Signal-To-Noise Ratio Dependence On Frame Time, Time Delay And Integration (TDI), And Pulse Shaping

The dependence of the signal-to-noise ratio (SNR) on three important focal plane design functions--frame time, time delay and integration (TDI), and pulse shaping--is examined. A general focal plane model is developed that permits the SNR, to be parameterized separately in terms of the three functions. The focal plane model treats both staring, mosaic sensors and scanning, line sensors as special cases of the model parameters, and accounts for the presence of multispectral detectors arranged in either a side-by-side or a sandwiched configuration. Both noise in the detectors (including photon noise) and CCD noise that arises in transferring the signal off the focal plane are considered, but it is assumed that the detectors are not limited by l/f noise. General parametric expressions for the SNR in terms of frame time, the number of samples per blur spot (pulse shaping), and the number of TDI steps are derived, and specific results for both a mosaic focal plane and a scanning line focal plane are presented. It is found that, regardless of the focal plane design, the SNR increases at least as the square root of the frame time and decreases at least as the square root of the number of samples per blur spot. The behavior of the SNR in terms of the number of TDI steps is more complicated and depends on the specific focal plane configuration. It can be stated generally, however, that the presence of CCD noise ultimately causes the SNR to peak and then decrease with increasing TDI. The peak SNR occurs at large TDI steps for scanning line sensors and at small TDI steps for mosaic sensors.