The optical transfer function and the Meijer-G function

The Meijer-G functions are applied in the calculation of the optical transfer function (OTF) for systems with circular pupil. The case of the defocused Gaussian pupil is examined as a standard paradigm for understanding the OTF in many imaging systems having that pupil. The OTF was obtained as the Fourier transform of the point-spread function and was examined analytically by means of a infinite series of Meijer-G functions, a parameter that characterizes the apodization, and the amount of defocus. A convergence test for the series expansion is provided to obtain a finite number of terms within the required accuracy. The agreement with published numerical results indicates that the Meijer-G functions turn out a useful approach in the analytic calculus of the OTF for the analysis of the imaging characteristics of systems working with apodized circular pupils.