AtLAST – quick survey of optics issues • Run through of options that I know of, mainly focused on what diffraction- limited field of view can be obtained. • For all cases assume a 50m-diameter aperture and do the ray trace for a 2 degree diameter FoV. (Place stop at the primary and size any other mirrors to pass this FoV. See note on slide 26.) • For now ignore the practical issues. • For each case show the ray trace plus a spot diagram on the focal plane (this is just ray optics – but it gives a good idea of what is going on). • The wavefront errors (in mm) as a function of radius in the focal plane, broken down into Zernike polynomials. Pink is Coma, green is Astigmatism. • A map of the FoV showing the 80% Strehl contours for 3mm, 1mm and 333μm wavelength.
1a. Comparisons • The throughput (“Étendue”) of a system is the product of the collecting area A and the solid angle accepted Ω. For a circular aperture and field with diameters D and Φ this gives: A Ω = η π 2 /16 (D Φ) 2 where η is a factor < 1 for blocking, losses, etc. • More relevant for many purposes is N, the number of independent modes that the system can support, which is roughly Ω / θ 2 where θ ~ λ/D is the beamwidth. This gives: N = k (D Φ / λ) 2 with k ~ 240 if D is in m, Φ in deg and λ in mm 1 . 1 Various other factors could be added here, e.g. x2 for polarization, /4 for detector spacing of 2 f λ in the focal plane, etc.
1b. Aberrations • The primary, or Seidel, aberrations can be expressed, in terms of the wavefront error W at a point, (ρ,θ) in the aperture, as 1 where α is the field angle and d is the radius of the aperture. • These 5 terms are Spherical, Coma, Astigmatism, Curvature and Distortion. • Spherical aberration can usually be eliminated by using conic surfaces. • Distortion means that the image is sharp but that a uniform pixel spacing in the detector does not produce a uniform spacing on the sky. For modest amounts of distortion we can correct this in the data processing, so I have ignored it here. • Curvature is a real problem and quite large for many of these designs. The instruments have to compensate for this. Note that I have done a best fit of the the focal surface, so the plots of Strehl ratio do not include curvature. • We are left with Coma and Astigmatism plus higher order aberrations. 1 https://www.telescope-optics.net/Seidel_aberrations.htm
2. Spherical Mirrors • Schmidt, FAST and Arecibo • All need correctors for spherical aberration • No obvious relevance for AtLAST?
3. Single-mirror on-axis With focal length of 50m, i.e. F/D =1. Dominated by Coma. DLFoV is < 0.1 deg even at 3mm. Note that Coma is linear in field angle. At Strehl 0.8, field diameter is ~36 times telescope beamwidth (FWHM) so ~250 independent beams.
4. Faster single-mirror on-axis For a typical radio F/D ratio of 0.4, i.e. focal length 20m. The Coma is even larger (scales as f –2 ) and the DLFoV is only a few beamwidths in diameter.
5. Two-mirror on-axis (Cassegrain) Keep parabolic primary F/D = 0.4 Secondary 12.5m diameter. Focus 3m behind primary gives f/1.8; 1deg ~ 1.6m Coma still dominates: Astigmatism significant. Note curvature of field: height ~ 225mm at edge.
6. Cassegrain plus flat: Nasmyth Add Flat on elevation axis. Need 8.6 by 6m ellipse. Back Foc Dist 12m gives f/2.55 1deg ~ 2.2m Spot size exaggerated by factor of 10 Flat could turn to feed 6(?) stations – 4 tilting, 2 horizontal Note FP Curvature now ~ 500mm
7. Ritchey-Crétien: correct Coma Allow non-parabolic primary. Readjust secondary. BFD still12m and f/2.55 1deg ~ 2.2m Exaggerate x10 Coma is removed. Slight increase in Astigmatism - now dominant. Number of beams goes as ν 1 .
7a. “Small” Ritchey-Crétien Faster parabolic primary 40m diameter F/D 0.36 Secondary 6m diameter. Target FoV 1deg diameter Focus 4m behind primary gives f/3.1; 0.5deg ~ 1.07m Exaggerate x10 Astigmatism dominant. Curvature: height ~ 275mm at edge.
7b. Astigmatism Through Focus spot diagrams for case on previous slide. • Once Coma is corrected Astigmatism is the aberration that limits the FoV. (Assumes that curvature is corrected.) • Astigmatism means that the focus in the radial direction is in a different place to that in the circumferential direction. • Proportional to field angle squared and 1/ f . • Requires lenses or mirrors with cylindrical surfaces to correct it in instrument.
8. Ritchey-Crétien plus 2 flats BFD now 21m. Gives f/3.3 1deg ~ 2.8m Exaggerate x10 The mirrors are 11.6 x 8.2 and 9.4 x 6.6m. The focal plane curvature is ~800mm at edge.
9. Two Symmetric mirrors plus Relay Intermediate focus plus 1:1 relay. f/1.62 1 deg = 1.4m. Exaggerate x10 The mirrors are 17.6 x 16.2 and 16.4 x 15.2m(!) The focal plane is almost flat but not telecentric.
9a. Telecentricity – not an aberration but important for instruments • A system is telecentric when the bundles of rays arriving at the instrument are all parallel to the axis of the telescope. • In optical terms, this means that the exit pupil (which is the image of the stop as seen at the instrument) is at infinity. • Pupil in front of instr (to right) Telecentric Pupil behind instr (to left) • Instrument squints. Looks straight ahead. Instrument “Wall-eyed” • For a camera design with “tubes” (see slide 24.) prisms can be inserted to correct for lack of telecentricity.
9b. Same as 9 but smaller secondary Intermediate focus plus relay. f/2. Actually works rather better. Mirrors a little smaller. FoV at 3mm little larger. Still completely impractical!
9c. Extension of this would be a Beam Waveguide system. This used on some communications antennas, e.g. the NASA deep space network. But single pixel. Even more impractical and I can’t make it work well anyway!
9d. Even more elaborate relays • SCUBA-2 optics on JCMT: 9 mirrors! • The original design of JCMT failed to take field of view into account at all. • Lesson in what not to do!
10. Three-mirror Anastigmat • With three conic mirrors one can correct spherical coma, astigmatism and curvature. • Korsch (1972)
11. LSST • Arranged to have the tertiary and primary made from same mirror blank. • Achieves optical quality (with additional corrector lenses) over a 3.5 deg field.
12. Three Symmetric Mirrors ~ LSST Tertiary limited to 12m diameter: in shadow of Secondary Pushed to f/1.5: 1 deg = 1.3m to fit in hole in Secondary Exaggerate x100 (!) DLFoV 1.8 deg at 333μm: 4.4x10 6 2fλ beams! Teritary ~2m in front of Prime vertex. Focal plane slightly curved (~80mm at edge). Telecentric.
12a. Seidel terms for this design • Just to see how the three-mirror scheme is working, here are the terms contributed by the three components. • These are in mm of wavefront error. • You can see that I have not attempted to cancel the curvature. That could be done but the geometry would be even less practical. • This calculation neglects the 6 th order terms, which do in fact remove most of the remaining astigmatism.
12b. TMA Faster version Primary F/D = 0.32. Tertiary continuous with primary. Final f/1.38: 1 deg = 1.21m. Trying to minimize blocking. Exaggerate x100 (!) Hard to match to instruments? Baffles still needed. FP curvature ~93mm at edge. ~Telecentric.
13. Three Symmetric Mirrors ~ ELT Two additional flats – beam on elevation axis? Intermediate focus f/1. Final focus f/3.7. 1 deg = 3.2m Exaggerate x100 Beam has to pass through hole in first flat. Tertiary diameter 16m! Focal plane almost perfectly flat (~13mm at edge). Not telecentric.
14. Off-Axis Telescopes Bell Labs 7m and GBT
15. More Off-axis Dishes • Allan Array, MeerKAT and the optical design of SKA dish
16. Asymmetric Systems – Gregorian No blockage. Receiver way above dish. 12m Secondary Prime focus ~f/0.83. Final focus f/1.6 1 deg ~ 1.4m Exaggerate x10 Correct Coma (RC equivalent) – Astigmatism dominates. Focal plane modestly convex (~100mm at edge). Not telecentric – real pupil in front of focus.
17. Asymmetric Systems – Cassegrain Tilt of axis goes other way. Still using 12m Secondary Prime focus ~f/1.1. Final focus f/2.53 1 deg ~ 2.2m Exaggerate x10 Coma corrected, astigmatism dominant, but other terms significant. Focal plane concave (~300mm at edge). Not far from telecentric. Compare DLFoV with slide 7.
17a. More compact Gregorian Faster primary. Secondary reduced to 10m. Lower Rx. Prime focus ~f/0.76. Final focus f/2.25 1 deg ~ 2m Exaggerate x10 Slightly larger FoV. Better match to instruments. Focal plane more convex (~400mm at edge). Not telecentric – real pupil in front of focus.
18. CCAT-prime • Crossed- Dragone layout • DLFoV with and without coma correction • 8 deg square • Strehl 0.8 at 75GHz (red) to 1500GHz (blue)
19. Crossed-Dragone Receiver near edge of primary (not on elevation axis here) Secondary diameter 41m! Final focus f/1.7 1 deg ~ 1.5m Exaggerate x10 Focal plane nearly flat and not far from telecentric. DLFoV better than other designs for ~ f/2
20. Dragone “Unique Arrangement” • PICO FoV ~10° x 8°
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