◄ 2.1. Light-gathering power   ▐    2.3. Telescope magnification
 

2.2. Telescope resolution

Resolution is another vital telescope function. Simply put, telescope resolution it is the limit to how small a detail can be detected in the image it forms. In the absence of aberrations, what determines limit to resolution is the effect of diffraction. Being subject to eye perception, resolution varies with detail's shape, contrast, brightness and wavelength. The conventional indicator of resolving power - commonly called diffraction resolution limit - is somewhat arbitrarily set forth by the wave theory as ~λ/D in radians, λ being the wavelength of light, and D the aperture diameter (expressed in arc seconds, it is 13.4/D for D in mm, or 4.5/D for D in inches, both for 550nm wavelength).

Linearly,  diffraction resolution limit is given by ~λF, F being the ratio number of the focal length to aperture diameter (F=f/D). Specifically, this is a limit to resolution of two point object images of near-equal intensity (FIG. 7). Resolution limit can vary significantly with other object types (FIG. 8).

Peak intensities of the two point-object images on Fig. 7 remain unchanged at the central separation of 1.22λ/D, and larger. At smaller separations (smaller the Rayleigh limit), the two peak intensities start to increase, at first slowly, then rather fast, with the combined intensity doubling as the two point-objects merge (this means that the left plot, illustrating two PSFs at Dawes' limit would be actually slightly higher if not normalized, with the initial peak intensity being at the level of the minima between the two peaks). The combined intensity of the two patterns (normalized to peak intensity of the point-object images) at any point is given by Ic=I'+I", with I' calculated from the PSF intensity profile relation for p'=(x-s/2)π/2, and I" for p"=(x+s/2)π/2, x being the point coordinate on the horizontal axis (with zero at the mid point between two PSF centeroids), and s being the pattern center separation, both in units of λF.

The separation at which the combined PSF flattens at the top occurs at the center separation 107/D in arc seconds, for D in mm (4.2/D for D in inches). It is so called Sparrow's limit, allowing detection  of close doubles based on visual elongation of the bright central spot of diffraction pattern. For closer separations, peak intensity of the combined pattern forms at the mid point between two Gaussian point-object images.

As mentioned, this limit applies to near-equally bright, contrasty point-object images at the optimum intensity level. Resolution limit for star pairs of unequal brightness, or those significantly above or bellow the optimum intensity level is lower. For other image forms, resolution limit also can and does deviate significantly, both, above and bellow the conventional limit. One example is a dark line on light background, whose diffraction image is defined with the images of the two bright edges enclosing it. These images are defined with the Edge Spread Function (ESF), whose configuration differs significantly from the PSF (FIG. 8). With its intensity drop within the main sequence being, on the other hand, quite similar to that of the PSF, resolution of this kind of detail is more likely to be limited by detector sensitivity, than by diffraction (in the sense that the intensity differential for the mid point between Gaussian images of the edges vs. intensity peaks, forms a non-zero contrast differential for any finite edge separation).

Formal premises and experimental results on telescopic resolution are covered in detail in Amateur Astronomer's Handbook from J.B. Sidgwick (p37-51). Naturally, resolution in general will deteriorate with introduction of wavefront aberrations.

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