Improved correction of axial geometrical distortion in index-mismatched fluorescent confocal microscopic images using high-aperture objective lenses

Extracting quantitative data from microscopic volume images is straightforward when the refractive indices of the immersion medium and the mounting medium are equal. The readings of the position of the specimen stage can be directly used to measure depth and width. Imperfectly matched immersion and mounting media result in axial geometrical distortion. Linear correction of the axial distortion using the paraxial estimate of the axial scaling factor yields results that may differ as much as 4% from the actual values. From calculations based on a theoretical expression of the 3-D point-spread function in the focal region of a high-aperture microscope focussing into a mismatched mounting medium, we derived axial scaling factors that result in quantitative results accurate to better than 1%. From a non-linear correction procedure, an improved formula for the paraxial estimate of the axial scaling factor is derived.