Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification

We present a numerical method for reconstructing large objects using a convolution method with an adjustable magnification. The method is based on the image locations and magnification relations of holography when the illuminating beam is a spherical wavefront. A modified version of the angular spectrum transfer function is proposed that allows the filtering in the spatial frequency spectrum. Experimental results confirm the suitability of the proposed method.

Large step-height measurements using multiple-wavelength holographic interferometry with tunable laser diodes

Accurate measurement of large step heights using multiple-wavelength holographic interferometry is realized using laser diodes. Due to the high-resolution wavelength tunability of such lasers, a pair of holograms with a wavelength difference of less than 0.01 nm is recorded and used to extract a phase difference having a large synthetic wavelength. Phase differences with synthetic wavelengths ranging from 2.5 to 73 mm are extracted by using pairs of holograms with wavelength differences between 0.3 and 0.01 nm. By combining the phase differences, measurements with a step height of 18 mm and an rms error of 0.04 mm could be achieved. The requirements for performing the phase unwrapping are discussed. Precise knowledge of the recording wavelengths is required to correctly perform this unwrapping.

High-fidelity numerical realization of multiple-step Fresnel propagation for the reconstruction of digital holograms

A cascaded Fresnel algorithm for the flexible reconstruction of digital holograms is proposed. Since the fast-Fourier-transform-based numerical realization of the Fresnel integral shows a dependency of its pixel resolution and its computation window size on the propagation distance different from that of the corresponding physical system, the computation window can be smaller than the actual physical diffraction field in the intermediate plane. Consequently, distortions in the final reconstruction may occur. A method is proposed to eliminate such distortion. The validity of this method is shown by both numerical simulations and experimental results.

Pixel-size-maintained image reconstruction of digital holograms on arbitrarily tilted planes by the angular spectrum method

We present an effective method for the pixel-size-maintained reconstruction of images on arbitrarily tilted planes in digital holography. The method is based on the plane wave expansion of the diffraction wave fields and the three-axis rotation of the wave vectors. The images on the tilted planes are reconstructed without loss of the frequency contents of the hologram and have the same pixel sizes. Our method shows good results in the extreme cases of large tilting angles and in the region closer than the paraxial case. The effectiveness of the method is demonstrated by both simulation and experiment.