Heterodyne Confocal and Solid Immersion Microscopy
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Optical phase is a wonderful thing—it can get you good topographical images of samples with no discernible amplitude contrast, for example, or allow you to disambiguate phase features from amplitude ones. My interest in phase-sensitive microscopes dates back to my graduate work—hence this paper. It gives design details and the theory of the heterodyne scanning laser microscope, including the point- and line-spread functions, plus a deconvolution method that can give resolution equivalent to an ordinary microscope working at λ0/2—ultraviolet resolution from a visible-light scope. Operating with a green Ar+2 laser (514.5 nm) and 0.9 NA, it attained a 10%-90% edge resolution of 90 nm.
This works because the interferometer makes it a confocal microscope, i.e. its amplitude point-spread function is the square of the illumination PSF. By the convolution theorem of Fourier transforms, that means that its bandwidth is twice as wide, i.e. ±2NA/λ. A bit of digital filtering turns the resulting nearly-triangular transfer function into something a bit more Gaussian-looking, which gives us a factor of 2 resolution improvement. Unlike the usual image processing ad-hockery, Fourier filtering makes absolutely no additional assumptions about the sample; the additional information comes from measuring both phase and amplitude, which is why you need an interferometer.