Can processed images be used to determine the modulation transfer function and detective quantum efficiency?

Purpose: The modulation transfer function (MTF) and detective quantum efficiency (DQE) of x-ray detectors are key Fourier metrics of performance, valid only for linear and shift-invariant (LSI) systems and generally measured following IEC guidelines requiring the use of raw (unprocessed) image data. However, many detectors incorporate processing in the imaging chain that is difficult or impossible to disable, raising questions about the practical relevance of MTF and DQE testing. We investigate the impact of convolution-based embedded processing on MTF and DQE measurements.

Approach: We use an impulse-sampled notation, consistent with a cascaded-systems analysis in spatial and spatial-frequency domains to determine the impact of discrete convolution (DC) on measured MTF and DQE following IEC guidelines.

Results: We show that digital systems remain LSI if we acknowledge both image pixel values and convolution kernels represent scaled Dirac $\delta$-functions with an implied sinc convolution of image data. This enables use of the Fourier transform (FT) to determine impact on presampling MTF and DQE measurements.

Conclusions: It is concluded that: (i) the MTF of DC is always an unbounded cosine series; (ii) the slanted-edge method yields the true presampling MTF, even when using processed images, with processing appearing as an analytic filter with cosine-series MTF applied to raw presampling image data; (iii) the DQE is unaffected by discrete-convolution-based processing with a possible exception near zero-points in the presampling MTF; and (iv) the FT of the impulse-sampled notation is equivalent to the $Z$ transform of image data.