Pasadena, California October 24-25, 2007 Contributors to the development effort: from IMTEC

TMT.OPT.PRE.07.057.REL01 HPS-280001-0105 – Volume-2 – October 24-25 2007 – Slide 1

TMT M1 Segment Support Assembly (SSA) Preliminary Design Review (PDR)

Volume-2: SYSTEM LEVEL CALCULATIONS

(See last slide for Revision History)Pasadena, CaliforniaOctober 24-25, 2007

Contributors to the development effort:from IMTEC

RJ Ponchione, Eric Ponslet, Shahriar Setoodeh, Vince Stephens, Alan Tubb, Eric Williams

from the TMT ProjectGeorge Angeli, Curt Baffes, Doug MacMynowski, Terry Mast, Jerry Nelson,

Ben Platt, Lennon Rodgers, Mark Sirota, Gary Sanders, Larry Stepp, Kei Szeto

TMT ConfidentialThe Information herein contains Cost Estimates and Business Strategies Proprietary to the TMT Project and may be

used by the recipient only for the purpose of performing a confidential internal review of the TMT Construction Proposal. Disclosure outside of the TMT Project and its External Advisory Panel is subject to the prior written

approval of the TMT Project Manager.

* Note: HYTEC, Inc. merged with IMTEC Inc. in March 2007.


OutlineVolume-2: System Level Calculations– M1 Segmentation – Segmentation Correction (for Variable Segment Geometry)– Budgets:

Installation & Alignment Edge GapActuator StrokeMass


SEGMENTATION(see Backup Slides for more detail)

System-Level Calculations


5566

4556

67

3646

5768

77

2837

4758

6978

2129

3848

5970

79

1522

3039

4960

7180

1016

2331

4050

6172

81

611

1724

3241

5162

73

37

1218

2533

4252

63

14

813

1926

3443

53

82

74

6475

25

914

2027

3544

5465

76

Sector-ASector-B

Sector-C Sector-F

Sector-D Sector-E

View from Sky

XM1

YM1

YM1

XM1

5566

4556

67

3646

5768

77

2837

4758

6978

2129

3848

5970

79

1522

3039

4960

7180

1016

2331

4050

6172

81

611

1724

3241

5162

73

37

1218

2533

4252

63

14

813

1926

3443

53

82

74

6475

25

914

2027

3544

5465

76

5566

4556

67

3646

5768

77

2837

4758

6978

2129

3848

5970

79

1522

3039

4960

7180

1016

2331

4050

6172

81

611

1724

3241

5162

73

37

1218

2533

4252

63

14

813

1926

3443

53

82

74

6475

25

914

2027

3544

5465

76

Sector-ASector-B

Sector-C Sector-F

Sector-D Sector-E

View from Sky

XM1

YM1

YM1

XM1

5566

4556

67

3646

5768

77

2837

4758

6978

2129

3848

5970

79

1522

3039

4960

7180

1016

2331

4050

6172

81

611

1724

3241

5162

73

37

1218

2533

4252

63

14

813

1926

3443

53

82

74

6475

25

914

2027

3544

5465

76

Sector-1Sector-2

Sector-3 Sector-6

Sector-4 Sector-5

View from Sky

XM1

YM1

YM1

XM1

5566

4556

67

3646

5768

77

2837

4758

6978

2129

3848

5970

79

1522

3039

4960

7180

1016

2331

4050

6172

81

611

1724

3241

5162

73

37

1218

2533

4252

63

14

813

1926

3443

53

82

74

6475

25

914

2027

3544

5465

76

5566

4556

67

3646

5768

77

2837

4758

6978

2129

3848

5970

79

1522

3039

4960

7180

1016

2331

4050

6172

81

611

1724

3241

5162

73

37

1218

2533

4252

63

14

813

1926

3443

53

82

74

6475

25

914

2027

3544

5465

76

Sector-1Sector-2

Sector-3 Sector-6

Sector-4 Sector-5

View from Sky

XM1

YM1

YM1

XM1

SegmentationM1 Array Segmentation– Six identical sectors of 82 unique

segmentsUnique hexagonal shapeUnique optical figureSegments (PSAs) clock 60 deg between sectors

xy

xyx

y

x

yx

yx

y

xy

xy

xy

x

yx

yx

y

B1

B2

C2

C1

AAA

A

xyPSA C-Sys. (XY)

Actuator & AAPLocations (Dots)


Segmentation SchemeSegmentation Overview:– Hexagons on a curved surface cannot be equal and regular (with regular gaps)– Segment outlines are determined by projecting a hexagonal array onto the

optical surface, resulting in irregular hexagons (varied size and shape):Constant gap segmentation

– Segment size and shape variations are important for many reasons:Affecting: Optical performance, Hex-correction, Size of mirror blanks, Length variation of Mirror Cell Top Chord members, AAP adjustment range…

– By stretching the Base Pattern in-plane before projection, we can affect these resulting characteristics.

XM1

ZM1

Base pattern: regular hex array

Scaled hex arrayScaling rule

project vertices and center onto optical surface, // ZM1

Vertices in optical surface

Center (scaled)(RM1)


Segmentation SchemeSegmentation studies :– Radial scaling of base pattern:

– 9 different objectives evaluated– “Rule 7” selected = 0.165

Minimize blank sizeOther metrics also favorable when = 0.165

2

2max

1

1

kRkR

RRscaled

Objectives evaluated:1. Minimize Irregularity2. Minimize Variation of Segment Area3. Minimize Variation of Circumscribed Dia.4. Minimize Cell top bar length range5. Minimize SSA aligner range6. Minimize Edge angle scatter (diffraction)7. Minimize diameter of largest circumscribed circle8. Minimize Max Pivot Shifts to rebalance Whiffletree9. Minimize Max figure residual after correction

Note: 1. Per Mast and Nelson

Where: is the scaling parameterRmax is the largest vertex radii (before scaling)R is the radial coordinate of a point in the base pattern to be scaledRscaled is the scaled radius of the point in the scaled pattern.k is the paraxial radius of curvature of M1

All coordinates in the M1 system

Scaling Rule1

(Only radial scaling studied, other parameters might be used for scaling, such as Azimuth)


0

1

2

3

4

5

6

7

8

9

10

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Nominal cell member length = 1.24m

1: Max. Irregularity (mm RMS)5: Max In-Plane Alignment Range

(mm)6: STD Edge Angle Scatter (mrad)

2: Range of segment area

(%)

3: Range Circum. Ø (%)

4: Range of Cell Bar Length (%)

7: Max. Circum

sc. Diam. –

1.21m

8: Max WT Pivot Shift (mm)

9: Max Pivot Shift resid.

(nm)

Valu

e of

met

ric

Value of tuning parameter

Segmentation SchemeSensitivity of objectives:

= 0.165


Segmentation SchemeImplementation:– Scaling rule affects the following:

Mirror shape and size– Coordinates of mirror vertices– Definition of optical origin and PSA coordinate systems (unique for each seg.)

Mirror cell node locations – Mirror cell top-chord length & variation

Position of AAP Post relative to Fixed Frame hole– Segmentation Database contains the following parameters:

PSA origins and Coordinate Axes in M1 Coordinate systemMirror vertices

– expressed in PSA and M1 coordinate systems

Location of Segment Clocking Mark in PSA XY-plane (Arrow points to center of M1)Coordinates of AAP mounting pads on mirror cell top chord Best fit radius for AAP mounting hole in Fixed Frame

– minimize adjustment range over 82 segments

Location of edge sensor positioning fiducials in PSA coordinate system– Segmentation Database under Revision Control at IMTEC

See backup slides for excerpt from Segmentation Database


SEGMENTATION CORRECTION(see Backup Slides for more detail)



Segmentation Correction ApproachSegment irregularity and size variations would degrade optical performance if not compensated forSingle support system design for all 82 types:– Adjusted for each segment geometry

Correction approach:– Rebalance each whiffletree:

Pivot-point shiftsAnalysis of each type required

– Drill holes for whiffletree pivots in custom locations for each segment type

Low cost, automated CNC operationBalance masses would raise part count and add mass

– Analysis of worst case correctionsMax pivot shift estimate: ~3.5 mmAxial RMS error increases ~ 10% (~1nm)


Segmentation Correction AnalysisCalculate unit cases (1gz applied to distorted segment)– Size Variations (Grow and Shrink)– Clocking– De-center (X,Y)– Irregularity

Seven postulated cases (an approximate set, not orthogonal)

Unit effects isolated by subtracting 1g RMS (in quadrature)Results show that pivot shifts are effective at compensating for segmentation (Next Slide)– Residual RMS is acceptable– Magnitude of pivot shifts practical

Note: This work was performed on the 1.2m segment– Results suggest the correction approach and have not been repeated on the

1.44m design.


Segmentation Correction AnalysisEvaluated 12 Cases Shown (for 1.2m segment)– Conclusion: Pivot shifts very effective correction method

Case Segmentation Shape Magnitude of Surface RMS, nm Residual RMS Error2 Max Pivot Point ShiftNo. Effect Analyzed1 Change Uncorrected Corrected Total,

nmPer Unit

Geometric EffectTotal, mm

Per Unit Geometric Effect

0 Nominal 0 mm 6.07 6.07 - - 0

Uniform Growth DR=10mm

Uniform Shrink DR=10mm

De-center X Dx=10mm

De-center Y Dy=10mm

Irregularity-a Dx=+/-10mm

Irregularity-b Dy=+/-10mm

Irregularity-c Dy=+/-10mm

Irregularity-d Dx=+/-10mm

Irregularity-e Dx=+10mm

Irregularity-f Dy=+10mm

Irregularity-g Dy=+/-10mm

Notes: 1) Distortions in SSA coordinate system.2) Determined by subtracting (in quadrature) from Case-0 result.

0.257

0.346

0.148

0.149

0.314

0.177

0.243

0.000

0.425

0.206

0.047

4.87

4.54

3.05

4.25

Geometric Effect

3 Clocking, 15 mrad

7.41

2.57

0.86

2.00

2.57

1.21

0.00

1.40

1.45 4.93

3.28

4.45

3.62

8.64

3.59

4.47

5.55

8.016.58

6.11

6.41

2.54

0.70

2.06

0.254

6.59

6.13

6.39

6.59

6.19

6.05

6.23

6.24

10

15

10

10

8.16

5.77

5.77

10

8.16

5.77

5.77

8.16

mm

mrad

mm

mm

mm, RMS

mm, RMS

mm, RMS

mm

mm, RMS

mm, RMS

mm, RMS

mm, RMS

12

10

11

8

9

1

2

6

7

4

5

nm/mm

nm/mm

nm/mrad

nm/mm

nm/mm

nm/mm

nm/mm

nm/mm

nm/mm

nm/mm

nm/mm

nm/mm

0.49 mm/mm

0.45 mm/mm

127.8

61.8

15.0

48.4

32.5

157.8

6.11

107.9

103.1

92.7

44.3

92.3

0.20 mm/mrad

0.80 mm/mm

0.86 mm/mm

0.62 mm/mm

0.77 mm/mm

0.68 mm/mm

0.60 mm/mm

0.57 mm/mm

0.77 mm/mm

0.44 mm/mm

10.2nm for 1.44m segment


Segmentation Correction AnalysisHardware Implementation of Pivot Shifts

Can shift Pivots Several mm in-plane


INSTALLATION & ALIGNMENT BUDGET



Installation & AlignmentAlignment & Registration– Estimate segment position errors

in-plane, clocking, piston and tip/tilt– Due to:

Registration - Clearance and RepeatabilityPMA Assembly Errors - Tower to Optical Origin/Axes/PlaneFixed Frame Alignment Errors - At TargetsTarget to Fixed Frame Tower-Attachment TolerancesSurveying Errors - Measurement Uncertainty (TMT Project Responsibility)

– Position error estimates are based on RSS of various effects– Requirements are:

In-plane alignment: +/-0.200mm (0.400mm range)Clocking alignment: +/-0.200mm at vertex (0.400mm range)

In-plane repeatability: +/-0.050mm (0.100mm range)Clocking repeatability: +/-0.050mm at vertex (0.100mm range


Installation & AlignmentAlignment & Registration Inputs & Assumptions

REQUIREMENTSInstallation Alignment.

In plane Dia of tolerance zone 0.400 mmClocking Range at vertex 0.400 mm Expect to violate this requirement, see bleow

Repeatability of registration features shall be:In plane Dia of tolerance zone 0.100 mm May slightly exceed this requirement

Expect [(0.070 clr + 0.025 Rep.)/Cos 30] = 0.110mmClocking Range at vertex 0.100 mm Will not meet this requirement.

Expect [(0.070 clr + 0.025 Rep.)* a/R_TOWER_INPLANE)] = 0.214mm

GEOMETRYSSA Geometry

Segment vertex radius a 720 mmDistance from optical origin to base of tower dz_Tower 334.125 mm

Distance from optical origin to guide flexure center of rotation dz_COR 55.739 mmRadius of Tower axial alignment features R_TOWER_AXIAL 320.000 mm

Radius of Tower In-plane/Clocking features R_TOWER_INPLANE 320.000 mmRadius of Actuators R_ACT 531.00 mm

Radius of Fixed Frame Targets R_TRGT 320.000 mmRadius of SSA Locks R_LOCK 200 mm

Radius of AAP's R_AAP 416.53 mm

With the tip/tilt error zeroed (this causes decenter). Segment shall be positioned such that the optical coordinate system is located in the desired theoretical location within the following tolerances:


Installation & AlignmentAlignment & Registration Inputs & Assumptions

ERROR TERMSRegistration - Clearance and Repeatability

In-Plane E_REG_IP 0.110 mm Dia of tol zone (.070 Max Clr + .025 repeat./Cos30) 120 deg kinematicsTip/Tilt E_REG_TT 0.010 mm Peak-Peak at radius R_TOWER_AXIAL

Clocking E_REG_CLK 0.095 mm Range of clocking tolerance at R_TOWER_INPLANE (0.070+0.050)Piston E_REG_Z 0.010 mm Range

PMA Assembly Errors - Tower to Optical Origin/Axes/PlaneIn-plane E_TWR_OPT_IP 0.025 mm Diameter of tolerance zone PMA Drawing - Revise (Figured on SSA)

Tip/Tilt E_TWR_OPT_TT 1.500 mm Peak-Valley at 1.44m Dia. PMA_DWG - Revise with 1.5mm ParallelismClocking E_TWR_OPT_CLK 0.025 mm P-P Range at R_Tower_InPlane PMA Drawing - Revise (Figured on SSA)

Piston E_TWR_OPT_Z 0.750 mm P-P Range PMA Drawing - Note 11Fixed Frame Alignment Errors - At Targets

In-plane E_FF_ALGN_IP 0.100 mm On the diameter Process prevents achieving desired alignmentsTip/Tilt E_FF_ALGN_TT 0.200 mm Peak-Valley "

Clocking E_FF_ALGN_CLK 0.100 mm P-P Range at R_TRGT "Piston E_FF_ALGN_Z 0.100 P-P Range "

Target to Fixed Frame Tower-Attachment TolerancesIn-plane E_FF_TRGT_IP 0.050 mm On the diameter Machining tolerances - Target to Tower-attachments

Tip/Tilt E_FF_TRGT_TT 0.050 mm Peak-Valley at R_Tower_Axial "Clocking E_FF_TRGT_CLK 0.050 mm P-P Range at R_Tower_InPlane "

Piston E_FF_TRGT_Z 0.050 P-P Range "Surveying Errors - Measurement Uncertainty (TMT Responsibility)

In-plane E_SVY_IP 0.100 mm On the diameterTip/Tilt E_SVY_TT 0.100 mm Peak-Valley at R_TRGT

Clocking E_SVY_CLK 0.100 mm P-P Range at R_TRGTPiston E_SVY_Z 0.100 mm P-P Range


Installation & AlignmentAlignment & Registration Results

PERFORMANCE ESTIMATESIn-Plane Error (Peak-Peak Range)

Tower to Optical Axes - In plane ERR_SSA_MFG_OPT_IP 0.025 mmTower to Optical Axes - Tip/Tilt DecenterERR_SSA_MFG_OPT_DECTR 0.116 mm Decenter from guide flexure only

Fixed Frame Alignment Error at Targets - In-Plane ERR_FF_ALIGN_IP 0.100 mmFixed Frame Alignment Error at Targets -Tip/Tilt Decenter ERR_FF_ALGN_DECTR 0.174 mm Tower rotates one way, guide flexure rotates opposite

Targets to Tower Attachments - In Plane ERR_TRGT_TWR_IP 0.050 mmTargets to Tower-attachments- Tip/Tilt Decenter ERR_TRG_TWR_DECTR 0.043 mm Tower rotates one way, guide flexure rotates opposite

SSA Only Performance RSS of Above 0.242 mm SSA REQUIREMENT: 0.400 mm P-P

Repeatability Error - In-Plane ERR_REG_IP 0.110 mmRepeatability Error - Decenter ERR_REG_DECTR 0.009 mm Tower rotates one way, guide flexure rotates opposite

Surveying Error - In-Plane ERR_SURVEY_IP 0.100 mmSurveying Error - Tip/Tilt Decenter ERR_SURVEY_DECTR 0.087 mm Tower rotates one way, guide flexure rotates opposite

Including Surveying & Repeatability Errors ERR_TOTAL_IP 0.297 mm P-P IN-PLANEClocking Error - Peak-Peak At Segment Vertex

Tower to Optical Axes - Clocking ERR_SSA_MFG_OPT_CLK 0.056 mmFixed Frame Alignment Error at Targets -Clocking ERR_FF_ALIGN_CLK 0.225 mm

Targets to Tower lateral/clocking features - Clocking ERR_TRGT_TWR_CLK 0.113 mmSSA Only Performance RSS of Above 0.258 mm SSA REQUIREMENT: 0.400 mm P-P

Repeatability Error - Clocking ERR_REG_CLK 0.247 mmSurveying Error - Clocking ERR_SURVEY_CLK 0.225 mm

Including Surveying & Repeatability Errors ERR_TOTAL_CLK 0.422 mm P-P CLOCKING


Installation & AlignmentOptical impact of these positioning errors– using Terry Mast’s sensitivities

Conclusion:– Design is very close to meeting requirements

Need relaxation of clocking requirements for alignment and repeatability– In-plane repeatability: 0.100 0.125mm– Clocking repeatability requirement: 0.100mm 0.225mm at vertex– Alignment clocking: 0.400 0.450mm at vertex

OPTICAL IMPACT OF THESE ERRORS [MFG, INSTALLATION, ALIGNMENT AND REPEATABILITY]Sensitivities due to Position Errors

Sensitivity to radial position errors averaged over array SENS_RAD_RMS 7.58 nm RMS/mm Per Mast's error budgetSENS_RAD_EE80 12.4 mas/mm Vol-II 7/9/07page 31.

Sensitivity to clocking position errors averaged over the array SENS_CLK_RMS 73.9 nm RMS/mm "SENS_CLK_EE80 83 mas/mm "

Surface RMSSurface RMS due to Radial Error 2.3 nm RMS

Surface RMS due to Clocking Error 31.2 nm RMS

Total Surface RMS Due to Installation before WH RSS of Above 31.3 nm RMS Averaged over array

WH Correction Factor WH_Factor 15.0 Factor of 15 reduction (Focus and Astigmatism)Residual RMS after WH correction SURF_RMS_AFTER_WH 2.1 nm RMS


GAP BUDGET



Gap Budget - Excluding SeismicNominal Segment-to-Segment Gap: 2.5 mmRandom Gap Reducing Effects:– PSA Manufacturing and Installation Tolerances 0.488 mmRSS Sum– Environmentally induced PSA motions 0.139 mmRSS Sum– Mirror cell deformations 0.486 mmRSS Sum

RSS = 0.702 mm

– Actuation Segment tip/tilt de-center: 0.754 mmAdjacent segments with full differential tiltFault Condition – Controller or Human Error

Linear Sum: 1.456 mm

– Gap Margin = 2.500 mm – 1.456 mm = 1.044 mm

Note: Linear sum of all effects gives 2.479 mm gap change – within budget

See back-up slides for more details

+ Linear Sum


Gap Budget - Including SeismicAssume 3.0g seismic with segment motions out of phase by 22.5 deg [0.39 factor * 3.0 * 0.203mm (1g deflection)] = 0.238 mmRandom Gap Reducing Effects:– PSA Manufacturing and Installation Tolerances 0.488 mmRSS Sum– Environmental PSA motions (w/seismic) 0.275 mmRSS Sum– Mirror cell deformations 0.486 mmRSS Sum

RSS = 0.744 mm

– Actuation Segment tip/tilt de-center: 0.754 mmAdjacent segments with full differential tiltFault Condition – Controller or Human Error

Linear Sum: 1.495 mm

– Gap Margin = 2.500 mm – 1.495 mm = 1.005 mm

Note: Linear sum of all effects gives 2.717 mm gap change– exceeds gap allowable (Segments may contact slightly during EQ.)

See back-up slides for more details

+ Linear Sum


Gap BudgetGap Budget Summary:– Gap margin appears acceptable using RSS summation– Conservative linear summation shows little or no margin– No changes recommended


ACTUATOR STROKE BUDGET



Actuator Stroke BudgetActuator Stroke Budget– PMA assembly errors are large terms, still being refined– Mirror Cell thermal distortion is significant TBD– 5mm actuator stroke seems sufficient

Estimate of Actuator Stroke Required to Overcome Manufacturing & Alignment ErrorsStroke

Change Values in Blue Cells only. Range, mm(P-P)

Piston EffectsSurveying Error (Measurement uncertainty) Piston 0.100PMA assembly error - Piston 0.750Fixed Frame alignment error - Piston 0.100Target to Tower-Attachment error - Piston 0.050SSA thermal distortion TBD SubtotalSegment thickness variation affects pocket depth and SSA height WRT Optical surface 1 0.250 Linear RSSActuator homing error 0.025 1.275 0.805

Tip/Tilt EffectsSubcell surveying error - Tip/Tilt 0.166PMA assembly error - Tip/Tilt 1.106Fixed Frame alignment error - Tip/Tilt 0.332 SubtotalTarget to Tower-Attachment error - Tip/Tilt 0.083 Linear RSSSurveying Error (Measurement uncertainty) Tip/Tilt 0.166 1.853 1.181

Mirror Cell gravity induced deflection - Stroke 1.800Mirror Cell thermal distortion TBD

RSS of above values 2.299Linear Sum of above values 4.928

Notes: Tip/Tilt values combined with max piston values (conservative)Tip/Tilt treated as motions of concentric circles for simplicity1) Segment thickness variation +/-0.5mm affects diaphragm pocket depth by half as much. SSA design would not compensate for this dimension.


MASS BUDGET



Mass EstimateCurrent design meets both fixed and moving mass limits:– Component sizing complete– Current CAD mass summary (no contingency included)

Component Mass (kg) Reqt.Whiffletrees 16.0

Warping Harness 4.2

Moving Frame 12.6

Lateral Support Tower & Locks 19.7

Fixed Frame 36.2

Adjustable Attachment Points 6.3

Fixed Mass 61.4

Moving Mass 35.5 ≤ 45.0

Total Mass 97 ≤ 90

Mirror Segment 153.0 kg


Acknowledgements

Acknowledgements:

The TMT Project gratefully acknowledges the support of the TMT partner institutions. They are the Association of Canadian Universities for Research in Astronomy (ACURA), the California Institute of Technology and the University of California. This work was supported as well by the Gordon and Betty Moore Foundation, the Canada Foundation for Innovation, the Ontario Ministry of Research and Innovation, the National Research Council of Canada, the Natural Sciences and Engineering Research Council of Canada, the British Columbia Knowledge Development Fund, the Association of Universities for Research in Astronomy (AURA) and the U.S. National Science Foundation.


BACKUP SLIDES



Primary Mirror Segmentation: Detailed Discussion Of Segmentation

Analysis

Credit: Eric Ponslet, IMTEC



M1 Segmentation ProblemDefine details of segmentation of M1 into hexagonal segments– M1 curvature and constant gaps leads to irregular hexagons

Infinite number of ways to define irregular hexagons on M1 surface – Limit choices by applying a radial scaling rule to an initial, regular hexagonal

base pattern, in projectionApproach (3D)– start with regular hexagonal array in the XYM1 plane (“base pattern”)– use a scaling rule to distort array in plane

Current rule has one adjustable parameter

– extrude (//ZM1) distorted array into optical surface– consider shape of resulting segments as projected into local frames

Implement gapsCalculate various metrics


M1 Segmentation ProblemTuning the scaling rule– Rule has one adjustable parameter– Parameter can be adjusted to achieve various goals– Tuning problem:

What are some useful goals to pursue?What are the best adjustments of the parameter to achieve those goals?

– Compromises…


Previous Work (1/3)Original work by others– TMT.OPT.TEC.06.025.DRF01: Excel spreadsheet with calculated coordinates of

1.2m segmentation patterns for three scaling rules (Larry Stepp)– T. Mast and J. Nelson, “TMT Primary-Mirror Segment Shape,” TMT Report No. 58,

TMT.OPT.TEC.04.001.REL01, November 2004.– L. Stepp, “Advantages and Disadvantages of Segment Geometries,”

TMT.OPT.TEC.05.031.DRF01, December 6, 2005.Initial presentations of HYTEC work– E. Ponslet, “Primary Mirror Segmentation: Issue with Rule #1,”

TMT.OPT.PRE.05.087.REL01 (HPS-280001-0045), January 17, 2006– E. Ponslet, “Primary Mirror Segmentation: Corrected Results,”

TMT.OPT.PRE.06.004.REL02 (HPS-280001-0046A), January 30, 2006 Detailed report– E. Ponslet, “TMT Primary Mirror Segmentation Studies,”

TMT.OPT.TEC.06.005.REL01 (HTN-280001-0007), June 7, 2006Other relevant documents:– T. Mast, G. Angeli, and S. Roberts, “TMT Coordinate Systems,”

TMT.SEN.TEC.05.016.DRF04, September 2005.

http://project.tmt.org:8080/docushare/dsweb/Get/Document-7650/Scaled%201_2-m%20segment%20dimensions%20061204.xls


Previous Work (2/3)Based on earlier scaling work by Larry Stepp & Jerry Nelson– Two scaling formulations– Three candidate goals for minimization (tuning of )

1. Maximum irregularity of any segment2. Range of segment area3. Range of circumscribed diameter

Introduced concept of Best Fit Regular Hexagon (BFRH)– Least-square fit performed in local XY plane (XYSEG)– Minimizes RMS value of distances from vertices of segment to vertices of BFRH

Adjust radius of BFRH (1 parameter)BFRH can be centered at OSEG or free to re-center (2 parameters)

BFRH can be aligned with XSEG or free to rotate (1 parameter)

– Residual of LSQ fit is a measure of irregularityIrregularity (and size variations) impacts performance (imperfect SuperHex correction)


Previous Work (3/3)Showed that– Both scaling formulations are equally effective / equivalent– All 3 goals can be achieved by proper tuning, using a single formulation

Goal 1: maximum irregularity reduced by factor 11 (with BFRH rotation)Goal 2: range of segment area reduced by factor 86Goal 3: range of circumscribed diameter reduced by factor 11

– Allowing rotation of BFRH results in large improvementsOnly a factor for Goal 1

– Re-center of BFRH has negligible impact Results in more complicated definition of XYZPSA

Abandoned to keep definition of center simple

2

2max

1

1

kRkR

RRscaled

from value without scaling


Irregularity: Definitionirregularity RMS distance between vertices of actual segment and vertices of LSQ best fit regular hexagon with arbitrary center, radius, and clocking angle– irregularity = RMS of residual of fit– general definition includes 4 variables: decenter (X & Y), radius, and clocking

angle

X

Y

Best fit regular hexago

nSegment outline in

{XY}SSA plane

d1

d2d3

d4

d5

d6

de-center

radius

clocking

6

1

2

,),(Minimize:fitbest LSQ

iiclockingradiuscenterded

6)RMS(tyIrregulari

6

1

2 i

i

i

dd


Re-centering BFRH has Negligible Impact

0

2

4

6

8

10

12

14

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Radial Scaling Parameter ()

Max

imum

Seg

men

t Irr

egul

arity

(mm

RM

S)

BFRH: no rotation, no centeringBFRH: rotation, no centeringBFRH: no rotation, centeringBFRH: rotation, centering

These results from Aplanatic Gregorian design with a=0.6m


Recent Changes and Additions (1/2)Modified definition of segment center– Was: mean of XYM1 coordinates of 6 vertices (after scaling, before gaps)– Changed to: scaled location of centers in base pattern– New definition is closer to BFRH center > re-centering now even less useful

~0.01mm difference in irregularity

New, more exact calculation of circumscribed circle– Was: centered at origin of local frame– Changed to: center is optimized to minimize diameter– Difference is small

Added representation of M1 cell– Cell nodes and Interface nodes

Added representation of SSA-Cell interface– 3 SSA support points per segment, at single location in local coordinate

systemRepresent SSA side of interface

XPSA

YPSA

Centered circle

Free circle


Recent Changes and Additions (2/2)Added six additional Tuning Goals

4. Minimize range of bar lengths in top layer of cell5. Minimize range of SSA alignment system6. Minimize width of diffraction spikes from segment edges7. Minimize largest circumscribed diameter (blank/boule size)8. Minimize magnitude of WT pivot shifts9. Minimize residual figure error from WT pivot shift correction

Repeated all calculations for Ritchey-Chrétien design and new segment size– Geometry and segmentation

K=60m, k=-1.00095a=0.716m, t=45mm, gap=2.4mm6*82=492 segments instead of 6*123=738

– WH pivot shift data not available for larger segmentsUsed sensitivities from a=0.6m – not directly applicable

– Observations:Optimal tuning almost identicalConclusions unchangedCan base decision on old baseline (a=0.6m, AG)


Segmentation Patterns

-2 0 2 4 6 8 10 12 14 160

5

10

15

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

XM1 (m)

YM

1 (m)

New baseline: 6×82, 1.432m segments


Coordinate SystemsXYZM1 / RθZM1

– OM1 at apex of M1 optical surface

– ZM1 along axis of symmetry of M1 optical surface, positive toward stars

XYZSEG

– OSEG in M1 optical surface, at center of segment

– ZSEG M1 optical surface

– XSEG in RZM1 plane

XYZTEMP* (= XYZSSA in TMT.SEN.TEC.05.016.DRF04)– OTEMP = OSEG

– ZTEMP = ZSEG

– XTEMP // XZM1 plane

XYZPSA*

– proposed as replacement for XYZSSA and XYZSEG in TMT.SEN.TEC.05.016.DRF04)

– OPSA = OTEMP

– ZPSA = ZTEMP

– (XPSA,XTEMP) = rotation to BFRH

– SSA uniquely located in XYZPSA

Coordinates of SSA features are invariant in XYZPSA

Suggest keeping only XYZM1 and XYZPSA as official systems– Possibly also XYSSEG if used by others

*Not currently an official TMT coordinate system (TMT.SEN.TEC.05.016.DRF04, September 2005)


Defining “PSA” Reference Frame

XM1

ZM1

Base pattern: regular hex array

Scaled hex array

X TEMP

Z TEMP

Scaling rule

extend vertices and center into optical surface // ZM1

center XYM1 = scaling rule × center

Outline in XY TEMP

BFRH

Vertices in

optica

l surface

Rotation about Z TEMP, f

rom XYZ TEMP to XYZ PSA

Z PSA

Y PSA

X PSA

X TEMPY TEMP

BFRH


Defining/Positioning Hardware Defining Segment outlines1) Begin with circular blank from polishing2) Engrave fiducials into optical surface of polished segment

Fiducials define location of XYZPSA reference frame

3) Cut segment outlines relative to fiducialssegment edges are straight lines in XYPSA plane (basic)

segment side faces // to ZPSA (basic)

4) Final-figure segments relative to XYZPSA

Optical prescription described in XYZPSA

Defining M1-Cell to SSA interface coordinates• All assembly tooling aligned to fiducials only

Physical outline or vertices are never used as datum• Coordinates of support points are identical in all segment types, when

expressed in PSA frame• Converting those coordinates back to XYZM1 frame provides global coordinates

of interface points


XM1

ZM1

X,Y PSAZ PSA

Cell Nodes (3) Interface Nodes (3)

SSA Supports (3)

Segment Vertices(before gaps)

Hcell

HSSA

RSSA

Cell Nodes and Cell-SSA InterfaceCell Nodes

– At given distance Hcell behind 3 of 6 pre-gap vertices, along local normal to optical surface

– Form irregular triangle whose geometry depends on scaling

Interface nodes– At 1/3 along length of cell members

SSA Supports– 3 points, representing nominal centers of AAP adjusters– At HSSA, RSSA from OPSA (same for all segments)

– HSSA and RSSA optimized to minimize maximum distance to interface nodes

XPSA

YPSA


Cell Nodes and Cell-SSA Interface

Cell Nodes

Interface Nodes

SSA Supports (“center” of adjusters)

HSSA

RSSA

XPSA

YPSA

ZPSA

Hcell

Local Normal to

optical surface


Cell Nodes and Cell-SSA Interface

-10

-5

0

5

10

15

20

25 -15

-10

-5

0

5

10

15

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

YM1 (m)

XM1 (m)

11 11.5 12 12.5 13

7.8

8

8.2

8.4

8.6

8.8

9

9.2

9.4

9.6

XM1 (m)

FormulationA-0.167-1-0: Segment Outlines in XYZM1

YM

1 (m)

-10-5

05

1015

2025 -15

-10

-5

0

5

10

15

0

0.5

1

1.5

YM1 (m)

XM1 (m)

NoScaling-0-1-0: Segment Outlines in XYZM1

-4 -2 0 2 4 6 8 10 12 140

5

10

15

XM1 (m)

FormulationA-0.167-1-0: Segment Outlines in XYZM1

YM

1 (m)


MATLAB Segmentation CodeProduces regular Hex base pattern in XYM1

– given segment size (a), and ID and OD of M1 (cropping) Scales the base pattern in radial direction

– Scaling rule adjusts radial coordinate (only) of centers and vertices of base pattern– Adjustable parameter (intensity of scaling)– Outermost vertex of array (at Rmax) is unchanged by definition of scaling rule

Extrudes segment centers and vertices into M1 optical surfaceDefines segment-local coordinate systems

– Z // normal to optical surface at segment centerCalculates coordinates of cell and interface nodes

– Top layer nodes and interface nodesImplements gapsCalculates size and rotation angle of BFRH

– Defines final local systems (XYZPSA)Establishes coordinates of SSA support pointsCalculates various metrics of resulting segmentationProduces outputs files (ASCII)

– segment vertex coordinates in M1 or PSA system– Cell node coordinates in M1 system

Creates various diagnostic plots– Distribution of metrics across array and corresponding statistical distributions– Segment outlines– 3D plots of array and cell


New Segmentation Goals (1/2)1. Minimize segment irregularity2. Minimize variation of segment area3. Minimize variation in segment size4. Minimize range of lengths of top members of cell

• Avoid having to build different length members• Metric = Max(L)/Min(L)-1, in percent

5. Minimize required range of SSA alignment system• Minimize maximum in-plane (XYPSA) distance between SSA support points and interface

nodes• Radial and depth location of SSA supports adjusted for best fit

6. Minimize width of diffraction spikes from segment edges• Based on edge angles projected on sky (?)• Minimize scatter of projected (into XYM1) angle of segment edges

Sort edges into 3 groups of angles (~0º, ~60º, ~120º)Calculate standard deviation within each group (Std0, Std60, Std120)

Metric = RMS(Std’s) = √ 1/3 (Std02+Std60

2+Std1202)

• This goal is optimized without scaling (=0): Std0 = Std60 = Std120 = 0


New Segmentation Goals (2/2)7. Minimize diameter of largest circumscribed circle

• Minimize size of glass boules/segment blanks• Now using exact calculation of circumscribed circle (free center)

8. Minimize magnitude of WT pivot shifts (rough estimate)• Whiffletree pivot shifts are used to fine-tune axial support to actual segment shapes

Custom machining of pivot features for each segment type

• Pivot shifts require “real estate” in the hub region of whiffletree componentsLarge shifts could be difficult to implement

• Estimates based on study of pivot shifts for various modes of segment shape variationsBased on “Correction of Segmentation Effects by Shifting Whiffletree Pivot Locations” TMT.OPT.TEC.06.009.REL01 (Eric Williams, June 2006)

• Metric = maximum estimated shift at any WT joint, for any segment

9. Minimize residual figure error after pivot shift (rough estimate)• Pivot shift is very effective, but not perfect

Figure error after optimal pivot shift is slightly worse than nominal value

• Estimates based on study of pivot shifts for various modes of segment shape variationsBased on “Correction of Segmentation Effects by Shifting Whiffletree Pivot Locations” TMT.OPT.TEC.06.009.REL01 (Eric Williams, June 2006)

• Metric = estimated value of √(RMScorrected2 – RMSnom

2), where RMSnom and RMScorrected are the RMS values of the SSA-induced surface errors, for a nominal regular segment (for which the WT geometry was designed) and the actual segment, after correction via WT pivot shifts, respectively


Goals 8 and 9: Axial Support Pivot ShiftsBFRH is optimally clocked no residual rotationCorrection for segment size (case 1) – using BFRH radius for size

• Requires pivot shifts up to 0.49mm per mm of radial growthUsed nominal segment radius = mean(BFRH radii) (could have used midrange value instead)

• Leaves residual figure error up to 0.425nm per mm of radial growth

Correction for Irregularity of segment (mean of cases 6 to 12)• Requires pivot shifts up to 0.636mm per mmRMS of irregularity• Leaves residual figure error up to 0.197nm per mmRMS of irregularity

Case Segmentation Shape Magnitude of Surface RMS, nm Residual RMS Error2 Max Pivot Point ShiftNo. Effect Analyzed1 Change Uncorrected Corrected Total,

nmPer Unit

Geometric EffectTotal, mm

Per Unit Geometric Effect

0 Nominal 0 mm 6.07 6.07 - - 0

Uniform Growth DR=10mm

Uniform Shrink DR=10mm

De-center X Dx=10mm

De-center Y Dy=10mm

Irregularity-a Dx=+/-10mm

Irregularity-b Dy=+/-10mm

Irregularity-c

Dy=+/-10mm

Irregularity-d

Dx=+/-10mm

Irregularity-e Dx=+10mm

Irregularity-f Dy=+10mm

Irregularity-g Dy=+/-10mm

Notes: 1) Distortions in SSA coordinate system.2) Determined by subtracting (in quadrature) from Case-0 result.

0.257

0.346

0.148

0.149

0.314

0.177

0.243

0.000

0.425

0.206

0.047

4.87

4.54

3.05

4.25

Geometric Effect

3 Clocking, 15 mrad

7.41

2.57

0.86

2.00

2.57

1.21

0.00

1.40

1.45 4.93

3.28

4.45

3.62

8.64

3.59

4.47

5.55

8.016.58

6.11

6.41

2.54

0.70

2.06

0.254

6.59

6.13

6.39

6.59

6.19

6.05

6.23

6.24

10

15

10

10

8.16

5.77

5.77

10

8.16

5.77

5.77

8.16

mm

mrad

mm

mm

mm, RMS

mm, RMS

mm, RMS

mm

mm, RMS

mm, RMS

mm, RMS

mm, RMS

12

10

11

8

9

1

2

6

7

4

5

nm/mm

nm/mm

nm/mrad

nm/mm

nm/mm

nm/mm

nm/mm

nm/mm

nm/mm

nm/mm

nm/mm

nm/mm

0.49 mm/mm

0.45 mm/mm

127.8

61.8

15.0

48.4

32.5

157.8

6.11

107.9

103.1

92.7

44.3

92.3

0.20 mm/mrad

0.80 mm/mm

0.86 mm/mm

0.62 mm/mm

0.77 mm/mm

0.68 mm/mm

0.60 mm/mm

0.57 mm/mm

0.77 mm/mm

0.44 mm/mm

Mean = 0.197 nmRMS/mmRMS

Mean = 0.636 mm/mmRMS

Table from “Correction of Segmentation Effects by Shifting Whiffletree Pivot Locations” TMT.OPT.TEC.06.009.REL01 (Eric Williams, June 2006)Applicable to a=0.6m


Goal 5: Range of SSA AlignersPlots show relative locations of SSA supports (blue dot, center of blue circles) and SSA support nodes (red dots)– Radial spacing between range circles is 0.5mm

-0.015 -0.01 -0.005 0 0.005 0.01 0.015-0.01

-0.005

0

0.005

0.01

0.015

XPSA (m)

YPS

A (m)

FormulationA-0-1-0: Cell interface nodes (red) and SSA support points (blue) seen from PSA frame (magnified)

-0.015 -0.01 -0.005 0 0.005 0.01 0.015-0.01

-0.005

0

0.005

0.01

0.015

XPSA (m)

YPS

A (m

)

FormulationA-0.167-1-0: Cell interface nodes (red) and SSA support points (blue) seen from PSA frame (magnified)

No Scaling (=0)Max distance = 5.6mm

Optimized (=0.167)Max distance = 1.9mm

Support nodes shown MUCH closer to one-another

than actual


Tuning Results for RC, a=0.716m

Goal:Minimize:

1Max(Irreg)

2 Rge(Area)

3Rge(Ø)

4Rge(L)

5Rge(Adj)

6Std()

7Max Ø

8Pivot Shift

9Fig. error

Optimal tuning = 0.243 = 0.122 = 0.160 = 0.161 = 0.167 = 0.000 = 0.165 = 0.230 = 0.141

Irreg. (mm RMS)% Relative to =0

0.505

5.0150

3.4534

3.4134

3.1631

10.08100

3.2432

0.737

4.2342

Area Range (%)% Relative to =0

2.7299

0.031

0.8531

0.8732

1.0137

2.74100

0.9635

2.4288

0.4316

Circum. Ø rge (%)% Relative to =0

1.3552

0.6525

0.229

0.229

0.2610

2.61100

0.249

1.1644

0.3513

Cell length rge (%)% Relative to =0

1.4453

1.3549

0.9535

0.9535

0.9735

2.75100

0.9635

1.3650

1.1341

SSA align. rge (mm)% Relative to =0

3.0248

3.2751

2.2936

2.2735

2.1834

6.46100

2.1934

2.8544

2.7843

Edge scatter (mrad)n/a

4.12-

2.07-

2.71-

2.73-

2.83-

0.00-

2.80-

3.90-

2.39-

Max(circumØ) (mm)% rel. to =0

≠ rel. to =0.165 (mm)

1450.698.85+6.4

1449.798.79+5.5

1444.398.42+0.2

1444.398.42+0.1

1444.298.42+0.1

1467.5100

+23.3

1444.298.41

0

1449.598.77+5.3

1446.998.60+2.8

Max pivot shift (mm)*% Relative to =0

2.6530

3.2137

2.9534

2.9434

2.9033

8.74100

2.9133

2.5629

3.0835

Max. fig. res. (nmRMS)*% Relative to =0

2.0873

0.9935

0.9433

0.9534

0.9935

2.83100

0.9834

1.8565

0.9032

* These metrics estimated using sensitivities calculated for a=0.600m

6×82, 1.432m segments


Tuning Results for RC, 492×1.432m

0

1

2

3

4

5

6

7

8

9

10

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Rotation, but no re-centering of BFRHNominal cell member length = 1.24m

1: Max. Irregularity (mm RMS)5: Max In-Plane Alignment Range (mm)

6: STD Edge Angle Scatter (mrad)

2: Range of segment area (%) 3: Range Circum. Ø (%)

4: Range of Cell Bar Length (%)

7: Max. Circumsc. Diam

. – 1.21m

8: Max WT Pivot Shift (mm)

9: Max Pivot Shift resid. (nm)

Goals 8 and 9 estimated using sensitivities from AG/a=0.600 design

Valu

e of

met

ric

Value of tuning parameter


Segmentation SummaryScaling effects are almost not affected by segment sizeGoals 4 and 5 are not achieved very effectively

– AAP adjustment range and cell member length variations remain significant after tuning the scaling rule

Metrics for both goals only reduced to 35% of their un-scaled valuesResidual AAP adjustment ~ 2.2mm (radial)Residual cell bar length variation ~ 12mm

– Definitions of node and/or support coordinates could (should?) be generalizedCurrent work based on extremely simple (and limited) definition of cellRequires better understanding of cell fabrication approach

Goal 7 can help save glass– Saves up to 23mm on blank diameter

Tuning for goals 8 and 9 only moderately effective– Pivot shifts and residual errors reduced to ~30% of their value without scaling– Estimated* pivot shift reduced from 8.7mm to 2.6mm

Relatively flat between =0.12 and 0.25– Estimated* residual error reduced from 2.8nmRMS to 0.9nmRMS

Negligible when added in quadrature with nominal error (~10nm)

Still no obvious, compelling reason to pick one particular tuning?– Which goal is most important?

Tuning range between ≈0.16 and 0.243 provides various compromises– Most goals are optimized closer to left edge of that band

Exception: irregularity* Sensitivity numbers obtained from study with a=0.6m


Segmentation DatabaseSegmentation Database Excerpt (for information)TMT M1 SEGMENTATION DATA - Eric Ponslet - HYTEC Inc. - 06-Mar-2007 15:14:15 This is the master segmentation data file HDB-280001-0003_Draft_3 generated by FinalSegm.m Matlab program This file is under revision control, please find current revision level in file name Latest official version resides on TMT Docushare document server, under document TMT.OPT.TEC.07.006.REL01 Unless otherwise specified, all linear dimensions are in meters, and all angles are in degrees ----------------------------------------------- SECTION 1: CONTROL PARAMETERS AND STATISTICS ----------------------------------------------1A: M1 GEOMETRY AND SEGMENTATION DATA M1 Radius of curvature: k = 60.000 m M1 Conic Constant: K = -1.000953000 Base pattern hex diameter: 1.4320 m Inter-segment gap: 0.00250 m (1/2 gap applied all around every segment (including outer edges of array) Segment chamfer width (projected into XY_PSA): 0.00035 m1B: SEGMENTATION PARAMETERS Scaling Parameter: alpha = 0.1650 (radial scaling = (1+alpha*(Rmax/k)^2)/(1+alpha*(R/k)^2) With rotation of PSA Without recentering of PSA 1C: NOMINAL SEGMENT SIZE Nominal segment diameter = 1.440000 m Best Fit Regular Hexagon (BFRH) statistics: Min BFRH diameter = 1.436839 m, or 3.16 mm smaller than nominal Mean BFRH diameter = 1.440312 m Max BFRH diameter = 1.443711 m, or 3.71 mm larger than nominal Location of AAP nodes in PSA system (at 90, 210, and 330 degrees about Z_PSA): Radius (R_PSA) = 0.418241 m Elevation (Z_PSA) = -0.368276 m1D: CELL DATA Distance from optical surface to cell nodes = 0.372501E: SEGMENTATION STATISTICS M1 Inner Diameters Gapped segments (glass): min diameter = 1.44808 m Optical surface: min diameter = 1.44849 m M1 Outer Diameters Gapped segments (glass): max diameter = 15.00049 m Optical surface: max diameter = 15.00010 m


Segmentation DatabaseSegmentation Database Excerpt (for information) Segment Irregularity (RMS): min = 0.112 mmRMS, at segment # 2 max = 3.245 mmRMS, at segment # 66 Segment area: min = 1.3409 m^2, at segment # 82 max = 1.3538 m^2, at segment # 2 spread (max/min-1) = 0.96 percent Circumscribed diameter: min = 1.44057 m, at segment # 55 max = 1.44406 m, at segment # 32 spread (max/min-1) = 0.24 percent BFRH Clocking angle: min = -13.8032 mrad, at segment # 82 max = -0.0000 mrad, at segment # 36 BFRH Radius: min = 0.71842 m, at segment # 66 max = 0.72186 m, at segment # 2 spread (max/min-1) = 0.48 percent Mean segment area = 1.35 m^2 Diameter of segment of mean area = 1.44032 m Mean diameter of BFRH = 1.44031 m Cell bar length: nominal = 1.24015 m (length of cell bar built on unscaled, planar array) min = 1.24870 m max = 1.26072 m range (max-min) = 12.017 mm spread (max/min-1) = 0.96 percent AAP Adjustments (if post centered on node): In plane min = 0.10 mm max = 2.19 mm Z_PSA min = -0.16 mm max = 0.16 mm Estimated WT pivot shifts: min = 0.98 mm, at segment # 2 max = 2.84 mm, at segment # 66 Estimated superhex correction residual: min = 0.36 nm, at segment # 28 max = 0.93 nm, at segment # 66


Segmentation DatabaseSegmentation Database Excerpt (for information) ----------------------------------------------- SECTION 2: DEFINITION OF PSA COORDINATE SYSTEMS -------------------------------------------DEFINITION OF PSA COORDINATE SYSTEMS - SECTOR A Origin of PSA Coordinate System given as coordinates of segment center (ctr) expressed in the M1 Coordinate System, in meters Segment center lies in the M1 optical surface Orientation of PSA frame in M1 frame given as coordinates of 1xPSA, 1yPSA, and 1zPSA unit vectors, expressed in the M1 system For sectors B through F, PSA Coordinate Systems are rotated about Z_M1 by 60 to 300 degrees 2A: SEGMENT CENTERS / ORIGINS OF PSA COORDINATE SYSTEMS (in meters) seg# X_M1(ctr) Y_M1(ctr) Z_M1(ctr) 1 0.000000000 2.505174820 0.052299152 2 1.084848967 1.879013530 0.039229897 3 0.000000000 3.756438643 0.117590151

----End of Excerpt


GAP BUDGET DETAILS



Gap Budget – Excluding SeismicEXCLUDING SEI SMI C LOADS

GAP CLOSURE EFFECT MAGNI TUDE MULTI PLI ER* GAP LOSS, mmSegment edge & PMA assembly tolerance 0.300 1.41 0.423

Per Polished Mirror Assembly Drawing: 280-TMT-01-11000. Edge profile tolerance +/-.300mm WRT TowerSubcell manufacturing/ assembly error (Target to Tower) 0.043 1.41 0.061

Accuracy from registration features to alignment targets. RSS of In-plane, Decenter and Clocking** (1/2 of P-P))Subcell initial alignment error 0.115 1.41 0.163

RSS of In-Plane, Decenter, & Clocking** (1/2 of P-P)Surveying Error 0.087 1.41 0.123

RSS of In-Plane, Decenter, & Clocking** (1/2 of P-P)SSA registration repeatability 0.083 1.41 0.117

RSS of In-Plane, Decenter, & Clocking** (1/2 of P-P)Gravity-induced PSA deformations 0.010 1.00 0.010

Assume max 5% difference in effective stiffness of neighboring PSA’s; 1g deflection=0.203mm based on fmin>35 hz.Seismic-induced PSA deformations - NONE 0.000 1.00 0.000

Not included in this budgetWind-induced PSA deformations 0.0005 1.41 0.001

5.8N load (DRD value scales by seg area for 1.44m) @ ~12N/μm = 0.48μm Temperature-Induced PSA translations 0.010 1.00 0.010

Temperature gradients, CTE non-uniformity, PSA-PSA variations… ???Temperature-Induced PSA rotations 0.138 1.00 0.138

Cell/Subcell CTE mismatch: Adjacent segment clocking is out of phase at sector boundary. 6.4 u-rad/C * DT=30Cmax = 192u-rad each Thermal expansion of cell 0.292 1.00 0.292

Assume nominal gap is set for 0°C; steel cell (CTE~11.7 ppm/°C), max neg. ΔT=-20°C, 1.247m between segment centers) Gravity-induced cell deflection 0.388 1.00 0.388

Change in Segment-Segment gap due to cell deformation, 2g load – from Nelson's analysis of DSL data, Feb 2007 (0.194mm).Maximum gap closure before tip/ tilt (RSS of above contributions) 0.702

Segment decenter due to full differential tip/ tilt 0.377 2.00 0.754Maximum gap closure after tip/ tilt (linear sum of two lines above) 1.456Nominal Gap Width 2.500Gap Margin 1.044* Multiplier relates single segment effect to total change in gap. Random effects on adjacent segments are RSS'd, giving the 1.41 factor. Linear Sum of All Effects 2.479** Clocking at vertex results in gap closure: DGap = Dq* sin(30) = 0.5*symbol


Gap Budget – Including SeismicINCLUDI NG SEI SMI C LOADS

GAP CLOSURE EFFECT MAGNITUDE MULTIPLIER* GAP LOSS, mmSegment edge & PMA assembly tolerance 0.300 1.41 0.423

Per Polished Mirror Assembly Drawing: 280-TMT-01-11000. Edge profile tolerance +/-.300mm WRT TowerSubcell manufacturing/ assembly error (Target to Tower) 0.043 1.41 0.061

Accuracy from registration features to alignment targets. RSS of In-plane, Decenter and Clocking** (1/2 of P-P))Subcell initial alignment error 0.115 1.41 0.163

RSS of In-Plane, Decenter, & Clocking** (1/2 of P-P)Surveying Error 0.087 1.41 0.123

RSS of In-Plane, Decenter, & Clocking** (1/2 of P-P)SSA registration repeatability 0.083 1.41 0.117

RSS of In-Plane, Decenter, & Clocking** (1/2 of P-P)Gravity-induced PSA deformations 0.010 1.00 0.010

Assume max 5% difference in effective stiffness of neighboring PSA’s; 1g deflection=0.203mm based on fmin>35 hz.Seismic-induced PSA deformations 0.238 1.00 0.238

Assume 3.0g response of PSAs. Adjacent PSAs out-of-phase by 22.5 deg.(0.390*3* .203) Basis: 1g deflection=0.203mm based on fmin>35 hz.Wind-induced PSA deformations 0.0005 1.41 0.001

5.8N load (DRD value scales by seg area for 1.44m) @ ~12N/μm = 0.48μm Temperature-I nduced PSA translations 0.010 1.00 0.010

Temperature gradients, CTE non-uniformity, PSA-PSA variations… ???Temperature-I nduced PSA rotations 0.138 1.00 0.138

Cell/Subcell CTE mismatch: Adjacent segment clocking is out of phase at sector boundary. 6.4 u-rad/C * DT=30Cmax = 192u-rad each Thermal expansion of cell 0.292 1.00 0.292

Assume nominal gap is set for 0°C; steel cell (CTE~11.7 ppm/°C), max neg. ΔT=-20°C, 1.247m between segment centers) Gravity-induced cell deflection 0.388 1.00 0.388

Change in Segment-Segment gap due to cell deformation, 2g load – from Nelson's analysis of DSL data, Feb 2007 (0.194mm).Maximum gap closure before tip/ tilt (RSS of above contributions) 0.741

Segment decenter due to full differential tip/ tilt 0.377 2.00 0.754Maximum gap closure after tip/ tilt (linear sum of two lines above) 1.495Nominal Gap Width 2.500Gap Margin 1.005* Multiplier relates single segment effect to total change in gap. Random effects on adjacent segments are RSS'd, giving the 1.41 factor. Linear Sum of All Effects 2.717** Clocking at vertex results in gap closure: DGap = Dq* sin(30) = 0.5*symbol


Gap BudgetSegment tip/tilt produces decenter:

– Center of rotation currently at ZPSA = - 55.739 mm

– Vertex location (due to curvature): ZPSA = +4.32 mm

– Radial location of actuators: R = 531 mm– Full differential tip/tilt results in 0.377 mm decenter (0.754 mm gap loss, worst case):

Assumes total actuator travel of 5mm

Center of tip/tilt rotation Tip/tilt angle:

5 mm over 796.5 mm = 0.63%

Lateral decenter at vertex0.63% of (60.059mm) = 0.377 mm

15.1 mm

axial edge motion0.63% of 720 mm = 4.5 mm 45mm

796.5 mm(1.5*531)

Radius to actuators = 531 mm

60.059 mmat vertex


Revision History11/13/07 Post PDR Corrections– Slide-7: Corrected location of vertical line to correspond to 0.165 value.

Documents

Pasadena, California October 24-25, 2007 Contributors to the development effort: from IMTEC