Bayesian approach to slanted-edge modulation transfer function measurements for lens and pixel-sensor systems.

Abstract

The Bayesian approach to slanted-edge modulation transfer function (MTF) measurements addresses several limitations inherent to the traditional methods. It effectively eliminates the need to differentiate noisy data, which typically require binning, smoothing, or data regularization techniques. Direct incorporation of the optical transfer function (OTF) into the parameter set allows for a more accurate fit to the measured data. The mathematical framework of this approach inherently includes the propagation of measurement noise to the resulting OTF and MTF, ensuring that the propagation of statistical errors is well understood. In addition, the method mitigates a small systematic error at the zero-frequency limit, which is commonly encountered in slanted-edge measurements. Although slanted-edge methods can be applied to a wide range of slant angles, we also demonstrate how problematic angles can be easily identified and addressed during the analysis of the edge image. The proposed method offers a significant improvement in precision at higher spatial frequencies, achieving uncertainties in the normalized MTF measurement of less than two percent point RMS up to the diffraction-limited cutoff, with typical data collection methods.