Domenico Bonaccini1
and
Paul Byard2
Osservatorio Astrofisico di Arcetri1
L.go E.Fermi 5
50125 Firenze - Italy
e-mail: domenico@arcetri.astro.it
The Ohio-State University - Dept. Astronomy2
174W 18th Ave.
Columbus, OH 43210 - USA
e-mail: byard@mps.ohio-state.edu
September 27, 1993
Introduction
Optical Specifications
Interferometric Mode and Field Specifications
1. Collimator Designs
Collimator Performance Evaluation
Introduction
The AO corrected image surfaces at the bent-Gregorian foci are collimated and the two beams combined to form an afocal system by two optical flats which direct the light parallel to the axes of the two primary mirrors (figure 1). An optomechanical set-up comprising an horizontal "T" pipe can be envisaged for the enclosure of the optics, in order to produce a vacuum and allow cooling the beam combiner optics. The combined image is formed by a camera accepting both these beams. The re-imaging approach of beam combination has several advantages over the previous design, i.e.: a) there is a real image of the pupil (M2 in this case) available for further AO correction, piston phasing or for M2 adaptive mirror diagnostics; b) the optical axes of the two beams are parallel to each other, eliminating differential tilts in image plane, present in the f/33 design; c) there are only three "warm" mirrors for the thermal infrared observations; d) the disadvantage of introducing more optical elements affecting throughput and thermal background with respect to the original f/33 design, is offset by the fact that in that case subsequent imaging cameras would have had to have extra optics, in order to give the proper image scales for sampling diffraction limited images at different wavelengths, as well as to provide a cold stop location for the reduction thermal background. This memo will begin to address the whole problem of using the LBT in an interferometric mode to cover a broad range of wavelengths, fields and imaging scales, rather than just provide a single combined beam focus, as was the case with the original f/33 focal station.
Optical Specifications
The Gregorian LBT has a real primary focus, and that makes it unique among other 8m class projects. This location can be used with a fiber source to test the optical train of the telescope itself, or else of the entire telescope+instrument assembly. As long as the spatial scale and the amplitude of the optical aberration are correctable by the AO servo, and the optical aberrations due to optical manufacturing or mounting errors are quantified, these can be fed back as a look-up table into the AO control algorithm (to give the ideal static configuration of the adaptive M2), in order to give perfect imaging at the scientific instrument rather than at the AO-wavefront sensor. Any remaining image defects being due to the atmosphere and enclosure alone. Ideally this procedure should be implemented in all of the LBT instruments, when an adaptive M2 is available.
The two downpointing flats reflect the beams from the collimators to produce a pair of collimated beams, with exit pupils meeting the (scaled) original entrance pupil geometry, so that beam combination and interferometry can be achieved. The chief rays through the two aperture stops are parallel, therefore any image plane curvature, if present, will be the same after the imaging cameras. As said, this is an improvement over the original baseline f/33 beam combiner design. The present (1993) mechanical design of the LBT foresees the beam combination axis at 8013.26 mm from M1 vertex, 3263.26 mm from the f/15 focus, 3500 mm on the opposite side of the C-shaped telescope elevation support, on a plane perpendicular to the elevation axis and symmetrical between the two primaries. This position actually corresponds to the location of the on axis image point when the LBT is viewed as one half of a "Four Shooter". In fact the required diameter of the camera lens can be reduced if the combination is allowed to take place on an axis through the line joining the pupil images. This places the combination axis slightly closer to the elevation axis. Refractive and reflective designs have been investigated for both collimators and cameras. The designs are for different wavelength bands, from the visible to the IR regions 1-2.5, 3-5, 8-12 microns.
An optical layout of the LBT in a beam combining mode is shown in Figure 1. The rays from the two primary mirrors M1 pass through a prime focus image surface in front of the Gregorian secondary mirrors M2, then are directed through the f/15 image surface by the tertiary flats M3 toward the beam combination axis. Prior to reaching this axis the chief rays are turned by the M4 mirrors to maintain the images of the pupils at the correct separation and orientation for interferometric combination. The figure shows the beam combination using refractive collimator lenses and a single spherical mirror as a camera. The whole design (the two telescopes collimators and camera combination) has been succesfully integrated using the Code-V optical design program. This will allow the study of the effects of radii and conic constant variations in the two interferometric paths to be studied to determine what the final tolerances have to be.
Interferometric Mode and Field Specifications
o. We can choose
well corrected stars within this field, as the reference for fringe tracking. However the corrected field
varies with the number of corrected modes. If only focus and tip-tilt is corrected by the AO system
(the lowest modes) the available field is increased in size over the isoplanatic field to what we call
here the isokinetic field. We have chosen the isokinetic field to be three times the usually defined
isoplanatic field. This is an average choice, because the real values are very dependent on the
turbulent layers distribution with height, their relative strength and some other AO servo parameters.
Anyway, the isokinetic field is the required field for the optical system, and is wavelength dependent.
Angular values of the diffraction limit and the isokinetic fields are plotted in figure 2.
1. Collimator Designs
In the designs that follow the aperture of the individual telescope exit pupils is 100 mm. To some
extent the choice is arbitrary. However smaller pupils would need larger field angles in the beam
combining cameras and larger pupils require excessively large optics. This value seems a fair
compromise, and requires a collimator effective focal length of 1500 mm, on the f/15 bent Cass beam.
The exit pupil (cold stop) is placed after the downpointing flats, to allow use of pupil location in the
camera designs and a test location for the phasing actuator. The optomechanical interface should
allow either a 
300 mm exit window after the (two) exit pupils or else the direct tight connection
of the camera.
There are three collimator designs, two reflective and one refractive. To achieve diffraction limited performances, the designs have to perform very well over what we call the isokinetic field. The isokinetic field is a seeing variable quantity, and a range of values is given using the Sandler et al. (1993) MK and MMK models for the isoplanatic angle. For the design of the collimator, the following are the basic resulting input parameters:
| Telescope focal plane | f/15 |
| Collimator aperture stop diameter | 100 mm. |
| Separation of aperture stop centers | 171.467 mm. |
| Diameter of camera entrance pupil | 271.467 mm. |
| Seeing Conditions (Mt. Graham) | 0.7" at 0.5 µ m |
| Resulting ro at 0.5, 1, 2, 5, 10, 20 µ m | 182, 417, 958, 2877, 6610 and 15187 mm resp. |
| Isokinetic angular diameters | 3.9-9", 9-20", 20-47", 62-142", 142-327", 326-752" |
| (MK-MMK models after Sandler et al. 1993) |
Collimator Performance Evaluation
The Strehl ratios (SR) obtainable at the various wavelengths and fields, with the different collimator
designs described below are shown in figures 3, 5 and 7. A comment is necessary. To evaluate the
telescope-collimator combination, a perfect lens is assumed for the camera, which does not make
complete justice since some aberrations can be compensated by the camera optimization on each
collimator-telescope combination. What is evaluated is the SR at the best focus of each field position,
at each wavelength.
Wavelength affects the SR performance by changing the value of the phase variance error when expressed in radians, which then enters the SR formula. It enters also in the chromatic effects for the refractive collimators. The off-axis reflective designs obviousely do not have a symmetric performance around the optical axis, having only one plane of symmetry normal to the off-axis
displacements. In our case the Y direction is the optics tilt-decenter direction, and it coincides with M1 optical axis (see figures on layouts below). In fact, our two reflective designs are limited in field in the Y-direction by the optics obstruction above ± 30", and evaluation beyond that value are done in the X field direction. In these reflective designs it should be clear that the operating field would be a strip with one (y) axis 
1' and the other axis as long as limited by the optics performance.
This is the name of the first of the collimator designs. Figure 3 shows one arm of the LBT
interferometer, with the reflective collimator solution BCOMB1. After the downpointing flat the light
is focussed by a perfect camera lens on the beam combination axis. It is made of an off-axis parabola
which is located 1500 mm after the f/15 bent Cass focus, and it makes a 100 mm pupil image 80 mm
before it, on a flat mirror. The flat mirror reflects the light to a downpointing flat. The collimator
involves three mirrors, only one of which with power. A perfect camera lens, not drawn in Fig 3, is
focussing the light at the LBT interferometric focus location. This design is simple and has the
advantage of a flat pupil image, useful for an adaptive mirror. However, the pupil is at 3343.26 mm
from the beam combination axis, therefore the beam hitting the downpointing flats becomes large as
soon as the field is increased. Also, the unvignetted field is limited in the collimator optics tilt
direction to BCOMB1
± 30", while of course there is no limitation in the other direction. Also, we are concerned
on the effects of differential distortion. There is a very limited distortion in this design, however it is
not symmetrical and it changes symmetry between the two arms. Indeed the chief rays aiming at the
same field point at, say, 30" field angle, hit the image plane apart by 1.16 diffraction limit FWHM
of a single telescope, at 1µm wavelength. We will have to explore later this effect more in detail, via
a full interferometric analysis. As for the diffraction limited performances of this collimator, figure
4 shows the Strehl Ratios obtained at different field positions, for different wavelengths. These Strehl
Ratios are obtained if a refocus is allowed over the field positions, i.e. they represent the best focus.
In the evaluation, the fields limits used are the isokinetic values given above.
This is a refractive collimator design. It is our preferred choice, because of the circular simmetry and
circular unvignetted field. It achieves the best optical performance. The design is a simple doublet, with a special choice of materials, ZnSe and CsI. This combination has excellent
performance over wavelength ranges from 1 to 18 microns with refocus. However, different
collimators, each optimized for the wavelength band of interest will probably have to be used because it will be difficult to find anti-reflective coatings covering the whole range
from 1 to 18 microns. The bands have been split
in the ranges 0.33-1.1 µ m, 1-2.5 µ m, 3-8 µm
and 5-18 µm, and all IR collimators have been
designed. The visible collimator has not yet
been optimized. Figure 5 shows the optical
layout of both arms of the beam combiner
collimator for the 3-8 µ m region. It also shows
the infrared camera mounted after the two
downpointing flats and the combined focus
image plane for two field positions. Collimators
for the other bands have similar layouts. Figure
6 shows the Strehl Ratio performance of these
refractive solutions. In all cases the performance
is above specifications, and it is the best of the
three collimator designs. The maximum size of
these lenses is 26 cm in diameter and the 4
different refractive collimators would be placed
in a rotating wheel inside the horizontal vacuum
tight pipe. They will also have to be cooled for
thermal IR uses. The lenses all consist of two
spherical elements. Both ZnSe and CsI can
probably be obtained in these sizes but the
properties of these materials, particularly the variation of refractive index with temperature and the
practicality of anti-reflection coatings will have to be studied before it can be seen whether the
theoretical designs can be used in a real instrument. It also remains to be explored the practical
durability of the chosen materials. BCOMB2
This is a reflective solution which makes a 100 mm diameter aperture stop just after the two
downpointing flats. It overcomes the beam size problems at the flats of BCOMB1, it has a real exit
pupil image, but it does not have a reflective flat exit pupil. Indeed this design takes into account the
idea that the adaptive correction is done at the secondary mirror, and/or on a transmissive liquid
crystal array. Figure 7 shows the two arms optical layout, from the f/15 focus to the reflective up-pointing camera mirror. Only small sections of the two off axis collimator mirrors are used. The
mirrors are aspheric, and probably the diamond turning technique is the production choice. The
position of the downpointing flats is 80 cm above the f/15 focus optical axis, determining the size of
the horizontal vacuum pipes. This solution is intermediate in performance between BCOMB1 and
BCOMB2, as indicated by figure 8. BCOMB3
2. Camera Designs
The Airy "disk" is the approximate separation of the first minima in diffraction pattern from the full
aperture of both telescopes. The camera f/ratios are calculated with the assumption that 4 pixels are
used to sample this distance which will give approximately two pixel sampling at the FWHM of the
diffraction peak. It should be noted that this would be an undersampled image in terms of the Raleigh
criterion for the resolution of two equally bright objects at the diffraction limit.
| Wavelength | 1µ m | 2.5µm | 3.5µm | 5.5µm | 10µm |
| Airy "disk" arcseconds | 0.022 | 0.055 | 0.077 | 0.121 | 0.22 |
| diameter of the angular isoplanatic field (MK model, 0.7" seeing) | 6.9" | 20.7" | 31.0" | 53.3" | 109.24" |
| Camera f/ratio 20 µ pixels | 33 | 13 | 9.4 | 6.0 | 3.3 |
| Camera focal length | 8.9 m. | 3.6 m. | 2.5 m. | 1.6 m. | 0.9 m |
| Camera isoplanatic field radius, pxl | 628 | 751 | 781 | 860 | 991.5 |
| Camera isoplanatic field radius, mm. | 12.56 | 15.03 | 15.63 | 17.21 | 19.83 |
Three camera designs are given, one for each of the ranges mentioned above.
Figure 9 shows the footprint of ray bundles at the focal surface of the 1 to 2.5 micron beam combining camera (large rectangle). The larger square encloses a field matching the isoplanatic patch for ro of 45 cm. The smaller square is equivalent to a 2048 x 2048 detector with 20 micron pixels. It is a section through the camera at the location of the focal surface. The array of pupils on the left of the figure represent the ray bundles from the corners of a field covering the isoplanatic patch at 2.5 microns as they pass close to the focal surface on their way to the spherical camera mirror. This mirror is offset by 200 mm, and forms images of objects represented by the ray bundles at the corner of the square in the center of the figure. An indication of the physical size of the isoplanatic patch is given by the small square to the right which is equivalent to a 2048 x 2048 detector with 20 micron pixels.
The field curvature in this design is 6 meters. Note that the physical extent of the field is very large; probably larger than any foreseeable detector! Also, the physical size of the third element is of some concern. This element could probably be sectioned into off axis pieces for different parts of the field. However the low power of the second and third elements prompted a search for a simpler solution. Between 8 and 12 microns the refractive index of germanium changes very little (at least at room temperature) i.e. the dispersion is very low. A single germanium lens can be used as a beam combining camera in this region . A simple camera of this form has a curved field with a curvature radius of about 1.2 meters. The Strehl ratio out to a camera field angle of 4.5 degrees (3.3 arc minutes telescopic field) exceeds 80%. The layout for this camera is shown in figure 12.
While the curvature of field looks excessive for this camera, it should be noted that the physical diameter of the field for which the Strehl ratio exceeds 80% is over 40 cm. Provided the detectors are not too large they can be tiled to match the curved focal surface.
DISCUSSION
Much work remains to be done. First, a study of the materials availability, and a "cold" refractive optics optimization. Moreover a study of the entire interferometer performance, once the optical solutions are chosen. Very recently we have been able (mostly Paul) to simulate the entire two arm interferometer, using the Code V the concept of non-sequential surfaces. We can thus assess the interferometer performance at the various field positions (assuming perfect adaptive optics correction), optomechanical tolerances, and evaluate the effects of polarization aberrations in the beam combiner system. To do this effectively, the optical coatings specification will have to be entered in the simulation. Also, starting from a model atmosphere with finite outer scale, and deriving the piston coefficients, it will be possible to evaluate the importance of the effects of piston errors due to the atmospheric turbulence. An exploratory work will be done by the adaptive optics group at Arcetri Astrophysical Observatory. At last, figure 13 shows the LBTI Point Spread Function for perfect phasing.
