Sinewave-based measurement of the modulation transfer function for noisy and distorted images

The modulation transfer function (MTF) is essential for assessing the spatial frequency characteristics of optical imaging systems. This study presents an innovative sinewave-based methodology for measuring the MTF, which demonstrates robustness against noise and applies to images exhibiting distortion. Slanted-sinusoidal fringe charts were utilized as test objects to simplify contrast calculations. The MTF for each frequency is determined by optimally fitting a sinusoidal function to unequally spaced pixel data using nonlinear least-squares estimation, enabling the derivation of optimal solutions that comply with Cramér-Rao bounds. This methodology enables MTF measurements in small-sized images with minimal distortion and at frequencies beyond the Nyquist limit. Numerical simulations and empirical camera experiments revealed that our proposed approach outperformed traditional edge-based methods.