Effects of undersampling on the proper interpretation of modulation transfer function, noise power spectra, and noise equivalent quanta of digital imaging systems

The proper understanding of modulation transfer function (MTF), noise power spectra (NPS), and noise equivalent quanta (NEQ) in digital systems is significantly hampered when the systems are undersampled. Undersampling leads to three significant complications: (1) MTF and NPS do not behave as transfer amplitude and variance, respectively, of a single sinusoid, (2) the response of a digital system to a delta function is not spatially invariant and therefore does not fulfill certain technical requirements of classical analysis, and (3) NEQ loses its common meaning as maximum available SNR2 (signal-to-noise) at a particular frequency. These three complications cause the comparisons of MTF and NEQ between undersampled digital systems to depend on the frequency content of the images being evaluated. A tutorial of MTF, NPS, and NEQ concepts for digital systems is presented, along with a complete theoretical treatment of the above-mentioned complications from undersampling.