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telescopeѲptics.net
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4.4. DefocusFormally, defocus wavefront aberration results from the image formed by a telescope objective being observed not at the location of the Gaussian image point, but at a point longitudinally displaced from it. Therefore, it is an actual aberration only when the Gaussian image point coincides with best focus. In such instances when this is not the case - such as the presence of spherical aberration, or astigmatism - certain amount of defocus from the Gaussian image point is necessary to shift to the actual best focus location. In other words, defocus can be balanced with another aberration in order to have the combined aberration minimized. In everyday's jargon, "defocus" has somewhat different meaning: it is simply an axial deviation from best focus location, correctable by mere refocusing. Back to best focus being coinciding with the Gaussian, defocus wavefront error is measured as the optical path difference between the perfect reference sphere for the point other than the Gaussian, and a perfect reference sphere for the Gaussian image point. It is expressed as: Wd= Pr2 (24) with r being the in-pupil ray height in units of the pupil radius, and P the peak aberration coefficient for defocus (equal to the p-v wavefront error) given by P= -Ld/8F2, (25) Ld being the longitudinal defocus (effectively, the difference in radii between the two reference spheres). It is radially symmetrical, with the blur diameter given simply by Ld/F. In units of the Airy disc diameter (2.44lF) the blur diameter is: Bd= 8P/2.44l = -Ld/2.44lF2 (26) which, in units of the wavelength becomes simply Bd=8P/2.44. The RMS wavefront error relates to blur diameter Bd as ω=2.44Bd/√768. The peak defocus aberration coefficient relates to the RMS error as ω=P/√12.
An important property of a telescope is its defocus sensitivity. As
Eq. 25 implies, it is
proportional to the longitudinal defocus Ld, and inversely proportional
to F2.
Taking as the maximum allowable P-V error of defocus P=xλ
(λ
being the wavelength of light)
in either direction from the exact focus, the longitudinal range (including both
sides of defocus) within
which defocus error will not exceed this level is given by Ld=16xlF2.
It is sometimes called focus depth (not to be confused with
field depth, a photographic term referring to the range of distance
in the object space within which the object image remains within a given
focus depth; irrelevant in astronomy, where all objects are very
distant). |