The recording density of multilevel photochromic memory is limited by the signal-to-noise ratio (SNR) of the readout signal. In this paper, shot noise and material noise are investigated through theoretical analysis of SNR. When the bandwidth of a system is less than 1MHz, the material noise takes a prominent position; when the bandwidth of the system is more than 10MHz, the shot noise becomes dominant. The thickness of recording layer can be optimized to maximize the SNR and reduce the influence of the bandwidth of the system on SNR.