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.     

Scheme to improve the reconstructed image in parallel quasi-phase-shifting digital holography

We propose a scheme to improve the reconstructed image in parallel quasi-phase-shifting digital holography. Parallel quasi-phase-shifting digital holography is a technique capable of noiseless instantaneous measurement of three-dimensional objects, and it implements four kinds of phase shifting at a time with an array of 2 x 2 phase-shifting devices located in the reference wave. In the phase-shifting calculation in the reconstruction process of the technique, the scheme assigns the 2 x 2 cell configuration for each pixel in the vertical direction and for each 1-pixel interval in the horizontal direction of the hologram recorded by the image sensor. We conduct both a numerical simulation and a preliminary experiment. The results show that the proposed scheme can improve the quality of the reconstructed image calculated by the conventional scheme of parallel quasi-phase-shifting digital holography we previously proposed, and then the effectiveness of the proposed scheme is verified.     

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.     

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.     

Fast acquisition system for digital holograms and image processing for three-dimensional display with data manipulation

A three-dimensional (3D) digital holographic display system with image processing is presented. By use of phase-shifting digital holography, we obtain the complex amplitude of a 3D object at a recording plane. Image processing techniques are introduced to improve the quality of the reconstructed 3D object or manipulate 3D objects for elimination and addition of information by modifying the complex amplitude. The results show that the information processing is effective in such manipulations of 3D objects. We also show a fast recording system of 3D objects based on phase-shifting digital holography for display with image processing. The acquisition of 3D object information at 500 Hz is demonstrated experimentally.     

Single-shot parallel four-step phase shifting using on-axis Fizeau interferometry

The purposes of the paper are threefold: (1) to show the possibility to perform parallel phase-shifting Fizeau interferometry by using a quarter waveplate with high flatness as a reference, (2) to present a comparative study between the phase-shifting algorithm and the off-axis geometry in surface microtopography measurement, and (3) to show the advantages of using the proposed common path Fizeau interferometry over the quasi-common path Michelson interferometry in terms of accuracy in measurement. The compelling advantage of the proposed parallel phase-shifting Fizeau interferometric technique is the long-term stability that leads to measuring objects with a high degree of accuracy.     

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.     

Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting

The use of an optical fringe projection method with two-step phase shifting for three-dimensional (3-D) shape measurement of small objects is described. In this method, sinusoidal linear fringes are projected onto an object's surface by a programmable liquid-crystal display (LCD) projector and a long-working-distance microscope (LWDM). The image of the fringe pattern is captured by another LWDM and a CCD camera and processed by a phase-shifting technique. Usually a minimum of three phase-shifted fringe patterns is necessary for extraction of the object shape. In this method, a new algorithm based on a two-step phase-shifting technique produces the 3-D object shape. Unlike in the conventional method, phase unwrapping is performed directly by use of an arccosine function without the need for a wrapped phase map. Hence, shape measurement can be speeded up greatly with this approach. A small coin is evaluated to demonstrate the validity of the proposed measurement method, and the experimental results are compared with those of the four-step phase-shifting method and the conventional mechanical stylus method.     

基于DMD的并行共焦图像处理方法研究

在并行共焦测量中,用于构造点光源阵列的光分束器件普遍存在参数固化、对不同测量对象适应性较差的缺点。将数字微镜器件（DMD）作为光分束器件应用于并行共焦测量,可以控制DMD构造柔性化点光源阵列,应对不同的测量场合。推导了DMD的空间光调制模型,规避了“泰伯效应”对并行共焦测量的影响,设计了可抑制光点横向漂移的远心光路,构建了基于DMD的并行共焦测量装置,对比了两种不同的并行共焦图像处理方法。实验结果表明,在没有设置高数值孔径物镜组的情况下,测量装置的纵向分辨率受到一定影响,但所设计的图像处理程序能够快速、准确地获取被测物面的形貌特征。     

Two-step phase-shifting fringe projection profilometry: intensity derivative approach

A new two-step phase-shifting fringe projection profilometry is proposed. The slowly variable background intensity of fringe patterns is removed by the use of an intensity differential algorithm. The high-resolution differential algorithm is achieved based on global interpolation of fringe gray level on a subpixel scale. Compared with the traditional three- or four-step phase-shifting method, the profile measurement is sped up with this approach. Computer simulation and experimental performance are evaluated to demonstrate the validity of the proposed measurement method. The experimental results compared with those of the four-step phase-shifting method are presented.     

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.     

Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram

A three-dimensional (3D) object reconstruction technique that uses only phase information of a phase-shifting digital hologram and a phase-only spatial-light modulator is proposed. It is well known that a digital hologram can store both amplitude and phase information of an optical electric field and can reconstruct the original 3D object in a computer. We demonstrate that it is possible to reconstruct optically 3D objects using only phase information of the optical field calculated from phase-shifting digital holograms. The use of phase-only information enables us to reduce the amount of data in the digital hologram and reconstruct optically the 3D objects using a liquid-crystal spatial light modulator without optical power loss. Numerical evaluation of the reconstructed 3D object is presented.     

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.     

Digitized holography: modern holography for 3D imaging of virtual and real objects

Recent developments in computer algorithms, image sensors, and microfabrication technologies make it possible to digitize the whole process of classical holography. This technique, referred to as digitized holography, allows us to create fine spatial three-dimensional (3D) images composed of virtual and real objects. In the technique, the wave field of real objects is captured in a wide area and at very high resolution using the technique of synthetic aperture digital holography. The captured field is incorporated in virtual 3D scenes including two-dimensional digital images and 3D polygon mesh objects. The synthetic field is optically reconstructed using the technique of computer-generated holograms. The reconstructed 3D images present all depth cues like classical holograms but are digitally editable, archivable, and transmittable unlike classical holograms. The synthetic hologram printed by a laser lithography system has a wide viewing zone in full-parallax and give viewers a strong sensation of depth, which has never been achieved by conventional 3D systems. A real hologram as well as the details of the technique is presented to verify the proposed technique.     

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.     

Space-bandwidth conditions for efficient phase-shifting digital holographic microscopy

Microscopy by holographic means is attractive because it permits true three-dimensional (3D) visualization and 3D display of the objects. We investigate the necessary condition on the object size and spatial bandwidth for complete 3D microscopic imaging with phase-shifting digital holography with various common arrangements. The cases for which a Fresnel holographic arrangement is sufficient and those for which object magnification is necessary are defined. Limitations set by digital sensors are analyzed in the Wigner domain. The trade-offs between the various holographic arrangements in terms of conditions on the object size and bandwidth, recording conditions required for complete representation, and complexity are discussed.     

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.     

Parallel two-step phase-shifting digital holograph microscopy based on a grating pair

An optical configuration for parallel two-step phase-shifting digital holographic microscopy (DHM) based on a grating pair is proposed for the purpose of real-time phase microscopy. Orthogonally circularly polarized object and reference waves are diffracted twice by a pair of gratings, and two parallel copies for each beams come into being. Combined with polarization elements, parallel two-step phase-shifting holograms are obtained. Based on the proposed configuration, two schemes of DHM, i.e., slightly off-axis and on-axis DHM, have been implemented. The slightly off-axis DHM suppresses the dc term by subtracting the two phase-shifting holograms from each other, thus the requirement on the off-axis angle and sampling power of the CCD camera is reduced greatly. The on-axis DHM has the least requirement on the resolving power of the CCD camera, while it requires that the reference wave is premeasured and its intensity is no less than 2 times the maximal intensity of the object wave.     

Parallel phase-shifting interferometry based on Michelson-like architecture

In this paper, we present a new scheme for parallel phase-shifting interferometry that employs a Michelson-like architecture and a simple polarization unit to generate two phase-shifting interferograms with phase shift of π/2 at a single camera exposure. The parallel phase-shifting unit is built with simple optical components, and the distance between the parallel interferograms can be adjusted conveniently. Phase reconstruction is performed by using an algorithm developed for two-step phase-shifting interferometry. The practicability of the proposed configuration and the reconstruction method is demonstrated by experiments.     

Shift-invariant three-dimensional object recognition by means of digital holography

We present an optoelectronic method to analyze three-dimensional (3D) scenes that is able to detect the presence, and also the position and orientation, of a reference 3D object. The data-acquisition procedure is based on digital holography. A phase-shifting interferometer records a single digital Fresnel hologram of the 3D scene with an intensity-recording device. Holographic information of the 3D reference object is also obtained with the same method. Correlation techniques are then applied to recognize the presence and position of the 3D reference object in the 3D scene. The technique also allows us to detect the 3D reference with a small out-of-plane rotation. Preliminary experimental results are presented that demonstrate the theory.