The imaging property of an astigmatic system is analysed in the matrix form. On the x-direotion spectrogram is conjugated vdth the image place. But on the y-direction the source place is conjugated with the image place. In this way the astigmatio system plays a role to average the noise on the y-direction. The source of noise of the laser plasma X-ray spectrogram are quantum noise of X-ray and granularity of the plate. The former is multiplicative to signal, but tho rear is added. The two types of the noise may bo averaged with an astigmatic system. Experimental results are represented.