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Optical System Design – S15 Reflector Telescopes Reflector Telescope Design Optical System Design – S15 Reflector Telescopes Reflector Telescope Design Objective: Describe the optical imaging performance of reflector telescopes. Telescope eyepieces are not discussed here, but must be designed carefully to not destroy the imaging capabilities of a telescope. + mirrors have no chromatic aberration (same telescope useful in uv-vis-IR) + mirrors have high reflectance over a very broad wavelength range + large mirrors can be built stronger and lighter than large lenses - mirrors easily get in the way of each other Joseph A. Shaw – Montana State University http://ngst.gsfc.nasa.gov/about.html 1 Optical System Design – S15 Reflector Telescopes Surface sag “sag” is the optical term for the shape of a surface that deviates from flat. 휌 2 2 Sag = 푅 − 푅2 − 휌2 = 푅 − 푅 1 − 푅 R r 2 2 휌 휌 푅2 − 푦2 Sag ≅ 푅 − 푅 1 − = sag 2푅2 2푅 휌2 Sag ≅ 2푅 …parabolic approximation of the sag of a spherical surface… Joseph A. Shaw – Montana State University Refs: J. M. Geary, Intro to Lens Design with practical Zemax examples, pp. 22-23. 2 Optical System Design – S15 Reflector Telescopes Conic Sections Joseph A. Shaw – Montana State University 3 Optical System Design – S15 Reflector Telescopes Conics A conic is a surface of revolution formed by spinning a conic section around the axis. 2 2 Equation for a conic centered on the z axis: r 2 Rz (k 1)z 0 r = radial coordinate ( r 2 x 2 y 2 ) R = vertex radius of curvature, k = conic constant. All conics satisfy Fermat’s principle (that is, have perfect imaging) at 2 conjugate points. Joseph A. Shaw – Montana State University 4 http://www.yahooligans.com/reference/dictionary/illus/pbloid.html Optical System Design – S15 Reflector Telescopes Conic constants 2 conic constant = K Eccentricity = e k e Shape eccentricity conic constant focal length sphere e = 0 k = 0 f < R/2 paraboloid e = 1 k = -1 f = R/2 Hyperboloid e > 1 k < -1 f > R/2 Prolate ellipsoid 0 < e < 1 -1 < k < 0 f < R/2 Oblate ellipsoid k > 0 Joseph A. Shaw – Montana State University 5 Optical System Design – S15 Reflector Telescopes Sag of aspheric surface The aspheric sag equation is found simply by solving the conic equation for z. r 2 R Sag for a conic: z 2 1 1 k 1 r R r 2 Sag for even asphere: z R a r46 a r ... 2 46 1 1 k 1 r R a’s = high-order aspheric coefficients R = vertex radius of curvature Refs: Zemax manual (ver 13, 2013), p. 329 D. Malacara, Optical Shop Testing, 2nd ed., Appendix A Joseph A. Shaw – Montana State University R. Shannon, Art and Science of Optical Design, sec. 7.1.6 6 Optical System Design – S15 Reflector Telescopes Spherical Mirror with stop at center of curvature When the aperture stop is at the mirror’s center of curvature, there are no “off-axis” rays and the image plane is a curved surface with radius equal to the mirror focal length. Coma and astigmatism are both zero, but the mirror still has spherical aberration. Joseph A. Shaw – Montana State University 7 Optical System Design – S15 Reflector Telescopes Paraboloidal Mirror Parabola defined as the locus of points in a plane whose distance to the focus equals the distance to a fixed line (called the directrix). A parabolic mirror has zero astigmatism when the aperture stop is located at the focus. But, B because spherical is also zero, A = B stop shifts do not affect coma. A Stigmatic imaging for parallel light (i.e., the “other” focus is at infinity) Joseph A. Shaw – Montana State University 8 Optical System Design – S15 Reflector Telescopes Paraboloidal one-mirror telescopes Herschellian (off-axis parabola) Newtonian (high obscuration ratio) Field always limited by coma for parabolas. Joseph A. Shaw – Montana State University (arc minutes at best) 9 Optical System Design – S15 Reflector Telescopes Ellipsoidal Mirror B Ellipse defined as the locus of points from which the A sum of distances to two foci (F1 and F2) is a constant. F1 F2 A + B = constant Optical property: A ray passing through one focus is reflected to pass through the other focus. Joseph A. Shaw – Montana State University 10 Optical System Design – S15 Reflector Telescopes Hyperboloid Mirror B Hyperbola is defined as the locus of points A for which the |difference of distances| to two foci is constant (points & foci in a common plane) |A-B| = constant Optical property: A ray that approaches a hyperbola from the side opposite a focus and pointing toward that focus reflects toward the other focus. Joseph A. Shaw – Montana State University 11 Optical System Design – S15 Reflector Telescopes Two-mirror telescopes b d a b a b n a Relationship between primary-mirror 4 3 2 and secondary-mirror conic constants y R m 1 k 1 2 1 k (k), radius of curvature (R), marginal 1 y 4 R3 2 m 1 ray heights (y), and magnifications 1 2 (m) for zero spherical aberration. D. Schroeder, Astro. Optics, p. 54 with m sign convention changed to match Smith’s. Ex: choose k2 = 0 (sphere), solve for k1 = -0.7696 (ellipse) … Dall-Kirkham Joseph A. Shaw – Montana State University (see references for many aberration equations) 12 Optical System Design – S15 Reflector Telescopes Gregorian Primary mirror = parabola Secondary = ellipsoid Spherical = 0 Field limited by … Joseph A. Shaw – Montana State University 13 Optical System Design – S15 Reflector Telescopes Cassegrain Primary mirror = parabola (k = -1) + very compact Secondary = hyberbola - convex secondary Spherical = 0 difficult to test Astigmatism larger than for parabola alone, but field usually limited by coma. Shorter than optically equivalent Gregorian Cassegrain – France 1672 Joseph A. Shaw – Montana State University 14 Optical System Design – S15 Reflector Telescopes Dall-Kirkham • Primary mirror = ellipse “poor man’s cassegrain” • Secondary = sphere (spherical 2ndary cheaper) • Spherical = 0 (on axis, obj at inf) + much easier to build and test • Spherical secondary generates than cassegrain (cheaper) additional aberrations … + less sensitive alignment • Field limited by coma, to about 1 ( m 2 1 ) times smaller than for 2 2 - larger aberrations classical cassegrain. Joseph A. Shaw – Montana State University 15 Optical System Design – S15 Reflector Telescopes Schmidt • “Catadioptric” system (combined reflector and refractor) • Spherical mirror + aspheric refracting (corrector) plate at center of curvature • Corrector plate at center leads to low off-axis aberrations • Corrector plate minimizes spherical + very compact + corrector plate easier to build than parabolic primary - images limited by spherochromatism and high-order astigmatism & spherical Joseph A. Shaw – Montana State University Schmidt – Estonia 1930 16 Optical System Design – S15 Reflector Telescopes Schmidt-Cassegrain Spherical primary and secondary plus aspheric corrector plate + very compact + easy to build and test - images contain some coma, astigmatism, spherochromatism … Joseph A. Shaw – Montana State University 17 Optical System Design – S15 Reflector Telescopes Maksutov Spherical primary and secondary plus meniscus corrector plate (sometimes elliptical primary … ex. AstroPhysics) + very compact + easy to build and test - images contain some coma, astigmatism, spherochromatism … correcting plate Maksutov – Russia 1941 & secondary Joseph A. Shaw – Montana State University 18 Optical System Design – S15 Reflector Telescopes Ritchey-Cretian “Aplanatic Cassegrain” ~ Cassegrain with + wider field of view than cc primary mirror = hyperboloid + spherical = coma = 0 secondary = hyperboloid - expensive to build (conic constant more negative than for classical cassegrain) - more difficult to test than other cassegrain types (Hubble = f/24 2.4 m R-C !) Spherical = coma = 0 (“aplanat”) Slightly more astigmatism than cc, but zero coma allows larger FOV Field limited by astigmatism (larger than coma-limit for cc because aberration symmetry) Joseph A. Shaw – Montana State University 19 Optical System Design – S15 Reflector Telescopes Hubble Space Telescope Ritchey-Cretian with 2.4-m primary and 0.3-m secondary (both hyberboloids) Hubble primary was ground to the wrong figure because of a slightly misplaced null lens during interferometric testing. The result was large Spherical aberration. Before COSTAR After Joseph A. Shaw – Montana State University 20 University State Montana – Shaw A. Joseph 21 0.6328 OBJ: 0.0000 (deg) OBJ: 0.0500 (deg) 100.00 IMA: 0.000 mm IMA: 50.238 mm Surface: IMA Spot Diagram Hubble Space Telescope Hubble spot diagrams diagrams spot Hubble designed as 3/9/2013 Units are µm. Airy– Radius: 18.52 µm Field : 1 2 RMS radius : 16.834 16.346 GEO radius : 22.852 23.295 Hubble_1(design).ZMX Scale bar : 100 Reference : Chief Ray Configuration 1 of 1 Optical System Design Design System Optical Reflector Telescopes Telescopes Reflector S15 – University State Montana – Shaw A. Joseph 22 0.6328 OBJ: 0.0000 (deg) OBJ: 0.0500 (deg) 1000.00 IMA: 0.000 mm IMA: 50.370 mm Surface: IMA Spot Diagram Hubble Space Telescope Hubble spot diagrams diagrams spot Hubble built as 3/9/2013 Units are µm. Airy– Radius: 18.61 µm Field : 1 2 RMS radius : 169.806 157.325 GEO radius : 290.329 245.825 Hubble_1(asbuilt).ZMX Scale bar : 1000 Reference : Chief Ray Configuration 1 of 1 Optical System Design Design System Optical Reflector Telescopes Telescopes Reflector S15 – Optical System Design – S15 Reflector Telescopes Hubble testing The test interferometer was accidentally focused on a metal cover over the null corrector spacing rod instead of on the rod itself, as intended (this happened because a black paint chip fell off, revealing a metal glint point). COSTAR corrective interferometric optics installed in 1993 null-lens test See Jeff Hecht, “Saving Hubble,” Optics and Photonics News, pp. 42-49, March 2013. Images: http://news.bbc.co.uk/1/hi/sci/tech/638187.stm Joseph A. Shaw – Montana State University 23 Optical System Design – S15 Reflector Telescopes Large Telescopes Modern mirrors can be made much larger than lenses, which would break or sag severely under their own weight.
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