Statement Of Copyright And Reprint Permission For

2y ago
13 Views
3 Downloads
790.91 KB
15 Pages
Last View : 1m ago
Last Download : 3m ago
Upload by : Rosa Marty
Transcription

Statement of copyright and reprint permission forPassive compensation of gravity flexure in optical instrumentsby Edward A. Hileman et al.Copyright 2004 Society of Photo-Optical Instrumentation EngineersThis paper was published in Proc. SPIE 5495, Astronomical Structures and MechanismsTechnology, eds. J. Antebi and D. Lemke, pp. 622-635, 2004,and is made available as an electronic reprint with permission of SPIE. One print orelectronic copy may be made for personal use only. Systematic or multiple reproduction,distribution to multiple locations via electronic or other means, duplication of anymaterial in this paper for a fee or for commercial purposes, or modification of the contentof the paper are prohibited.

Passive compensation of gravity flexure in optical instrumentsE. Hileman, J. Elias, R. Joyce, R. Probst, M. Liang, E. PearsonNational Optical Astronomy Observatory, 950 N. Cherry Ave., Tucson, Arizona, USA 85719ABSTRACTWe present case studies on the application of passive compensation in two large astronomical instruments: the GeminiNear Infrared Spectrograph (GNIRS), including actual performance, and the NOAO Extremely Wide Field InfraredMosaic (NEWFIRM) camera. Image motion due to gravity flexure is a problem in large astronomical instruments. Wepresent solutions for two different cases using passive mechanical compensation of the optical train. For the GeminiNear Infrared Spectrograph (GNIRS), articulation of a single sensitive optic is used. Adjustable cantilevered weights,designed to respond to specific gravity components, are employed to drive tilt flexures connected to the collimatormirror. An additional requirement is that cryocooler vibration must not dynamically excite this mirror. Performancetesting of the complete instrument shows that image motion has been satisfactorily compensated. Some image blur dueto dynamic excitation by the cryocoolers was noted. A successful damping scheme has been developed experimentally.For the NOAO Extremely Wide Field Infrared Mosaic camera (NEWFIRM), the entire optical support structure ismechanically tuned to deflect and rotate precisely as a rigid body relative to the telescope focal plane. This causes theoptical train to remain pointed at a fixed position in the focal plane, minimizing image motion on the science detector.This instrument is still in fabrication.Keywords: flexure, compensation1. INTRODUCTIONModern astronomical instruments mounted on large aperture telescopes are of such a scale (typical dimensions 1 m;weights 1000 kg) that mechanicaldeflection within the instrument isinevitable as the telescope movesabout the sky, yet they must also meetvery stringent requirements ongravitationally induced image motionat the detector. For example, theGNIRS image motion from gravityinduced flexure is budgeted to notexceed 2.7 microns at the sciencedetector during a one hour exposure(15 degree change in gravity vector).The NEWFIRM instrument isbudgeted to not exceed 2.5 microns atthe science detector during a 15minute exposure (4 degree change ingravity vector).Gravity flexure may be broken intotwo categories: (1) flexure occurringwithin the Optical Support Structure(OSS) itself, including mechanisms,causing optics to misalign with respectto one another, and (2) ‘rigid body’motion of the entire OSS with respectFigure 1. GNIRS Optical path through the OSS bench assembly. The collimatorto the instrument mounting locationmirror has substantial leverage to reposition the image at the science detector.

due to flexure ofstructure connecting theOSS to the mountinglocation. GNIRSemploys a wave frontsensor mounted to theOSS housing assemblythat nullifies rigid bodyflexure of the OSS bycommanding smallpointing corrections ofthe telescope. Thus, weare primarily concernedwith deflection withinthe OSS itself.NEWFIRM, unlikeGNIRS, does not havean onboard wave frontsensing device mountedto the OSS. A separatetelescope guider,attached to the trussconnecting the OSS tothe telescope mirrorcell, is included onNEWFIRM. Gravityflexure of all structurebetween the guider andthe OSS will thereforecontribute toward imagemotion at the detector.These differentinstrument architecturesled us to two distinctsolutions of the flexureproblem.Figure 2. Finite element models used for flexure analysis of GNIRS. Upper model addresses rigidbody motion of the OSS optical bench with respect to the telescope interface due to flexure of thesupporting structure. Shown here is deflected shape (inches) for 1G in the y direction. Portions of thismodel not displayed for clarity. The Onboard instrument wavefront sensor (OIWFS) mounted to thebench corrects for image motion due to this flexure. Lower model addresses flexure within the benchitself. Deflections of nodes at optic vertices are used to determine image motion at the detector.Shown here is the deflected shape (inches) for 1G in the minus y direction.2.0 GNIRS METHODOLOGY2.1 Flexure control strategy for GNIRSWithin the GNIRS OSS housings, the optical beam path is complex and long, magnifying small mechanism andhousing distortions (figure 1). Structural deflection of the OSS from changing gravity loads was analyzed utilizingFinite Element Analysis (figure2). Mechanical flexure was measured directly at room temperature for the threemechanisms carrying relevant optical elements, and these flexure values were also included in the model. Flexureinduced image motion in excess of the specified maximum was indicated (figure 3). Compensation was thereforenecessary.

Load Case1 G in XMotion on Detector(micron)43-161 G in Y1 G in ZMotion direction (GlobalCoordinates)ZYLateral to slitParallel to slit48ZLateral to slit17YParallel to slit0ZLateral to slit0YParallel to slitFigure 3. Image motion on GNIRS detector when moving to gravity in x or y directions assuming alignment whengravity is in z direction. Slit tracked by wavefront sensor.Because of its location, the GNIRS collimator mirror has high sensitivity to affect image motion via tilt. It was decidedto utilize this optic for compensation. Also, the modeling showed that corrections applied at the collimator would bevery similar for different instrument configurations, allowing a passive compensator to be used. A totally passivesystem was desirable so as to avoid the complexity, risk, and integration effort associated with an active system.2.1.1 GNIRS compensatorA passive compensation assembly, connecting between the back of the collimator mirror and the OSS, was designed,fabricated, tested and integrated into the instrument. At the time of its design, the magnitude and direction ofcompensation needed was only known approximately. Therefore, the goal with the compensator is to provide tiltingcorrection in any direction and of adjustable magnitude given a gravity direction. This will allow compensation ofgravity induced repeatable linear errors regardless of their magnitude (within limits) or direction. For example, ifgravity is in the y direction, the mechanism shall be capable of corrective tilt about the collimator’s x axis or the y axisor both. Both the sign and magnitude of the corrective tilt shall be adjustable.2.1.2 Design configurationConfiguration of the GNIRS passive compensator is shown in figure 4. The collimator mirror is supported from thebase housing by three tangentially stiff support brackets located at 120 degree intervals about the mirror perimeter. Thebrackets are designed to be radiallycompliant, so as to allow thermalmismatch and minimize mechanicaldistortion of the mirror. The bracketlocated on the –x face is stiff in the z(optical axis) direction. The othertwo brackets have flexures machinedinto them so as to be compliant in thez direction. Pushing or pulling theseflexures along z tilts the collimatormirror about the x or the y axes. Thebrackets are stiff in thecircumferential direction, whichrigidly locates the mirror with respectto translation in the x or y direction.Arms equipped with flexural pivotsand adjustable counterweights(termed the “Actuators”) provide thenecessary push/pull force on theflexures.The compensator utilizes two groupsof three actuators; one group on the –y side of the x axis, the other, aFigure 4. GNIRS collimator mirror compensator assembly.

mirror image, on the y side of the x axis. Each group is comprised of an x direction actuator, y direction actuator and zdirection actuator. That is, these are actuators that supply z direction force due to gravity loads in the x, y, or zdirections respectively. The actuators are aligned orthogonal to one another. This ensures that a gravity component inone direction will have no effect on the other two actuators. Shown in figure 5 is a single group of actuators. The“output” (z direction) forces of all three actuators are tied together at a common point, via ‘cross’ flexures, and actuatethe support bracket through a post linking the actuator arms to the mirror support bracket.2.1.3 OperationOperation of the compensationmechanism can be illustrated byconsidering an example. Suppose forgravity in the x direction, we need thecollimator mirror to tilt negativeabout the x axis. Because of theorthogonal layout, solely the xdirection actuators will create anactuation force. Depending on xactuator counterweight adjustment,gravity will cause the x actuator ofgroup 1 (-y side of x axis) to pull inthe z direction on the supportbracket, lifting that side of the mirror.Likewise, the group 2 ( y side of xaxis) x actuator can be adjusted topush an equal amount in the –zdirection on its respective supportbracket, thereby lowering that side ofthe mirror. The combined effect is totilt the mirror about the x axis with anegative sense. By biasing theweights so that the pull force ofFigure 5. Actuator group B assembly. A group is comprised of three actuators, eachgroup 1 is greater than the push forceof which respond only to gravity components in the x, y, or z directions respectively.of group 2, one can also cause aEach actuator is tied together by the cross flexures. Each will generate z directionsimultaneous tilt about the y-axis in apush/pull forces on linkage assembly. The x and y direction actuator counter weightsnegative sense. Extrapolating theand arms are biased toward the z side of their pivots.above scenario, we can visualize howit is possible to achieve varied magnitude of or – tilt about either or both axes for only a single gravity direction. Asimilar argument applies to the other two gravity directions as well. Simultaneous application of gravity components inall three dimensions cause mirror tilt which is the superposition of the individual component cases.2.1.4 Design considerations and details2.1.4.1 CounterweightsBased on preliminary structural analysis of the OSS, we designed for 3 arc-sec (15 micro-radian) of compensation tilt.To achieve this, the primary counterweights are about 0.37 pounds, and the larger z counterweight is 2.20 lbs. Ifnecessary, the size of the weights may easily be modified. The counterweights are fabricated from machineable tungstenalloy (density 17.0 g/cm 3) to maintain a necessarily compact space envelope behind the collimator. Counterweightsare threaded onto the actuator arms providing easily quantifiable adjustment. Once adjusted, the counterweights areclamped to the arm threads with cap screws. Each weight is slotted through nearly its entire diameter to provide thenecessary clamping flexibility.The range of motion of the weights was about 0.5 inch for the Z weights and 1.5 inches for the x and y weights, in orderto provide the range of adjustment indicated previously. The weight position adjustments could easily be made to 0.02inches or better, providing more that the required resolution.

The z direction compensator counterweight is much larger than the other two counterweights in the group. In addition tosupplying corrective tilt forces, it must also equalize the weight of the collimator mirror for z direction gravity force,since the support brackets are compliant in that direction. Employing larger weights on the shortest possible arm is alsoa goal because the resonant frequency of the system is minimized. 1Two counterweights are provided on each of the x and y actuator arms. This allows a continuous range of adjustmentfrom plus to minus. The range of motion for these weights is not equally spaced because the locations at which thesupport brackets hold the mirror lie in a plane not coincident with mirror center of gravity. Bracket attachment holes inthe sides of the mirror are biased toward the back face to reduce local distortion reaching the working side of the mirror.This causes the mirror to tilt slightly when no compensators are attached. For instance, when gravity is in the xdirection, the mirror wants to tilt negative about the y-axis. Biasing of the x direction counterweights counteracts thistendency.2.1.4.2 Support BracketsIn addition to the z directionflexure, support bracketsincorporate flexures on their ‘feet’to allow for thermal growthmismatch between the titaniumbracket and the aluminum base towhich it is bolted (figure 6).Machined into each support bracketis a semi-gimbaled flexure where acap screw mounts the bracket to thesides of the collimator mirror. Thisgimbal flexure reduces reactionmoments due to mirror tilt.Dimensionally small features of thebracket flexures and the substantialstress resulting within them fromassembly and testing forcesdictated the use of a high strengthmaterial. Titanium 4Al 2.5Sn waschosen for its high strength andgood toughness at cryogenictemperatures. Wire EDM was usedto cut out the bracket shapeincluding the z flexure blades andpart of the gimbal flexure. Millingprocedures created the remainingfeatures.Figure 6. Compensator support bracket flexure with detail view of mirror attachment.Flexure allows tip-tilt of mirror but not decenter.1If d is the moment arm length between pivot and weight, and the mass of the weight m is varied with d such that the product of mgd(the moment) is constant, then the fundamental frequency Z of a simple cantilevered mass on an arm pivoting about a fixed pointagainst a torsional spring will vary with d as the ratio:ω1d2 ω2d1

2.1.4.3 ActuatorsActuator arms are fabricated fromaluminum 6061-T651 plate andincorporate stainless steel Lucas flexpivots at their rotation axes. Where thethree actuation arms (x,y,z) intersect, a‘cross’ flexure attaching one x or y armto the z arm is employed (figure 7). It isdesigned to transfer shear force betweenarms while reducing moment reactionswhen the actuators displace.Connecting the actuator arms to thesupport bracket is a titanium link rod. Itis axially stiff to transfer actuator outputforce, but compliant in bending so as notto restrain small lateral offset of its endsduring assembly, test and operation.Figure 7. ’Cross’ flexure detail with FEA used to determine spring rate(374 lb/in)the finite element model developed todetermine the natural frequency of thesystem. Beam elements, lumpedmass elements, and spring elementsare used in lieu of the actual actuatorand bracket components to simplifythe model and minimize run time.Spring rates are determined fromseparate models of the supportbracket and the ‘cross’ flexure alone(figures 7 and 9). In its worstconfiguration (all weights atmaximum travel away from thepivot), the fundamental naturalfrequency is about 80 Hz. Lackingquantified vibration inputcharacterization (such as powerspectral density), we made theengineering decision that the naturalfrequency was sufficiently high sothat excitation would not besignificant. As a backup measure, weconsidered the potential use ofvibration dampening material to helpattenuate response.2.1.5 Design analysisLowering the resonant frequency of thecollimator mirror assembly is a primaryissue with regard to compensator design.Cryocooler impulse noise excitation isthe main concern. Shown in figure 8 isFigure 8. Compensator FEA model showing response of the mirror to gravity in they and x directions separately. Model also used to predict the fundamental frequencyof 80 Hz. Note counterweight magnitude and position in the tuned final version is notas shown here.

Figure 9. Stiffness analysis of collimator mirror support bracket. Stiffness results fromupper left clockwise: Tangential to mirror 129,600 lb/in, Optical axis direction 3850lb/in, Thermal mismatch 3.73 lb reaction on each foot, Radial to mirror 182 lb/in.3.0 GNIRS COMPENSATOR TESTING3.1 Stand-alone testingFollowing fabrication and assembly, the compensator unit including the off axis collimator mirror was tested as a standalone assembly using both optical and mechanical measurements. The first set of tests were done with the collimator inan expanding Zygo beam and a flat reflecting the collimated beam back onto itself; an autocollimating mode with thecollimator itself in double pass. This set up orientation allowed testing of only the y direction actuators (gravity in the ydirection). By symmetry one would expect the behavior of the x and y compensators to be the same.Initial tests were performed with the pushrods connecting the compensation actuators not connected to the mirrorsupport flexures. The intent was to see if the wavefront quality was degraded by the three support studs threaded intothe mirror independent of any additional stresses that might have been introduced by compensating mechanism (figure6). The wavefront quality was somewhat better than that measured with the mirror unmounted. Installation of the threesupport studs did not appear to introduce any distortion.Next, with the y counterweights set to an initial configuration, the tilt on the Zygo was zeroed. The weights were thenmoved along the actuator arm a prescribed amount, and the resulting tilt measured from fringes on the interferogram. Inthis configuration, four tests were done: motion of the A and B primary weights individually, tandem motion of theweights both in phase and out of phase. Results of the y actuator test are summarized in figure 10.

Y Actuator test resultsGroup AGroup BTilt (Prad)0.75” in0.000.75” out0.75” in0.000.75” in0.75” out0.75” out10.611.52310.6Predicted Tilt(µrad)12.912.92213.6Predicted Axis AngleTilt Axis Angle 30-30090 20 -20 0 90Z Actuator test resultsGroup AGroup B0.5” in0.00.5” out0.5” out0.00.5” in0.5” out0.5” inA actuator motion(µinches)-138 -5 135 140B actuator motion(µinches) 10-140 135-140Figure 10. GNIRS collimator compensatorpre-installation test results.At least two items are worth noting.First, the individual weight motionproduces a mirror tilt that is not exactlyat the 30 degree angle of the flexurewith respect to the horizontal, butslightly less. This might suggest someinteraction with the other flexures.When the weights were moved intandem, measured tilt angle about the xaxis was as expected, suggesting themotion of the flexures was equal. Whenthe weights were moved out of phase,however, the magnitude of the tilt aboutthe y axis was significantly less thanthat predicted. While in this set up, wealso varied the position of the x and zcounterweights. No tilt change wasnoted on the interferogram as expecteddemonstrating independence of x, y,and z actuators.The collimator assembly was thenplaced on a granite table with gravityFigure 11. Flexure testing of GNIRS at the NOAO flexure test facility inoriented in the z direction. Because theTucson, Arizona.Zygo cannot be used in thisconfiguration, remaining tilt measurements were made with precision indicators. Test precision of 0.1 micron waspossible, similar to that of the optical tilt measurement. The spring constant of the flexures was measured directly bypushing on A and B pushrod assemblies separately with a force gauge and measuring the motion of the flexure. A 5 lb.force yielded a deflection of 1100 micro-inches for both the A and B pushrod assemblies, equivalent to a springconstant of 4545 lb/inch, slightly more than measured prior to installation of the mirror. Next, the same series of zweight motions (individual, tandem in and out of phase) was tested. Results of the z actuator test are also summarized infigure 10. We note the results are consistent with equal spring constants for the two flexures and independent motion ofthe two flexures.Dynamic response of the compensator assembly was also tested. The signal from an accelerometer placed on the backface of the collimator mirror was displayed on an oscilloscope. The mirror was gently tapped and the responseobserved. The lowest response frequency noted was around 90 Hz.

3.1.2 Testing after integration into the instrumentWith the collimator mirror and compensator installed into the instrument and cooled to operating temperature (65K),flexure of the optical bench and mechanisms was determined. This was done using pinholes or other fiducials in the slitwhile placing the instrument in various gravity orientations on the NOAO Flexure Test Facility (figure 11).Laboratory testing of the instrumentrevealed that the actual internalflexure was almost twice the modelpredictions. We were able toaccommodate this by either movingweights from one side of the pivot tothe other, or (in one case) byfabricating a weight with somewhathigher moment. Representative dataafter the initial iterations are shown infigure 12; the motion on the detectorhas been reduced by roughly a factorof 6. The larger flexure observed inthe instrument beyond that predicted(figure 3) is almost certainly due todifferent flexure of the mechanisms at65K in vacuum, compared with themeasured performance at roomtemperature in air. The mechanismsare also almost certainly the source ofthe hysteresis seen in the figure,which effectively limits thecompensator performance.LBC (slit to det)1.0Shift (pixels)0.5DxDy0.0-0.5-1.0-90-60-300306090X Angle (deg)Figure 12. Typical data for GNIRS flexure compensation. The apparent motion ofa pinhole at the spectrograph slit on the detector, in both X and Y, during rotationof the instrument about the Z axis. A motion of 1 pixel corresponds to uncorrectedflexure of 27 microns, or about 9 micro-radians of tilt at the collimator. Note theeffects of hysteresis, especially in the Y axis.The tests also showed that thecryocoolers used to cool the instrument’s internal structure were capable of exciting resonance in the compensator byenough to produce small but measurable tilts of the collimator (image blurring). These resonant frequencies lay between100 and 200 Hz, and comprised motion in the actuator assemblies and in the mirror/mount assembly. The actuatorassemblies were damped by slightly loosening the clamping screws of the largest (Z) weights, effectively decouplingthe weights from the rest of the system. Additional damping was achieved by attaching a tightly wound coil of copperbraid between the mirror support point and the bracket body in the triangular opening of the mirror support brackets(Figure 6 - braid not shown in the figure). These two remedies reduced both the amplitude and damping time of thecollimator system response to impulsive input from the cryocoolers by roughly an order of magnitude, though not theyare not entirely eliminated.4.0NEWFIRM METHODOLOGY4.1 Flexure control strategy for NEWFIRMThe NEWFIRM instrument features a relatively simple, single pass, straight through optical path with all opticsclustered together in a fairly small space with the exception of lens 1, the field lens (figure 13). None of the opticsarticulate via mechanisms (except filters) eliminating mechanism flexure as a source of error. Compactness of theoptical train allows design of the OSS to be quite stiff having internal gravity deflection well under that needed tomaintain image motion specification. “Rigid body” deflection of the OSS with respect to the guider is therefore aprimary concern with this instrument.

The NEWFIRM OSS ismounted to the telescope ina somewhat flexible manner.By design, rotation of theOSS by gravity loads causethe optic train therein to“look at” a constant point onthe telescope focal planeregardless of instrumentorientation. This actionminimizes image motion atthe detector.4.1.1 NEWFIRMcompensationIt is difficult to providesufficient stiffness for aninstrument the weight andsize of NEWFIRM so as tomaintain position of the OSSwith respect to an externalguider within tighttolerances needed to meetthe tracking image motionrequirement. Instead theNEWFIRM OSSFigure 13. NEWFIRM optical path through guider, into dewar, and OSS housings. Theincorporates a supporttangent bars connecting OSS to truss provide some flexibility for rigid body rotation of theOSS.structure that allows gravityforces to purposefully rotatethe OSS in a controlled manner designed to compensatefor the gravity-induced sag of the instrument.4.1.2 Design configurationThe collimator and camera lenses, filter wheel, anddetector assembly are contained in the OSS housingsassembly. This comprises the 310 kg ‘cold mass’ of theinstrument, to be maintained at 65K (detector at 30K).The OSS is held in place at its upper end by three‘tangent’ bars spaced at 120 degree intervals which, inturn, connect to the inside face of the dewar girth ring.On the girth ring outer face directly opposite the tangentbar connections are attachments to the instrument supporttruss. The load path for the OSS is: from OSS, throughtangent bars, through dewar girth ring, throughinstrument support truss, to telescope mirror cell. Referto figure 14. Also connected to the support truss close tothe telescope focus is the guider assembly.4.1.3 OperationLateral gravity components deflect laterally the entiredewar and cold mass within. Similarly, the guider is alsodeflected to a lesser extent. If uncorrected, this actioncauses the optic train within the OSS to ‘look at’ avarying point on the telescope focal plane resulting inFigure 14. NEWFIRM instrument cutaway view showing theOSS support scheme and load path; OSS to tangent bars to girthring to truss to telescope mirror cell.

image motion on the detector. The tangent bars are designed to correct for the majority of this error by allowing theOSS to rotate by an amount necessary to nullify translation of the truss. Rotation occurs because the OSS center ofgravity is below the connection centerline of the supporting tangent bars, creating a moment that flexes the tangent barsby a prescribed amount. The tangent bars maintain high stiffness against lateral translation of the OSS, yet allow theOSS to shrink when cold without significant stress or decenter.4.1.4 Design considerations and details4.1.4.1 Tangent barsThe tangent bars control rotation of theOSS by bending stiffness about theirstrong axis. Geometry of the bar crosssection is adjusted to structurally tunethis stiffness in accordance with theOSS rotation needed for correction.The tangent bars are offset in the zdirection to provide clearance for thefilter wheel assembly.Because the tangent bars connectdirectly between the cold OSS (65K)and the warm dewar girth ring(ambient), thermal conduction throughthe bars is a concern. Titanium 6Al 4Vis chosen for the tangent bars for acombination of reasons; low thermalFigure 15. Thermally induced stress and displacement of NEWFIRM tangent barsconductivity, low thermal expansion,following cool down from 293K to 60K. Displacement scale factor is 50x.predictable stiffness performanceMaximum induced bending stress is 20 ksi (138 Mpa). Displacement of the OSS in(Young’s modulus well determined),z at the tangent bar connection location is 0.029 inch. Reaction force at ends ofand high strength. Mechanicaltangent bars is 2000 lb.connection of the bars to both the dewarwall and the OSS utilizes a split tapered cone insert locating into a conical hole in the bar and against the shank of ashoulder bolt aligned and threaded into the mating part. A G10 washer separates the two pieces. Heat loss through the3 tangent bars including connections from OSS to girth ring are estimated at 14 watts, well within the cooling loadbudget.Rotation of optical axis 52 micro Radian-5 degreeK 5 degreeKFigure 16. Temperature variation across the girth ring diameter results inrotation of the OSS due to thermal expansion of the tangent bars and theiroffset geometry.Thermal contraction of the bars axiallycreates in plane bending loads on the bars andreaction forces on the girth ring. Bendingloads arise from the offset shape of the bar.Shown in figure 15 are the FEA results forthermally induced stress and displacement ofthe bars. Reaction force on the girth ring is8.9 kN which is acceptable for both the girthring and the connection. Small non-uniformvariation of temperature in the bars with timewill induce OSS pointing errors andconsequent image motion at the detector.Presented in figure 16 is a scenario wheretangent bar ends at the dewar become 10Kdifferent across the girth ring diameter. Theresulting OSS rotation causes image drift onthe detector of approximately 25 microns.When compared to the budgeted amount fromthis source (1.25micron/0.25 hour, one half

the total acceptable drift), this result suggests spatial temperature variation across the dewar diameter not exceed about1K/hour. Given the temperature stability of the telescope enclosure environment, this is limit is reasonable.4.1.4.2 Instrument support trussThe instrument support truss is a space frame designed to be stiff with low cost and weight (figure 14). At the dewarconnection, it provides a lateral stiffness of 57.6 kN/mm and weighs 270 kg. Geometry of the truss causes dewardeflection to be translation only with no rotation. Connection with the dewar girth ring is designed to allow piston andtilt adjustment of the dewar with respect to the mounting face on the telescope mirror cell. Carbon steel mechanicaltubing comprises most of the truss.4.1.4.3 Dewar vesselThe 400mm diameter field lens of the NEWFIRM optical train serves also as the entrance window into the dewarvessel. I

The actuators are aligned orthogonal to one another. This ensures that a gravity component in one direction will have no effect on the other two actuators. Shown in figure 5 is a single group of actuators. The “output” (z direction) forces of all three actuators are tied toge

Related Documents:

Revised reprint January 1998 Revised reprint October 2001 Revised reprint June 2003 Revised reprint March 2006 Revised reprint June 2007 Revised reprint June 2008 . Chapter II—The Executive Government 18 Chapter III—The Judicature 20 Chapter IV—Finance and Trade 22

MATHEMATICS AND STATISTICS The Institute of Cost Accountants of India CMA Bhawan, 12, Sudder Street, Kolkata - 700 016 SYLLABUS - 2016. First Edition : August 2016 Reprint : April 2017 Reprint : March 2018 Edition : August 2019 Reprint : March 2020 Reprint : October 2020 Reprint : January 2021

2 The Government of the Hong Kong Special Administrative Region First published, March 1992 Reprinted, April 1993 Second reprint, March 1994 Third reprint, July 1995 Fourth reprint, August 1996 Fifth reprint, December 1997 Sixth reprint, November 1998

foreign bank for processing Paper statement (per statement) (no charge for e-statements) 4.00 in account currency 4.00 in account currency NA Account transaction print (per statement) 3.00 3.00 No charge Statement reprint (per page on plain paper) 5.00 5.00 No charge Statement reprint (per page on statement paper) 10.00 10.00 No charge

range is -120 to 120 dots. 0 Left Position This option is used to adjust print position horizontally on the label. The range is -9999 to 9999 dots. 0000 Reprint Mode When reprint mode is enabled, you can reprint the last label printer by pressing “UP” button on printer’s control pane

registration in Brunei Darussalam. ii) Arrangement of Sections Part I - deals with subsistence, ownership and duration of copyright which cover areas on rights of the copyright owner, acts permitted to copyright works, moral rights, dealing with rights in copyright works, remedies for infringement,

A. The scope of copyright protection 1. Protect only the works required to be protected as copyright works 2. Grant copyright owners only the rights required to be granted List of Boxes B. The duration of copyright protection C. The limitations and exceptions 1. Allow parallel import 2.

Mass of Christ the Savior 30103878 Dan Schutte We are pleased to grant permission to reprint these assembly editions at no charge through November 26, 2011. Reprints must include title, composer's name and full copyright notice as it appears on this document. Copies must be destroyed after this date or a Reprint License must