The optical hyperfine pumping clock approach relies on the detection of a low level fluorescence. The clock stability is a function of the signal-to-noise ratio (SNR). This paper exhaustively analyzes the properties of spurious noise in the high-gain trans-impedance amplification of the low noise PIN photodiode signal. It is shown that long-term data acquisition and statistical analysis is an appropriate tool to characterize such phenomena. The few existing literature would attribute the spurious to the operational amplifiers. In contrast, it turns out that the photodiode itself is the source of the spurious.