In this paper, an exact signal-to-noise-ratio (SNR) analysis is carried out for spectral amplitude coding optical code division multiple access (SAC-OCDMA) system with spectral direct detection (SDD). Unlike to the early calculated SNR expression based on SAC-OCDMA with balanced detection decoder scheme, which cannot be applied to SAC-OCDMA system with SDD; exact SNR formulas are derived and compared for two SDD schemes. We also mathematically clarify the justification to use the proposed approaches. Based on these approaches, the SNR formulas of SAC-OCDMA system with both SDD schemes, for various zero cross correlation (ZCC) codes, are accurately determined.