Abstract

1 Introduction

1.1 Should the F/15 Secondary be Cassegrain or Gregorian?

This choice of secondary optical design is clearly a complex issue and an important decision. Section 2 of this memo is my attempt to summarize the arguments and state the facts as we know them. Thanks to R. Angel, B. Atwood, D. Bonaccini, P. Byard, G. Rieke, P. Salinari and N. Woolf for their contributions in sweat and blood to this discussion.

The most important and/or most distinguishing issues in this debate are: the power required for chopping, the length of the telescope tube and the size of the dome, testing capability for adaptive optics, and the flexibility of telescope operations. These and other points of discussion are expanded below.

1.2 Result

2 Points of Discussion

2.1 Adaptive Secondary --- Access to Prime Focus

From J. R. P. Angel: ``Adaptive correction can be made at a secondary, at a warm adaptive relay mirror or at a cooled adaptive relay. An adaptive secondary is challenging to make, but has the advantages that it is available for any instrument, and there are no additional warm surfaces. ........ Gregorian secondaries have the great advantage that they can be readily tested in manufacture and use. Moreover, complete system tests of the adaptive system can be made at any time by placing an artificial star at prime focus. For example, if capacitive sensors are used in the secondary, they could be calibrated by interferometry as often as necessary, at any time of the day or night and regardless of seeing conditions. Reconstructor performance would be optimized with the aid of an artificial star with known controlled aberrations. We could not bring our present (ACME) system into operation without an artificial star. System tune up would be to adaptive optics what flat fields are to CCDs.''

It appears that this issue is the one that must sell the Gregorian as having scientific benefit. (JMH's opinion)

2.2 Easier Secondary Testing

2.3 Telescope Length

2.4 Enclosure Height

2.5 Flip-Top Geometry

2.6 Rapid Exchange

2.7 Seeing Conjugate

2.8 Secondary Diameter

2.9 Moment of Inertia

2.10 Wind Force

2.11 Focal Plane Compatibility

Preferred Curvature: What is the preferred curvature of an instrument which reimages through a cold pupil? Would choosing a Cassegrain or Gregorian provide general improvement to the optical designs of LBT instruments? How much can the curvature contribution from the instrument be adjusted with the optical design? None of the LBT optical expertise has been able to answer this question in even a qualitative way. We have looked at some examples, but they have not yet provided a general conclusion. It must depend on the arrangement and combination of lenses and mirrors in the instrument.

How do the field characteristics change between Cassegrain and Gregorian telescopes? The image quality is essentially the same, but the Gregorian has slightly less field curvature (13% at F/15) of opposite sign.

Field Limitations: What are the field limitations for ``seeing-limited'' imaging and for ``diffraction-limited'' imaging? For this discussion (and the spreadsheet below), ``seeing-limited'' or ``wide-field'' imaging is defined to be imaging or spectroscopy with the pixel size set so there are N pixels (usually 2) sampling the seeing disk without any wavefront correction. The field-of-view is limited by the optics of the telescope and instrument and not by the isoplanatic patch since we have no requirement for tip-tilt or adaptive correction. We will define ``diffraction-limited'' imaging to be imaging or spectroscopy with the pixel size set so there are N pixels (usually 2) sampling the airy disk. Thus, the pixel size on the sky is a function of wavelength as is the isoplanatic patch where the image can be corrected over the entire field. In order to quantify the effects in this discussion, we developed a spreadsheet calculation for reimaging cameras at the Columbus Optics meeting in October.

Assumptions for ``the spreadsheet'':

• The camera and collimator are curvature neutral. So the instrument only changes the reimaged focal plane curvature by the amount expected from the magnification or demagnification.

• We are matching physical pixel sizes of 24, 30, 60 and 100 microns respectively for the visible, near-infrared, mid-infrared and thermal-infrared detectors (see the table). This clearly involves some assumptions about detector technology.

• Detectors are flat, so the field of view with aberration-free optics is limited by the depth of focus. The seeing-limited depth of focus is given by ± 0.2 F * pixelsize. The diffraction-limited depth of focus is given by ± 2 F ² * , where F is the final focal ratio at the detector and is the wavelength.

• The instrument is designed for ``good'' seeing. We assumed that the seeing (telescope plus atmosphere) is 0.5 arcsec FWHM in the visible and that the isoplanatic patch is 5 arcsec in radius in the visible.

• The design sampling is assumed to be two pixels across the seeing disk or the Airy disk. This makes a seeing-limited pixel equal to the HWHM, and a diffraction-limited pixel is 1.2 / D, where DS is the telescope diameter.

• Calculate the pixel size in arcseconds to match either the seeing disk or the Airy disk for N=2 sampling.

• Compute the camera focal ratio required to match the physical pixel size to this sampling.

• Use the camera focal ratio to compute the depth-of-focus for the seeing and diffraction-limited cases.

• Use the depth-of-focus and the magnified field curvature to calculate the radius of the useful field in arcminutes and in pixels.

• Compare this field with the isoplanatic patch at each wavelength.

• Seeing-limited F/15 cameras (that is --- cameras which use the F/15 secondary) have ~ 2 arcminute diameter flat focal planes at all wavelengths (using depth of focus as defined above). These focal planes are roughly 500 -- 700 pixels in diameter.

• At 2 microns, the seeing-limited camera reimages to F/4 to match 30 micron physical pixels. (This probably means that J and H band imaging should use the F/4 secondary without reimaging and with baffles.)

• At 2 microns, the diffraction-limited camera reimages to F/12.5 to match 30 micron physical pixels.

• The telescope is frequently diffraction-limited without adaptive optics beyond 5 microns. Note in the tables that the seeing-limited pixels are apparently smaller than the diffraction-limited pixels for wavelengths longer than 5 microns (the definition of diffraction-limited?). This transition from seeing-limited to diffraction-limited is indicated by a horizontal line in the seeing-limited section of the tables. There is therefore no need for a seeing-limited camera in the thermal infrared. (The diffraction-limited camera will already have a wide field at those wavelengths, if you can build enough pixels.)

• Diffraction-limited imagers are limited by the isoplanatic patch (rather than field curvature) shortward of 20 microns (depends on physical pixel size). This transition is indicated by a horizontal line in the diffraction-limited section of the tables. So field curvature is not a problem for diffraction-limited imaging except in the thermal infrared. We have ignored the distinction between the isoplanatic patch and the isokinetic patch.

• The Gregorian F/15 focal plane has a 6 % larger flat field than the Cassegrain F/15 focal plane. It has slightly less field curvature (1.0 m vs 0.9 m radius-of-curvature).

• Changing an instrument (moving it) from a Cassegrain to a Gregorian telescope doesn't significantly change the size of the usable flat field unless the instrument optics have intrinsic curvature correction.

• For the same camera (instrument), moving from the MMT F/15 to LBT F/15 will reduce the field to 0.77 of its previous size because the pixels are smaller (focal length is longer). .... Then by some more calculation .... The field loss due to curvature change between a focal plane matched (curved) to MMT F/15 Cass and LBT F/15 Gregorian is duplicated by the loss due to scale. i.e. There is no loss unless you had extra pixels at the MMT to begin with.

• A 2 micron wide-field imager only has incompatibility between Cassegrain and Gregorian when the number of pixels across a diameter approaches 1000 (4 x 4 NICMOS3 detectors).

Input			Seeing-Limited				Diffraction-Limited
µ m	pixel µ m	d arcmin	pixel arcsec	F/ #	field radius arcmin pixels		pixel arcsec	F/ #	field radius arcmin pixels
0.32	24	0.05	0.273	2.79	1.27	278	0.012	62.50	0.77	3801
0.50	24	0.08	0.250	3.05	1.21	290	0.019	40.00	0.96	3041
0.80	24	0.15	0.228	3.35	1.16	304	0.030	25.00	1.22	2404
1.00	24	0.19	0.218	3.50	1.13	311	0.038	20.00	1.36	2150
1.60	30	0.34	0.198	4.80	1.08	326	0.061	15.62	1.73	1700
2.00	30	0.44	0.189	5.02	1.05	333	0.076	12.50	1.93	1520
2.50	30	0.57	0.181	5.25	1.03	341	0.095	10.00	2.16	1360
3.50	30	0.86	0.169	5.62	1.00	353	0.133	7.14	2.55	1149
5.00	30	1.32	0.158	6.03	0.96	365	0.190	5.00	3.05	961
8.50	60	2.50	0.142	13.42	0.91	385	0.324	5.88	3.98	737
10.0	60	3.03	0.137	13.86	0.90	392	0.381	5.00	4.31	680
12.0	60	3.78	0.132	14.37	0.88	399	0.457	4.17	4.73	620
20.0	100	6.97	0.120	26.54	0.84	420	0.761	4.17	6.10	480
30.0	100	11.34	0.110	28.78	0.80	437	1.142	2.78	7.47	392

Input			Seeing-Limited				Diffraction-Limited
µ m	pixel µ m	d arcmin	pixel arcsec	F/ #	field radius arcmin pixels		pixel arcsec	F/ #	field radius arcmin pixels
0.32	24	0.05	0.273	2.15	1.18	258	0.009	62.50	0.63	4017
0.50	24	0.08	0.250	2.36	1.13	270	0.015	40.00	0.79	3214
0.80	24	0.15	0.228	2.59	1.07	283	0.024	25.00	1.00	2541
1.00	24	0.19	0.218	2.71	1.05	289	0.029	20.00	1.12	2272
1.60	30	0.34	0.198	3.71	1.00	303	0.047	15.62	1.41	1796
2.00	30	0.44	0.189	3.88	0.98	310	0.059	12.50	1.58	1607
2.50	30	0.57	0.181	4.06	0.96	317	0.074	10.00	1.76	1437
3.50	30	0.86	0.169	4.34	0.93	328	0.103	7.14	2.09	1214
5.00	30	1.32	0.158	4.67	0.89	340	0.147	5.00	2.49	1016
8.50	60	2.50	0.142	10.38	0.85	358	0.250	5.88	3.25	779
10.0	60	3.03	0.137	10.72	0.83	364	0.294	5.00	3.53	718
12.0	60	3.78	0.132	11.12	0.82	371	0.353	4.17	3.86	656
20.0	100	6.97	0.120	20.52	0.78	390	0.589	4.17	4.99	508
30.0	100	11.34	0.110	22.25	0.75	406	0.883	2.78	6.11	414

Input			Seeing-Limited				Diffraction-Limited
µ m	pixel µ m	d arcmin	pixel arcsec	F/ #	field radius arcmin pixels		pixel arcsec	F/ #	field radius arcmin pixels
0.32	24	0.05	0.273	2.15	1.25	273	0.009	62.50	0.67	4256
0.50	24	0.08	0.250	2.36	1.19	286	0.015	40.00	0.84	3405
0.80	24	0.15	0.228	2.59	1.14	300	0.024	25.00	1.06	2692
1.00	24	0.19	0.218	2.71	1.11	306	0.029	20.00	1.18	2407
1.60	30	0.34	0.198	3.71	1.06	321	0.047	15.62	1.49	1903
2.00	30	0.44	0.189	3.88	1.04	328	0.059	12.50	1.67	1702
2.50	30	0.57	0.181	4.06	1.02	336	0.074	10.00	1.87	1522
3.50	30	0.86	0.169	4.34	0.98	347	0.103	7.14	2.21	1287
5.00	30	1.32	0.158	4.67	0.95	360	0.147	5.00	2.64	1076
8.50	60	2.50	0.142	10.38	0.90	379	0.250	5.88	3.44	825
10.0	60	3.03	0.137	10.72	0.88	386	0.294	5.00	3.74	761
12.0	60	3.78	0.132	11.12	0.87	393	0.353	4.17	4.09	695
20.0	100	6.97	0.120	20.52	0.82	413	0.589	4.17	5.28	538
30.0	100	11.34	0.110	22.25	0.79	431	0.883	2.78	6.47	439

Conclusions from ray tracing tests on the baseline optical spectrograph (Bonaccini and Byard): Moving the optical spectrograph (VDS) optimized for F/15 Cassegrain to F/15 Gregorian produced 15 % worse spotsize at the camera. But, the flatter telescope field makes the slit images better, so much of the light loss is recovered.

Conclusions from ray tracing tests on the infrared spectrometer being built for the MMT (Rieke and Thompson): The instrument does work over the 512x512 field with slightly less design margin.

2.12 Cold Pupil Compatibility

If the entrance pupil is the primary mirror, then the positions of the exit pupil in the telescope and the cold stop do NOT change between Cassegrain and Gregorian telescope configurations.

If the entrance pupil is the secondary mirror, then the position of the cold stop at the image of the secondary formed by the collimator clearly does move. The amount of linear shift goes as the inverse square of the magnification between the pupil and the secondary. The fractional shift compared to the stop diameter goes as the inverse of the magnification. For a 10 mm diameter cold stop (beam size), changing LBT from F/15 Cassegrain to Gregorian moves the stop by 0.289 mm (0.3 % of stop diameter). For a 100 mm diameter cold stop, the shift increases to 28.9 mm (2.9 % of stop diameter). For all stop sizes, changing LBT from Cassegrain to Gregorian increases the difference between LBT F/15 and MMT F/15 Cassegrain by 62 %. (Note that the pupil is strongly curved --- whether or not the aperture stop is at the secondary.)

2.13 Instrument Optics

Question: How do we know that the Gregorian Telescope / Refractive Collimator combination proposed by Shectman in Magellan report #38 does not have an analog in reflecting collimators? And does a system exist which could provide a similarly wide field on the MMT F/9 Cassegrain focus? Shectman says that the success of his design is due to the fact that the inherent curvature of his collimator lens exactly matches the curvature of the telescope focal plane. Thus having chosen a beam size and designed the field lens of the collimator, the F/11 Gregorian secondary is chosen to produce the correct field curvature. This gives good images (< 0.1 arcsec) over a 24 arcminute field. Similar systems with Cassegrain secondaries are typically limited to fields 1/3 this size.

Hypothesis: That an inverted Cassegrain collimator should be able to match the curvature of a Gregorian telescope, or vice versa that an inverted Gregorian telescope should be able to match a Cassegrain telescope.

Experimental Test: Does the curvature match occur at any interesting focal ratio or beam size?

Results: Indeed, I find that the Magellan F/11 Gregorian focal plane with its radius of curvature of --1.5 meters can be matched with an inverted Cassegrain F/11 collimator which has an ~ F/8 primary which is 0.325 meters in diameter. BUT, the problem is that the hole in the primary of collimator must be large enough to accommodate the telescope field-of-view (bigger than the collimator primary). Thus the inverted F/11 collimator can only work if we want to make a beam size of order 1 meter or if we are able to work off-axis.

Then, I checked the MMT F/5.25 naked Cassegrain focus. In this case, an inverted Gregorian F/5.25 collimator with a 0.325 meter ~ F/2.7 primary matches the 2.1 meter radius of curvature of the telescope. 10 arcminutes on the telescope focal plane is only 0.1 meter diameter. BUT, the Gregorian secondary of the collimator completely obstructs the beam --- we lose again. In this case, the images of the bare collimator are not within spec, but they are close enough to suggest that a couple of field corrector lenses could fix things up.

Now, the question is: Can an off-axis collimator be optimized to give adequate images? Bonaccini tried an off-axis Cassegrain to reimage the LBT F/15 Gregorian focus, but he didn't explicitly try to constrain the field curvature.

2.14 Aplanatic F/15

2.15 Coronography / Polarimetry

2.16 Slow Primary

3 Conclusion