# Performance Estimation of Intensity Accumulation Display by Computer-Generated Holograms
## 4 Discussions  
The important parameters obtained from the empirical formula are listed in Table 1. In particular, we consider the PSNR at different propagations (\(P\)) or different numbers of intensity accumulation (\(N\)). The concern of different propagations is for the evaluation of the computing-capacity-limited case, in which the binary CGHs must be generated using a limited computing power (e.g., the real-time display). The concern of different numbers of intensity accumulation is for the evaluation of the frame-rate-limited case, in which the frame rate is limited but the computing power is not a constraint (i.e., non-real-time applications). From Equations (8) and (9) and for \(N\rightarrow\infty\), we can also define a maximum achievable PSNR as \(20\log_{10}\left(S\sqrt{K}\right)\). In other words, the image quality cannot be infinitely  
Figure 6: PSNR of the reconstructed image by LRDS binary CGHs (\(k=4\)) as a function of accumulation number. The values of parameters \((S,K)\) of the fitting curve are \((2.08,12.79)\). Figure 7: PSNR of the reconstructed image by LRDS binary CGHs (\(k=4\)) together with AIA as a function of accumulation number. The values of the parameters \((S,K)\) of the fitting curve are \((2.24,42.4)\). improved via intensity accumulation. This is very different from previous studies [19; 20; 27], in which the noise was assumed to be proportional to \(1/\sqrt{N}\) and thus the quality could be continuously improved. For the MIFA method (Figure 4), the \(S\) value raises to above 3, but \(K\) decreases, in comparison with the RP method. For MIFA with 10 iterations (Figure 5), the \(S\) value increases further than that of MIFA, with five iterations. It is postulated that a greater iteration number can increase the maximum achievable PSNR. On the contrary, the maximum achievable PSNR decreases slightly in the case of more iterations. This counterintuitive result can be explained by the fact that the iteration in producing one hologram is a procedure of signal enhancement. Meanwhile, the same procedure also increases the correlation between different holograms, which effectively reduces the value of \(K\) in the average process. The significantly reduced \(K\) also results in another problem. The efficiency (PSNR at 100 propagations) of intensity accumulation by MIFA CGHs is the worst among all discussed methods. Accordingly, MIFA is not recommended for the intensity accumulation, provided the computing cost is the main concern. The characteristics of LRDS CGH (Figure 6) are almost the same as those of RP CGH. This implies that the randomness generated by random phase and by random down-sampling can be regarded to be identical in practice. Therefore, for a pointwise CGH algorithm (e.g., [28]), the use of random down-sampling can significantly reduce the computing load without degrading the display quality. The fitting model is not applicable for the LRDS+AIA method (Figure 7). The reason is that AIA is an adaptive method to improve the quality of reconstruction globally. Therefore, the statistical randomness of each binary hologram has been broken in this method. According to the above discussion and Table 1, we can conclude that the RP method and the LRDS method are better for the computing-capacity-limited case, while MIFA method can provide a better PSNR for the frame-rate-limited case. The LRDS + AIA method always exhibits the best PSNR, except for the case of a small number of propagations (\(P=10\)). Finally, we will consider the design strategy of intensity accumulation. Since there is a maximum achievable PSNR, the display by using many numbers of intensity accumulation is a waste of computing power. Our goal is to find a reasonable number of intensity accumulation to achieve a PSNR only slightly lower than the maximum achievable PSNR.