Parallel three-step phase-shifting digital holography

We propose parallel three-step phase-shifting digital holography as a technique capable of noiseless instantaneous measurement of three-dimensional objects based on phase-shifting interferometry. The proposed digital holography carries out three-step phase shifting at the same time by using a phase-shifting array device located in the reference beam. The array device has a periodic three-step phase distribution, and its configuration is simplified compared with that required for conventional parallel phase-shifting digital holography. Therefore the optical system of the proposed parallel phase-shifting digital holography is more suitable for the realization of the proposed holography. We conduct both a numerical simulation and a preliminary experiment. The results of the simulation and experiment agree well with those of the conventional phase-shifting method and are superior to the results obtained by conventional digital holography by using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.     

Parallel two-step phase-shifting digital holography

We propose a parallel two-step phase-shifting digital holography technique capable of instantaneous measurement of three-dimensional objects, with a view toward measurement of dynamically moving objects. The technique is based on phase-shifting interferometry. The proposed technique carries out the two-step phase-shifting method at one time and can be optically implemented by using a phase-shifting array device located in the reference beam. The array device has a periodic two-step phase distribution, and its configuration is simplified compared with that required for three-step and four-step parallel phase-shifting digital holographies. Therefore the optical system of the proposed technique is more suitable for the realization of a parallel phase-shifting digital holography system. We conduct both a numerical simulation and a preliminary experiment in the proposed technique. The results of the simulation and the experiment agree well with those of sequential phase-shifting digital holography, and results are superior to those obtained by conventional digital holography using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.     

Simultaneous two-wavelength Doppler phase-shifting digital holography

This paper presents a method based on the use of an image sensor for obtaining the complex amplitudes of beams diffracted from an object at two different wavelengths. The complex amplitude for each wavelength is extracted by the Doppler phase-shifting method. The principle underlying the proposed method is experimentally verified by using the method with two lasers having different wavelengths to measure the surface shape of a concave mirror.     

Free-viewpoint images captured using phase-shifting synthetic aperture digital holography

Free-viewpoint images obtained from phase-shifting synthetic aperture digital holography are given for scenes that include multiple objects and a concave object. The synthetic aperture technique is used to enlarge the effective sensor size and to make it possible to widen the range of changing perspective in the numerical reconstruction. The lensless Fourier setup and its aliasing-free zone are used to avoid aliasing errors arising at the sensor edge and to overcome a common problem in digital holography, namely, a narrow field of view. A change of viewpoint is realized by a double numerical propagation and by clipping the wave field by a given pupil. The computational complexity for calculating an image in the given perspective from the base complex-valued image is estimated at a double fast Fourier transform. The experimental results illustrate the natural change of appearance in cases of both multiple objects and a concave object.     

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.     

Compression of interference patterns with application to phase-shifting digital holography

A compression method of phase-shifting digital holographic data is presented. Three interference patterns are recorded, and holographic information is extracted from them by phase-shifting interferometry. The scheme uses standard baseline Joint Photographic Experts Group (JPEG) or standard JPEG-2000 image compression techniques on the recorded interference patterns to reduce the amount of data to be stored. High compression rates are achieved for good reconstructed object image quality. The utility of the proposed method is experimentally verified with real holographic data. Results for compression rates using JPEG-2000 and JPEG of approximately 27 and 20, respectively, for a normalized root-mean-square error of approximately 0.7 are demonstrated.     

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.     

Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator

Parallel phase-shifting digital holography using a phase-mode spatial light modulator (SLM) is proposed. The phase-mode SLM implements spatial distribution of phase retardation required in the parallel phase-shifting digital holography. This SLM can also compensate dynamically the phase distortion caused by optical elements such as beam splitters, lenses, and air fluctuation. Experimental demonstration using a static object is presented.     

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.     

Three-dimensional displacement measurement for diffuse object using phase-shifting digital holography with polarization imaging camera

The amount of displacement of a diffused object can be measured using phase-shifting digital holography with a polarization imaging camera. Four digital holograms in quadrature are extracted from the polarization imaging camera and used to calculate the phase hologram. Two Fourier transforms of the phase holograms are calculated before and after the displacement of the object. A phase slope is subsequently obtained from the phase distribution of division between the two Fourier transforms. The slope of the phase distribution is proportional to the lateral displacement of the object. The sensitivity is less than one pixel size in the lateral direction of the movement. The longitudinal component of the displacement can be also measured separately from the intercept on the phase axis along the phase distribution of the division between two Fourier transforms of the phase holograms.     

Noise and aliases in off-axis and phase-shifting holography

We have compared the respective efficiencies of off-axis and phase-shifting holography in terms of noise and aliases removal. The comparison is made by analyzing holograms of a USAF target backlit with laser illumination, recorded with a charge-coupled device camera. We show that it is essential to remove the local oscillator beam noise, especially at low illumination levels.     

Drying process in a solvent-based paint analyzed by phase-shifting digital holography and an estimation of time for tack free

A technique to study the drying of paints, based on phase-shifting digital holography, is presented. The technique is applied to the drying process of solvent-based paint on a three-dimensional surface at different substrate temperatures. For processing the data, a cross-correlation function and phase change derived from reconstructed complex amplitudes are calculated to visualize and to evaluate the local variations in the dryness of paint. The relationship between the optical signal obtained by the holographic method and the actual microscopic variations occurring in the paint film is also investigated using the gravimetric technique and a microscope. It is shown that the holographic technique can determine the stationary state of a painted surface corresponding to the end of the falling rate period in the drying process. The holographic technique detects mainly the activity on the surface and is applicable to assessment of the early drying process of paint.     

Phase-error correction in digital holography

The quality of images computed from digital holograms or heterodyne array imaging is degraded by phase errors in the object and/or reference beams at the time of measurement. This paper describes computer simulations used to compare the performance of digital shearing laser interferometry and various sharpness metrics for the correction of such phase errors when imaging a diffuse object. These algorithms are intended for scenarios in which multiple holograms can be recorded with independent object speckle realizations and a static phase error. Algorithm performance is explored as a function of the number of available speckle realizations and signal-to-noise ratio (SNR). The performance of various sharpness metrics is examined in detail and is shown to vary widely. Under ideal conditions with >15 speckle realizations and high SNR, phase corrections better than lambda/50 root-mean-square (RMS) were obtained. Corrections better than lambda/10 RMS were obtained in the high SNR regime with as few as two speckle realizations and at object beam signal levels as low as 2.5 photons/speckle with six speckle realizations.     

Light-in-flight digital holography display

We present a digital speckle-pattern interferometric setup that can be operated at TV frame rates (30 ms) to display the locus of the points at which the optical-path difference between the reference and object beams is within the coherence length. Experimental results are shown.     

Exact complex-wave reconstruction in digital holography

We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, one can achieve exact complex-wave reconstruction in the absence of noise. A feature of the proposed technique is that the zero-order artifact, which is commonly encountered in hologram reconstruction, can be completely suppressed in the absence of noise. The technique is noniterative and nonlinear. We also establish a connection between the reconstruction technique and homomorphic signal processing, which enables an interpretation of the technique from the perspective of deconvolution. Another key contribution of this paper is a direct link between the reconstruction technique and the two-dimensional Hilbert transform formalism proposed by Hahn. We show that this connection leads to explicit Hilbert transform relations between the magnitude and phase of the complex wave encoded in the hologram. We also provide results on simulated as well as experimental data to validate the accuracy of the reconstruction technique.     

Comparison of two-, three-, and four-exposure quadrature phase-shifting holography

In standard (four-exposure) quadrature phase-shifting holography (QPSH), two holograms and two intensity maps are acquired for zero-order-free and twin-image-free reconstruction. The measurement of the intensity map of the object light can be omitted in three-exposure QPSH. Furthermore, the measurements of the two intensity maps can be omitted in two-exposure QPSH, and the acquisition time of the overall holographic recording process is reduced. In this paper we examine the quality of the reconstructed images in two-, three-, and four-exposure QPSH, in simulations as well as in optical experiments. Various intensity ratios of the object light and the reference light are taken into account. Simulations show that two- and three-exposure QPSH can provide reconstructed images with quality comparable to that of four-exposure QPSH at a low intensity ratio. In practice the intensity ratio is limited by visibility, and thus four-exposure QPSH exhibits the best quality of the reconstructed image. The uniformity and the phase error of the reference light are also discussed. We found in most cases there is no significant difference between the reconstructed images in two- and three-exposure QPSH, and the quality of the reconstructed images is acceptable for visual applications such as the acquisition of three-dimensional scene for display or particle tracking.     

数字同轴和数字离轴全息系统分析

利用最高空间频率分析法,通过逐点分析记录在 CCD 上的空间频率信息,研究了物体可允许记录的最大横向尺寸、最小记录距离、全息图的信息量、空间分辨力、再现像的横向分辨力、轴向分辨力及散斑大小,并得到了数学表达式。理论分析和实验结果表明,数字同轴全息系统放宽了对 CCD 分辨力的要求,有较高的分辨力,较低的散斑噪声、灵活、简单的系统结构及较高的 CCD 空间带宽利用率,在增强系统性能方面要优于数字离轴全息系统。这一研究为数字全息系统的设计和操作提供了一定的理论和实验指导。     

Reconstruction domain compression of phase-shifting digital holograms

Phase-shifting digital hologram compression has been mainly studied in the recording domain, where data possess a rather randomlike appearance, yielding reduced compression efficiency. We carry out the compression of such data in the reconstruction domain, which benefits from the spatial correlation of the data yielding, increased efficiency. Real holographic data are used to demonstrate the performance of the new approach. It is also shown that the reconstruction is not limited to the initially obtained view, as additional views can still be obtained with appropriate postprocessing.