Estimation of point-spread functions and modulation-transfer functions of optical devices by statistical properties of randomly distributed surfaces

The point-spread function a(PSF) and the modulation-transfer function (MTF) are important tools to characterize the information transfer through optical devices. They give useful information about the resolution. Several methods have already been achieved to calculate the PSF and the MTF from theoretical aspects of wave propagation or from experimental results. I present a novel way of estimating these two functions. It deals with statistical considerations for a randomly distributed surface involving a statistical determination of the PSF and the MTF. Indeed, in this case the theoretical shape of the autocorrelation function of such surface profiles is known. It is a decaying exponential function α[exp(-β|x|)]. Comparingthe theoretical autocorrelation-function profile with the experimental one and deconvolving in Fourier space leads to an estimation of the MTF of the imaging device. Applying the inverse Fourier transform to the MTF involves the computation of the PSF, assuming that the latter has no imaginary part and is symmetrical. The two-dimensional images are regarded as an iteration of one-dimensional ones according to the orthogonal direction. The MTF's and PSF's are therefore one-dimensional. Different results are presented. The first result proceeds from investigation with scanning near-field microscopy and illustrates the method step by step. The tunneling effect is detected assuming that the information transfer is linear. The last result concerns an optical profilometer, and the influence of the microscope objective is studied.