Effects of quantization in phase-shifting digital holography

We discuss quantization effects of hologram recording on the quality of reconstructed images in phase-shifting digital holography. We vary bit depths of phase-shifted holograms in both numerical simulation and experiments and then derived the complex amplitude, which is subjected to Fresnel transformation for the image reconstruction. The influence of bit-depth limitation in quantization has been demonstrated in a numerical simulation for spot-array patterns with linearly varying intensities and a continuous intensity object. The objects are provided with uniform and random phase modulation. In experiments, digital holograms are originally recorded at 8 bits and the bit depths are changed to deliver holograms at bit depths of 1 to 8 bits for the image reconstruction. The quality of the reconstructed images has been evaluated for the different quantization levels.     

Surface shape measurement by phase-shifting digital holography with a wavelength shift

Surface contouring by phase-shifting digital holography is proposed and verified by experiments and numerical simulations. Digital holograms are recorded before and after mode hopping of a laser diode subject to current tuning, and the difference of the reconstructed phases at each wavelength is computed to deliver surface contours of a diffusely reflecting surface. Since normal incidence on the object is employed, the method does not need the removal of the tilt component and is free from the shadowing effect as advantages over the dual-incidence method proposed before by the first author.     

Image reconstruction only by phase data in phase-shifting digital holography

We describe data compression in phase-shifting digital holography. We demonstrate by experimentation that an image of a diffusely reflecting object can be reconstructed only by phase data of the derived complex amplitude. It is shown that reduction of the bit depth of the phase data does not seriously damage the image even down to 1 bit. We observe enhancement of halo in the image with low bit depths. This tendency is verified quantitatively by a one-dimensional simulation. Our procedure for smoothing the images that result from the data-compression methods is shown to be effective.     

Image formation in phase-shifting digital holography and applications to microscopy

We discuss image formation in phase-shifting digital holography by developing an analytical formulation based on the Fresnel-Kirchhoff diffraction theory. Image-plane position and imaging magnification are derived for general configurations in which a spherical reference is employed. The influences of discrete sampling of the resulting interference patterns by a CCD and numerical reconstruction on qualities of point images are investigated. Dependence of the point images on the ratio of the minimum fringe spacing to pixel pitch of the CCD is numerically analyzed. Two-point resolution and magnification are also investigated as a function of pixel numbers by a simulation using a one-dimensional model. In experiments magnified images of biological objects and a resolution target were reconstructed with the same quality as by conventional microscopy.     

Compensation algorithm for the phase-shift error of polarization-based parallel two-step phase-shifting digital holography

We propose an algorithm for compensating the phase-shift error of polarization-based parallel two-step phase-shifting digital holography, which is a technique for recording a spatial two-step phase-shifted hologram. Although a polarization-based system of the technique has been experimentally demonstrated, there had been the problem that the phase difference of two phase-shifted holograms had been changed by the extinction ratio of the micropolarizer array attached to the image sensor used in the system. To improve the performance of the system, we established and formulated an algorithm for compensating the phase-shift error. Accurate spatial phase-shifting interferometry in the system can be conducted by the algorithm regardless of phase-shift error due to the extinction ratio. By the numerical simulation, the proposed algorithm was capable of reducing the root mean square errors of the reconstructed image by 1/4 and 1/5 in amplitude and phase, respectively. Also, the algorithm was experimentally demonstrated, and the experimental results showed that the system employing the proposed algorithm suppressed the conjugate image, which slightly appeared in the image reconstructed by the system not employing the algorithm, even when the extinction ratio was 10:1. Thus, the effectiveness of the proposed algorithm was numerically and experimentally verified.     

Improvement of color reproduction in color digital holography by using spectral estimation technique

We propose a color digital holography by using spectral estimation technique to improve the color reproduction of objects. In conventional color digital holography, there is insufficient spectral information in holograms, and the color of the reconstructed images depend on only reflectances at three discrete wavelengths used in the recording of holograms. Therefore the color-composite image of the three reconstructed images is not accurate in color reproduction. However, in our proposed method, the spectral estimation technique was applied, which has been reported in multispectral imaging. According to the spectral estimation technique, the continuous spectrum of object can be estimated and the color reproduction is improved. The effectiveness of the proposed method was confirmed by a numerical simulation and an experiment, and, in the results, the average color differences are decreased from 35.81 to 7.88 and from 43.60 to 25.28, respectively.     

Some opportunities for vibration analysis with time averaging in digital Fresnel holography

Features offered by the combination of time averaging and digital Fresnel holography are investigated. In particular, we introduce the concept of the zero-crossing phase of Bessel fringes, which allows a highly contrasted determination of the dark fringes in the hologram. We discuss some particularities of the digital reconstruction and show how time-averaged digital holography can be used to study vibration drifts. Experiment results are presented in the case of a loudspeaker under a sinusoidal excitation; digital and analogical holography are also compared.     

Size measurement of bubbles in a cavitation tunnel by digital in-line holography

Digital in-line holography (DIH) with a divergent beam is used to measure size and concentration of cavitation bubbles (6-100 μm) in hydrodynamic facilities. A sampling probe is directly inserted in the cavitation tunnel, and the holograms of the bubbles are recorded through a transparent test section specially designed for DIH measurements. The recording beam coming from a fiber-coupled laser diode illuminates the sample volume, and holograms are recorded by a CMOS camera. From each hologram, the sampling volume can be reconstructed slice by slice by applying a wavelet-based reconstruction method. Because of the geometry of the recording beam, a magnification ratio must be introduced for recovering the 3D location and size of each bubble. The method used for processing holograms recorded in such a configuration is presented. Then, statistical results obtained from 5000 holograms recorded under different pressures in the cavitation tunnel are compared and discussed.     

Resolution improvement in digital holography by angular and polarization multiplexing

Angular and polarization multiplexing techniques are utilized in both object and reference arms in the digital holographic microscopy system to improve its resolution. The angular multiplexing provides on-axis and off-axis illumination and reference beams with different carrier frequencies. Polarization multiplexing prohibits the occurrence of interference between low and high object spatial frequencies and reference beams. The proposed system does not require special light sources or filtering masks. Experimental results show that the resolution of the synthesized image exceeds the resolution determined by the numerical aperture of the imaging microscope objective.     

Reduction of speckle in digital holography by discrete Fourier filtering

We present a digital signal processing technique that reduces the speckle content in reconstructed digital holograms. The method is based on sequential sampling of the discrete Fourier transform of the reconstructed image field. Speckle reduction is achieved at the expense of a reduced intensity and resolution, but this trade-off is shown to be greatly superior to that imposed by the traditional mean and median filtering techniques. In particular, we show that the speckle can be reduced by half with no loss of resolution (according to standard definitions of both metrics).     

Superresolved imaging in digital holography by superposition of tilted wavefronts

A technique based on superresolution by digital holographic microscopic imaging is presented. We used a two dimensional (2-D) vertical-cavity self-emitting laser (VCSEL) array as spherical-wave illumination sources. The method is defined in terms of an incoherent superposition of tilted wavefronts. The tilted spherical wave originating from the 2-D VCSEL elements illuminates the target in transmission mode to obtain a hologram in a Mach-Zehnder interferometer configuration. Superresolved images of the input object above the common lens diffraction limit are generated by sequential recording of the individual holograms and numerical reconstruction of the image with the extended spatial frequency range. We have experimentally tested the approach for a microscope objective with an exact 2-D reconstruction image of the input object. The proposed approach has implementation advantages for applications in biological imaging or the microelectronic industry in which structured targets are being inspected.     

Damage process in heterogeneous materials analyzed by a lattice model simulation

Several materials of technological interest could be considered as heterogeneous and their random nature can be accounted to be the cause of the nonlinear behavior. The quantitative evaluation of damage in materials subjected to stress or strain states has great importance due to the critical character of these phenomena, which, at a certain point, may suddenly give rise to catastrophic failure. In previous studies, Carpinteri and his coworkers have presented different aspects of the damage process characterization in heterogeneous materials. Three of these aspects demand our attention: (i) the brittleness number to measure the brittleness level of the structure under investigation; (ii) the fractal dimension in which the damage process develops; and (iii) the global indexes obtained for the Acoustic Emission (AE) analysis. In the present work, a version of the discrete element method formed by bars is used to explore these concepts. A set of quasi-brittle material specimens is simulated and, when it is possible, the numerical results are compared with experimental data. Moreover, a discussion of the obtained results aids to better understand the behavior of this kind of materials, describing the numerical method as a viable tool to extract information from experimental tests on the damage process.     

Improvement of accuracy in digital holography by use of multiple holograms

Speckle pattern decorrelation reduces the accuracy of interferometric shape and deformation measurements. We introduce a technique for the reduction of speckle noise in digital holography. The method is not based on classical filtering techniques such as median filters. Instead it utilizes the shift theorem of the Fourier transform. For this method several holograms of the same object under test are recorded. The reconstruction leads to a set of object wave fields with different speckle patterns. A proper averaging procedure, taking into account the properties of the wrapped phases, leads to an improvement of the accuracy in the resulting phase difference. The theory of the applied method is described and our first results for technical components with an improvement of accuracy up to 1/57 of the wavelength are presented.     

Recognition and classification of three-dimensional phase objects by digital Fresnel holography

We demonstrate the validity of wavelet-based processing for recognition and classification of three-dimensional phase objects. One Fresnel digital hologram of each of the three-dimensional (3-D) phase objects to be classified is recorded. The electronic holograms are processed digitally to permit 3-D object information to be retrieved as two-dimensional digital complex images. We use a Mexican-hat wavelet- matched filter (WMF) to enhance the correlation peak and discriminate between the objects. The WMF performs a wavelet transform (WT) to enhance the significant features of the images and the correlation of the WT coefficients thus obtained. We compare the feasibility of a WMF-based object classifier with the matched-filter-based classifier to classify our four 3-D phase objects in a 3-D scene into true or false classes with minimal error.     

Spatial filtering for zero-order and twin-image elimination in digital off-axis holography

Off-axis holograms recorded with a CCD camera are numerically reconstructed with a calculation of scalar diffraction in the Fresnel approximation. We show that the zero order of diffraction and the twin image can be digitally eliminated by means of filtering their associated spatial frequencies in the computed Fourier transform of the hologram. We show that this operation enhances the contrast of the reconstructed images and reduces the noise produced by parasitic reflections reaching the hologram plane with an incidence angle other than that of the object wave.     

Simple method for direct determination of bending strains by use of digital holography

A computer-based technique is described for direct determination of bending strains in beam and plate structures. First a displacement-related phase-change map is constructed by digital holography and computer-vision techniques. Subsequently the computer generates an exact replica of the phase-change map, then overlays the two identical maps and, finally, rotates one of the maps through 180 degrees relative to the other in their planes about a point of interest. The local curvatures and the local twist of the bent surface at the point of interest are determined from the conic sections that are reconstructed from the algebraic sum of the phase changes at the vicinity of this point, thus permitting further calculation for determination of the local bending strains. When the need arises, bending moments and stresses may be determined concurrently. As the optical setup is simple, with computer-based data acquisition and processing, the entire system is user friendly, and rapid measurement is achieved.     

Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies

When a digital holographic reconstruction is performed, digital diffraction effects occur at the borders when the hologram amplitudes at the two opposite border points are different on each vertical or horizontal line. We propose a method of digital hologram extension to reduce such diffraction effects. The method consists of extending the size of the digital hologram and of filling the extended part by complex values that minimize, according to a numerical criterion, the highest spatial frequencies. The theoretical aspects of the method are given and the results from a demonstration are provided.     

Phase-shifting digital holography with a low-coherence light source for reconstruction of a digital relief object hidden behind a light-scattering medium

Hiding image data with a light-scattering medium is effective as a basic data protection technique. The hidden image data can be observed only by using a low-coherence interference technique and is thus protected from unauthorized access. Unlike an intensity-distributed object, a digital relief object has no intensity distribution, making it possible to hide its existence by using a dilute light-scattering medium. To reconstruct the digital relief object through the light-scattering medium, we developed phase-shifting digital holography with a low-coherence light source. The experimental performance, including the spatial resolution and phase error of the reconstructed image, is estimated.     

Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain

Digital holography techniques can be utilized to implement image watermarking schemes. In a previous method proposed by Takai and Mifune [Appl. Opt. 41,865 (2002)], a watermark image is transformed into a digital Fourier hologram, which then is directly superposed onto a content image to perform the embedding process. In the detection stage, the watermark is extracted based on the inverse Fourier transform and optical holography techniques. A method in which the hologram is superposed on the discrete-cosine-transform domain of the content image is proposed to significantly improve Takai and Mifune's method. The proposed method can greatly reduce the degradation on the superposed image, which is the major drawback in Takai and Mifune's method. Simulation results also demonstrate that the watermark can be successfully extracted under different kinds of attack.     

Simultaneous depth determination of multiple objects by focus analysis in digital holography

Focus analysis techniques from computer vision are applied to digital holography to determine the depth (range) of multiple objects and their surfaces from a single hologram capture. With this method the depths of objects can be determined from a single hologram capture without the need for manual focusing and without prior information on object location. Variance and the Laplacian of Gaussian are analyzed as focus measures, and techniques are proposed for focus plane determination from the focus measure curves. The algorithm is described in detail and demonstrated through simulation and optical experiment.