TMT'OPT'PRE'07'057'REL01

1
TMT M1 Segment Support Assembly (SSA) Preliminary
Design Review (PDR)Volume-2 SYSTEM LEVEL
CALCULATIONS(See last slide for Revision History)

• Pasadena, California
• October 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 Project
• George Angeli, Curt Baffes, Doug MacMynowski,
  Terry Mast, Jerry Nelson, Ben Platt, Lennon
  Rodgers, Mark Sirota, Gary Sanders, Larry Stepp,
  Kei Szeto
• TMT Confidential
• The 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.

2
Outline

• Volume-2 System Level Calculations
• M1 Segmentation
• Segmentation Correction (for Variable Segment
  Geometry)
• Budgets
• Installation Alignment
• Edge Gap
• Actuator Stroke
• Mass

3
System-Level Calculations
SEGMENTATION(see Backup Slides for more detail)
4
Segmentation

• M1 Array Segmentation
• Six identical sectors of 82 unique segments
• Unique hexagonal shape
• Unique optical figure
• Segments (PSAs) clock 60 deg between sectors

A
A
A
A
B2
B1
C2
C1
PSA C-Sys. (XY) Actuator AAP Locations (Dots)
5
Segmentation Scheme

• Segmentation 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.

Vertices in optical surface
ZM1
project vertices and center onto optical
surface, // ZM1
XM1
Center (scaled)
(RM1)
Scaled hex array
Scaling rule
Base pattern regular hex array
6
Segmentation Scheme

• Segmentation studies
• Radial scaling of base pattern
• 9 different objectives evaluated
• Rule 7 selected a 0.165
• Minimize blank size
• Other metrics also favorable
• when a 0.165

(Only radial scaling studied, other parameters
might be used for scaling, such as Azimuth)
Where a is the scaling parameter Rmax is the
largest vertex radii (before scaling) R is the
radial coordinate of a point in the base pattern
to be scaled Rscaled 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

• Objectives evaluated
• Minimize Irregularity
• Minimize Variation of Segment Area
• Minimize Variation of Circumscribed Dia.
• Minimize Cell top bar length range
• Minimize SSA aligner range
• Minimize Edge angle scatter (diffraction)
• Minimize diameter of largest circumscribed circle
• Minimize Max Pivot Shifts to rebalance
  Whiffletree
• Minimize Max figure residual after correction

Note 1. Per Mast and Nelson
7
Segmentation Scheme

• Sensitivity of objectives

a 0.165
Nominal cell member length 1.24m
7 Max. Circumsc. Diam. 1.21m
1 Max. Irregularity (mm RMS)
8 Max WT Pivot Shift (mm)
Value of metric
5 Max In-Plane Alignment Range (mm)
6 STD Edge Angle Scatter (mrad)
9 Max Pivot Shift resid. (nm)
4 Range of Cell Bar Length ()
2 Range of segment area ()
3 Range Circum. Ø ()
Value of tuning parameter a
8
Segmentation Scheme

• Implementation
• 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
  system
• Mirror 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

9
System-Level Calculations
SEGMENTATION CORRECTION(see Backup Slides for
more detail)
10
Segmentation Correction Approach

• Segment irregularity and size variations would
  degrade optical performance if not compensated
  for
• Single support system design for all 82 types
• Adjusted for each segment geometry
• Correction approach
• Rebalance each whiffletree
• Pivot-point shifts
• Analysis of each type required
• Drill holes for whiffletree pivots in custom
  locations for each segment type
• Low cost, automated CNC operation
• Balance masses would raise part count and add
  mass
• Analysis of worst case corrections
• Max pivot shift estimate 3.5 mm
• Axial RMS error increases 10 (1nm)

11
Segmentation Correction Analysis

• Calculate 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.

12
Segmentation Correction Analysis

• Evaluated 12 Cases Shown (for 1.2m segment)
• Conclusion Pivot shifts very effective
  correction method

10.2nm for 1.44m segment
13
Segmentation Correction Analysis

• Hardware Implementation of Pivot Shifts

Can shift Pivots Several mm in-plane
14
System-Level Calculations
INSTALLATION ALIGNMENT BUDGET
15
Installation Alignment

• Alignment Registration
• Estimate segment position errors
• in-plane, clocking, piston and tip/tilt
• Due to
• Registration - Clearance and Repeatability
• PMA Assembly Errors - Tower to Optical
  Origin/Axes/Plane
• Fixed Frame Alignment Errors - At Targets
• Target to Fixed Frame Tower-Attachment Tolerances
• Surveying 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

16
Installation Alignment

• Alignment Registration Inputs Assumptions

17
Installation Alignment

• Alignment Registration Inputs Assumptions

18
Installation Alignment

• Alignment Registration Results

19
Installation Alignment

• Optical impact of these positioning errors
• using Terry Masts 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

20
System-Level Calculations
GAP BUDGET
21
Gap Budget - Excluding Seismic

• Nominal Segment-to-Segment Gap 2.5 mm
• Random Gap Reducing Effects
• PSA Manufacturing and Installation
  Tolerances 0.488 mm RSS Sum
• Environmentally induced PSA motions 0.139 mm RSS
  Sum
• Mirror cell deformations 0.486 mm RSS Sum
• RSS 0.702 mm
• Actuation Segment tip/tilt de-center 0.754 mm
• Adjacent segments with full differential tilt
• Fault 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
22
Gap Budget - Including Seismic

• Assume 3.0g seismic with segment motions out of
  phase by 22.5 deg 0.39 factor 3.0 0.203mm
  (1g deflection) 0.238 mm
• Random Gap Reducing Effects
• PSA Manufacturing and Installation
  Tolerances 0.488 mm RSS Sum
• Environmental PSA motions (w/seismic) 0.275
  mm RSS Sum
• Mirror cell deformations 0.486 mm RSS Sum
• RSS 0.744 mm
• Actuation Segment tip/tilt de-center 0.754 mm
• Adjacent segments with full differential tilt
• Fault 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
23
Gap Budget

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

24
System-Level Calculations
ACTUATOR STROKE BUDGET
25
Actuator Stroke Budget

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

26
System-Level Calculations
MASS BUDGET
27
Mass Estimate

• Current design meets both fixed and moving mass
  limits
• Component sizing complete
• Current CAD mass summary (no contingency included)

28
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.
29
System-Level Calculations
BACKUP SLIDES
30
Primary Mirror Segmentation Detailed Discussion
Of Segmentation Analysis
System-Level Calculations

• Credit Eric Ponslet, IMTEC

31
M1 Segmentation Problem

• Define 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
  projection
• Approach (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 gaps
• Calculate various metrics

32
M1 Segmentation Problem

• Tuning 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

33
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, 2006
• Other relevant documents
• T. Mast, G. Angeli, and S. Roberts, TMT
  Coordinate Systems, TMT.SEN.TEC.05.016.DRF04,
  September 2005.

34
Previous Work (2/3)

• Based on earlier scaling work by Larry Stepp
  Jerry Nelson
• Two scaling formulations
• Three candidate goals for minimization (tuning of
  a)
• Maximum irregularity of any segment
• Range of segment area
• 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 irregularity
• Irregularity (and size variations) impacts
  performance (imperfect SuperHex correction)

35
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
  86
• Goal 3 range of circumscribed diameter reduced
  by factor 11
• Allowing rotation of BFRH results in large
  improvements
• Only 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

from value without scaling
36
Irregularity Definition

• irregularity ? 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

37
Re-centering BFRH has Negligible Impact
These results from Aplanatic Gregorian design
with a0.6m
38
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 gt
  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 system
• Represent SSA side of interface

YPSA
XPSA
Free circle
Centered circle
39
Recent Changes and Additions (2/2)

• Added six additional Tuning Goals
• Minimize range of bar lengths in top layer of
  cell
• Minimize range of SSA alignment system
• Minimize width of diffraction spikes from segment
  edges
• Minimize largest circumscribed diameter
  (blank/boule size)
• Minimize magnitude of WT pivot shifts
• Minimize residual figure error from WT pivot
  shift correction
• Repeated all calculations for Ritchey-Chrétien
  design and new segment size
• Geometry and segmentation
• K60m, k-1.00095
• a0.716m, t45mm, gap2.4mm
• 682492 segments instead of 6123738
• WH pivot shift data not available for larger
  segments
• Used sensitivities from a0.6m not directly
  applicable
• Observations
• Optimal tuning almost identical
• Conclusions unchanged
• Can base decision on old baseline (a0.6m, AG)

40
Segmentation Patterns
New baseline 682, 1.432m segments
41
Coordinate Systems

• XYZM1 / R?ZM1
• 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

Not currently an official TMT coordinate system
(TMT.SEN.TEC.05.016.DRF04, September 2005)
42
Defining PSA Reference Frame
YTEMP
XPSA
XTEMP
YPSA
Rotation about ZTEMP, from XYZTEMP to XYZPSA
BFRH
BFRH
Outline in XYTEMP
Vertices in optical surface
ZTEMP
ZPSA
XTEMP
ZM1
extend vertices and center into optical surface
// ZM1
XM1
center XYM1 scaling rule center
Scaled hex array
Scaling rule
Base pattern regular hex array
43
Defining/Positioning Hardware

• Defining Segment outlines
• Begin with circular blank from polishing
• Engrave fiducials into optical surface of
  polished segment
• Fiducials define location of XYZPSA reference
  frame
• Cut segment outlines relative to fiducials
• segment edges are straight lines in XYPSA plane
  (basic)
• segment side faces // to ZPSA (basic)
• 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

44
Cell Nodes and Cell-SSA Interface

• Cell 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

YPSA
ZPSA
X,YPSA
Segment Vertices (before gaps)
ZM1
HSSA
XPSA
SSA Supports (3)
RSSA
XM1
Hcell
Cell Nodes (3)
Interface Nodes (3)
45
Cell Nodes and Cell-SSA Interface
ZPSA
Local Normal to optical surface
XPSA
YPSA
Hcell
HSSA
Cell Nodes
RSSA
SSA Supports (center of adjusters)
Interface Nodes
46
Cell Nodes and Cell-SSA Interface
47
MATLAB Segmentation Code

• Produces 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 a (intensity of scaling)
• Outermost vertex of array (at Rmax) is unchanged
  by definition of scaling rule
• Extrudes segment centers and vertices into M1
  optical surface
• Defines segment-local coordinate systems
• Z // normal to optical surface at segment center
• Calculates coordinates of cell and interface
  nodes
• Top layer nodes and interface nodes
• Implements gaps
• Calculates size and rotation angle of BFRH
• Defines final local systems (XYZPSA)
• Establishes coordinates of SSA support points
• Calculates various metrics of resulting
  segmentation
• Produces outputs files (ASCII)
• segment vertex coordinates in M1 or PSA system
• Cell node coordinates in M1 system

48
New Segmentation Goals (1/2)

• Minimize segment irregularity
• Minimize variation of segment area
• Minimize variation in segment size
• Minimize range of lengths of top members of cell
• Avoid having to build different length members
• Metric Max(L)/Min(L)-1, in percent
• 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
• 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(Stds) v 1/3 (Std02Std602Std1202)
  
• This goal is optimized without scaling (a0)
  Std0 Std60 Std120 0

49
New Segmentation Goals (2/2)

• Minimize diameter of largest circumscribed circle
• Minimize size of glass boules/segment blanks
• Now using exact calculation of circumscribed
  circle (free center)
• 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 components
• Large shifts could be difficult to implement
• Estimates based on study of pivot shifts for
  various modes of segment shape variations
• Based 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
• 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 variations
• Based on Correction of Segmentation Effects by
  Shifting Whiffletree Pivot Locations
  TMT.OPT.TEC.06.009.REL01 (Eric Williams, June
  2006)
• Metric estimated value of v(RMScorrected2
  RMSnom2),
• 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

50
Goals 8 and 9 Axial Support Pivot Shifts

• BFRH is optimally clocked ? no residual rotation
• Correction for segment size (case 1) using BFRH
  radius for size
• Requires pivot shifts up to 0.49mm per mm of
  radial growth
• Used 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

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 a0.6m
51
Goal 5 Range of SSA Aligners

• Plots 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

No Scaling (a0) Max distance 5.6mm
Optimized (a0.167) Max distance 1.9mm
Support nodes shown MUCH closer to one-another
than actual
52
Tuning Results for RC, a0.716m

• 682, 1.432m segments

53
Tuning Results for RC, 4921.432m
Rotation, but no re-centering of BFRH
Nominal cell member length 1.24m
Goals 8 and 9 estimated using sensitivities from
AG/a0.600 design
1 Max. Irregularity (mm RMS)
7 Max. Circumsc. Diam. 1.21m
8 Max WT Pivot Shift (mm)
Value of metric
5 Max In-Plane Alignment Range (mm)
6 STD Edge Angle Scatter (mrad)
9 Max Pivot Shift resid. (nm)
4 Range of Cell Bar Length ()
2 Range of segment area ()
3 Range Circum. Ø ()
Value of tuning parameter a
54
Segmentation Summary

• Scaling effects are almost not affected by
  segment size
• Goals 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 values
• Residual AAP adjustment 2.2mm (radial)
• Residual cell bar length variation 12mm
• Definitions of node and/or support coordinates
  could (should?) be generalized
• Current work based on extremely simple (and
  limited) definition of cell
• Requires 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 a0.12 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?

Sensitivity numbers obtained from study with
a0.6m
55
Segmentation Database

• Segmentation Database Excerpt (for information)

TMT M1 SEGMENTATION DATA - Eric Ponslet - HYTEC
Inc. - 06-Mar-2007 151415 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 m 1B SEGMENTATION PARAMETERS
Scaling Parameter alpha 0.1650 (radial
scaling (1alpha(Rmax/k)2)/(1alpha(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 m 1D CELL DATA
Distance from optical surface to cell nodes
0.37250 1E 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
56
Segmentation Database

• Segmentation 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 m2, at segment
82 max 1.3538 m2, 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 m2 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
57
Segmentation Database

• Segmentation Database Excerpt (for information)

-----------------------------------------------
SECTION 2 DEFINITION OF PSA COORDINATE SYSTEMS
------------------------------------------- DEFINI
TION 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
58
System-Level Calculations
GAP BUDGET DETAILS
59
Gap Budget Excluding Seismic
60
Gap Budget Including Seismic
61
Gap Budget

• Segment 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

Lateral decenter at vertex 0.63 of (60.059mm)
0.377 mm
axial edge motion 0.63 of 720 mm 4.5 mm
45mm
60.059 mm at vertex
Radius to actuators 531 mm
15.1 mm
Center of tip/tilt rotation
Tip/tilt angle 5 mm over 796.5 mm 0.63
796.5 mm (1.5531)
62
Revision History

• 11/13/07 Post PDR Corrections
• Slide-7 Corrected location of vertical line to
  correspond to 0.165 value.