Abstract: This paper inquires in detail the synthetic aperturemicrowave radiometer(SAMR) on satellite according to the coherent theory, and presents the generalexpression for the SAMR respones to the earth's radiation. When the earth's radicationsource is incoherent, the formula for reconstructing the earth's brightnesstemperature distribution is derived for the narrow- band SAMR. When the earth's radiation soure is coherent, the SAMR outputs do not include the usefrulinformation about the earth's brightness temperature distribution.