Signal and noise in modulation transfer function determinations using the slit, wire, and edge techniques.

Abstract

The modulation transfer function (MTF) of an idealized imaging system can be determined from the Fourier transform of the system's line-spread function (LSF). Three techniques of experimentally determining the LSF require imaging either a slit, wire, or edge. In this paper, these three techniques are modeled theoretically to determine the noise in the calculated MTFs as a function of spatial frequency resulting from both quantum fluctuations and stochastic detector noise. The techniques are compared using the signal-to-noise ratio (SNR) in the MTF, defined as the ratio of the MTF value to the standard deviation in an ensemble of MTF determinations from independent measurements. It is shown that for a specified photon fluence, the edge method MTF has the highest SNR at low spatial frequencies, while that of the slit method is superior at high frequencies. The wire method SNR is always inferior to that of the slit technique. This suggests that the edge method is preferable for measuring parameters such as the low-frequency drop, and the slit method is preferable for determining high-frequency response. The cross-over frequency at which the slit and edge methods are equal (f(e)) for quantum-noise limited systems is a function of the slit width and the length over which the LSF is measured. For detector-noise limited systems, f(e) is dependent on the slit width only. The SNR in all but the quantum-noise limited slit method can therefore be increased by decreasing the length over which the LSF is measured, smoothing the tails of the LSF, or by fitting the tails to an analytic expression.