# Fast Image Reconstruction Technique for Parallel Phase-Shifting Digital Holography
## 3 Experiments  
The proposed technique was verified experimentally. The experimental system was constructed based on the Fresnel incoherent correlation holography (FINCH) [3, 4, 5, 6, 7]. Figure 4 illustrates the FINCH recording system. The objective lens provides a converging wavefront with incoherent light diffracted from an object. The polarizer transforms the incoherent light into linearly polarized light with a polarization angle of 45\({}^{\circ}\). The phase-modulation spatial light modulator (SLM) modulates the phase of the linearly polarized light in either the horizontal direction or the vertical direction but does not modulate the phase of the linearly polarized light in the orthogonal direction. A quadratic phase distribution is displayed on the phase-modulation SLM so that the horizontally and vertically polarized lights have wavefronts with different radii of curvature. Then, the quarter-wave plate transforms the horizontally and vertically polarized lights into right-handed and left-handed circularly polarized lights. Finally, the polarization image sensor is used to record the interference of the two circularly polarized lights. An LED with a central wavelength of 525 nm and a bandwidth of 30 nm was used as an incoherent light source. We used SLM-100 (Santec Corporation, Aichi, Japan) with a resolution of 1440 \(\times\) 1050 as a phase-modulation SLM; a pixel pitch of 10.4 \(\upmu\)m was used. The polarization camera was VP-TRI050S-P (Lucid Vision Labs, Inc., Richmond, BC, Canada), which had a resolution of 2448 \(\times\) 2048 and a pixel pitch of 3.45 \(\upmu\)m. The central 2048 \(\times\) 2048 pixels were used for hologram recording. The focal length of the objective lens was 20 mm, and the focal length of the quadratic phase distribution displayed on the SLM was 600 mm. The theoretical minimum resolvable distance was 1.60 \(\upmu\)m [6]. A negative test target USAF1951 was used as a recording object. The calculations were performed using a personal computer (Intel Core i7-8550U 4.0 GHz CPU, 8 GB RAM). Figure 5a-c shows the reconstructed images obtained using the conventional technique and Figure 5d-f show those obtained using the proposed technique. For the image  
Figure 4: Experimental system based on Fresnel incoherent correlation holography (FINCH). interpolations, we used the bilinear, bicubic, and Lanczos-3 algorithms with the kernel sizes of \(3\times 3\), \(7\times 7\), and \(11\times 11\), respectively. The peak signal-to-noise ratios (PSNRs) between the images calculated using the conventional and proposed techniques for the bilinear, bicubic, and Lanczos-3 algorithms were 61.2, 61.3, and 62.1 dB, respectively. Thus, the reconstructed images obtained by the two techniques were virtually equivalent. Table 1 shows a comparison of the calculation time required by the different algorithms. The calculation time was measured separately for object wave generation and diffraction calculations. The results were averages of 100 calculations. The proposed technique effectively reduced the calculation time for the object wave generation. The time required for the object wave generation did not depend on the kernel size of the interpolation. The diffraction calculation time for the proposed technique was slightly longer than that for the conventional technique because the multiplication operations of the Fourier transform of the interpolation kernel were added to the diffraction calculation. Figure 6 shows the magnified reconstructed images obtained using the proposed technique for comparing the effects of the interpolation algorithms. The highest spatial frequency line group was extracted. From top to bottom, the line spacings were 2.76, 2.46, and 2.19 \(\upmu\)m. In [32], the authors reported that in the reconstructed images, the bicubic interpolation produced smaller errors than the bilinear interpolation; however, the calculation time required for the bicubic interpolation was approximately twice as