Accuracy of a simple method for deriving the presampled modulation transfer function of a digital radiographic system from an edge image

Several methods for accurately deriving the presampled modulation transfer function (MTF) of a pixelated detector from the image of a slightly slanted edge have been described in the literature. In this paper we report on a simple variant of the edge method that produces sufficiently accurate MTF values for frequencies up to the Nyquist frequency limit of the detector with little effort in edge alignment and computation. The oversampled ESF is constructed in a very simple manner by rearranging the pixel data of N consecutive lines corresponding to a lateral shift of the edge by one pixel. A regular subsampling pitch is assumed for the oversampled ESF, which is given by the original pixel sampling distance divided by the integer number N. This allows the original data to be used for further computational analysis (differentiation and Fourier transform) without data preprocessing. Since the number of lines leading to an edge shift by one pixel generally is a fractional number rather than an integer, a systematic error may be introduced into the presampled MTF. Simulations and theoretical investigations show that this error is proportional to 1/N and increases with spatial frequency. For all frequencies up to the Nyquist limit, the relative error delta MTF/MTF is smaller than 1/(2N). It can thus be kept below a given threshold by suitably selecting N, which furnishes a certain maximum edge angle. The method is especially useful for applications where the presampled MTF is needed only for frequencies up to the Nyquist frequency limit, such as the determination of the detective quantum efficiency (DQE).