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Optical metrology for two large highly aspheric
telescope mirrors
S. C. West, J. H. Burge, R. S. Young,
D. S. Anderson,
C. Murgiuc,
D. A. Ketelsen,
and H. M. Martin
We describe a relatively simple, but highly effective, approach to the system design and alignment of an
all-refractive Offner null corrector and phase-measuring Shack cube interferometer. In addition we
outline procedures for fabricating and testing the optical components. Allowable errors for all
parameters are determined by a tolerance analysis that separates axisymmetric and residual figure
errors. An open construction optics frame provides a high degree of metering flexibility by incorporating
simple kinematic mounts that provide adjustment of each lens while also allowing the lens to be removed
and replaced with < 2-pLmabsolute repeatability. Nonaxisymmetric alignment errors are removed by
rotating the optics on a high-precision bearing. Axial spacings are measured with contact transducers
attached to both ends of an Invar metering rod. Two completed systems have guided the stressed-lap
polishing of 1.8-mf/ 1.0 and 3.5-m f/ 1.5 aspheric mirrors.
Key words: Interferometry, optical testing, metrology, null correctors, polishing.
1.
Introduction
The Steward Observatory Mirror Laboratory has
developed technology to cast and polish lightweight
honeycomb sandwich mirrors up to 8.4 m in diameter. 1 -4 Considerations of stiffness and the economy
of the resulting telescopes require that these mirros
be polished with focal ratios near 1. The surface
accuracy of these mirrors must meet the extremely
demanding specifications set by the requirement that
the telescope not degrade the atmospheric wave front
expected from the best nights of seeing and that the
optics produce rms images of <0.1 arcsec over 1°
fields.5 Specifically,the optics must not cause wavefront distortions that are greater than those introduced by a 0.125-arcsec full width at half-maximum
atmosphere and must scatter < 20% of the light at a
wavelength of 350 nm. The surface figure irregularity of the primary mirror is specified as a structure
function. Typical values of the rms surface difference between points range from 20 nm rms for
separations of < 5 cm to 600 nm rms at 5-m separation. We must maintain the conic constant to a few
parts in 104 to provide proper matching to the
secondary mirror while holding the position of the
The authors are with the Steward Observatory, University of
Arizona, Tucson, Arizona 85721.
Received 28 February 1992.
0003-6935/92/347191-07$05.00/0.
©
1992 Optical Society of America.
focal plane to several centimeters. The successful
figuring of a primary mirror to these specifications
translates into an extremely tight error budget for
the optical metrology system.
Two highly aspheric primary mirrors-the Lennon
1.8-m f/1.0 and Phillips Laboratory Starfire Optical
Range 3.5-m f/1.5 mirrors-have recently been polished to rms surface accuracies of 17 and 21 nm,
respectively.6 Here we report on the methods and
procedures used in the development of the optical
metrology systems that guided stressed-lap polishing
of these mirrors. Sufficient detail is included to be of
value to others working on similar projects. A description of the optical system and its tolerance,
manufacture, and testing is in Section 2. Mechanical support and remote positioning are discussed in
Section 3. The optical alignment scheme, which is
capable of controlling component runouts to ± 1.5 [im
and axial spacings to ±5 jim, is outlined in Section 4.
The remaining sections describe the large optics test
tower and the procedures used to verify the nullcorrector performance.
2. Optical System
The optical system (Fig. 1) consists of a phasemeasuring Shack-cube interferometer, an Offner refractive null lens, a stabilized He-Ne laser, and an
imaging system. The null corrector is used to transform a spherical diverging wave front into a highly
aspheric wave front that accurately matches the
1 December 1992 / Vol. 31, No. 34 / APPLIED OPTICS
7191
CCD
Relay Lens
FielLens
Shac~
Fig. 1. Offner null corrector and Shack-cube interferometer used
to perform the null test of the primary mirrors (not to scale). See
text for explanation.
desired shape of the primary mirror. On reflection
from the mirror the light returns through the null
lens, is converted into a spherical wave front, and is
coherently added to the reference light from the
spherical surface of the Shack cube, which gives
fringes of interference that indicate deviations of the
mirror from the desired shape. For our purposes
the refractive Offner7 null corrector provides two
major advantages over reflective optics. The error
budget is less sensitive to the surface accuracy of the
components (although it is highly sensitive to index
homogeneity), and the optics have no central obstruction, which allows for simplified axial metering as
well as visibility of a reference sphere inserted into
the primary-mirror perforation.
We chose a Shack-cube interferometer because it
requires only one precise spherical component and is
inexpensive, compact, and easily phase shifted.8 9
The Shack cubes (constructed by Tucson Optical
Research Corporation) are phase shifted with a Burleigh piezoelectric drive. The interferometer includes a stabilized He-Ne laser, beam-steering flats,
and relay optics to image the mirror onto a CCD
camera.
A. Tolerance Analysis
We performed a thorough tolerance analysis of the
null lens to determine the precise correspondence
between uncertainties in the null corrector and specific errors in the primary mirror, such as the conicconstant error and the surface irregularities with the
conic error removed. Because the telescope allows
for a small variation in the conic constant, it was
separated from the other errors.
The procedure for creating the error budget was
derived from the procedure that the opticians use to
test the mirror. The interference pattern is used as
a guide for positioning the null corrector to obtain the
best wave front. The interferometer is moved vertically to eliminate focus, laterally to eliminate tilt and
is gimbaled about the lateral axes to eliminate coma.
This is tantamount to positioning the mirror surface
with respect to the null corrector to achieve the best
fit with the generated wave front. The compensation procedure in the tolerance analysis used optical
design software (Super Oslo) to follow this test
procedure exactly. For example, the influence of a
single parameter of the null lens is determined by
7192
APPLIED OPTICS / Vol. 31, No. 34 / 1 December 1992
varying it an appropriate amount and then reoptimizing for minimum wave-front variance by changing
the position, orientation, and conic constant of the
mirror. This directly yields the uncertainty in both
the conic constant and the rms wave front corresponding to each parameter. We evaluated errors occurring in the manufacture of the null corrector and
interferometer by using the above procedure and
then added in quadrature to determine the resulting
error in the primary-mirror figure. The results
showed that axial spacings and edge runouts must be
held near 5-10 jim for all optical components.
Table 1 summarizes the uncertainties in the conic
constant and the rms surface figure that result from
the errors incurred during the assembly of the interferometer and the manufacture of the optics. The
uncertainties represent upper limits because nonaxisymmetric errors (e.g., index inhomogeneity), which
can be removed by rotating the test optics with
respect to the mirror, are included. The mirror
asphericity is expressed as a deviation from the
vertex-matching sphere in He-Ne waves. The contribution of each null-lens parameter to the conic constant and wave-front uncertainties is shown in Fig. 2.
B.
Optics Manufacture and Testing
We chose to use Schott BK7 H4 glass because of its
excellent refractive-index homogeneity, reasonable
cost, and availability. The glass blanks were certified to have a maximum index variation of < 0.5 x
10-6. Interferograms of the blanks show a slowly
varying diametric error that principally causes tilt in
the wave front and does not affect the null test.
All the test plates and lenses for the Phillips
Laboratory null corrector were manufactured at our
laboratory. (The Lennon optics were manufactured
at Tucson Optical Research Corporation.) The lens
blanks were generated to the appropriate radii and
thicknesses, then ground and polished to match the
test plates to < 1 fringe of power and 0.1 fringes of
irregularity. The rear surface of the test plate for
the relay lens required a steep compensating curve for
us to view the Fizeau fringes during polishing. The
wedge requirements were significantly relaxed because the surfaces were spherical and the alignment
scheme (Section 4) provided for independent tilt and
centration adjustments.
The optical parameters of the test plates and lenses
for both correctors were carefully verified. Using a
standard method,1 0 we measured the radii of curvature on a lens bench constructed jointly by the Optical
Sciences Center and Steward Observatory. It consisted of a 1.6-m Gaertner optical bench, a 1-m
Table1. Asphericity
VersusCumulative
ErrorsResultingfromthe
Fabrication
of theNullCorrectors
Mirror
Phillips Laboratory, 3.5 m
Lennon, 1.8 m
Asphericity
Conic
rms Surface
(Waves) Uncertainty Uncertainty
1612
2908
0.00012
0.00028
0.025 wave
0.033 wave
0.000100
Primary radius
uncertaintyof 1
0.000090
E
0.000080
0.000070
E
c
=L
c,
O
CU
a,
CD
a 0.000060
O
0
Z7
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o
CC
0.000050
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0C
co
0.000030
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~
t
~
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aI
a~)
6 0.000040
C
CD
CD
c)
~a),
=3
a,
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ID
~~~~~~CD
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,CD
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~~~~~~~~U
_
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=3
~~~~~~~~~a'
a,
-a
c
I
-
-
0
0.000020
0.000010
0.000000
ShackCube
Field Lens
Relay Lens
(a)
0.0500
-
0.0450
co
0.0400
-
F
~~~~~~~~~~~~a
Cd)
E
co~~~~~~~~~~~~~~
0.)
0.0350
CD0
CN4
Co
Cq
CD
0.0300
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a
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c
~
tc
,
CD
00
g.
TO
,
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-
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,5
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ad
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0.0150
.m
B'
U~~~~~~~~
a
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o
,
-~~~~~~~~~~~~~~~~~c
o
L
|~~~~~~~~~~E
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i:
a
=3
0
>,
a,
=
co
0
CD
co~~~~~~~~~~0
0.0200
>
CD~~~~~~~~~~C
a,
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a,0)
_D
II. I
0.0100
0.0050
~~~CD
'0,0
0.0000
ShackCube
Field Lens
RelayLens
(b)
Fig. 2. Contributions of each error in the null lens to the uncertainty in (a) the conic constant and (b) the wave front for the Phillips
Laboratory primary mirror. Only the parameters with the greatest effect are labeled.
Mitutoyo linear scale (with 1-jim resolution), and a
Zygo Mk II-01 phase-measuring interferometer with
several diverger lenses. The same interferometer
was used to measure surface irregularities. Lens
thickness were measured with a Cadillac gauge and a
Mitutoyo probe placed on a precision granite table
and then independently verified with stacked gauge
blocks.
The pinhole of the Shack cube must be precisely
positioned at the center of curvature of the cube's
reference surface to minimize aberrations. The focus of a fast lens (of the Zygo interferometer) is
1 December 1992 / Vol. 31, No. 34 / APPLIED OPTICS
7193
positioned precisely at the center of curvature of the
cube's reference surface by nulling the fringes in
retroreflection off that surface. The pinhole (which
is mounted on a glass spacer) is positioned with a
translation stage until light throughput is maximized
and cemented in place.
3.
Top View
Centration
Optics Frame
The optomechanical schematic of the interferometer
is shown in Fig. 3. The main parts of the unit are
the interferometer, null corrector, CCD camera and
relay optics, Invar optics frame, adjustable kinematic
lens mounts, high-precision rotary table, and a remotely controllable five-axis positioner. The Invar
frame provides for 50 C temperature tolerance for
the axial spacings. The design details of the various
parts are described below.
A.
Kinematic Lens Mounts
The optics structure provides a high degree of metering flexibility resulting from the design of versatile
lens mounts that combine nearly strain-free lens
supports and five axes of adjustment with highprecision kinematic mounts (shown in Fig. 4 for the
relay lens). The lenses can be removed and replaced
from the optics frame with < 2-jim-p.v. repeatability.
Within the kinematic support each lens is held in
slight compression both axially and laterally. Axial
(and some radial) support is provided by spring
loading each lens on three axial points around its
periphery. Additional radial constraints consist of
three sections of Tygon tubing compressed between
the edge of the lens and its mount. The kinematic
support has the canonical hole-slot-flat construction
Beam
CCD & Camera
Kinematic Supports
Invar Frame
Lens Adjusters
5-Axis
LI
I
Fig.3. Schematic of the test optics for the Lennon 1.8-mf/I.0 and
Phillips Laboratory 3.5-m fl 1.5 primary mirrors.
7194
APPLIED OPTICS / Vol. 31, No. 34 / 1 December 1992
Side View
Tip-Tilt
Mechanism
X-Y
Stage
Brass Jacks
Fig. 4. Kinematic lens supports permit nearly strain-free lens
mounting, five axes of adjustment, and the ability to remove and
replace the lens with extremely high-positioning repeatability.
with several refinements that allow for high-precision
adjustments. Tip-tilt adjustment is provided by pistoning two tooling balls with 60-pitch screws. The
balls cannot rotate while being jacked so that ball
runout cannot produce lateral movement. Except
for our oversight of the Shack cube, we kept the plane
defined by the three tooling balls close to the lens
vertices to minimize cross talk between centration
and tip tilt. Centration is provided by attaching the
third tooling ball to a lockable XY stage (Daedal
3927). The hole, slot, and flat are made of precision
ground steel mounted into large brass rotationally
constrained piston screws. All moving parts are
locked with split-ring clamps.
B. Remote Positioning
The optics frame is micropositioned near the center of
curvature of the mirror being polished with a five-axis
positioner (Fig. 3). The translation and tip-tilt resolutions (0.25 jim and 0.1 arcsec, respectively) are set
by the motions that produce a < 0.1-wave-p.voptical
path distance error in the interferogram. The gimbal is chosen to produce pure Zernike coma without
tilt (two-thirds of the way from the paraxial to the
marginal center of curvature).
X-Y-Z translation is provided by a stack of three
linear slides with open construction (Design Components, Inc. HM 80) driven by microstepped motors
[American Precision Industries (API) M233]. The
upper two slides are tilted by 15 deg and are driven in
tandem to provide X and Z motion. Providing Z
motion in this fashion is preferable to a vertical slide,
which would be bulky, suffer from flexure, and have
to drive the entire weight of the unit directly in
against gravity. The two-axis gimbal is constructed
with four flex pivots (Bendix Aerospace 5024-400)
and driven by two microstepped linear actuators (API
A231).
In addition the optics may be precisely ro-
tated about the Z axis with a Klinger RT-200 rotary
table. An 8752 microprocessor controller provides
for remote selection of the axis to be moved, direction,
speed, and programmable jogs by sending digital
signals to API P325 microstepping drives.
4.
Optical Alignment
System alignment is based on a variation of the
methods that use a high-precision rotary table to
1 3 Tolerances near 5 jim,
define the optic axis.11combined with the fact that we have nonperforated
refractive components, suggest that mechanical (rather than interferometric) metering provides a straightforward approach (Fig. 5). The Invar optics frame is
built onto a rotary table that we verified to have +3
arcsec of ball race wobble and ± 2.5 jim of concentricity runout. A stationary I beam provides the platform for mounting the metering probes. The edge
probes (Mitutoyo 519-899 leverhead and 519-817
mu-checker) are stationary and extend through perforations in the rotary table and structural top plate so
that the runouts may be sensed while the optics
rotate without interference from the frame. The
axial metering rod is mounted on a five-axis adjust-
able stage that is attached kinematically to the I
beam. The rod itself is an Invar bar with highprecision compliant contact sensors mounted to each
end [Schaevitz PCA-375-PR-010linear variable differ-
ential transformers (LVDT's) with DTR-451 readers).
Coalignment of the rotary table and lens axes
typically consists of several iterations of the following.
First all other lenses are removed so that the axial
edge probes can be installed on each surface [Fig.
5(a)]. While rotating the optics frame, we minimized the sum of the edge probe readings. (The sum
is primarily sensitive to decentering and the lens
wedge. Then nulling an individual surface removes
tilt. To set the axial spacing, we removed one edge
probe, installed another lens for reference, and inserted and adjusted the metering rod until the LVDT's
touched the vertices [Fig. 5(b)]. A misalignment of
the metering rod from each vertex produces a cosine
tilt error and an error resulting from lens curvature.
For typical spacings and curvatures here, optical
tolerances can be maintained if the rod misses each
vertex by as much as 0.5-1 mm. In practice one
insures proper metering by insisting that gimbaling
the rod in any direction increases its length and that
the distance remains constant as the optics are
rotated on the bearing. Alternatively one could manufacture a field cap. We used the brass jacks (Fig. 4)
to piston the lens while monitoring tip tilt with the
remaining edge probe.
The entire procedure is performed in a laboratory
whose temperature is controlled to 0.50 C. The
metering rod is calibrated with a large high-precision
micrometer (Mitutoyo 103 series) and calibrated
length standard corrected for thermal expansion.
5.
Testing Tower
The optical test tower used for the Phillips Laboratory mirror is shown in Fig. 6. It was designed by
W. A. Siegmund (University of Washington, Seattle,
Wash. 98105) and consists of 4572 kg (45 tons) of
structural steel built onto a 37,592-kg (370-ton)
concrete base, which is pneumatically isolated with
40 100-psi isolators. The lowest internal resonant
frequency is 10 Hz, and the isolator resonant frequency is 1.2 Hz. The Phillips Laboratory metrology system is mounted on the lowest platform. The
Lennon metrology system is mounted onto a polishing machine dedicated for that mirror.
6.
Fig. 5. Procedure used to align the relay lens of the null corrector
with respect to the field lens.
(a) The edge metering
of two
surfaces removes tip-tilt, wedge,and decentration. (b) Vertex-tovertex axial adjustments were made whilethe tip tilt was monitored.
A high degree of metering flexibility is provided by the removable
kinematic lens mounts.
Performance Verification
Constructing these systems instills a deep appreciation of the enormous difficulties and potentiality for
errors that plague any optomechanical project built to
tight tolerances. Our goal was to produce a metrology system that would guide the primary mirrors
within their specified error budgets. The two main
concerns are nonaxisymmetric errors (tip tilt, centration, deformation scalloping, and index inhomogenieties) and the more elusive axisymmetric errors that
produce spherical aberration or conic-constant errors.
The latter arise from improper axial metering, errors
in lens radii and thicknesses, and improper placement
of the pinhole of the Shack cube.
1 December 1992 / Vol. 31, No. 34 / APPLIED OPTICS
7195
14.5m
1
11.5m
Pneumatic Isolation
Fig. 6. Schematic of the test tower for large optics. Shown are
the concrete base and steel structure providing five individual
testing platforms at heights ranging from 11.5 to 23.5 m. The
platforms are offset horizontally (out of the plane of the page) to
provide clearance for all test paths. Vibration isolation is provided with 40 100-psi pneumatic isolators (not shown). The
Phillips Laboratory metrology system is mounted to the lowest
platform.
To test for the nonaxisymmetric errors, we deliberately built in a high-precision rotary table. Those
errors were determined simply by rotating the system
about the mirror's axis. Figure 7 shows a phase
contour map of the nonaxisymmetric errors for the
null corrector used to polish the Lennon 1.8-m mirror.
VATT 1. M
Phase
0 .
0.013
Map
a18 ,......
xx
0 .008
-E
.....;
. 001
-9.06
-0. 011
-0. 16
-0. 021
-0.9025
ms:
.90061A
P.v.:
0.043A
04:59:91 11-27-91
Fig. 7. Phase map showing the nonaxisymmetric errors of the
null corrector and Shack cube for the Lennon 1.8-m f1.0 mirror
determined by rotating the interferometer with the high-precision
rotary table. The corresponding surface error is 0.0061wave rms
and 0.043 wave p.v. and is slightly better than that for the Phillips
Laboratory corrector. The contour step is 0.005 wavePTS.
7196
APPLIED OPTICS / Vol. 31, No. 34 / 1 December 1992
Traditionally axisymmetric errors are the most
troublesome.'4' 6 Ideally one wants to test the null
corrector against another built of a different design or
the same type of system assembled by an independent
team. Unfortunately this can quite time-consuming
and expensive. Our procedure for polishing the Phillips Laboratory mirror provided a starting check
because loose abrasive grinding required the use of a
10-jim interferometer and null optics. On changing
to the visible system, we required that the two agree
to 1-jim-rms spherical aberration before proceeding
without a detailed investigation. Better agreement
would be unrealistic because the IR system was
working beyond its specifications by the time we were
ready for pitch polishing. This is no guarantee that
the visible null lens is correct. 5 1 6
As the final word on the radial figure verification,
we are implementing a scanning pentaprism for the
Lennon mirror.' 6 The test will be described in detail
elsewhere. Preliminary results show that the conic
constant is -0.996 ± 0.001 compared with the design
specification of -0.9958 ± 0.0005. The test is currently limited by misalignment of the rail on which
the pentaprism slides.
7.
Conclusion
We have described in detail our procedures for manufacturing, constructing, and verifying optical metrology systems for two highly aspheric telescope primary
mirrors. A powerful optical tolerance analysis decoupled the conic-constant uncertainty from the surface
irregularity and guided the system design. The optomechanical supports and alignment methods outlined here provided accuracies of ± 1.5-jim edge runout
and ± 5,m 6f axial spacing.
Currently we have reconfigured the Lennon optics
frame to perform metrology on the Astrophysical
Research Consortium 3.5-m f/1.75 primary mirror.
In addition we are designing a similar metrology
system for the 6.5-m f/1.25 primary mirror for the
Multiple Mirror Telescopeupgrade. Several improvements will be implemented in this unit. We will
replace the three vertical posts that make up the
optics frame with a truss to achieve greater stiffness.
Better kinematic repeatability will be realized by
replacing the X-Y table contained in each mount with
a flexure. The great difficulty in aligning the Shack
cube will be eliminated by forcing the tooling ball
plane to be near the vertex, as it is with the null
corrector elements. A perforated reflective field stop
near the relay camera will permit remote beam
finding. Brakes on the tilted tables of the remote
positioner will eliminate an occasional annoyance
when the power to the stepping motors is interrupted.
Although nonaxisymmetric errors are easily tracked
with the rotary table, future efforts require earlier
verification of potential spherical aberration errors.
We intend to either build an inverse null lens or
implement a pentaprism verification immediately after loose abrasive grinding.
Many talented people contributed to the success of
this project. Warren Davison provided valuable mechanical design advice. Mike Orr, Jeff Urban, Ivan
Lanum, and Bob Miller machined difficult parts with
great expertise. Tom Trebisky programmed the 8752
controller. Barry McClendon, Julie Barnes, Ken
Duffek, and Vince Moreno provided unparalleled electronics support. Richard Kraff was invaluable during the installation of the units. We are indebted to
Dick Sumner of the Optical Sciences Center for his
expertise and support throughout our use of the Zygo
interferometer amid heavy schedule constraints.
We gratefully acknowledge support from the National Science Foundation cooperative agreement AST
89011701 and an Air Force Phillips Laboratory con-
tact.
We dedicate this paper to the late Dick Young.
He was both a colleague and a dear friend. His
natural optomechanical talent contributed almost
singularly to the success of countless projects during
his 15-year tenure at Steward Observatory.
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