Parallel two-step phase-shifting digital holography is a technique for single-shot implementation of phase-shifting interferometry and requires only the intensity distribution of the reference wave and spatial two phase-shifted holograms. We constructed a system of parallel two-step phase-shifting digital holography and experimentally demonstrated the technique, for the first time. The system uses an originally fabricated image sensor having an array of 2 × 1 micro polarizers. Each micro polarizer was attached on pixel by pixel. In the experiment, the unwanted images, the zero-order diffraction wave and the conjugate image, are removed from the reconstructed image of objects by the system, while the images superimpose on the image of objects reconstructed by Fresnel transform alone. Also the capability of single-shot and three-dimensional imaging is demonstrated by the system.
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Digital holography [1–4] is a technique for recording a hologram using an image sensor and reconstructing the wavefront of objects. The technique is capable of instantaneous three-dimensional (3-D) measurement, and is researched in many fields: microscopy [3,5,6], particle and flow measurement [7,8], object recognition [9,10], shape measurement [11–13], vibration Analysis , and so on. However, the pixel size of an image sensor is too large to record fine interference fringes. Therefore, the angle between the direction of the object wave and that of reference wave has to be less than few degrees. Then the unwanted images, which are the 0-th diffraction wave and the conjugate image, are superimposed on the image of objects. Phase-shifting digital holography  was proposed to reconstruct only the desired image, which is the image of the objects, and can achieve high-accuracy 3-D measurement. However, the technique is impossible to measure instantaneous 3-D information because it requires sequential recording of three or more holograms. In recent years, to achieve both instantaneous and high-quality 3-D measurement, parallel phase-shifting digital holography [16–29] has been studied. This technique records several phase-shifted holograms with a single-shot exposure by using space-division multiplexing technique. Several types of parallel phase-shifting digital holographies have been reported in terms of the number of phase shifts, and the parallel two-step technique can achieve the highest-quality imaging among them . Although parallel four-step technique has been experimentally verified [19,26,28], only a numerical simulation and an experimental simulation utilizing sequential recording of holograms were attempted for the parallel two-step phase-shifting digital holography because the array of phase-shifting device for implementation of two phase-shifts has not been developed. In this paper, we report a construction of a system of parallel two-step phase-shifting digital holography using a camera having an image sensor on which an array of 2 × 1 micro polarizers was attached, and experimental demonstration of the technique, for the first time.
Figure 1 shows the basic concept of the parallel two-step phase-shifting digital holography. In this technique, an image sensor simultaneously records the information of two phase-shifted holograms with a single-shot exposure using space-division multiplexing of reference waves. Multiple holograms required for the phase-shifting interferometry are generated from the recorded single hologram by applying the pixel extraction and interpolation to the recorded hologram. The complex amplitude of an object wave on the image sensor plane is calculated from the generated multiple holograms and the intensity distribution of the reference wave by phase-shifting interferometry. The complex amplitude of the object wave at arbitrary position is obtained by applying diffraction calculation to that on the image sensor.
Schematic diagram of the constructed system of parallel two-step phase-shifting digital holography is shown in Fig. 2(a) . A perpendicularly polarized light beam is emitted from the laser. The laser beam is split into two beams by a beam combiner. One beam illuminates the objects. The scattered light from the objects passes through the polarizer and is changed to the perpendicularly polarized light. And then the scattered light arrives at the image sensor of the originally developed camera and becomes the object wave. The other beam passes through the quarter wave plate (QWP), and then arrives at the image sensor. This wave is the reference wave. The developed camera has an image sensor on which an array of 2 × 1-cell of micro-polarizers is attached to implement 90° phase-shift of the reference wave as shown in Fig. 2(b). Each cell of the micro-polarizer array corresponds with each pixel of the image sensor. Figure 2(c) shows the polarization orientation of the micro-polarizer array. Transmission axis of each cell is tilted 45° against that of the polarizer placed between the object and the beam splitter, and parallel or orthogonal to the fast or the slow axis of the QWP. After passing the micro-polarizer array, the object wave and the reference wave which passes through the fast axis of the QWP form a hologram. On the other hand, those passes through the slow axis of the QWP form a hologram with the 90° phase-shifted reference wave. Thus, the single image sensor can acquire the information of two phase-shifted holograms required for two-step phase-shifting technique  with a single-shot exposure. 3-D image of the objects is reconstructed by using the image reconstruction procedure described in Ref. 22 from the recorded single hologram. Although the configuration of the system has been proposed by Nomura et al. , the system of the Nomura’s technique has not only been constructed yet but also is essentially impossible to apply instantaneous measurement because it requires the intensity distribution of the object wave for reconstructing the image of the objects.
To construct the system, we developed a camera having an image sensor on which an array of 2 × 1-cell of micro polarizers was attached. We adopted the fabrication technique of the photonic crystal reported in Ref. 31 to develop the polarizer array, and realized the camera as shown in Fig. 3 . The number of cells of micro polarizers was 1164(H) × 874(V). Each cell was attached on pixel by pixel of the image sensor. The micro polarizers were optimized for the light of 532nm wavelength.
To verify the validity of the parallel two-step phase-shifting digital holography, we conducted an experiment using the developed camera. A U.S. one cent coin and a die shown in Fig. 4 were set as a 3-D object and were located at 520mm and 650mm away from the image sensor plane. A Nd:YVO4 laser operated at 532nm was used as a light source.
Figures 5(a) and 5(c) show the images reconstructed by the constructed system at the position away from 520 mm, and 650 mm, respectively. In Fig. 5(a), the embossment of the coin can be seen, and the dot of the die is blurred. On the other hand, the embossment of the coin is blurred, and the edge of the dot of the die is clear in Fig. 5(c). Thus, the 3-D imaging capability of the constructed system was experimentally demonstrated.
Also focused images of the objects were reconstructed from the same hologram by Fresnel transform alone, for comparison, and shown in Figs. 5(b) and 5(d). The focused images reconstructed by Fresnel transform alone are unclear because of the superposition of the 0-th diffraction and the conjugate images. On the other hand, the images reconstructed by the constructed system are much clearer than those by Fresnel transform alone. Thus, it was confirmed that the 0-th diffraction and the conjugate images are removed from the reconstructed image by the parallel two-step technique. Thus, the effectiveness of the technique is verified.
In conclusion, we have constructed a parallel two-step phase-shifting digital holography system and experimentally demonstrated the effectiveness of the technique, for the first time. This technique is possible for not only single-shot 3-D imaging of high speed phenomena by applying a pulsed laser but also 3-D motion picture (4-D) measurement by continuous recording of holograms. The technique will contribute to 3-D measurement of particles, fluidics, behavior of living cells, and so on.
This study was partially supported by Industrial Technology Research Grant Program from New Energy and Industrial Technology Development Organization (NEDO) of Japan.
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