AtLAST quick survey of optics issues Run through of options that I - - PowerPoint PPT Presentation

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 π2/16 (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 / θ2 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 mm1.

1Various other factors could be added here, e.g. x2 for polarization, /4 for detector spacing of 2f 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, as1 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?

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.

• 3. Single-mirror on-axis

For a typical radio F/D ratio

• f 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.

• 4. Faster single-mirror on-axis

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.

• 5. Two-mirror on-axis (Cassegrain)

Add Flat on elevation axis. Need 8.6 by 6m ellipse. Back Foc Dist 12m gives f/2.55 1deg ~ 2.2m Flat could turn to feed 6(?) stations – 4 tilting, 2 horizontal Note FP Curvature now ~ 500mm

• 6. Cassegrain plus flat: Nasmyth

Spot size exaggerated by factor of 10

Allow non-parabolic primary. Readjust secondary. BFD still12m and f/2.55 1deg ~ 2.2m Coma is removed. Slight increase in Astigmatism - now dominant. Number of beams goes as ν1.

• 7. Ritchey-Crétien: correct Coma

Exaggerate x10

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 Astigmatism dominant. Curvature: height ~ 275mm at edge.

• 7a. “Small” Ritchey-Crétien

Exaggerate x10

• 7b. Astigmatism
• 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.

Through Focus spot diagrams for case on previous slide.

BFD now 21m. Gives f/3.3 1deg ~ 2.8m The mirrors are 11.6 x 8.2 and 9.4 x 6.6m. The focal plane curvature is ~800mm at edge.

• 8. Ritchey-Crétien plus 2 flats

Exaggerate x10

Intermediate focus plus 1:1 relay. f/1.62 1 deg = 1.4m. The mirrors are 17.6 x 16.2 and 16.4 x 15.2m(!) The focal plane is almost flat but not telecentric.

• 9. Two Symmetric mirrors plus Relay

Exaggerate x10

• 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.

Intermediate focus plus relay. f/2. Actually works rather better. Mirrors a little smaller. FoV at 3mm little larger. Still completely impractical!

• 9b. Same as 9 but smaller secondary

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!

• 9c. Extension of this would be a Beam Waveguide system.

• 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.

Tertiary limited to 12m diameter: in shadow of Secondary Pushed to f/1.5: 1 deg = 1.3m to fit in hole in Secondary

DLFoV 1.8 deg at 333μm: 4.4x106 2fλ beams!

Teritary ~2m in front of Prime vertex. Focal plane slightly curved (~80mm at edge). Telecentric.

• 12. Three Symmetric Mirrors ~ LSST

Exaggerate x100 (!)

• 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 6th order terms, which do in fact remove most of

the remaining astigmatism.

Primary F/D = 0.32. Tertiary continuous with primary. Final f/1.38: 1 deg = 1.21m. Trying to minimize blocking. Hard to match to instruments? Baffles still needed. FP curvature ~93mm at edge. ~Telecentric.

• 12b. TMA Faster version

Exaggerate x100 (!)

Two additional flats – beam on elevation axis? Intermediate focus f/1. Final focus f/3.7. 1 deg = 3.2m Beam has to pass through hole in first flat. Tertiary diameter 16m! Focal plane almost perfectly flat (~13mm at edge). Not telecentric.

• 13. Three Symmetric Mirrors ~ ELT

Exaggerate x100

• 14. Off-Axis Telescopes

Bell Labs 7m and GBT

• 15. More Off-axis Dishes
• Allan Array, MeerKAT and the
• ptical design of SKA dish

No blockage. Receiver way above dish. 12m Secondary Prime focus ~f/0.83. Final focus f/1.6 1 deg ~ 1.4m Correct Coma (RC equivalent) – Astigmatism dominates. Focal plane modestly convex (~100mm at edge). Not telecentric – real pupil in front of focus.

• 16. Asymmetric Systems – Gregorian

Exaggerate x10

Tilt of axis goes other way. Still using 12m Secondary Prime focus ~f/1.1. Final focus f/2.53 1 deg ~ 2.2m Coma corrected, astigmatism dominant, but other terms significant. Focal plane concave (~300mm at edge). Not far from telecentric. Compare DLFoV with slide 7.

• 17. Asymmetric Systems – Cassegrain

Exaggerate x10

Faster primary. Secondary reduced to 10m. Lower Rx. Prime focus ~f/0.76. Final focus f/2.25 1 deg ~ 2m Slightly larger FoV. Better match to instruments. Focal plane more convex (~400mm at edge). Not telecentric – real pupil in front of focus.

• 17a. More compact Gregorian

Exaggerate x10

• 18. CCAT-prime
• Crossed-

Dragone layout

• DLFoV with and without coma correction
• 8 deg square
• Strehl 0.8 at

75GHz (red) to 1500GHz (blue)

Receiver near edge of primary (not on elevation axis here) Secondary diameter 41m! Final focus f/1.7 1 deg ~ 1.5m Focal plane nearly flat and not far from telecentric. DLFoV better than other designs for ~ f/2

• 19. Crossed-Dragone

Exaggerate x10

• 20. Dragone “Unique Arrangement”
• PICO

FoV ~10° x 8°

• 21. Three-Mirror Off-Axis
• Steve Padin’s proposal for a CMB S-4 telescope.
• 5m aperture. Secondary ~4m Tertiary ~5.5m.
• This version f/3.3. 10deg field is ~3m diameter.
• Strehl map at 1mm

Pushed angles to clear beams. No blocking or narcissus. 2nd & 3rd Mirrors 12m diam. Final focus f/2.5 1 deg ~ 2.2m. Coma and Astigmatism corrected. Almost as good as “LSST” case. Focal plane slightly concave and small tilt. Not far from telecentric.

• 22. Three Mirror Off-Axis, Korsch 1

Exaggerate x100

With intermediate focus between 2nd and 3rd Mirrors. 2nd & 3rd Mirrors 12m diam. Final focus f/2.5 1 deg ~ 2.2m. Coma and Astigmatism nearly corrected. DLFoV good at 1mm. Focal plane somwhat convex. Pupil in front of focal plane so far from telecentric.

• 23. Three Mirror Off-Axis, Korsch 2

Exaggerate x100

• 24. Aberration Correction in the Instruments
• For an RC telescope the residual aberrations

are curvature and astigmatism.

• For a camera built of “tubes” the bulk curvature

may be matched by staggering them axially.

• This leaves a tilt in the focal plane and a

cylindrical wavefront error to be corrected in the lenses or perhaps by adding an extra lens.

Field Lens L2 Stop L3 Detector

• 25. Area of DLFoV versus
• bserving frequency
• Recall that this has curvature

removed but no other correction in instruments.

• These are in square degrees and

are for Strehl ratio 0.8

0.05 0.2 0.8 3.2

100 200 400 800

DLFoV (sq deg) Frequency (GHz)

Field of View versus Frequency

Off Greg RC + 1flat RC + 2flat Cross Drag Sym 3 Mirr Off 3 Mirr Small RC

• 26. Note on placing of stop.
• Choice when setting up optical model.
• Effects size of secondary and (slightly) the

f-ratio and aberrations. A) Nominal 2nd, sized for on-axis beam B) Stop on prime – oversized 2nd C) Stop on secondary – undersized 2nd outer part of primary not used.

• Real situation is that stop is in instrument.

If you illuminate whole secondary you will get spill-over onto the ground with A or B.

• Suggestion is to use oversized secondary

but set stop size in instrument so that you illuminate nearly to edge of primary.

B A C