Signal-to-noise ratio, contrast-to-noise ratio, and exposure time for imaging systems with photon-limited noise

We present simple, mathematically tractable definitions of signal-to-noise ratio (SNR), contrast, and contrast-to-noise ratio (CNR) for imaging systems when photon-counting statistics are the dominant source of noise. These definitions lead to a simple expression for CNR that is convenient for comparing images taken under different conditions and/or in different wave bands. Furthermore, this real-space CNR is directly proportional to the SNR in Fourier space. The sampling factor Q with which a focal plane array records an image is shown to be a primary determinant of exposure time and of SNR. If Q is known (or assumed), the f-number, resolution, and pixel size are not required. (C) 2006 Society of Photo-Optical Instrumentation Engineers.