Method and apparatus for determining best focus using dark-field imaging

Abstract

A method and apparatus () for determining a best focus position of an object () relative to a reference position (e.g., axis A) of a dark-field optical imaging system (), with an effective focusing range up to 10 times of the depth of field of the system. The method includes the steps of first forming a dark-field image of the object at different focus positions (z). Each dark-field image has a corresponding image intensity distribution with an average intensity and a variance of intensity. The next step is forming a set of contrast values by calculating a contrast value (C) for each dark-field image based on the variance and the average intensity. The last step is determining the best focus position by fitting a Lorentzian function to the set of contrast values plotted as a function of the different focus positions and identifying the focus position associated with the maximum contract value (C). The second step includes digitizing each dark-field image such that the image intensity distribution for each the dark-field image is a digitized image intensity distribution comprising discrete gray-scale intensity levels (I) corresponding to a discrete plurality of n pixels, and then arranging each the digitized image intensity distribution into a histogram (H(I)) of an amount of the pixels having a given the gray-scale intensity level (I).