Telescope Ѳ ptics.net ▪ ▪ ▪ ▪ ▪▪▪▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪◄▐ ►3.5.1. Seidel aberrations, wavefront aberration functionA brief look at the aberration functionhelps clarify basic terminology often used with primary aberrations.
FIGURE 29: All three primaryaberrations affecting point-image quality cause diffraction peak (best focus) to shift away from paraxial(Gaussian) focus. In the past, these aberrations were evaluated atparaxial (Gaussian) focus, hence the name 'classical aberrations'. Whilethey remain a part of optical textbooks, it is best focusaberrations, called balanced, or orthogonal, that are ofpractical importance.
Several Aberration Expressions from the Seidel Sums 38. Such as spherical aberration, coma, astigmatism, field curvature and distortion, as. B terms are primary or Seidel aberrations: spherical, coma, astigmatism, curvature. Amount of distortion increases as image size increases.
'Orthogonal' relates to a characteristic of the calculations used toextract them; 'balanced' refers to balancing the principal primaryaberration with one or more other aberrations in order to have itminimized. In effect, the shift fromparaxial to best focus location is determining best-fit reference spherefor the aberrated wavefront.For classicalprimary spherical aberration, balancing aberration isdefocus, numerically equal to the amount of spherical aberration(expressed as the peak aberration coefficient), but ofthe opposite sign.
Resulting aberration - nowbalanced primary spherical aberration - at the best ordiffraction focus ( B') is only 1/4 of the primary sphericalaberration at Gaussian, or paraxial focus ( P'). The gray shaded areasdo notrepresent the wavefront itself ( W), rather its grosslyexaggerated deviation from aperfect reference sphere ( B), centered at the best focus ( B').The deviation is zero at the center and the edge, reaching the maximumat the 0.707 zone. While the actual wavefront doesn't changeits shape, the wavefront deviation plot changes when it presents deviationof the actual wavefront from another reference sphere, such as the onecentered at paraxial ( P') or marginal ( M') focus.Similarly, balancing aberration for classicalprimary coma is wavefront tilt, which is practically a rotationof the Gaussian reference sphere ( G) centered at the Gaussianimage point ( G')around its vertex, so that better fitting sphere to the tilted wavefrontis found. The new reference sphere ( B) is centered at the best focus ( B'),and the wavefront error for that point - the focal point forbalanced primary coma - is only 1/3of the error at the Gaussian focus (classical coma error). Unlikespherical aberration, where the point of peak diffraction intensity(best focus) is found in another plane in the image space, best focusfor balanced coma is in the same plane (practically, considering verysmall angle of rotation) as the classical focus.Finally, balancing aberration for classical primary astigmatism isdefocus.
Shown to the left is astigmatism of a concave mirror, for whichthe wavefront section in the tangential (vertical) plane ( T),being of smaller diameter, focuses shorter than the wavefront section insagittal (perpendicular to it) plane ( S), with the intermediatewavefront sections focusing in between. Aberration balancing is accomplished by defocusing to the mid point betweensagittal ( S')and tangential ( T') foci, where is located best focus. Thispoint becomes center ofcurvature for the perfect reference sphere B forbalanced primary astigmatism. While the P-V error remainsidentical to that at either tangential or sagittal foci, the RMS errorat the best focus is smaller by a factor 0.82 (note that cylindrical wavefrontdeviations at T' and S' are from the respective referencespheres centered at those points).below shows differences in the size of aberration, and otherspecific properties at paraxial and best focus for the three point-imagequality aberrations, in terms of the peak aberration coefficient ( S,C, A for spherical aberration, coma and astigmatism,respectively), normalized height in the pupil ρ (0.
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