Requirements for the LBT Combined Focus

J. M. Hill, Steward Observatory

Large Binocular Telescope Project

Technical Memo

October 29, 1993

UA-93-07
http://medusa.as.arizona.edu/lbtwww/tech/ua9307.htm

Abstract

1. Introduction

2. Scientific Requirements

3 An Algebra of Beam Combiner Design

4 Practicalities

5 Optical Requirements

6 Beam Combiner Options

7 Conclusions

8 Acknowledgements

9 Bibliography

List of Figures

Abstract

A summary of the scientific requirements and the optical design requirements for the Large Binocular Telescope Project beam combining optics is presented. Interferometry requires combining the focal planes from the two telescopes. Adaptive correction of the individual telescopes can increase the sensitivity of the interferometer at wavelengths where the individual elements are not diffraction-limited. Beam combination optics should deliver diffraction-limited images over the full isoplanatic 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.

1. Introduction

This memo 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 November 1986 memo ``Phased Focus for the Two-Shooter Telescope'' (UA-86-06). That memo puts the interferometric focus in a somewhat broader context of telescope design. McCarthy et. al. (1988) provide some simulations to illustrate the performance of the 8 meter binocular.

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 memo discuss the tradeoffs of the various types of beam combination optics for LBT and its instruments. Bonaccini and Byard (OAA-93-01) have recently studied several optical designs which produce the combined focus by reimaging.

2. Scientific Requirements

2.1 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 microns (where the field is small, ~ 5 arcsec diameter) to 20 microns (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 microns, 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.

2.2 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 1.

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 1.8m, 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 (McCarthy 1986, McCarthy et. al. 1988, Hill 1990). In this case the practical minimum number of mirrors to get to the combined focal plane is four. See the examples in Figures 2 and 3.

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.

The reader should not confuse these classes of beam combiners with the types of telescope arrays described by Beckers (1986). This memo is primarily discussing what Beckers would call Type 0 or Type 1 arrays.

2.3 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), 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 dual (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 Traub (1986). Beckers (1990) discusses the tolerances required for cophasing.

2.4 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.) An example of lateral offset can be seen in Figure 4 which is the side view of Figure 3.

2.5 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. This document will not consider adjustments to the mirror spacing. See McCarthy et. al. (1988) for additional discussion.

2.6 Isoplanatic Patch and Field Size

The size (angular diameter) of the isoplanatic patch (field of similar phase) is given by Beckers et. al. (1986) 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. Multiconjugate adaptive systems are beyond the scope of this discussion. See Sandler et. al. (1993) for 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. All star images in the isoplanatic field can be corrected and phased with the same wavefront reference. 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 (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 microns, and 1.9 -- 9.4 arcminutes at 10 microns. (These ranges should be typical of the best 20 % of the nights.) 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.

2.7 Isokinetic 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.

The size (angular diameter) of the isokinetic patch (field of similar centroid) scales as D/H (Angel, private communication); where H is the average distance to the seeing layer and D is the diameter of the telescope (see also Woolf 1982). The isokinetic patch for an 8-meter aperture should be several arcminutes in diameter. This means that reference stars for tip-tilt correction will be available over even larger fields than those specified above for the isoplanatic patch at wavelengths where r0 is smaller than D. (What happens when r0 is larger than D? --- Even tilt becomes less important compared to the diffraction limit.) The isokinetic patch size (defined by angular motion) is independent of wavelength, but the isokinetic patch size (defined by motion as a fraction of the Airy disk) increases linearly with wavelength.

Lloyd-Hart et. al. (1993) have measured the isokinetic patch using binary stars at the MMT. They find that the isokinetic patch at 2 microns is 90 arcsec diameter under median conditions (r 0 (2 µ m) = 0.9 m). They also measure the high-altitude seeing layer at a height of 5000 -- 6000 m.

(This discussion refers to tip-tilt correction on the image centroid. In practice, one may wish to track the brightest speckle where wavelength effects will be significant. The centroid is relevant in the visible where there are many speckles or in the thermal infrared where there is only one speckle.)

2.8 Isopistonic Patch and Field Size

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.

Simulations indicate that the size of the isopistonic patch is ......... (Stay tuned for a future memo.)

2.9 Vignetting Considerations

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. The field radius, X (m), of the beam combiner at height (of the apex), H (m), is approximately given by

X = (P cos(aa) tan(ai) H) / ( P cos(aa) - H)

where P (m) is the distance from the exit pupil to the focal plane, aa (rad) is the half-angle of the combined chief rays, and ai (rad) is the interior half angle (empty space between the beams). These two angles describe the pupil geometry. However, the equation is changed by reimaging, so this equation is only relevant for combiners of the second class.

For LBT with the traditional 4-mirror beam combiner at F/33, this means that the beam combiner apex must be 11.5 meters above the focal plane to give a 5 arcminute diameter unvignetted field-of-view.

2.10 Depth of Focus 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 ± 2F 2 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 microns wavelength would have a depth of focus of ±8 mm.

Since the focal plane tilt is fixed by the telescope (entrance pupil) geometry, the depth of focus increases linearly with wavelength and the isoplanatic field increases with the 1.2 power of the wavelength, the longest wavelength provides the most severe constraint of the focal ratio. The tilt angle of the LBT focal planes is given by (14.417 / 8.408) * arctan( 1 /F) . Using = 10 microns, and a field radius of 2.5 arcminutes, we can set the tilted height at the edge of the field equal to the diffraction depth of focus and solve for the minimum focal ratio (F). For the LBT entrance pupil, the secondary focal ratio must be slower than F/23 to preserve coherence across the tilted focal planes with a 5 arcminute diameter field at 10 microns.

For the reimaging beam combiner, the tilt of the focal planes may be either increased or decreased by the reimaging optics if they are off-axis. Ideally, we would like the focal planes to coincide with the constant phase plane.

2.11 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. That 80% diameter for selected wavelengths and a primary diameter of 8.408 m is:

0.5 microns 0.03 arcsec
1.0 microns 0.06 arcsec
2.0 microns 0.12 arcsec
5.0 microns 0.29 arcsec
10.0 microns 0.59 arcsec

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. At visible wavelengths, other parts of the telescope error budget will dominate. In the mid- and far-infrared, the telescope optics should easily (given 5 years and $60M) be able to deliver diffraction-limited images.

2.12 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 microns (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. (Hill in UA-88-14 assumed that the images should overlap to 0.1 ( / B) for a 6 arcminute field, where B is the telescope baseline. This implies a match to 1 part in 20000. Whether this tolerance is 1:2500 or 1:20000 has a big effect on beam combiner design and primary fabrication.)

2.13 Field Curvature

Harvey and Ftaclas (1990) and Weaver, Fender and De Hainaut (1988) 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 my 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. (Again from my analysis,) 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. The 4-mirror F/33 configuration for LBT has a field radius of curvature of 1.03 meters. The sag at the edge of a 6 arcminute diameter field is 28 mm. This means that the images are separated by 1.1 arcsec on the curved combined surface. If we apply the same overlap criterion as for scale and distortion (0.24 ( / D ) ~ 0.06 arcsec), then the field radius is limited to only 0.7 arcminutes! The critical related question is whether the surface of common phase (where the detector should actually be) is also curved? (see raytrace results below) IF the surface of common phase remains flat, then the images are not separated by field curvature. The images may still be separated because the chief rays at the edge of the field are not perpendicular to the paraxial focal plane (a form of non-telecentricity). That separation is given by tilt angle between the focal planes times the field radius times the angle deviation from perpendicular. For the LBT F/33 case, the tilted focal planes at a radius of 3 arcminutes (or 242 mm) are separated by 12.5 mm, so the images are separated by 0.07 arcsec.

For class two beam combination, the effects of field curvature relative to the diffraction depth of focus decrease linearly with final focal ratio. Decreasing the focal ratio by a factor of two doubles the radius of curvature of the focal plane and cuts the field radius in half. This reduces the sag across the focal plane by a factor of eight while the depth of focus only decreases by a factor of four. Of course, the penalties for the faster focal ratio would be more vignetting at the beam combiner and a larger secondary mirror.

Raytracing the LBT moving phased Gregorian focus with the OSLO program (rev 3.20) indicates that the surface of common optical pathlength from the entrance pupil (conjugate to the infrared secondary) of a single telescope has only a slight curvature, radius = 32.4 meters with sign opposite the field curvature. The Gregorian F/15 focus has a surface of common optical pathlength with a radius of 13.1 meters, also opposite in curvature from the curved focal plane with best images.

2.14 Field Rotation

Because the telescopes are mounted on an altitude-azimuth mount, we must also pay attention to field rotation effects. This influences the integration times rather than the optical design requirements.

2.15 Atmospheric Dispersion

Bonaccini and Byard pointed out in October 1992 that atmospheric dispersion correction may be needed for broad band imaging or spectroscopy now that the pixel size is approaching the diffraction limit. From OSU-DBPB-OPIM-1 (Columbus IDT Memo) we learn that the spread between the 1.0 and 2.0 micron image is ~0.25 arcsec at a zenith distance of 45 degrees. The image blurs caused by atmospheric dispersion at J 1.25µ m , H 1.6µ m , K 2.2µ m and L 3.4µ m bands are 0.08, 0.035, 0.02 and 0.005 arcsec respectively (compared to diffraction-limited slit sizes of 0.027, 0.035, 0.048 and 0.074 arcsec). Broad band imaging at the diffraction limit of the interferometer starts to become impractical because the filter bandwidths will tend to reduce the fringe contrast. The bandwidths for Johnson J, H, K and L bands are between 20% and 30%.

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: 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.

3.2 Algebra examples

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.

4 Practicalities

In addition to the scientific and optical requirements, there are certain practicalities that we would like to consider in the design process.

5 Optical Requirements

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

6 Beam Combiner Options

 This section provides an executive summary of how the design process got to where it is. Perceived strengths and weaknesses of the various optical options are listed.

6.1 September 1992 politics

If I may be so bold, I would now like to summarize the ``politics'' of the various beam combining options --- as perceived in September 1992. I perceive that there are three camps.

The visible camp: This group would use 7 mirrors and a reimaged F/15 bent Cass focus to produce a phased focus with an intermediate pupil accessible to an adaptive mirror (like Beam Combiner Design 1). They don't require much field, so beam combiner height isn't an issue. Warm mirrors also present no problem.

The 2 micron camp: This group is attempting to find a 5 mirror solution to a reimaged bent Cass F/15 focus (like Beam Combiner Design 2). This allows the phased focus to share a common secondary with the normal F/15 Cass focus optimized for the infrared. Since the baseline F/33 secondaries would not be needed in this option, it carries substantial support from the telescope engineering and budget points of view. At this writing (9/92), we do not yet have an adequate optical design for the finite conjugate reimaging/combining optics. An adaptive secondary offers a substantial sensitivity to this focal station at near and mid-IR wavelengths.

The 10 micron camp: In the deep thermal infrared, every reflection adds emissivity, so the baseline F/33 combined focus (Beam Combiner Design 0) is still preferred. The baseline optics provide a 4 arcminute flat field with diffraction-limited images. A separate adaptive secondary would be needed for F/33 (or else an adaptive beam combiner), but this capability is only needed at wavelengths shorter than 5 microns. This focal station offers performance that no other telescope currently under design can approach. Neither ESO's VLT nor Keck I+II nor individual 8 meter telescopes can provide the combination of baseline plus field plus low emissivity.

6.2 June 1993 solution

Between October 1992 and June 1993, the telescope design group evolved its thinking on the combined focus. The ``politics'' described above consider 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. Pros and cons of the various options are discussed below. The concept we have in mind is described by Bonaccini and Byard (OAA-93-01). The refractive version of this concept is discussed here as Beam Combiner Design 3.

6.3 Beam Combiner Design 0

This design is the classic Columbus ``4 mirrors to focus'' design at F/33. See Figures 2 and 3.

6.4 Beam Combiner Design 1

This design is the 7 mirror reflective reimaging system designed by Bonaccini in 1991. It reimages the F/15 bent Cass focus with ``spectrograph style'' reflective optics. See Figure 3 of Bonaccini and Byard (OAA-93-01).

6.5 Beam Combiner Design 2

This design 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. See Figure 5.

6.6 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. At least three sets of lenses would be required to cover the visible, near infrared and thermal infrared. 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.

6.7 Optical Examples

View Figure 1 here

View Figure 2 here

View Figure 3 here

View Figure 4 here

View Figure 5 here

7 Conclusions

8 Acknowledgements

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

9 Bibliography