The spatial heterodyne spectrometer used for high precision atmospheric CO2 remote sensing adopts array detector to collect the two-dimensional interferogram at the same time. According to the response nonlinearity and non-uniformity existing in array detector simultaneously, the influence on the interferogram and the recovered spectrum is analyzed respectively. It is pointed out that, at the same detector non-uniform noise, the higher the spectral resolution, the higher noise in recovered spectrum is. The nonlinearity not only impacts the effective spectral range, but also brings nonzero value below the spectral cutoff frequency. A method of correction nonlinearity by several uniform radiances and non-uniformity by a single uniform radiance is reported. The experiments are fulfilled, and the response non-uniformity improves from 4.04% to 0.14%. The recovered spectrum from the corrected interferogram is smooth due to the non-uniformity noise reduction greatly, and the data out of the spectrum cutoff frequency have zero values for correction the response nonlinearity.