The raw output of many scanning radiometers is a small, rapidly varying signal superimposed on a large background that varies more slowly, due to thermal drifts and 1/f noise. To isolate the signal, it is necessary to perform a differential measurement: measure a known reference and subtract it from each of the raw outputs, cancelling the common-mode background. Calibration is also a differential measurement: the difference between two outputs is divided by the difference between the two known references that produced them to determine the gain. The GOES-I Imager views space as its background subtraction reference and a full-aperture blackbody as its second reference for calibration. The background suppression efficiency of a differential measurement algorithm depends on its timing. The Imager measures space references before and after each scan line and performs interpolated background subtraction: a unique, linearly weighted average of the two references is subtracted from each scene sample in that line, cancelling both constant bias and linear drift. Our model quantifies the Gaussian noise and 1/f noise terms in the noise equivalent bandwidth, which is minimized to optimize the algorithm. We have obtained excellent agreement between our analytical predictions and Monte Carlo computer simulations.