We have studied the usefulness of both pre- and post-ADC frame summing for the purpose of reducing the effect of quantum noise and digitization noise in portal imaging systems. The study is based on the fluorescent-screen video-camera type of system. The study predicts the not-surprising result that provided the noise level at the ADC input is sufficiently large, the overall SNR can be increased by a factor of square root of M1M2, where M1 and M2 are the number of frames summed before and after the ADC. The study also predicts, somewhat unexpectedly, that there is an operating region in which increasing M1 actually decreases the SNR in the final image. To avoid this region M1 must be less than approximately 6 x 2(2B) (1 + -delta-1)1/2/(iaccf), where B is the number of ADC bits, -delta is the mean number of optical photons detected by the video camera per detected x-ray photon, iacc is the open-field number of detected x-ray photons per accelerator pulse per pixel, and f is the patient transmission factor. An equivalent statement is that the rms noise at the input to the ADC, sigma in, must exceed approximately 0.4q where q is the quantization interval of the ADC. It is possible that some systems operate in or close to this region. A second feature of this anomalous behavior is that the final image is not necessarily improved by increasing the number M2 of post-ADC-summed frames. For example, when sigma in/q = 0.2, there is no improvement in the overall rms error for M2 > 32.(ABSTRACT TRUNCATED AT 250 WORDS)