8.4.1. Off-axis Newtonian

FIGURE 70: Off-axis segment of a paraboloid focuses pencil of incoming light out of its path. Reflecting flat directing converging light to a more convenient location is also out of the incoming light path, allowing unobstructed system. The parent mirror is usually ~ƒ/4, which is about the upper limit to its relative aperture, both, in regard to econo production and the amount of aberration leftover in the off-axis segment mirror (usually f/10 to f/12 effective f-ratio). Segment of any other conic would produce axial aberrations.

FIGURE 71: Along the axis of aberration, comatic wavefront deviation for a full aperture mirror has two lobe-like formations of opposite signs. Deformation of the portion of the wavefront reflected from an off-axis segment - green shaded - is mostly astigmatic, despite it being originating from mainly comatic deformation of the wavefront as a whole. Section of the wavefront reflected from the segment will have the radius along the axis of aberration - imaginary central vertical line on the plot - more strongly curved than in the direction perpendicular to it. The P-V wavefront error of the segment is determined by the P-V wavefront error of the appropriate portion of the comatic wavefront over its effective pupil (aperture). Since this astigmatic wavefront deformation originates from the parent mirror coma, it changes linearly, with the field angle - not with the square of it, as astigmatism does when it originates from the incoming wavefront being tilted with respect to the optical surface (which is the "usual" astigmatism form for off-axis image points). Variation of wavefront profile with the wavefront incoming angle also produces peculiar image field.

FIGURE 72: Wavefront profile along the axis of aberration (dotted green) for the parent mirror wavefront over the pupil radius d is a basis for calculating approximate P-V error of astigmatism (as the dominant aberration) in an off-axis section mirror. Perfect reference sphere for this wavefront (solid red) determines relative actual wavefront deviation at any pupil height r normalized to 1, according to ρ3-2ρ/3 (Eq.12); for the axis of aberration, θ=0). For a given segment diameter 2Ωd, whose upper edge nearly coincides with that of the parent mirror, the P-V wavefront error with respect to the same reference sphere is identical to the P-V wavefront error over the entire radius d, equal to W=W1+W2. However, it has an obvious tilt element in regard to that reference sphere, which is centered at the best focus for the comatic wavefront as a whole. Best focus of the wavefront segment lies in a slightly different direction; in effect, it is shifted in respect to that of the parent mirror wavefront. Best reference sphere for the segment portion of the wavefront is the one centered at the segment's diffraction focus (dashed red). It is corrected for the tilt error, with the P-V error along the axis of aberration reduced to WΩ~W'+W". The segment wavefront radius shown is in the tangential (vertical) plane, thus determining the tangential astigmatic focus, slightly farther away from the pupil than sagittal focus, which is determined by the perpendicular  wavefront radius (the focus is formed to the left, hence the convex to the left wavefront deformation indicates wavefront surface flatter than the reference sphere). Best focus lies midway between the tangential and sagittal foci of the wavefront segment, perhaps only slightly deviating from best focus location for pure astigmatism.