Autofocusing in microscopy based on the OTF and sampling

Abstract

In the literature many autofocus algorithms have been proposed and compared (Groen et al 1985, Firestone et al 1991, Yeo et al 1993, Price and Gough 1994) for use in optical microscopy (bright field and fluorescence microscopy). Most of the focus criteria measure the high frequency contents of a recorded image as a measure of focus. In this paper we show that a focus criteria should measure the signal power of the middle frequency, since defocusing mainly reduces the frequencies around half the cut-off frequency of the optical system. The filter that provides the required band-pass filtering depends strongly on the sampling density of the camera. There are two practical combinations of sampling density and one-dimensional digital band-pass filter: Sampling at the Nyquist frequency and the {1, 0, -1} filter; Sampling at half the Nyquist frequency and the {1, -1} filter. The latter is to be preferred due to noise considerations and the fact that it uses four times fewer sample points. Calculation speed can also be increased by further reducing the sampling density perpendicular to the filter (on chip or in software) down to 1/8 of the Nyquist frequency. We have designed a three-phase autofocus algorithm that works well in fluorescence and bright field microscopy. The phases are: Coarse: find the region near focus (step size of typically a few microns); Fine: find a quadratic region around focus (step size around one micron); Refine: use a quadratic fit on samples around the peak to find the in-focus position. We found that the final focus error is smaller than the mechanical reproducibility of our ζ-axis (~50 nm) for light levels down to 400 photo-electrons per pixel (sampling at the Nyquist frequency using a cooled CCD camera with pixels of 6.8 x 6.8 μm).