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

In a computer system, a method of determining the best focus position of an object relative to a reference position, based on a plurality of dark-field images of the object, comprising the steps of:

• a) storing, in a computer readable medium, data corresponding to the plurality of dark-field images, each said dark-field image being associated with a different focus position and having an associated image intensity distribution with an average and a variance;
• b) forming, in said computer system, a set of contrast values by calculating a contrast for each said dark-field image, based on said variance and said average;
• and
• c) determining, in said computer system, the best focus position by fitting a Lorentzian function to said set of contrast values slotted as a function of said different focus positions;
• wherein said step b) further includes the steps of:
• d) digitizing each said dark-field image with said image intensity distribution for each said dark-field image having a digitized image intensity distribution comprising discrete gray-scale intensity levels, In corresponding to a discrete plurality of n pixels;
• and
• e) arranging each said digitized image intensity distribution into a histogram, H(In), of an amount of said pixels having a given said gray-scale intensity level, In.

A computer readable medium capable of holding data corresponding to at least four dark-field image intensity distributions measured at different focus positions, and holding instructions for determining a best focus position based on said data, by performing the steps of:

• a) calculating an average intensity and a variance for each of said dark-field image intensity distributions;
• b) forming a set of contrast values by calculating a contrast value for each image intensity distribution based on said variance and said average intensity;
• and
• c) determining the best focus position by fitting a Lorentzian function to said set of contrast values clotted as a function of said different focus positions
• wherein said step b) further includes the steps of:
• d) digitizing each said dark-field image such that said image intensity distribution for each said dark-field image is a digitized image intensity distribution comprising discrete gray-scale intensity levels, In, corresponding to a discrete plurality of n pixels;
• and
• e) arranging each said digitized image intensity distribution into a histogram, H(In), of an amount of said pixels having a given said gray-scale intensity level, In.