Strategy for Interferometry with the Large Binocular Telescope

J. M. Hill

University of Arizona, Large Binocular Telescope Project

Steward Observatory, Tucson, AZ 85721

email: jhill@as.arizona.edu

http://medusa.as.arizona.edu/lbtwww/tech/spiecomb.htm

Proceedings of SPIE conference on Amplitude and Intensity Spatial Interferometry II, 2200, p. 248 (1994)

2. Optical Design Considerations

3. An Algebra of Beam Combiner Design

5. Optical Design Requirements

List of Figures:

Figure 1 Figure 2 Figure 3
Figure 4 Figure 5 Figure 6

A summary of the scientific requirements and the optical design requirements for the Large Binocular Telescope (LBT, former Columbus Project) beam combining optics is presented. Our goal for LBT is to produce a phased focal plane combining the beams from two 8.408 m diameter primaries on a common mount (14.417 m center-center). This provides an interferometric baseline of 22.825 m (edge-edge). This combined focal plane should be phased, in-focus and unvignetted over a field covering most or all of the isoplanatic patch in the best seeing conditions. These field requirements should be met for wavelengths from 0.4 to 20 µ m. This allows the observer to obtain the maximum amount of diffraction-limited imaging information around each reference source. The individual telescope images should be close to diffraction-limited over the isoplanatic patch in order to facilitate adaptive correction of the interferometric field. A minimum number of warm reflections and minimum obstruction of the beams should be used in order to reduce the emissivity. The two-shooter telescope will be uniquely powerful in the thermal infrared (based on the combination of interferometric baseline and single element diffraction limit). We will be discussing several related classes of beam combiners to evaluate design tradeoffs for LBT. An earlier design considered direct combination of the beams from two F/33 secondary mirrors with long back focal distance. We have also considered reimaging the F/15 Gregorian focal planes with a number of optical designs.

1. Introduction

This paper restates the optical requirements for the Large Binocular Telescope Project (LBT) combined or phased focus. This effort was precipitated by the study of a number of options for how to implement the combined or interferometric focus on the two-shooter telescope. This discussion will be oriented to combining the light from two primary mirrors, but the philosophy should also be applicable to N-telescope combination as well.

Two-shooter beam combination strategy was originally outlined by Don McCarthy in his memo ``Phased Focus for the Two-Shooter Telescope''¹. That memo puts the interferometric focus in a somewhat broader context of telescope design. McCarthy et. al. ² provide some simulations to illustrate the performance of the 8 meter binocular. The classical Columbus beam combination scheme is illustrated in Figure 1.

Here we concentrate specifically on the optical design implications. Specifically, what constraints does the astronomy impose on the optical and mechanical designs of the telescope? The later sections of this paper discuss the tradeoffs of the various types of beam combination optics for LBT and its instruments. Byard and Bonaccini³ have recently studied several optical designs which produce the combined focus by reimaging.

View Figure 1 here

1.1 Goals

Our goal for LBT is to produce a phased focal plane combining the beams from two 8.408 m diameter primaries separated by 6.0 m on a common mount (14.417 m center-center). This provides an interferometric baseline of 22.825 m (edge-edge).

This combined focal plane should be phased, in-focus and unvignetted over a field covering most or all of the isoplanatic patch in the best seeing conditions. We have assumed that the best seeing corresponds to r _{0 (0.5 µ m)} = 45 cm; or 0.22 arcsec FWHM in the visible. This field requirement should be met for wavelengths from 0.4 µ m (where the field is small, ~ 5 arcsec diameter) to 20 µ m (where the field is ~ 10 arcminutes diameter). This allows us to obtain the maximum amount of diffraction-limited imaging information around each reference source.

The individual images from each telescope should be close to diffraction-limited over the isoplanatic patch in order to facilitate adaptive correction of the field (correction of seeing and telescope imperfections). Even ``bad seeing'' (~1 arcsec) images will contain the interferometric information in the speckle pattern, but the sensitivity of the interferometer can be increased by orders of magnitude if adaptive correction can be used to reduce the size of the overlapping images. The telescope/instrument combination should facilitate correction with an adaptive mirror.

A minimum number of warm reflections and minimum obstruction of the beams should be used in order to reduce the emissivity. The two-shooter telescope will be uniquely powerful in the thermal infrared (based on the combination of interferometric baseline and single element diffraction limit). Beyond 5 µ m, the images from the individual telescopes will often be diffraction-limited without adaptive correction (beyond tip-tilt). This allows the two-shooter telescope to have smaller images and therefore much more sensitivity than smaller aperture telescopes with similar baselines. (Since the diffraction peak from a point source has higher contrast against the background.)

Near-UV and sub-millimeter observations with the interferometer will not be excluded, but they are not considered to be important design drivers.

2. Optical Design Considerations

2.1 Types of Beam Combiners

We will be discussing several related classes of beam combiners. The first class combines the light from two (N) afocal telescopes using a single combining telescope. In this case, the best flat focal surfaces of the individual telescopes and the plane of common phase are coincident. The practical minimum number of mirrors to get to the combined focal plane is five (four in some special arrangements). An example is shown in Figure 2. The second class uses flat combining optics to bring together the focal planes of two (N) telescopes with long back focal distances. In this case, the flat focal planes of the individual telescopes are slightly tilted with respect to one another. The MMT (6 x 1.8 m, with modified beam combiner) is an example of this second class. A beam combiner of this type has been used in the classical Columbus baseline design^2,4. The examples in Figures 1 and 3 show that the practical minimum number of mirrors to get to the combined focal plane is four. There is also a nearly trivial class of beam combiner composed of off-axis pieces of a single mirror telescope. An example of this zeroth class beam combiner is shown in Figure 4. Of course, life is never that simple --- one of the motivations of this summary is to explore beam combiner options where short back focal distance telescopes have their principal focal planes reimaged onto the phased/combined focal plane. The reimaging optics can be either of the two classes mentioned above. These reimaging systems require at least five mirrors to get to the combined focal plane. Reimaging potentially allows access to real pupil locations with adaptive elements ahead of the combined focal plane. Examples of reimaging beam combination are shown in Figures 5 and 6. The reader should not confuse these classes of beam combiners with the types of telescope arrays described by Beckers⁵. This paper is primarily discussing what Beckers would call Type 0 or Type 1 arrays.

2.2 Phasing the Field and Preserving the Sine Condition

Light from the two (N) telescopes can be phased at a single point in the focal plane by assuring that the optical path length on both sides (all N telescopes) is equal. When you wish to phase an extended field (you always do in astronomy), you face additional requirements. The most important additional requirement is that the geometry of the light cones converging on the combined focal plane must exactly preserve the entrance pupil geometry of the telescopes. This is known as (is equivalent to) preserving the Sine Condition, since the sine of each ray angle in the cones must be exactly proportional to the position of that ray in the multiple entrance pupil. An important result is that for combining simple Cassegrain or Gregorian telescopes, the combined beam (rays travelling from beam combiner mirrors toward the focal plane) must travel in a direction parallel to the axes of the primary mirrors (i.e. when the telescope is zenith pointing, the combined beam must go down rather than up or horizontal or some other angle.). After the beam combiner, any number of flat mirrors can be used in the combined beam to adjust the location and angle of the final focal plane in space. The optical explanation for this geometry is elaborated most clearly by Traub⁶.

2.3 Lateral Offset

The combined axis may be offset laterally off of the center line between the primaries. This symmetry or lack thereof only applies to a two-shooter or an irregular array. For combiners of the second class, this offset causes the plane containing the two chief rays to tilt relative to the optical axes of the telescopes. (Think about the two-shooter as half of a four-shooter geometry. In that case the lateral offset would be half the center-center separation.)

2.4 Baseline

The interferometric baseline of the telescopes limits the resolution that can be obtained. The baseline for Columbus/LBT was set to provide essentially continuous coverage in the u-v plane while still providing a substantially longer baseline than the equivalent circular aperture.

2.5 Isoplanatic Patch and Field Size

The angular diameter of the isoplanatic patch (field of similar phase) is given by Beckers et. al. ⁷ as (2 /3) * r₀ / H where H is the average distance to the seeing layer. We'll leave it to the adaptive optics and seeing experts to make more complicated / realistic multilayer models of the atmosphere. Sandler et. al. ⁸ provide a more extensive discussion of adaptive optics and properties of the atmosphere. Fried's parameter, r₀, increases as a function of wavelength by lambda to the power 1.2. For our present purposes, we need an estimate of the size of the isoplanatic field at various wavelengths. Assume H is between 4000 m and 20000 m. Also assume that r _{0 (0.5 µ m)} = 0.45 m on the best 20% of the nights (This value refers only to the contribution from high altitude layers, not to local seeing around the telescope.), so r _{0 (2 µ
m)} = 2.4 m and r _{0 (10 µ m)} = 16.4 m. This means that the isoplanatic patch size is 3 -- 15 arcsec at 500 nm, 16 -- 82 arcsec at 2 µ m, and 1.9 -- 9.4 arcminutes at 10 µ m. The full isoplanatic patch is needed to provide the largest possible field-of-view for imaging. A larger field-of-view also increases the number of bright reference stars that are available for phasing and adaptive correction.

2.6 Isokinetic Patch, Isopistonic Patch and Field Size

Why are we interested in the size of the isokinetic patch? In the thermal infrared, simple tip-tilt corrections should be sufficient to recover the diffraction patterns of the individual telescopes. This means that more complicated wavefront correction beyond piston and tilt is not needed for interferometry. At shorter wavelengths (2 µ m) adaptive optics systems can correct the wavefronts using laser beacons. The laser guide star does not permit correction for global piston and tilt because of its common path through the atmosphere. Thus, a natural field star is needed for tilt correction. Some ground-based measurements indicate that the isokinetic patch at 2 µ m is 90 arcsec diameter under typical conditions.

Even with the two (N) telescopes providing perfect, overlapping, diffraction-limited images, the interferometer still requires a phase reference for the combined focal plane. Phase errors are caused by anisoplanicity between the two (N) paths through the atmosphere as well as by thermal and mechanical distortions in the telescope. The obvious candidate to correct the relative phase of the atmosphere and the telescope simultaneously is a field star.

2.7 Depth of Focus and Vignetting Considerations

In the second class of beam combiner with tilted focal planes, the focal ratio must be slow enough to allow the two (N) images to have an overlapping depth of focus across the phased field. The separation of the tilted focal planes must be less than the diffraction depth of focus of ± 2F²

where F is the focal ratio and

is the wavelength. This depth of focus corresponds to reducing the Strehl intensity to 80% (see the discussion of the intensity distribution near diffraction focus by Born and Wolf). For example, an F/20 beam at 10 µ m wavelength would have a depth of focus of ±8 mm.

In order to keep the useful phased field unvignetted, the light cones from the edges of the field for each of the two (N) telescopes must have separated before they have reached the beam combiner mirrors (considered as looking up from the focal plane). Therefore, the minimum height of the beam combiner is a function of the field diameter, the final focal ratio and the entrance pupil geometry. We can calculate this height for an unvignetted field by requiring that the interior marginal ray from the edge of the field cross the combination center line.

2.8 Diffraction-limited Images

A diffraction-limited image from one of the individual telescopes contains 80% of the energy in a circle of angular diameter 2.4 (

/ D), where D is the primary diameter and

is the wavelength. The goal we have adopted for the combined beam optical design is that the images in the combined focal plane be diffraction-limited at the edge of the isoplanatic patch for all wavelengths longer than 1 micron. To maintain high fringe visibility, the relevant definition of diffraction-limited is a Strehl ratio of 80%. This optical design specification must be considered in light of the total telescope error budget and the expected image sizes.

2.9 Scale and Distortion

The design of the beam combiner should obviously allow images from the two (N) telescopes to overlap simultaneously in all parts of the field --- thus permitting interference. This limits the amount of asymmetric distortion that is permitted in the reimaging process. It also limits how well the platescale of the two (N) telescopes must match. Presumably the two (N) images should overlap within about 10% of the diffraction-limited image diameter. To set the scale and distortion tolerances, let us assume that the images from the two (N) individual telescopes must overlap within 0.24 (

/ D), where D is the telescope diameter. Assuming a 5 arcminute field diameter at a wavelength of 10 µ m (see below) the scale of the two telescopes must match to 1 part in 2500. This corresponds to an image separation of 0.06 arcsec. Differential distortion (asymmetric terms) would need to be less than 0.05% between the two focal planes.

2.10 Field Curvature

Harvey and Ftaclas ⁹ and Weaver, Fender and DeHainaut¹⁰ discuss field curvature of the individual telescopes as a fundamental limitation on the off-axis performance of phased telescope arrays (with afocal combination --- class one). Field curvature of the individual array elements has two effects. First, curvature in the individual telescopes cause the images from the individual telescopes in the combined focal plane to separate (because their chief rays are not parallel). From our analysis, the separation of the individual images depends on the telescope spacing, the sag of the focal planes and inversely on the combining lens focal length. Second, the field curvature (which is a field dependent defocus) produces wavefront degradation of the combined pupil.

For class two beam combination with tilted focal planes, the field curvature also causes the images from the two (N) telescopes to separate. The amount of separation depends on where the detector is placed. If the detector is located on the curved surface midway between the curved focal planes, the image separation due to field curvature is the focal plane sag times the tilt angle between the focal planes.

3. An Algebra of Beam Combiner Design

Faced with an ever increasing number of telescope and beam combiner geometries to evaluate, Hill, Atwood and Davison have developed the following rules for deciding whether a particular scheme preserves the entrance pupil correctly. Consider the following prescription:

3.1 Phasing prescription

Count each of the following on one side of your telescope:

focal planes which real rays pass through
(A Cassegrain telescope has 1; a Gregorian telescope has 2.)
mirrors
(Count everything from the primary to the beam combining optics.)
(Folding or reimaging AFTER the beams are combined doesn't count.)
(Lenses don't count.)
crossings of the centerline (symmetry axis) of the multi-telescope system
beam combiner direction changes parallel to the incoming light
(0 if beam combiner sends light down; 1 if up;
other angles can't ever be used.)

If the total is an odd number, you should have preserved the entrance pupil. If the total is an even number, your telescope is not phased over the field.

Example: The ``historical'' Columbus F/33 Cassegrain focus known as ``moving phased'' has 1 focal plane, 4 mirrors (primary, secondary, tertiary, beam combiner), doesn't cross the centerline and combines going down. So it correctly gets an odd score of 5.

Example: The ``hypothetical'' LBT F/33 Gregorian focus known as ``moving phased'' has 2 focal planes, 4 mirrors (primary, secondary, tertiary, beam combiner), crosses the centerline and combines going down. So it correctly gets an odd score of 7.

View Figure 6 here

4. Practical Considerations

In addition to the scientific and optical requirements, there are certain practicalities that we would like to consider in the design process. These refer mainly to how the optical design of the telescope interacts with the mechanical structure of the telescope. Hill and Salinari¹¹ describe the mechanical design of LBT.

We would like the beam combining optics and the phased instrument to fit within the nominal envelope of the telescope structure.
The beams are not permitted to pass through the edge of the primary mirrors or important structural components of the telescope.
In the case of separate phased focus secondary mirrors, the secondary should live within the thermal shadow of the normal infrared secondary that it is ``flipped'' with.
The secondary and tertiary mirrors should also hide within the shadow of the hole in the primary mirror.
We would also like to provide a second combined focus that has sufficient back focal distance to reach to a fixed gravity location below the telescope. This has been named the ``coudé'' focus, even though it is not a classical coudé. At least 6 mirrors are required to reach the coudé focal plane.
The secondary focal ratio must be as fast as possible to avoid severe focal plane curvature. Increasing the back focal distance also flattens the field.

5. Optical Design Requirements

Based on the discussion above, we have developed the following ``requirements'' to serve as a starting point for optical design explorations.

The combined beam focal plane (combining axis) should lie along the symmetry plane between the two telescopes.
The combined focal plane should be offset laterally by 2.0 -- 4.0 meters from the centerline between the two telescopes (prefer 3.5 m).
The combined focal plane should be 1.5 to 3.5 meters below the plane containing the primary vertices (prefer 2.5 m to match other instruments, but other options are possible).
The final focal ratio of the individual beams at the combined focal plane should be between F/25 and F/35. If reimaging beam combination is used, the focal ratio becomes an issue of matching diffraction-limited pixels. In that case, different cameras would be used for different wavelengths. (For combiners of the second class, it appears that instruments will reimage at wavelengths shorter than 1 micron for reasons of scale, and will reimage at wavelengths longer than 2.4 µ m to form a cold pupil.)
The images (from optical design) at the combined focal plane should contain 80% of the energy inside a diameter of 0.12 arcsec at a field radius of 30 arcsec. This is an alternate statement that the images should be diffraction-limited within the isoplanatic patch (see the discussion above). The important point is that the image quality requirement varies linearly with field angle.
The unvignetted field diameter should be at least 4 arcminutes to cover the isoplanatic patch in the thermal infrared. For combiners of the second class, this implies a beam combiner height of 8 meters above the focal plane at F/33.
The differential distortion between the two focal planes should be no more than 0.05%.

6. Beam Combiner Options

During 1992/1993, the LBT telescope design group evolved its thinking on the combined focus. We had initially considered a combined focus followed by a series of instruments. Our enlightened ``solution'' came in considering the beam combiner and instrument as a single unit followed by a detector module. All of the previous strawman instruments needed to reimage to form a pupil stop and to produce the proper plate scale regardless of whether an intermediate pupil was already formed before the combined focal plane. By including the beam combiner into an instrument which is built into the telescope, we are able to offer improved performance at all wavelengths. The concept we have in mind is described by Byard and Bonaccini ³. The refractive version of this concept is shown in Figure 6 as Beam Combiner Design 3.

6.1 Beam Combiner Design 0

Beam Combiner Design 0 is the classic Columbus ``4 mirrors to focus'' design at F/33 shown in Figure 1. The Gregorian version of the design considered for LBT is shown in Figure 3. The strengths of this design include: diffraction-limited images over a large field; a ~4 arcminute unvignetted flat field; being fully achromatic; having only flat combining optics; and providing a simple option to feed the coudé focus. This design has only 4 warm reflections before the dewar window. The main weaknesses of this design are that: it requires high structure in the center of the telescope; it requires separate F/33 secondaries; it requires reimaging in the instrument for most wavelengths; there is no real pupil before the focal plane; and the large focal plane requires a large entrance window to the dewar (~40 cm). These weaknesses led us to explore other optical design possibilities.

6.2 Beam Combiner Design 1

Beam Combiner Design 1 is the 7 mirror reflective reimaging system designed by Bonaccini in 1991. It reimages the F/15 bent Cassegrain focus with ``spectrograph style'' reflective optics. This design works at all wavelengths but the field is severely limited by vignetting in the reimaging optics.

6.3 Beam Combiner Design 2

Beam Combiner Design 2 uses finite conjugate ellipsoidal mirrors to reimage the F/15 focal planes to the combined focus. The tertiary and a fold flat feed the beams to the reimaging/combining mirrors. An example is shown in Figure 5. The strengths of this design are that it uses fully achromatic reflective optics and the existing F/15 secondaries. The weaknesses are that it uses 3 to 5 warm reflections before the focal plane and requires high structure in the center of the telescope. The differential (asymmetric) distortion appears to be the fatal flaw unless optical designs with symmetrical distortion can be found.

6.4 Beam Combiner Design 3

This infinite conjugate design uses lenses to reimage the F/15 focal plane through a cold pupil inside a dewar. A collimator lens outside the F/15 focus forms a cold pupil before a beam combiner mirror. Then a camera lens reimages the focal plane on the detector. This scheme combines the functions of the telescope and the instrument, so that what we think of as the instrument would now be only a detector. In the other beam combiner options (0,2) a reimaging instrument in a dewar would still be needed after the combined focal plane. The strengths of this design include: using pre-existing F/15 secondaries; having the F/15 focal planes accessible for guiding/sensing; only three warm reflections are needed; reimaging optics can be enclosed in a dewar after the tertiary; the cost and complexity of instruments are greatly reduced; a small dewar window is possible (15 -- 20 cm); easy access to a transmissive pupil and parallel beams provide locations for atmospheric dispersion correction. The weaknesses of this design include: possible non-achromatic optics which would require separate lenses for 0.5, 2 and 10 µ m; a sizable dewar is required on/in the telescope; phase measurement at short wavelength is more difficult; optical design work is still needed because field size is still uncertain.

7. Conclusions

Interferometry requires us to combine the focal planes from the two (N) telescopes. This combined focus should be of high optical quality and mechanically stable.
Adaptive correction of the individual telescopes can increase the sensitivity of the interferometer at wavelengths where the individual elements are not diffraction-limited.
We want beam combination optics which deliver diffraction-limited images over the full isoplanatic angle. This allows us to take full advantage of natural reference stars, even if the available detectors cannot image the full isoplanatic field.
Useful piston and tilt reference stars may be used over the full isokinetic angle.
After considering a number of optical configurations, we feel that a system which reimages the bent F/15 Gregorian focus offers the best combination of performance, flexibility and cost.

8. Acknowledgements

This work has benefited greatly from discussions with Roger Angel, Bruce Atwood, Domenico Bonaccini, Jim Burge, Paul Byard, Warren Davison, Michael Lloyd-Hart, Don McCarthy, Piero Salinari, and Nick Woolf.

9. References

McCarthy, D. 1986, ``Phased Focus for the Two-Shooter Telescope'', Columbus Project Technical Memo UA-86-06, 13/11/86.
McCarthy, D. W., Hege, E. K., Freeman, J. D., Blanco, D. R., Sjogren, J. C., Janes, C. C., Montgomery, J. W. and Shaklan, S. B. 1988, ``Interferometry with the Columbus Telescope: Design Considerations Based on MMT Experience and Imaging Simulations'',
Very Large Telescopes and their Instrumentation, ed. M.-H. Ulrich, (Munich:ESO), pp. 787-803.
Byard, P. and Bonaccini, D. 1994, (These proceedings).
Hill, J. M. 1990, ``Optical Design, Error Budget and Specifications for the Columbus Project Telescope'', S.P.I.E., 1236, pp. 86-107.
Beckers, J. M. 1986, ``Field of View Considerations for Telescope Arrays'', S.P.I.E. 628, pp. 255-260.
Traub, W. A. 1986, ``Combining Beams from Separated Telescopes'', Applied Optics 25, pp. 528-532.
Beckers, J. M., Roddier, F. J., Eisenhardt, P. R., Goad, L. E. and Shu, K-L. 1986, ``NOAO Infrared Adaptive Optics Program I: General Description'', S.P.I.E. 628, pp. 290-297.
Sandler, D. G., Stahl, S., Angel, J. R. P., Lloyd-Hart, M. and McCarthy, D. 1993, ``Adaptive Optics for Diffraction-Limited Infrared Imaging with 8m Telescopes'', JOSA A, in press.
Harvey, J. E. and Ftaclas, C. 1990, ``Fundamental Limitations on Off-axis Performance of Phased Telescope Arrays'', S.P.I.E. 1236, pp. 390-404.
Weaver, L. D., Fender, J. S. and DeHainaut, C. R. 1988, ``Design considerations for multiple telescope imaging arrays'', Optical Engineering, 27, pp. 730-735.
Hill, J. M. and Salinari, P. 1994, S.P.I.E.}, 2199 (Companion proceedings).