The theory of diffraction-limited resolution in microparticle image velocimetry

A theory of diffraction-limited spot size is developed for infinity-corrected microscope optics. Previously reported formulae were originally derived using a single-lens system. In addition, the previously reported relationship between f-number and numerical aperture assumed a paraxial approximation and was limited to air-immersion lenses. Here, a new relationship between f-number and numerical aperture is developed, and is valid for all numerical apertures and all immersion media. In addition, a new theory is developed that estimates the effective numerical aperture of an oil-immersion lens when imaging into fluid of a lower refractive index, such as water. The results indicated that when imaging into water, high numerical aperture NA = 1.0 or 1.2 water-immersion lenses provide comparable and sometimes better diffraction-limited resolution than NA = 1.4 oil-immersion lenses. In addition, when imaging into water, water-immersion lenses may provide superior image quality, because they are corrected for aberrations resulting from the water/glass interface.