# Enhancing the Quality of Sampled Phase-Only Hologram (SPOH) Based on Time-Division Comb Filtering
## 4 Experimental Results  
To demonstrate our proposed method, a SPOH of the source image in Figure 2a is generated with the optical setting in Table 1. Downsampling factor \(\tau=16\) is adopted as it leads to a reconstructed image with better uniformity in intensity distribution. The correlation score between the source image, and the reconstructed image of the SPOH (shown in Figure 2e) is 0.6387, reflecting that the 2 images are similar. TDCF is applied to the numerical reconstructed image in Figure 2e. The average of four shifted versions of the image, based on Equation (14), is computed and the result is shown in Figure 7a. Similar to Figure 2e, the image intensity is normalized to \([0,1]\) and the dynamic range is shown with a greyscale bar. It can be seen that the sparsity of the reconstructed image has been reduced considerably after applying TDCF. The correlation score between the source image, and the reconstructed image of the phase-only hologram obtained with the incorporation of TDCF is 0.7231, which is higher than the reconstructed image of the SPOH. Next, we employ a phase-only SLM to display the holograms. The SLM is made by Jasper Display Corp. and the model number is JD955B. The resolution is \(1920\times 1080\), the pixel pitch is 6.4 micron, and the maximum frame rate is 60 Hz. The SLM is reflective, and has \(2\pi\) phase modulation (256 levels) at 532 nm. No calibration is made before the experiment. A diode-pumped solid state (DPSS) laser with wavelength \(\lambda=532\) nm is expanded and used to illuminate the SLM, and the reconstructed image is recorded with a Canon (m6 mark II) with 6960\(\times\)4640 resolution and pixel pitch 3.19 micron. The four shifted version of the SPOH representing the source image is sequentially displayed in a repetitive manner. As the reconstructed image is contributed by sequentially displaying the 4 holograms on the SLM, the maximum frame rate is reduced to one quarter of that of the SLM, i.e., 60/4 = 15 frames per second. The four reconstructed images, each corresponding to a shifted version of the SPOH, is captured by the camera. The mean of the four reconstructed images is obtained to simulate the persistence of vision property of human eyes. Optical reconstruction of the SPOH before and after TDCF are shown in Figure 7b,c, respectively. The dynamic range of the image intensity is normalized to \([0,1]\), with 0 and 1 representing the smallest and the largest intensity in the image. A green-scale bar is associated with each image to reflect the relative intensity. Due to imperfection of the optical system, the optical reconstruction is not as good as the numerical reconstruction. However, we observe that with the incorporation of TDCF, the quality of the optical reconstructed image is superior to that of the original SPOH, which is in line with the results obtained in numerical reconstruction. Notably, in Figure 7c, the empty voids that are caused by the down-sampling are reduced, resulting in a more solid and smooth appearance. Figure 6: Two-dimensional time-division comb filtering (TDCF) for enhancing the reconstructed image of a SPOH. To further illustrate the effect of TDCF, refer to a row of the source image, highlighted in grey, in Figure 8a. The intensity variation of this row of pixel for the source image, the reconstructed images of the SPOH before and after applying our proposed method, are shown in Figure 8b-d, respectively. It can be seen that both reconstructed images in Figure 8c,d are down-sampled versions of the source image. However, the sampling interval of the reconstructed image corresponding to our proposed method in Figure 8d is smaller than that of the SPOH in Figure 8c. Figure 7: (**a**) Numerical reconstructed of the SPOH of the source image, based on down-sampling factor \(\tau=16\), in Figure 1a after applying TDCF, (**b**) optical reconstructed image of the SPOH, (**c**) optical reconstructed image of the SPOH after applying TDCF. Analysis on the same row of pixels is conducted on the optical reconstructed images.