Pattern matching for three-dimensional tracking of sub-micron fluorescent particles

A microscope objective of NA = 0.6 designed for air medium has been used to generate diffraction patterns of sub-micron fluorescent particles with various defocus distances through a thick cover glass with a mismatched refractive index. The diffraction pattern centers were located by a cross-correlation analysis between the central Airy disk of the diffraction pattern and a template with the standard Airy intensity distribution. The locating accuracy of the diffraction pattern centers was 0.02-0.04 mu m (0.1-0.2 pixels). Cross-correlation analyses were also performed to match the measured particle diffraction pattern to a calculated intensity distribution with the Gibson and Lanni scalar diffraction model to determine the particle defocus distance. The matching results showed that, unlike the product cross-correlation function, the least-squares error function, which has been extensively used to recognize objects in images, could be used to match the intensity distributions with a simple weight function. The defocus distances of particles under a 1.1 mm thick cover glass with the defocus distances larger than about 13 mu m could be determined at an accuracy better than 0.1 mu m by intensity distribution matching.