Telescope Optics: A Primer for Amateur Astronomers Part 2: Optical aberrations Marc Baril West Hawaii Astronomy Club, October 13, 2009

Overview Quick recap from August. What is an optical aberration? The Seidel aberrations Chromatic aberration Example: Cassegrains Example, fast catadioptric astrographs

Examples of most commonly used telescopes Schmidt Cassegrain (catadioptric) Newtonian reflector (Dobson mount) Air spaced doublet refractor

Optical aberrations, what are they? The ideal telescope images every point in the object plane to exactly a point in the image plane (within the diffraction limit). All the rays traced from a point source at infinity should intersect at one point in the image plane, neglecting diffraction. A plot that shows the intersection of an assorted number of rays traced from the object in the image plane is called a spot diagram. Ideally, an aberration free system (i.e. a diffraction limited system) will have >70 % of its rays contained inside the airy disk diameter in a spot diagram. Aberrations that affect the image of a point source (the point spread function) are; spherical aberration, coma and astigmatism. Also, the telescope must faithfully reproduce straight lines in the source object. Failure to do so is called distortion. Furthermore, it is assumed that the best image surface is a plane as this is the most generally useful for cameras and eyepieces. Deviation of the image surface from a plane is called field curvature.

Spherical aberration Spherical mirror Parabolic mirror Note: Spherical aberration is unaffected by the field position.

Best focusInside focusOutside focus Negative S.A. None Positive S.A. Diffraction disk in the presence of pure spherical aberration (S.A.)

Coma Coma is an off-axis aberration that increases linearly with the field position. Using the same eyepiece, coma will appear the same in any Newtonian telescopes of a certain focal ratio. Coma increases as the inverse of the focal ratio of the Newtonian.

Astigmatism (3 rd order) 3 rd order astigmatism occurs for objects off-axis and occurs when sagittal and tangential rays come to a different focus. 3 rd order astigmatism increases as the square of the angular field distance – bad, bad bad! The other form of astigmatism is due to non-rotationally symmetric optics due to poor fabrication (e.g. the human eye) or by deliberate design (e.g. Shiefspiegler). Sagittal plane Tangential plane

Aberrations of the field – distortion and field curvature Barrel distortionPincushion distortion Field curvature or Petzval curvature occurs when the focal plane is not planar. In the presence of astigmatism there are two additional focal planes for the best sagittal and tangential focus. In such a case the best focus plane may lie anywhere between the three planes, depending on the relative strength of other aberrations present.

Chromatic aberration Like spherical aberration, (longitudinal) chromatic aberration affects axial and off-axis images equally. For the catadioptric telescope systems we will be looking at in this talk it is a minor aberration in all cases when the lenses are correctly manufactured. A regular achromat is designed to bring two colors to a common focus. An apochromat brings three colors to a common focus as well as correcting for S.A. at two colors. A superachromat combines four colors in the same focal plane.

Example: The Cassegrain reflector Compare 3 different 2-mirror cassegrains, all with a 20 cm aperture, f/10 with typical separation between primary and secondary (set to produce a 30% linear central obstruction).

…All have have curved fields (the diagrams are drawn on the curved field!). Dall Kirkham – ellipsoidal primary / spherical secondaryClassical – paraboloidal primary / hyperboloidal secondary Ritchey-Chretien – hyperboloidal primary and secondaryRitchey-Chretien – flat focal plane… Focal plane radius: 22.5 cm Focal plane radius: 15 cm Focal plane radius: 14.4 cm Focal plane radius: infinity Spot diagrams

Schmidt and Maksutov Cassegrains Maksutov (“rumak”) Typical Schmidt Cassegrain (SCT)

SCT Rumak Focal plane radius: 48.5 cm Focal plane radius: 31 cm

Improving things: Adding one surface with a conic constant… What happens when the secondary is made aspheric (in this case almost paraboloidal). This is the principle behind Meade’s “ACF” (advanced coma free) design (a.k.a. RCX). Focal plane radius: 22 cm

Fast (less than f/4) astrographs: Schmidt and Wright Newtonians In the Schmidt Newtonian the primary is spherical, in the Wright Newtonian the primary is an oblate ellipsoid to correct for coma. Commercial example of a Schmidt Newtonian: Meade LXD-75 series: SN-6, SN-8 & SN-10

… More f/4 astrographs: Maksutov Newtonians Somewhat improved performance over a Schmidt Newtonian at the cost of a more expensive to fabricate lens. If the primary is made aspheric (oblate, but half as much as in the Wright design), Wright camera performance is approached.

Sub-aperture coma correctors: The Wynne Corrector Ross style correctors (very poor performance). Wynne corrector (3 elements). For both correctors, performance is improved if the primary is slightly hyperboloidal. In this case the corrector must be designed to match the primary mirror! Wynne corrector for an f/4 parabolic mirror (optimized to maintain 42% or less central obstruction ratio) Uses inexpensive common glasses; BSL-7, LAL54 & FSL5

The Wynne corrector is the basis of the ASA astrographs. Their “type-h” astrographs use a hyperbolic primary mirror to further improve the performance by reducing the astigmatism. …But this performance comes at a steep price.