Wavefront control of the Large Optics Test and Integration Site (LOTIS) 65m Collimator

Wavefront control of the Large Optics Test andIntegration Site (LOTIS) 6:5 m Collimator

Steven C. West,1,* Samuel H. Bailey,1 James H. Burge,2 Brian Cuerden,1

Jeff Hagen,1 Hubert M. Martin,1 and Michael T. Tuell1

1Steward Observatory, University of Arizona, Tucson, Arizona 85721, USA2Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA

*Corresponding author: [email protected]

Received 17 February 2010; revised 21 May 2010; accepted 22 May 2010;posted 24 May 2010 (Doc. ID 124340); published 14 June 2010

The LOTIS Collimator provides scene projection within a 6:5 m diameter collimated beam used foroptical testing research in air and vacuum. Diffraction-limited performance (0.4 to 5 μm wavelength)requires active wavefront control of the alignment and primary mirror shape. A hexapod corrects sec-ondary mirror alignment using measurements from collimated sources directed into the system withnine scanning pentaprisms. The primary mirror shape is controlled with 104 adjustable force actuatorsbased on figure measurements from a center-of-curvature test. A variation of the Hartmann test mea-sures slopes by monitoring the reflections from 36 small mirrors bonded to the optical surface of theprimary mirror. The Hartmann source and detector are located at the f =15 Cassegrain focus. Initialoperation has demonstrated a closed-loop 110 nm rms wavefront error in ambient air over the 6:5 mcollimated beam. © 2010 Optical Society of AmericaOCIS codes: 110.0110, 120.0120, 220.0220, 110.6770, 120.1680, 220.1080.

1. Introduction

The University of Arizona was contracted by Lock-heed Martin Space Systems Corporation (LMSSC)to design, build, and install a 6:5 m diametervacuum-compatible horizon-pointing collimatingtelescope for their Large Optical Test and Integra-tion Site (LOTIS) located in Sunnyvale, California.The intent of the LOTIS facility is to allow imagingspacecraft (up to 6:5 m in diameter) to make test-like-you-fly verifications in vacuum and air fromwavelengths 0.4 to 5 μm. Descriptions of theLOTIS facility and the Collimator are found else-where [1–4].

Wavefront measurement and correction systemscompensate for manufacturing uncertainties and en-vironmental variations. Although the test chamber islarge, it is far too short to implement the distant

point-source forms of wavefront sensing used inground-based astronomy (see, e.g., [5,6]). The con-struction of a horizon-pointing 6:5 m diameter auto-collimating flat mirror was not practical, due toprohibitive expense and interference with the opticalmeasurement of a test article. The challenge was tocreate in situ wavefront sensing systems commensu-rate with the physical size of the chamber, whileavoiding the chamber volume for the test article.Therefore, the systems for maintaining wavefrontquality are mostly incorporated into the optomech-anical structure of the Collimator itself.

The University of Arizona solved the unique wave-front measurement and control constraints by usinga combination of traditional and novel methods, asexplained in the sections below. The wavefront errorfor the complete LOTIS Collimator is estimated bycombining separate measurements of the primarymirror figure and Collimator alignments. Individualmeasurement systems do have some overlap, provid-ing for limited consistency checks.

0003-6935/10/183522-16$15.00/0© 2010 Optical Society of America

3522 APPLIED OPTICS / Vol. 49, No. 18 / 20 June 2010

Prior to shipment to LMSSC, the LOTIS Col-limator underwent testing and integration at theUniversity of Arizona Steward Observatory MirrorLaboratory (SOML), which concluded in October2007. After delivery to LMSSC Sunnyvale, the LO-TIS Collimator was reassembled and retested in aclass 100000 high bay. It was moved into the vacuumchamber, and initial nonvacuum operation began inNovember 2008. Although rated for hard vacuum(10−6 Torr), the Collimator has not yet undergonevacuum tests.

Section 2 provides a brief overview of the Col-limator. Sections 3 and 4 summarize the manufac-ture and wavefront control systems of the primaryand secondary mirrors and their alignment. Section5 presents the results of the thermal analysis forhigh vacuum operation of the Collimator. Section 6presents results from the first wavefront measure-ments in air at the LOTIS facility.

2. LOTIS Collimator Overview

The LOTIS Collimator and wavefront systems areshown schematically in Fig. 1, and the assembledsystem is shown installed into the high vacuumchamber at Lockheed Martin in Fig. 2. The Collima-tor is designed as a 6:5 m diameter f =15 Ritchey–Chrétien telescope operated in reverse with a 97:5 m

effective focal length and 5 arc-minute field of view.Any system this large requires active controls tomaintain performance. These systems are brieflyoutlined next.

The secondary mirror alignment is measured witha pentaprism system, consisting of three bearingrails (attached to the Collimator headring), each con-taining three movable pentaprisms and a fiber-fedcollimated projector beam. The optical structure spa-cing the secondary and primary mirrors is manufac-tured from low-expansion Invar in order to minimizesensitivity to thermal variations of the chamber. Theprimary mirror shape is initially measured in situwith a null lens and interferometer located at thecenter-of-curvature and corrected with 104 activeaxial actuators. The primary mirror shape is thentransferred to a novel Hartmann slope-measuringsystem, consisting of 36 mirrors bonded onto the pri-mary mirror surface, thus allowing the null lens andinterferometer station to be removed from the cham-ber. The focal plane contains a 4 k × 4 k imaging sen-sor to record slope changes seen by the pentaprismand Hartmann systems and a laser source for illumi-nating the Hartmann mirrors.

The above systems are sufficient to fully estimatethe 6:5 m diameter collimated wavefront. An inde-pendent subaperture verification of the wavefront

Fig. 1. Schematic depiction of the LOTIS Collimator system. The components are described in the text.

20 June 2010 / Vol. 49, No. 18 / APPLIED OPTICS 3523

is provided by an autocollimation test using a SchottZerodur 1:8 m diameter flat mirror (manufacturedby ITT Corporation, Rochester, New York) and focalplane interferometer (PhaseCam 5020, 4D Technol-ogy, Incorporated, Tucson, Arizona). An enormousX-Y positioner (InPlace, Incorporated, Milwaukee,Wisconsin) locates the flat mirror anywhere in theoutput beam or in a parking position. This system,however, is not discussed here.

Table 1 expands the level of detail by listing eachcomponent of the active wavefront control along withthe control and feedback mechanisms and the correc-tion frequencies. Sections 3 and 4 provide detaileddescriptions of these control elements in the orderin which they appear in the table. The system wave-front budget is shown in Table 2 for vacuum and airoperation. The vacuum budget is the result of ex-tensive analysis, and each row is detailed in the sec-tions below. The air budget is an arbitrary goal fornonvacuum operation. The principal differences be-tween the specifications are that thermo-opticalperformance has been optimized for vacuum opera-tion, and the vacuum measurements are free of airturbulence and convective heat transfer.

Fig. 2. LOTIS Collimator in the vacuum chamber at LMSSCSunnyvale, California. Shown from front to back are the center-of-curvature interferometer system, the large xy flat mirror posi-tioner, the pentaprism system and Collimator headring, and the6:5 m primary mirror with its attached Hartmann system. Noticethe two engineers in clean room attire along the right side.

Table 1. Active Wavefront Control Components of LOTIS Collimatora

Component Degree of FreedomControlMechanism

FeedbackMechanism

CorrectionFrequency

Primary mirrorsolid-body forces,moments,and positioning

Solid bodyx, y, z, Mx, My, Mz

x: two active lateralactuators

Hexapod platform positionerthat also measures the globalmirror forces and torqueswith load cells

10 min

y, Mz: four active verticalactuators

z, Mx, My: 104 active axialactuators

Primary mirrorfigure

Surface distortion 104 active axial actuatorsto bend mirror

Absolute figure:center-of-curvaturenull lens interferometer

6 months

Extensive thermalanalysis andthermal preconditioner

Relative figure: 36-mirrorHartmann system: sourceand sensor at Cassegrain focus

1 h

Relatively thick honeycombstructured OharaE6 borosilicate substrate

Secondary mirrorfigure

Surface distortion Passive high-performancesupports

SOML horizon-pointing measurementin mirror cell using a holographictest plate and interferometer

Never

Relatively thick low-expansionULE substrate

Secondary mirroralignmentand focal planeplacement

z axis, rotation aboutzero-coma location,rotation aboutsecondary mirrorcenter-of-curvaturepoint

Six-axis hexapod positioner Absolute: six-prism scanningpentaprism test

8 h

Invar OSS for excellentpassive performance

Relative: nine-prism staringpentaprism test

1 h

Independent wavefrontverificationand smallscale wavefront

System 1:8 m Zerodur flat withpositioning system tolocate flat anywhere inCollimator output beam(with coarse and finetip/tilt adjustments)

Autocollimation test withfocal plane interferometer

As needed

aSections 3–5 of the text describe these components in detail.


3. Primary Mirror

A. Manufacture

The 6:5 m diameter f =1:25 honeycomb primary mir-ror was cast, generated, and stressed-lap polishedat the University of Arizona SOML from Ohara E6borosilicate glass (Ohara, Incorporated, Kanagawa,Japan). The large mirror manufacturing process atthe University of Arizona is described elsewherefor spin casting, stressed-lap polishing, and opticaltesting [7–10]. The as-fabricated primary mirrorhas a 16; 256� 0:5 mm vertex radius of curvatureand a conic constant of −1:00177� 0:00009. The pri-mary mirror was aluminized (no overcoat) at SOMLby Multiple Mirror Telescope Observatory (MMTO)personnel in a process similar to that used for the6:5 m conversion of the MMTO [11]. The bare alumi-num coating errors are 3 nm rms wavefront over theentire mirror (estimated from separate coatings ofwitness samples).

B. Surface Figure Measurement and Horizon-PointingOptimization

Before the primary mirror figure can be optimized,the global forces and moments acting upon the mir-ror must be removed. This is accomplished with sixstruts that connect the back plate of the mirror withthe mirror cell weldment working in conjunctionwith the active support system. The lengths of thestruts place the mirror precisely within the cell.The force along the axis of each strut is measuredwith a load cell specified to have �2 N nonrepeatingerrors. The six strut forces are used to compute thesolid-body forces and moments acting between themirror and cell. Any force error acting along the pri-mary mirror optical axis (z) or moments acting aboutgravity (y) or the horizontal axis (x) are removed byforce offset or gradients (respectively) placed into theactive axial supports. Force error along the x axis isremoved with two active lateral actuators placedalong the x axis. Force error along the y axis andclocking error about the optical axis are removedwith four actuators acting along the gravity direc-tion. Each strut has protection mechanical fuses act-ing in compression and tension that protect theprimary mirror from high stresses caused fromearthquakes or other support system malfunctions.

The absolute primary mirror figure is measuredwith a horizon-pointing Offner null lens and phase-

measuring interferometer (4D Technology, Incor-porated, Phasecam 4010 using 4Sight software,Tucson, Arizona) located at the mirror center-of-curvature caustic and encased in a pressure vesselfor vacuum operation. Separate computer-generatedholograms (CGH) for vacuum and air can be movedinto the beam for certifying the null correctors [12].

The primary mirror shape is controlled with 104axial force actuators built into the mirror supportsystem. In all, the primary mirror support systemcontains 104 axial force actuators, 50 passive lateralactuators (which act vertically to balance the mirroragainst gravity), 4 adjustable vertical actuators, and2 adjustable lateral actuators perpendicular to grav-ity. High actuator stability is achieved using counter-weights to achieve the ideal force distribution,determined with a finite element mechanical model.Allowable axial nonrepeating errors are 0:3N rms,including friction. Adjustable actuators have springcage force bias applied to the counterweight levers.The conversion of measured surface figure errorsto the corresponding axial force correction distribu-tion is described elsewhere [13,14]. A detailed modebending analysis for large honeycomb borosilicatemirrors has also been published [15]. For this work,the influence of each actuator upon a distributionof nodes on the mirror surface was calculated fromfinite element models. Phase errors derived fromany measurement method are resampled onto thisnode distribution, and the linear superposition ofactuator surface influences that correct the phaseerrors is calculated from a least-squares analysis.The resulting actuator forces are downloaded tothe active axial supports to correct the mirror figure.

Phase maps of the primary mirror residual er-rors, as measured using full aperture interfero-metry through a null corrector, are shown in Fig. 3.The upper map shows the zenith-pointing mirror inthe polishing cell after polishing was finished. Thezenith-pointing wavefront error (WFE) measuredin the polishing cell is 31 nm rms with 23 Zernikesremoved (polynomial set defined in Ref. [16]). Thelower figure shows the horizon-pointing primarymir-ror mounted in the Collimator support system. Theresidual WFE is 40 nm rms. The Collimator center-of-curvature interferometer sees a silhouette of theheadring system, which includes the pentaprism sys-tem and the secondary mirror support system. Thishardware creates 10 isolated phase islands in theprimary mirror phase map. Although the 4Sight soft-ware allows manual adjustment of phase islands, itdoes not provide for the removal of imaging distor-tion in the null lens optics. Distortions in the nulllens corrector system were measured by imagingfiducials precisely placed on the primarymirror. Soft-ware was written to remove these distortions auto-matically based on a seventh-order least-squaressolution. This reduces imaging distortion in the nulllens system that peaks near 360 mm in amplitude toabout 20 mm on the primary mirror surface.

Table 2. System Wavefront Error Budget (nm rms)Versus System Subaperture Diameter

6:5 m 2:5 m 1:0 m 0:4 m

Primary mirror 60 41 30 22Secondary mirror 61 38 27 21Alignment 43 15 4 0Sum (vacuum) 96 58 41 30Air specification (∼3 · vacuum) 255 165 115 80`The specification for ambient air operation is simply scaled from

the vacuum results.


C. Slope-Measuring Hartmann System

Once the primary mirror shape is optimized accord-ing to the interferometric measurements, the surfaceslope distribution is sampled at 36 locations via anovel Hartmann system consisting of thirty-six100 mm diameter mirrors bonded to the primarymirror surface in three concentric rings. This imple-mentation is a variation of traditional Hartmanntests [6] but is designed specifically for measuringthe primary mirror figure. The technique resemblesthose used in the past with holographic optical ele-ments [17,18]. The Hartmann mirrors (manufac-tured by SESO, France) have substantial wedge(up to 10°) in order to point at the focus of the pri-mary mirror [Fig. 4, top]. They are illuminatedwith 405 nm light from a single-mode laser (CUBE,Coherent, Incorporated, Santa Clara, California)

located at the focus of the Collimator and pointedat the secondary mirror. A holographic diverger(Point Source, Incorporated, Hamble, UK) matchesthe beam size to the secondary mirror. Light reflectedby the Hartmann mirrors returns to the secondarymirror and back to the focal plane instrument wherea beam splitter directs the spots to a CCD camera(Spectral Instruments, Tucson, Arizona, model 800 Smodified for vacuum environment operation). Theprimary mirror wavefront slopes are thus recordedas ðx; yÞ spot locations. Subsequent mirror shape op-timizations return the spots to the baseline pattern,therefore restoring the mirror shape obtained with

Fig. 3. Residual as-polished zenith-pointing primary mirror fig-ure phase map with 23 Zernike polynomials removed (top) is31 nm rms wavefront. The horizon-pointing residual mirror figure(40 Zernikes removed) measured in the Collimator is 40 nm rmswavefront (bottom). The silhouettes are the secondary mirror hub,support vanes, pentaprism rail system (which appear magnifieddue to the center-of-curvature perspective), andHartmannmirrorsbonded onto the primary mirror. Scale bars are nm wavefront, andxy units are in pixels in the phase image file and have no relation-ship to the Collimator scale.

Fig. 4. (Color online) (Top) Concept of the Hartmann mirror sys-tem formeasuring changes in the primarymirror shape. Thirty-six100 mmmirrors are bonded to the primary mirror surface and arepointed at its focus. They are illuminated by a single-mode laserlocated at the focal plane that fills the secondary mirror. The re-flected beams return to the secondary mirror and then back intothe focal plane package where a beam splitter reflects them to aCCD camera (not shown). (Bottom) Image of the Hartmann spotsformed on the focal plane detector. The large boxes are the areaswhere the computer expects to find each spot, and the small boxesare centered on the computer-determined centroid. The largerspot at the lower center is the pointing alignment spot describedin Subsection 4.B.


the null lens interferometer. Although the Hartmannsystem is designed to measure and correct 17 modes,thermal models conclude that during vacuum opera-tion, only astigmatism will need correcting. Once thebaseline slopes are transferred to the sensor, the nulllens interferometer can optionally be removed fromthe test chamber, and the primary mirror shape ismaintained with the Hartmann slope-measuringsystem.

Bonding the Hartmann mirrors to the primarymirror surface received considerable attention. Thewavefront budget called for a bond stability produ-cing no more than 31 nrad rms mirror tilt variations.Bonding tests were conducted at the University ofArizona Optical Sciences Center. The testing sub-strates were similar to the actual Hartmann mirrorsin geometry and mass. Three bonding pads were cre-ated by acid etching each test substrate, and thenthey were bonded onto a glass reference block. Thestability of the substrate was measured with capaci-tive gap sensors manufactured onto the glass parts.Tests included vacuum, thermal, humidity, and loadcycling versus various bonding agents, microspheremixtures, and tripod pad geometries. All require-ments were met with three 8 mm diameter bondingpads, each bonded with approximately 40 nanolitersof Norland Optical Adhesive 61 with 0.5% (byvolume) microspheres of 1 μm diameter. The bond-ing pad surfaces are contoured to match the best-fit sphere at each primary mirror location.

The placement of the Hartmann mirrors on theprimary mirror surface was done after (i) the Colli-mator was assembled, (ii) the primary mirror figurewas optimized with the null lens interferometer, and(iii) the secondary mirror and focal plane instrumentwere aligned to the primary mirror with the pentapr-ism system (described later). A vacuum jig held eachHartmann mirror to the primary mirror surface,while its orientation was adjusted to steer the spotimage it created onto the desired detector location.The adhesive was then cured with a UV lamp. Thespot pattern created on the detector is shown atthe bottom of Fig. 4.

D. Wavefront Error Budget for Primary Mirror

The wavefront errors (nm rms) versus collimatedoutput beam subaperture diameter are shown inTable 3. The measured, as-polished, zenith-pointingmirror has 23 Zernike modes mathematically

removed (Z1–Z22 and Z28). Mirror support errorsinclude allowable actuator force errors, random fric-tion, and thermal effects. The zenith to horizon figureerrors represent the support errors that are producedfrom polishing the mirror zenith pointing, but thenusing it horizon pointing. This component cannotbe corrected by the same support locations. Thetemperature gradient row contains the flow-down re-quirements for the thermal performance of the mir-ror in vacuum. The center-of-curvature test errorsinclude the calibration hologram manufacture andmeasurement noise of both the primary mirror andhologram. The Hartmann test error includes the gluestability of the bonds to the primarymirror, the clock-ing uncertainty of the Hartmann mirrors, and cen-troid errors on the focal plane sensor. Only theuncertainty for measuring astigmatism is shown inthe table; however, the Hartmann system iscapable of measuring 17 modes if required, but themeasurement uncertainty increases to 46 nm rmsin vacuum.

4. Secondary Mirror

A. Manufacture and Surface Figure Measurement

The 655 mm diameter secondary mirror is manu-factured from ultra-low-expansion (ULE) glass(Corning, Incorporated, Corning, New York). The as-finished surface has 1751:1� 0:1 mm vertex radiusof curvature and a conic constant of −1:4167�0:0005. The blank was generated at SOML. Polishingwas completed through an iteration of passive toolsat SOML and ion polishing at ITT Corporation. Test-ing was done at SOML using a CGH in close proxi-mity to the mirror surface (see Fig. 13 in [19]). Themirror was aluminized (no overcoat) using the 2:2 mchamber at the University of Arizona Sunnysidefacility.

Table 3. Wavefront Error Budget for Primary Mirror (nm rms)Versus System Subaperture Diameter

6:5 m 2:5 m 1:2 m 0:4 m

As-polished figure 31 24 22 18Mirror supports 12 7 5 3Zenith to horizon support change 34 27 17 9Temperature gradients 20 12 8 5Center-of-curvature test 20 12 8 5Hartmann measurement 22 3 0 0Sum 60 41 30 22

Fig. 5. Horizon-pointing wavefront phase error map of the ULEsecondary mirror supported in the Collimator cell is 46 nm rms.The three edge high points are from clamps used during ionpolishing and are outside of the optical aperture. Scale bar unitis wavefront nm.


The secondary mirror is the only component ofthe Collimator that is not actively controlled. Afterpolishing was completed, the mirror was placed intothe Collimator support cell, and a final CGH mea-surement established the phase error map for thelifetime of the Collimator at 46 nm rms over theclear aperture [Fig. 5]. Because of its small size, highstiffness, and low coefficient of thermal expansion,the secondary mirror is supported passively on flex-ures with no mechanism for further shape control.

The wavefront budget for the secondary mirrormanufacture and testing is shown in Table 4. Theas-polished figure was from the horizon-pointingmeasurement described above. The support varia-tions were determined by analysis.

B. Alignment Strategy

The secondary mirror must be placed relative to theprimary mirror so that on-axis coma, power, andspherical aberration due to misalignments are mini-mized. Additionally, wide-field optical systems suchas the LOTIS Collimator require that misalign-ment-induced field astigmatism be controlled. Thesecondary mirror is precisely positioned with a hex-apod using feedback from a unique pentaprism sys-tem that measures the alignment wavefront, and it iscombined with absolute pointing references manu-factured into the Collimator as explained below.

Misalignment of the secondary mirror causes foureffects:

• power and spherical aberration, which are con-stant across the field;

• coma, which is constant across the field;• astigmatism, which is zero on axis but in-

creases linearly with field of view; and• a shift in the line of sight.

Once spherical deformation in the mirror figureshas been eliminated, the remaining spherical WFEis created by a spacing error between the primaryand secondary mirrors (conic matching). The spacingis initially controlled using measurements from a la-ser tracker and then refined by minimizing sphericalaberration using the pentaprism system and second-ary piston motion. Once the spacing is correct, resi-dual wavefront power is eliminated with the properpositioning of the focal plane along the optical axis.Fine adjustments are made by moving the secondarymirror with the hexapod.

On-axis coma error can be corrected with eitherlateral displacement or tilt motion of the secondarymirror, but the measurement is incapable of differen-

tiating between the two. Furthermore, astigmatismcreated by misalignments is zero on the optical axisand grows with the field, so no on-axis measurementcan detect it. However, misalignment astigmatismcan be controlled indirectly by maintaining boththe coma and the system pointing [20–22].

In order to accomplish this, the coma wavefrontmeasurement is combined with two alignment refer-ences manufactured into the Collimator. The firstpointing reference consists of a small sphere ma-chined into the center of the secondary mirror opticalsurface. The angular offset of the sphere is measuredrelative to the secondary mirror optical axis duringmanufacture. When illuminated by the focal planelaser source, the alignment sphere produces a spotthat is precisely placed on the focal plane detector[shown in Fig. 4]. Any tilt of the mirror shows upas a displacement of the spot in the focal plane.

However, the proper placement of this pointingspot image requires the focal plane source and sensorto be referenced to the primary mirror optical axis.This is accomplished with a reticle plate that con-tains the orientation of the primary mirror opticalaxis [Fig. 6]. The plate indexes to the primary mirrorcentral perforation. The plate is aligned so its cross-hair intersects the primary mirror optical axis andits surface is perpendicular to it, as determinedby rotating the mirror underneath the center-of-curvature interferometer. The crosshair center isrefined until the change in coma seen by the interfe-rometer due to mirror rotation is sufficiently small[23,24]. The reticle plate tilt is adjusted to be perpen-dicular to the line between the crosshair and theinterferometer axis. During assembly of the Collima-tor, the focal plane source and sensor are alignedto this reticle using an autocollimating alignmenttelescope.

Table 4. Wavefront Error Budget for Manufacture and Testing ofSecondary Mirror Versus System Subaperture Diameter

6:5 m 2:5 m 1:2 m 0:4 m

As-polished figure 57 36 26 20Measurement 20 12 8 5Support variations 6 2 1 0Sum 61 38 27 21

Fig. 6. (Color online) Controlling Collimator pointing using a sec-ondary mirror sphere and an alignment reticle to transfer the pri-mary mirror axis to the focal plane detector. This arrangementcontrols field astigmatism by controlling absolute Collimatorpointing. See Subsection 4.B for more details.


The position of the secondary mirror is controlledwith a hexapod programmed for two virtual pivotrotations and piston [Fig. 7]. Rotation about the sec-ondary mirror center-of-curvature changes coma butnot pointing. Rotation about the zero-coma pointchanges pointing but produces canceling amountsof coma from mirror rotation and centration. On-axiscoma error is corrected with a center-of-curvature ro-tation. Then a zero-coma rotation of the secondarymirror places the alignment sphere image onto thepredetermined detector location without changingcoma. Table 5 shows the wavefront and pointingchanges associated with each motion of the second-ary mirror (M2) shown in Fig. 7. In this way, the fieldastigmatism of the Collimator can be kept minimal,despite the Collimator having no off-axis wavefrontsensing ability.

C. Slope-Measuring Pentaprism System

The alignment wavefront is measured with a pen-taprism system attached to the headring of theCollimator, illustrated in Fig. 8. The pentaprisms si-mulate rays from a wavefront created by a distantpoint source and have been successfully used for op-tical metrology in the past [25–27]. The pentaprismssend collimated beams into the LOTIS Collimatorand parallel to its optical axis. Each beam is brought

to a focus at the LOTIS Collimator’s Cassegrain fo-cus, where the displacement of the focused spot isproportional to the system’s wavefront slope erroron the path sampled by that beam. Each rail has asingle fiber-fed collimated beam that supplies lightto all three prisms on the rail. The prisms have beenmanufactured (Precision Optical, Costa Mesa, Cali-fornia) with special beam splitters so that a fractionof the light feeds the LOTIS Collimator and a frac-tion is passed to the next prism. The outside prisms(A and C) have movement ranges limited to the outerparts of the Collimator aperture, although the posi-tions are fixed in different locations for each of thetwo pentaprism tests. The scanning prism (B) iscapable of traversing most of the aperture. Digitalautocollimators (UDT Instruments, San Diego, Cali-fornia) measure prism yaw.

Pentaprisms are used to redirect the 50 mm colli-mated beam to provide insensitivity to the scanningmotion. The pentaprisms deviate the light by nomin-ally 90 degrees in the pitch direction (along the railaxis), and the angle of deviation does not change asthe prism is rotated by small amounts. Therefore,along the pitch direction of the prism, or the in-scan direction of the motion, the slope changes ofan optical system may be measured precisely with-out interference from small prism pitch angle errors.However, the beam deviation in the perpendicular di-rection (hereafter called cross scan) contains no use-ful information, because it is easily dominated by anymechanism that changes prism roll or yaw angle.The in-scan beam deviation is sensitive to changesin pitch of the beam projector, including changescaused by a tilt or distortion of the entire pentaprismrail. For that reason, the system is designed to mea-sure differential motion between the spot from ascanning pentaprism and that from a fixed referencepentaprism. Any change in orientation of the beamprojector is common to all pentaprisms on a rail,so it is removed in the differential measurement.

The LOTIS pentaprism test uses three rails ar-ranged in an “A” configuration [shown in Figs. 1and 2], each containing three moveable pentaprismsfor a total of nine prisms. The “A-frame” geometrywas chosen to measure power, astigmatism, coma,and spherical aberration. The wavefront slopes pro-jected onto the in-scan prism directions are shown inFig. 9 for power, astigmatism, coma, spherical, andtrefoil wavefront slope errors. These simulatedcurves are the wavefront x and y slope errors pro-jected onto the pitch direction of the prism for eachaberration considered. Only one mode of trefoil can

Fig. 7. Principal hexapod motions used to align the secondarymirror. The center-of-curvature rotation (top) corrects coma with-out affecting pointing. The zero-coma rotation (center) correctspointing without changing coma. Piston along the optic axis(bottom) corrects power.

Table 5. Wavefront Error (nm rms) Corresponding to Control Actions of Secondary Positioner Shown in Fig. 7

MotionBack Focal Distance

Change (μm)Power WFE(nm rms)

Spherical WFE(nm rms)

Pointing Change(μrad)

Coma WFE(nm rms)

1 μm Piston 144 23 0.23 0 0Sensor shift 1000 161 0 0 01 μrad M2 CoC 0 0 0 0 2.01 μrad M2 zero coma point 0 0 0 0.11 0


be measured with this geometry, but the triangularrail geometry used here is only used for measuringalignment wavefront errors and astigmatism.

The pentaprisms are used in two modes during op-eration of the LOTIS Collimator. One mode is calledthe scanning mode, where the “B” prism from eachrail is moved across the LOTIS Collimator pupil in20 to 40 locations. The scanning mode utilizes the“A” prisms in fixed positions near the edge of the LO-TIS pupil so that only “B–A”measurements are usedto compute the wavefront errors. This mode mea-sures the absolute alignment wavefront by fittingpolynomials to the slope changes measured versusthe position of the “B–A” prism within the Collimatorpupil. In practice, this operation takes about 30 min-utes. The second mode of operation is called the star-ing mode. The nine prisms are moved to fixedlocations within the LOTIS Collimator pupil. Thechanges in alignment aberrations are measured bythe slope changes at these nine locations only. Thestaring pentaprism mode uses “B–A” and “B–C” dif-ferential slopes in the computation of wavefrontchanges. In this fashion, changes in alignment aremeasured and corrected quickly using the staringmode, but the time-consuming absolute alignmentneed only be measured infrequently.

Twomain sources of in-scan systematic errorsmustbe controlled. The first is due to intensity, wavefronterror, and diffraction within the collimated projectorbeamilluminating theprisms.Duringa scan, changesin the “B” prism lateral position cause it to “see” a dif-ferent portion of the projector wavefront. Therefore,the projector beam must be of very high quality. The“B” prism has motors to intentionally create prismdisplacements (called the dither mode) used for mea-suring the effect that the projector beam aberrationshave on the in-scan beam deviations. The projector

lens housing has tip, tilt, and piston adjustments,allowing it to be positioned precisely with respect tothe fiber launch using feedback from the prism dithermode. In this way, the projector wavefront can bemade good enough so that some displacement ofthe “B” prism within the projector beam can be toler-ated during the prism’s long walk down the rail. Ahologram printed on the projector lens flattens theintensity profile of the beam. Adjustable stops onthe pentaprisms reduce sensitivity to diffraction atthe edge of the projector beam and make this effectinsignificant.

Coupling between prism yaw and roll can also pro-duce unwanted in-scan slope error in the pentaprismtest. To the first order, prism pitch has no effect onbeam deviation, while roll and yaw cause onlycross-scan deviations. Coupling of these attitude er-rors causes weak second-order in-scan beam devia-tions. There is a family of yaw and roll values thatminimizes the in-scan deviations. For a given roll,the optimum yaw can be determined by measuringthe in-scan deviation (the second-order coupling)as a function of yaw. The relationship was measuredand is shown in Fig. 10. The farther the prism atti-tude is from the vertex of the parabolic curve, themore sensitive the in-scan deviation is to small var-iations of prism attitude. All prism housings havesmall stepper motors (Diamond Motion, Incorpo-rated, Port Angeles, Washington), to adjust yaw androll. Once the prism attitude is set to the vertex of thecurve, the yaw angle is measured by a digital auto-collimator, and the roll angle is constrained to asmall tolerance at the focal plane detector [as seenin Fig. 11], thereby insuring that the yaw-roll cou-pling slope error is small. This procedure is describedby Mallik et al. [28].

Fig. 8. Concept for a single rail of the LOTIS pentaprism system. See Subsection 4.C for an explanation.


In Fig. 12, data from two pentaprism scans areshown. The first scan is directly after the alignmentof the secondary mirror using a laser tracker. Thesecond scan was taken after using the pentaprismsystem to correct secondary position. The secondaryposition errors corresponding to these scans [shown

in Tables 5 and 6] allow their conversion to wave-front error.

High-frequency slope errors on the primary andsecondary mirror surfaces make spurious contribu-tions to the wavefront alignment slope errors. Thepentaprism scan does not have adequate spatial

Fig. 9. Simulated measurements of the wavefront slope errors projected onto the scanning direction of the three LOTIS pentaprism railsversus 1 μm amplitude of power (Z3), astigmatism (Z4,5), coma (Z6,7), spherical aberration (Z8), and trefoil (Z9,10), Zernike wavefronterrors. The rail geometry can onlymeasure onemode of trefoil, but is designed to provide an excellent geometry for measurement of on-axisalignment wavefront errors and system astigmatism.


resolution to resolve these surface errors, so they con-tribute noise to the measurement of low-order slopeaberrations. The residual slopes from a pentaprismscan (created by removing the fitted Zernike polyno-mials from the data) are compared to a simulation ofa scan over the phase maps of the horizon-pointingprimary and secondary mirrors [Fig. 13]. The mea-sured slope residuals from the pentaprism scanare similar in magnitude to the slope errors in theoptics simulation, so this effect probably contributesa significant fraction of the residual slopes.

From Fig. 13, the pentaprism system accuracy islimited by the 0:3 μrad rms residual wavefront slopeerrors occurring uniformly through the data. Using a

Monte Carlo simulation, a scanning measurementwith 40 points per pentaprism rail operating ontop of these high-frequency slope errors translatesinto the following uncertainties in low-order aber-rations (compared to the predicted measurement un-certainties in parentheses for each item): 15 nm rmswavefront in focus (21), 40 nm rms astigmatism (52),20 nm rms coma (17), and 9 nm rms spherical aber-ration (7). It should be noted that the on-axis systemastigmatism is not part of the pentaprism alignmentbudget, because it is a system verification measure-ment. Further improvements to the pentaprism ac-curacy will be realized by increasing the number ofpoints per scan as well as “cherry-picking” the scan

Fig. 10. Measurement of the in-scan angle error produced by anabsolute prism yaw angle error. The absolute yaw must be alignedto the beam projector axis to 0:2 mrad to keep the unwantedin-scan error coupling to 5 nrads.

Fig. 11. Focal plane image during a pentaprism scan. The threestationary “A” prisms are used to correct pointing errors for thescanned “B” prisms. The large boxes are the regions of interest,where the computer expects to find each spot. The parallel linesare the allowed roll angle tolerances for each prism, which areset to �10 μrads.

Fig. 12. Pentaprism scan taken directly after the secondary waspositioned with the laser tracker during initial assembly of theCollimator (top) and the scan taken after two corrections of posi-tion using the pentaprism system and hexapod. Tables 5 and 6allow the conversion of these curves to wavefront error.

Table 6. Improvement in Secondary Position of Laser TrackerAlignment Compared to That after Two Alignment Corrections

Using Scanning Pentaprism System Measurementsto Change Secondary Position

Secondary MirrorAlignment Term

Laser TrackerSetup

After Using ScanningPentaprism

Primary to secondaryspacing (μm)

870 0.1

Pitch angle (μrad) 150 4Yaw angle (μrad) 290 15


locations so as to avoid regions of high slope changesin the polished mirror surfaces.

D. Wavefront Error Budget for Secondary Mirror andAlignment

The wavefront error budget for the secondary and itsalignment are shown in Table 7. The first entryshows the error for determining the absolute align-ment coma, power, and spherical aberration usingthe scanning pentaprism system, while the secondrow shows the measurement error for maintainingfocus with the staring pentaprism system. The next

entries show the errors resulting from the accuracyof the secondary mirror positioning system. The fieldastigmatism error results from the accuracy of ad-justing the absolute Collimator pointing, using thealignment sphere manufactured into the secondarymirror. Controlling field astigmatism to 10 nm rmsat the edge of the 5 arc-minute field of view corre-sponds to locating the alignment spot to an accuracyof 100 μrads (1 mm on the focal plane detector). Thesecondary mirror motion error between 1 h correc-tions with the staring test is shown for the vacuumoperation derived from the thermal analysis dis-cussed in the next section.

5. Thermal Analysis Results

A thermal analysis of the Collimator was performedfor hard vacuum operation (10−6 Torr), but was notperformed for ambient air operation in the chamber(because the latter is not the primary use of theCollimator). The results are included here for com-pleteness, even though vacuum operation of the Col-limator has not yet been initiated.

Thermal analysis for the vacuum operation of theLOTIS Collimator was performed using ANSYS andTMG analysis software, with all critical runs beingperformed on both platforms. The chamber thermalenvironment was physically measured to provide theboundary conditions. During pump down, the cham-ber air temperature transiently drops 7 °C, coolingexposed surfaces and the chamber walls.

The primary mirror, being Ohara E6 glass with athermal expansion coefficient of 2:9 ppm=°C, can suf-fer significant optical distortion if the temperaturedifference between any two points on the mirror ex-ceeds 0:01 °C excluding linearly varying and certainlow-order distributions. This sensitivity is small com-pared to the diurnal and spatial temperature varia-tions in the chamber after pump down. A passivethermal solution is employed to obtain acceptablethermal response from the primary. The primaryand its steel cell are enclosed inmultilayer insulation(MLI) blankets having a nominal emissivity, e�, of0.08. The primary face is exposed, but because it isaluminum coated, e∼ 0:02 in the IR, heat transferto the chamber walls from the face is acceptablylow (although an MLI shroud forward of the primaryface is used to further reduce heat transfer by redu-cing the view factor from the primary face to thechamber walls). Within the insulated enclosurearound the primary and cell, radiant heat transferfrom the mirror back plate to the cell front plateand then to the cell webs provides enough heat trans-fer in the lateral directions to equalize temperaturesthroughout this volume. Internal heat loads of morethan about 1=4 W continuously applied at a point inthis enclosed volume would detract from the thermalperformance, so all heat loads and heat leaksthrough the enclosure are controlled by specifica-tions on the Collimator systems.

Thermal distortion of the Collimator structure af-fects optical performance by misaligning the various

Fig. 13. Residual errors measured in the pentaprism test (top)versus a simulation over the as-polished phase maps of the pri-mary and secondary mirror figures (bottom). The phase mapsare not phased to the measured data, but show that the measuredresiduals are consistent with those expected from high-frequencypolishing slope errors on the optics.

Table 7. Wavefront Error Alignment Budget Including Secondary MirrorPositioner Accuracy Versus System Subaperture Diameter

Aperture Diameter 6:5 m 2:5 m 1:0 m 0:4 m

Scanning pentaprism(coma, spherical, power)

36 14 4 0

Staring pentaprism (focus) 13 2 0 00:5 μm axial resolution 12 2 0 03 μm lateral resolution (coma) 8 2 0 04 μrad tilt resolution (coma) 8 3 1 0Secondary pointing (field astigmatism) 10 2 0 0Motion between corrections 6 1 0 0Sum 43 15 4 0


optical and wavefront sensing systems. The tempera-ture distributions that cause these distortions arecontrolled by selecting surface treatments with emis-sivities that give acceptable performance. In somecases, the required emissivity is not the lowestobtainable value. Some structural elements needto have moderate emissivities so they can obtainequilibrium with the chamber environment in a rea-sonable time after being chilled during the pumpdown.

Finite element analysis was used to predict theperformance of the Collimator. The analyses typi-cally started with an expected temperature distribu-tion before pump down, exposed external surfaces ofthe Collimator to convective heat loss during pumpdown, and then simulated about 200 h of post–pump-down response, with the chamber wall tem-peratures being set to the measured values. Therequired optical performance is achieved 78 h afterpump down starts with improving performance outto about 180 h. The analysis results for alignment

and primary mirror figure changes are comparedto the wavefront budget and presented in Table 8.The analysis accounts for hourly focus and coma cor-rection from the staring pentaprism system and cor-rection of astigmatism every 8 h by the Hartmannsystem. These corrections are modeled by extractingthe specific data that would be measured in opera-tion and adjusting the finite element result basedonly on this data using an algorithm identical to thatto be employed in operation.

6. Results

A. Initial Collimator Wavefront

Initial wavefront tests were conducted in the class10000 ambient environment of the LOTIS test cham-ber at 65:8 °F and 35,000 cubic feet per minute (cfm)air exchange. Per requirements, the Collimator WFEis characterized as the average rms wavefront versussubaperture diameter. The procedure for measuringand correcting the LOTIS Collimator wavefront is asfollows:

1. The primary mirror: the strut platform forcesensors and active mirror supports are used to re-move the global forces and moments on the mirror.The center-of-curvature null lens interferometermeasures the aluminized horizon-pointing mirror

Table 8. Summary of Analysis of Wavefront Error Contributions(nm rms) to Primary Mirror Figure and Secondary Alignment

for Time >78 h after Chamber Depressurization(Compared to Thermal Wavefront Error Budget)a

Case

SecondaryAlignment

WFE(nm rms)

PrimaryMirrorWFE

(nm rms)

Primary mirror support system(10 cycles=h)

0 4.6

Scene generator radiation 0 0.2Pentaprism scan drive power 0.29 0Scene generator power 0 7.1Power umbilicals 0 3.7Chamber pump-down effects 4.2 7.5Initial air temperature �0:5 °C 0 6.4Primary figure change in 8 h 0 2.6Primary coating “e” variation 0 2.5MLI e� variation 0 8.0Other 0 3.0Total 4.2 16.4Error Budget 6 20

aThe analysis assumes hourly correction of focus, coma, and pri-mary mirror astigmatism (not including the measurement errors,which are shown in the other wavefront error budget tables).

Fig. 14. Subaperture diameter versus average rms WFE for theinitial wavefront tests of the LOTIS Collimator. The vacuum (bot-tom curve) and ambient air (top curve) goals are shown. The grayregion identifies the measured Collimator wavefront error includ-ing the 1-sigma measurement uncertainty spread.

Table 9. Average Subaperture WFE (nm rms) with and without Measurement Uncertainties Versus Component for FirstLOTIS Collimator Ambient Air Wavefront Correction Tests at LMSSC Facility

WFE Component 6:5 m 2:5 m 1:0 m 0:4 m

Primary mirror horizon-pointing optimization 98 59 19 3Secondary mirror horizon-pointing figure 48 40 24 13Secondary mirror Al coating 1.6 1.4 0.6 0.2PPS Collimator alignment errors (Z3, Z6, Z7) scanning þ starting 30 14 2 0.4Hartmann 17-mode measurement 15 7 3 0.6Collimator wavefront constructed from measurements 102 74 43 21PPS measurement uncertainty (scanning þ starting) 57 24 4 0.6Hartmann measurement uncertainty (17 modes) 8 2 0.8 0.15CoC measurement uncertainty 17 modes 105 25 7 1Wavefront including 1-sigma measurement uncertainties 170 81 44 21


figure, and the 104 axial force actuators optimize itsshape. The slope data from the optimized mirror, asmeasured with the 36-mirror Hartmann system, arestored as the target for subsequent operations.

2. The secondary mirror: The final uncoated hor-izon-pointing phase map of the secondary mirror

(mounted in the Collimator cell) was measured atSOML. The aluminum coating wavefront error is es-timated fromwitness samples are added to the figuremeasurement.

3. Alignment: the focal plane package is moved toeliminate power and aligned to the primary mirror

Fig. 15. Nine-hour stability of Collimator power, coma and astigmatism were measured with the staring pentaprism system duringoperation in ambient air. No corrections were made the Collimator wavefront control systems during these tests. For reference,28 nm rms of power corresponds to 1 μm secondary mirror piston, and 2 nm rms coma corresponds to 1 μrad of secondary mirror rotationabout its center-of-curvature. Astigmatism and coma graphs show only one set of error bars to limit confusion.


optical axes with the boresight alignment reticleplate (one time only). The alignment wavefront ismeasured with the three slope-measuring scanningpentaprisms. The reflection from the alignmentsphere manufactured into the secondary is used tocorrect Collimator pointing. The secondary mirroris positioned using a hexapod based on these data.The alignment wavefront is transferred to thenine-prism staring pentaprism configuration.

4. Alignment is maintained using the nine-prismstaring pentaprism and the pointing sphere manu-factured into the secondary mirror, and the primarymirror figure is maintained with the slope-measur-ing Hartmann system at typical frequency of onceper hour. Recalibration of absolute alignment withthe scanning pentaprism can be performed severaltimes a day, and the primary mirror phase mapremeasurement with the center-of-curvature interfe-rometer is expected semiannually.

The results of the first system wavefront measure-ments of the Collimator are graphically summarizedin Fig. 14, and the component measurements and un-certainties are listed in Table 9, which shows all ofthe Collimator wavefront error measurement resultsfor the ambient air tests described in this paper. Thefirst five rows are the measured wavefront errors,which then lead to row six, which is the Collimatorwavefront error combined from the individual tests.These results can be compared with the variouswavefront budgets shown in Table 3 through Table7. The last portion of Table 9 shows the uncertaintiesobtained from repeating the measurements severaltimes. The uncertainties are larger than those shownin the wavefront budgets because the latter arederived from an optimized Collimator working invacuum, while these data were collected in air.The shaded area of Fig. 14 is delimited by the mea-surement and its uncertainty. The vacuum specifica-tion and the air performance goals are shown in thegraph for comparison.

B. Measurements Versus Design

The wavefront changes corresponding to motions ofthe secondary mirror and astigmatic bending ofthe primarymirror (to simulate system astigmatism)were measured with both the scanning and staringpentaprism tests (Table 10). The design alignmentwavefront errors per unit secondary motion areshown versus the pentaprism measurement. Simi-larly, the measured system astigmatism change isexpressed as a percentage of the commanded pri-mary mirror astigmatic bending. A useful sanitycheck incorporated the Hartmann system tomeasurethe alignment error changes (not shown in theTable), and gave twice the sensitivity of the pentapr-ism test (because the Hartmann is double-pass offthe secondary mirror).

Table 11 shows the Hartmann measurement effi-ciency versus the change in primary mirror shapefor astigmatism and trefoil. No other modes weretested because during future vacuum operation, onlyastigmatism will be sensed and corrected with theHartmann system, as shown by the thermal analysisof Section 5.

C. Long-Term Stability

Long-term stability of power, coma, and astigmatismweremeasured for 9 h, respectively, using the staringpentaprism system without any wavefront correc-tions applied to the Collimator [Fig. 15]. The staringpentaprism measurement uncertainty of astigma-tism is far worse than that for the Hartmann system,but this is the only stability test run at the time ofthis paper. The stability of such a large Collimatorwavefront is a testament to both the design of theLMSSC test chamber environmental control, the ac-tive vibration isolation bench supporting the Colli-mator, and the design of the Collimator. Powerstability particularly benefits from the Invar trussmembers that space the primary and secondary mir-rors, and astigmatism stability benefits from thenear-frictionless primary mirror supports and goodthermal design. These results show that the focusand coma change is about 60 nm rms over the9 h period, and the astigmatism change is approxi-mately 100 nm rms. Therefore, the designed goalof correcting alignment and mirror bending onceeach hour seems appropriate. Additionally, the ran-dom beam tilt errors of the Collimator chamber were

Table 10. Commanded Secondary Motions and Astigmatic Bending of Primary Mirror Versus WavefrontChanges Measured with Both Scanning and Staring Pentaprism Systemsa

M2 Pitchnm rms=μrad

M2 Yawnm rms=μrad

M2 Z3nm rms=μrad

M2 Z8nm rms=μrad

CCD Defocusnm rms=μrad

M1Z 4%

M1Z 5%

Design 2.0 2.0 23 0.23 161 100 100Measuredscan

2:2� 0:14 2:4� 0:11 24:2� 1:1 0.20 167 101� 1 100� 1

Measuredstare

2:1� 0:13 2:0� 0:23 22:5� 1:6 – – 96� 6 95� 3

aThe staring pentaprism geometry was designed to limit spherical aberration aliasing with power and, therefore, is not used to measurespherical aberration. The CCD defocus is the change in power resulting from changing the focal plane position of the detector.

Table 11. Change in Hartmann Wavefront Fit CoefficientExpressed as Percentage of Commanded Primary Mirror

Astigmatism and Trefoil Bending Averaged for Many BendsMeasured during Collimator Setup

Z4 Z5 Z9 Z10

89� 8 89� 4 93� 4 91� 7


measured to be 55 nrads rms, derived from an anal-ysis of Hartmann spot position variations with achamber flow rate of 35,000 cfm.

7. Conclusions

This paper summarizes the wavefront control con-cepts and first results for the wide-field 6:5 mdiameter vacuum-compatible LOTIS Collimator de-signed and built by the University of Arizona andcurrently in use by Lockheed Martin Space SystemsCorporation in Sunnyvale, California. The uniquewavefront control systems consist of a pentaprismsystem for measuring and maintaining alignmentsand a null lens interferometer and Hartmannslope-measuring system for optimizing and main-taining the primary mirror figure. Active optics sys-tems shape the primary mirror and adjust thealignment of the secondary mirror to the changingenvironmental conditions during use. The first testsin ambient air have achieved 110 nm rms wavefronterror over the full 6:5 m collimated beam. Vacuumoperation has not yet begun.

The success of this project depended on many peo-ple at the University of Arizona’s Steward Observa-tory (SO) and College of Optical Sciences (COS), theMMTObservatory (MMTO), and outside vendors. Weacknowledge several people for major contributions:Kurt Kenagy, Steve Miller, Blain Olbert, Buddy Po-well, andMichael Ward (SO), J. T. Williams (MMTO),Tom Zobrist (COS), and Harvey Wong, Bob Nelson,Sheldon Hutchison, Greg Cuzner, Mike Spier, andStephen Borota (Lockheed Martin Space SystemsCompany). The Kaman Aerospace Electro-Optics De-velopment Center made contributions early in theproject. We thank the reviewers who made this a bet-ter paper. This project was funded by the LockheedCorporation Space and Strategic Missiles (contractSA01T2801GM).

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Documents

Wavefront control of the Large Optics Test and Integration Site (LOTIS) 65m Collimator