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Star image appearance in large ground-based telescopes is determined by the properties of the Optical Path Difference (OPD) fluctuation associated with the image-forming wave potions collected by the telescope aperture. The principal properties are the root mean square (rms) OPD fluctuation and the autocorrelation function of the OPD fluctuation. The OPD properties ultimately depend on the combined effects of turbulence in the atmospheric path, the fixed aberrations of the telescope and, if appropriate, the corrective effects of Adaptive Optics (AO). The equations given in this paper relating star image properties to the OPD properties (and also the inverse relations) apply to all large ground-based reflector telescopes, including ELTs. They apply equally to telescopes with and without AO. The OPD properties can be obtained directly from an image of an unresolved star. This image represents the intensity Point Spread Function (PSF) corresponding to the entire end-to-end imaging path. To obtain the full OPD information compliment, however, the image must be formed at a wavelength that delivers the most general type of star image: a core and halo image. Once the OPD properties have been obtained from such an image, the intensity PSF for the telescope/atmosphere/AO combination can immediately be calculated for any other wavelengths of interest in the extended optical wavelength range, 0.3 μm – 1000 μm. There are numerous applications for the mathematical relationships set out in this paper, including characterization of atmospheric paths, assessment of telescope/AO imaging performance, establishing wave front tolerances for ELTs and other large ground-based telescopes, and the rapid identification of sweetspot wavelength regions where highest resolution is achieved and star images attain maximum central intensity.
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