LIGO
LIGO- T1100445
–v5
LIGO Laboratory / LIGO Scientific Collaboration
LIGO
LIGO- T1100445-v5
3/9/12
AOS SLC
Signal Recycling Cavity Baffles
Final Design
Michael Smith, Lisa C. Austin, Mike Hillard, Heidy Kelman, Tim Nguyen, Manuel Ruiz, Jesse
Terrazas, Virginio Sannibale
Distribution of this document:
LIGO Scientific Collaboration
This is an internal working note
of the LIGO Laboratory.
California Institute of Technology
LIGO Project – MS 18-34
1200 E. California Blvd.
Pasadena, CA 91125
Phone (626) 395-2129
Fax (626) 304-9834
E-mail: info@ligo.caltech.edu
Massachusetts Institute of Technology
LIGO Project – NW22-295
185 Albany St
Cambridge, MA 02139
Phone (617) 253-4824
Fax (617) 253-7014
E-mail: info@ligo.mit.edu
LIGO Hanford Observatory
P.O. Box 159
Richland WA 99352
Phone 509-372-8106
Fax 509-372-8137
LIGO Livingston Observatory
P.O. Box 940
Livingston, LA 70754
Phone 225-686-3100
Fax 225-686-7189
http://www.ligo.caltech.edu/
LIGO
LIGO- T1100445
–v5
2
LIGO
LIGO- T1100445
–v5
Table of Contents
1
INTRODUCTION....................................................................................................................... 7
1.1 Scope .............................................................................................................................................. 7
1.2 Final Design Review Checklist..................................................................................................... 7
1.2.1
Final requirements – any changes or refinements from PDR? ........................................... 7
1.2.1.1 Direct Requirements ....................................................................................................... 7
1.2.1.2 Hartmann Baffle Requirements—NEW ......................................................................... 7
1.2.1.3 Ghost Beam Baffle Requirements .................................................................................. 7
1.2.1.4 Clear Aperture Requirements ......................................................................................... 7
1.2.2
Resolutions of action items from SLC PDR ....................................................................... 7
1.2.2.1 Lower BRDF Material for Baffles .................................................................................. 7
1.2.3
Final Parts Lists and Drawing Package .............................................................................. 8
1.2.4
Final specifications ............................................................................................................. 8
1.2.5
Final interface control documents....................................................................................... 8
1.2.6
Relevant RODA changes and actions completed ............................................................... 8
1.2.7
Signed Hazard Analysis ...................................................................................................... 8
1.2.8
Final Failure Modes and Effects Analysis .......................................................................... 8
1.2.9
Risk Registry items discussed............................................................................................. 8
1.2.10 Design analysis and engineering test data .......................................................................... 8
1.2.11 Software detailed design ..................................................................................................... 8
1.2.12 Final approach to safety and use issues .............................................................................. 8
1.2.13 Production Plans for Acquisition of Parts, Components, Materials Needed For
Fabrication .................................................................................................................................. 8
1.2.14 Installation Plans and Procedures ....................................................................................... 9
1.2.15 Final hardware test plans .................................................................................................... 9
1.2.16 Final software test plans ..................................................................................................... 9
1.2.17 Cost compatibility with cost book ...................................................................................... 9
1.2.18 Fabrication, installation and test schedule .......................................................................... 9
1.2.19 Lessons Learned Documented, Circulated ......................................................................... 9
1.2.20 Porcelainizing ..................................................................................................................... 9
1.2.21 Problems and concerns ....................................................................................................... 9
1.3 Applicable Documents .................................................................................................................. 9
2
SIGNAL RECYCLING CAVITY BAFFLES .......................................................................... 10
2.1 FUNCTION ................................................................................................................................. 10
2.1.1
SR3 HR BAFFLE ............................................................................................................. 10
2.1.2
SR3 AR BAFFLE ............................................................................................................. 10
2.1.3
SR2 SCRAPER BAFFLE ................................................................................................. 10
2.1.4
HAM SCRAPER BAFFLE .............................................................................................. 10
2.1.5
SRM AR BAFFLE............................................................................................................ 10
2.2 ZEMAX LAYOUT ..................................................................................................................... 10
2.2.1
H1 & L1 IFO ZEMAX LAYOUT .................................................................................... 10
2.2.2
H2 IFO ZEMAX LAYOUT ............................................................................................. 16
2.3 BEAM SIZES .............................................................................................................................. 18
3
LIGO
LIGO- T1100445
–v5
2.3.1
H1/L1 BEAM SIZES IN SIGNAL RECYCLING CAVITY ........................................... 18
2.3.1.1 H1/L1 ZEMAX PHYSICAL OPTICS PROPAGATION MODEL ............................. 18
2.3.2
H2 BEAM SIZES IN SIGNAL RECYCLING CAVITY ................................................ 27
2.3.2.1 H2 ZEMAX PHYSICAL OPTICS PROPAGATION MODEL................................... 27
3
DESCRIPTIONS OF SIGNAL RECYCLING CAVITY BAFFLES...................................... 36
3.1 SR3 HR BAFFLE........................................................................................................................ 36
3.1.1
SR3 HR BAFFLE Characteristics .................................................................................... 37
3.2 SR3 AR BAFFLE ........................................................................................................................ 38
3.2.1
SR3 AR BAFFLE Characteristics .................................................................................... 39
3.3 SR2 SCRAPER BAFFLE ........................................................................................................... 40
3.3.1
SR2 Scraper Baffle Characteristics................................................................................... 42
3.4 HAM SCRAPER BAFFLE ........................................................................................................ 43
3.4.1
HAM Scraper Baffle Characteristics ................................................................................ 46
3.5 SRM AR BAFFLE ...................................................................................................................... 47
3.5.1
SRM AR Baffle Characteristics ........................................................................................ 47
3.6 BAFFLE HEIGHTS ................................................................................................................... 48
3.7 OPTICAL INTERFACES ......................................................................................................... 48
4
SCATTERED LIGHT DISPLACEMENT NOISE ................................................................. 50
4.1 Scattered Light Requirement .................................................................................................... 50
4.1.1
Scattered Light Parameters ............................................................................................... 52
4.1.2
BRDF of Baffle Surfaces .................................................................................................. 57
4.1.3
HAM ISI Seismic Motion ................................................................................................. 57
4.1.4
Naming Convention for Wedged Optics .......................................................................... 58
4.1.5
SR3 HR Baffle Scatter ...................................................................................................... 60
4.1.6
SR3 AR Baffle Scatter ...................................................................................................... 60
4.1.6.1 Transmission of Signal Recycling Cavity Main Beam through SR3 HR ..................... 60
4.1.6.2 SR3 GBAR3 Ghost Beam............................................................................................. 61
4.1.6.3 SR3 GBHR3 Ghost Beam............................................................................................. 62
4.1.7
SR2 Scraper Baffle Scatter ............................................................................................... 63
4.1.7.1 ITM Ghosts Beams ....................................................................................................... 64
4.1.7.2 BS Ghosts Beam ........................................................................................................... 65
4.1.7.3 CP Ghosts Beam ........................................................................................................... 65
4.1.7.3.1 CP_GBAR1 H1..................................................................................................... 66
4.1.7.3.1.1 CP_GBAR3 H1 .............................................................................................. 66
4.1.7.4 Summary SR2 Scraper Baffle Scatter ........................................................................... 67
4.1.7.5 SRM GBAR3 Ghost Beam ........................................................................................... 67
4.1.7.6 SRM GBHR3 Ghost Beam ........................................................................................... 68
4.1.7.7 Summary SR3, SR2, SRM Ghost Beam Scatter ........................................................... 69
4.1.8
H2 Hartmann Y Scatter..................................................................................................... 69
4.1.8.1 Scattered Light Displacement Noise from H2 HWSYM1............................................ 69
4.1.8.2 Scattered Light Displacement Noise from H2 HWSYM2............................................ 70
4.1.8.3 Scattered Light Displacement Noise from H2 HWSYM3............................................ 71
4
LIGO
LIGO- T1100445
–v5
4.1.8.4 Scattered Light Displacement Noise from H2 DCBS1Y.............................................. 72
4.1.8.5 Scattered Light Displacement Noise from H2 VAC LENSY ....................................... 73
4.1.8.6 H2 Hartmann Y Viewport Scatter ................................................................................ 73
4.1.8.7 H2 Hartmann Y Viewport Reflection, HAM Chamber Scatter .................................... 74
4.1.8.8 Summary of H2 Hartmann Y Scatter ............................................................................ 75
4.1.9
H2 Hartmann X Scatter..................................................................................................... 76
4.1.9.1 Scattered Light Displacement Noise from H2 HWSXM1............................................ 76
4.1.9.2 Scattered Light Displacement Noise from H2 DCBS1X.............................................. 77
4.1.9.3 Scattered Light Displacement Noise from H2 VAC LENSX ....................................... 78
4.1.9.4 Scattered Light Displacement Noise from H2 HWSXM2............................................ 79
4.1.9.5 H2 Scattered Light Displacement Noise from H2 HWSXM3 ...................................... 80
4.1.9.6 H2 Hartmann X Viewport Scatter ................................................................................ 81
4.1.9.7 H2 Hartmann X Viewport Reflection, HAM Chamber Scatter .................................... 82
4.1.9.8 Summary of H2 Hartmann X Scatter ............................................................................ 83
4.1.10 H1 & L1 Hartmann Beam Scatter..................................................................................... 84
4.1.10.1
H1 & L1 Hartmann X Arm ....................................................................................... 84
4.1.10.2
Summary of H1 & L1 Hartmann X Scatter .............................................................. 87
4.1.10.3
H1 & L1 Hartmann Y Arm ....................................................................................... 87
4.1.10.4
Summary of H1 & L1 Hartmann Y Scatter .............................................................. 89
5
INTERFACE CONTROL DOCUMENT................................................................................. 90
Table of Figures
Figure 1: H1 & L1 HAM4: SR2 Scraper Baffle, SR2 AR Baffle, HAM Scraper Baffle.................... 11
Figure 2: H1& L1 HAM5: SR3 HR Baffle, SR3 AR Baffle, SRM AR Baffle..................................... 15
Figure 3: HAM5 Elevation View ...................................................................................................... 16
Figure 4: H2 HAM10: SR2 Scraper Baffle, SR2 AR Baffle, HAM Scraper Baffle ........................... 17
Figure 5: H2 HAM11: SR3 HR Baffle, SR3 AR Baffle, SRM AR Baffle ........................................... 18
Figure 6: 3D Layout, H1/L1 Physical Optics Propagation.............................................................. 19
Figure 7: H1/L1 SR3, Horizontal Beam Profile ............................................................................... 20
Figure 8: H1/L1 SR3, Vertical Beam Profile ................................................................................... 21
Figure 9: : H1/L1 SR2 Scraper Baffle, Horizontal Beam Profile .................................................... 22
Figure 10: H1/L1 SR2 Scraper Baffle, Vertical Beam Profile ......................................................... 23
Figure 11: H1/L1 HAM Scraper Baffle (SR2 AR Baffle), Horizontal Beam Profile ........................ 24
Figure 12: H1/L1 HAM Scraper Baffle (SR2 AR Baffle), Vertical Beam Profile ............................ 25
Figure 13: H1/L1 SRM, Horizontal Beam Profile ............................................................................ 26
Figure 14: H1/L1 SRM, Vertical Beam Profile ................................................................................ 27
Figure 15: 3D Layout, H2 Physical Optics Propagation ................................................................. 28
Figure 16: H2 SR3, Horizontal Beam Profile .................................................................................. 29
Figure 17: H2 SR3, Vertical Beam Profile ....................................................................................... 30
Figure 18: : H2 SR2 Scraper Baffle, Horizontal Beam Profile ........................................................ 31
Figure 19: H2 SR2 Scraper Baffle, Vertical Beam Profile............................................................... 32
Figure 20: H2 HAM Scraper Baffle (SR2 AR Baffle), Horizontal Beam Profile ............................. 33
Figure 21: H2 HAM Scraper Baffle (SR2 AR Baffle), Vertical Beam Profile .................................. 34
Figure 22: H2 SRM, Horizontal Beam Profile ................................................................................. 35
Figure 23: H2 SRM, Vertical Beam Profile ..................................................................................... 36
Figure 24: SR3 HR Baffle ................................................................................................................. 37
Figure 25: SR3 AR Baffle ................................................................................................................. 39
5
LIGO
LIGO- T1100445
–v5
Figure 26: SR2 Scraper Baffle, H2 ................................................................................................... 41
Figure 27: SR2 Scraper Baffle with HAM Table Extension ............................................................. 42
Figure 28: HAM Scraper Baffle ....................................................................................................... 44
Figure 29: Internal Frequencies of HAM Scraper Baffle Assembly ................................................ 46
Figure 30: SRM AR Baffle ................................................................................................................ 47
Figure 31: Scattered Light Noise Transfer Functions ...................................................................... 52
Figure 32: HAM optics table Seismic Motion, m/rtHz ..................................................................... 58
Figure 33: Wedged Core Optic ghost beam naming convention...................................................... 59
Figure 34: BS ghost beam naming convention .............................................................................. 59
Figure 35: SR2 Scraper Baffle Scatter ............................................................................................. 67
Figure 36: Summary of SR Ghost Beam Scatter............................................................................... 69
Figure 37: Summary of H2 Hartmann Y Surfaces Scatter ............................................................... 76
Figure 38: Summary of H2 Hartmann X Surfaces Scatter ............................................................... 84
Figure 39: Summary of H1 & L1 Hartmann X ................................................................................. 87
Figure 40: Summary of H1 & L1 Hartmann Y Scatter ................................................................. 90
Table of Tables
Table 1: SR3 HR BAFFLE Characteristics ...................................................................................... 37
Table 1: SR3 AR BAFFLE Characteristics....................................................................................... 39
Table 1: SR2 Scraper Baffle Characteristics .................................................................................... 42
Table 1: HAM Scraper Baffle Characteristics ................................................................................. 46
Table 1: SRM AR Baffle Characteristics .......................................................................................... 48
Table 1: Heights and Sizes of SR Baffles .......................................................................................... 48
6
LIGO
LIGO- T1100445
–v5
1 INTRODUCTION
1.1 Scope
This document provides the final designs for the Signal Recycling Cavity Baffle for aLIGO.
1.2 Final Design Review Checklist
1.2.1 Final requirements – any changes or refinements from PDR?

The updated requirements for the Signal Recycling Cavity Baffles are listed in T070061 Stray
Light Control Design Requirements.

The Hartmann Viewport Beam Dumps were eliminated; see section Error! Reference source
ot found..
1.2.1.1 Direct Requirements
Phase noise due to scattered light fields injected into the interferometer is treated as a technical
noise source. Therefore, the total scattered light phase noise, expressed in equivalent displacement
noise, must be < 1/10th of the quadrature sum of the suspension thermal noise and the test mass
thermal noise (referred to as the SRD), as given in Figure 1 of M060056-06, Advanced LIGO
Reference Design.
1.2.1.2 Hartmann Baffle Requirements—NEW
Baffles shall be placed to mitigate the scattered displacement noise caused by scatter from
Hartmann optics in the Hartmann sensing train for the ITM mirrors; the total scattered light
displacement noise, must be < 1/10th of the quadrature sum of the suspension thermal noise and the
test mass thermal noise (referred to as the SRD), as given in Figure 1 of M060056-06, Advanced
LIGO Reference Design.
1.2.1.3 Ghost Beam Baffle Requirements
Baffles shall be placed to mitigate the scattered light displacement noise caused by scatter from the
ghost beams generated by the wedged optics, ITM, FM, BS, SR3, SR2, and SRM; the total
scattered light displacement noise, must be < 1/10th of the quadrature sum of the suspension
thermal noise and the test mass thermal noise (referred to as the SRD), as given in Figure 1 of
M060056-06, Advanced LIGO Reference Design.
1.2.1.4 Clear Aperture Requirements
All Scraper Baffles shall not vignette the recycling cavity beam > 100 ppm power loss;
1.2.2 Resolutions of action items from SLC PDR
Refer to: LIGO-L0900119-v1
1.2.2.1 Lower BRDF Material for Baffles
We suggest the team consider a lower-BRDF material for the more critical baffles,
and in particular suggest looking at the electro-static frit black-enameled steel as an option
7
LIGO
LIGO- T1100445
–v5
that would give better optical performance.
Ans: The lowest BRDF material that is practical at the moment is oxidized polished stainless
steel.
1.2.3 Final Parts Lists and Drawing Package
TBD
1.2.4 Final specifications
E1100842 Specification for Mirror Finished (Super #8) Stainless Steel to be used in the LIGO
Ultra-High Vacuum System
E0900364-v8 Metal components intended for use in the Adv LIGO Vacuum System
1.2.5 Final interface control documents
TBD The mechanical and optical interfaces of the Signal Recycling Cavity Baffles are described in
E110XXX-v1AOS SLC Signal Recycling Cavity Baffles Interface Control Doc.
1.2.6 Relevant RODA changes and actions completed
NO Rodas!
1.2.7 Signed Hazard Analysis
E1100984 SLC Signal Recycling Cavity Baffle Install Hazard Analysis
1.2.8 Final Failure Modes and Effects Analysis
Not Required
1.2.9 Risk Registry items discussed
None for this subsystem
1.2.10 Design analysis and engineering test data
See Section 3, Descriptions of Signal Recycling Cavity Baffles and Section 4, Scattered Light
Displacement Noise
1.2.11 Software detailed design
Not applicable
1.2.12 Final approach to safety and use issues
No operational safety issues
1.2.13 Production Plans for Acquisition of Parts, Components, Materials Needed For
Fabrication
E1101001-v1_AOS SLC Signal Recycling Cavity Baffles production plan
8
LIGO
LIGO- T1100445
–v5
1.2.14 Installation Plans and Procedures
This will be deferred until after FDR
1.2.15 Final hardware test plans
See E1101023 Signal Recycling Cavity Baffles Fabrication, Installation, and Test Plan
1.2.16 Final software test plans
Not applicable.
1.2.17 Cost compatibility with cost book
See E1101001-v1_AOS SLC Signal Recycling Cavity Baffles production plan
1.2.18 Fabrication, installation and test schedule
See E1101023 Signal Recycling Cavity Baffles Fabrication, Installation, and Test Plan
1.2.19 Lessons Learned Documented, Circulated
1.2.20 Porcelainizing
The baffles will be constructed of oxidized polished stainless steel to avoid shedding of the
porcelain surface.
1.2.21 Problems and concerns
There are presently no problems or concerns with the recycling cavity baffles.
1.3 Applicable Documents
T070303 Arm Cavity Finesse for aLIGO
T070247 aLIGO ISC Conceptual Design
E0900364-v8 LIGO Metal in Vacuum
E1101023 Signal Recycling Cavity Baffles Fabrication, Installation, and Test Plan
T060073-00 Transfer Functions of Injected Noise
T070061-v2 Stray light Control Design Requirements
T0900269-v2 Stray Light Control (SLC) Preliminary Design
T1100056-v2 Arm Cavity Baffle Edge Scatter
E1100984_SLC Signal Recycling Cavity Baffle Install Hazard Analysis
E1101001-v1_AOS SLC Signal Recycling Cavity Baffles production plan
TBD E110XXX-v1AOS SLC Signal Recycling Cavity Baffles Interface Control Doc.
9
LIGO
LIGO- T1100445
–v5
2 SIGNAL RECYCLING CAVITY BAFFLES
2.1 FUNCTION
2.1.1 SR3 HR BAFFLE
The SR3 HR Baffle catches, on its recycling cavity side, some of the ghost beams from the ITM,
CP, and BS; the stray light that is not absorbed is reflected toward the mode cleaner tube baffle
near HAM5 and HAM11.
2.1.2 SR3 AR BAFFLE
The SR3 AR Baffle catches and absorbs the signal recycling cavity power that leaks through the
SR3AR surface.
2.1.3 SR2 SCRAPER BAFFLE
The SR2 Scraper Baffle catches most of the ghost beams from ITM, CP, and BS. It also catches, on
the side facing the SR2 mirror, some of the SR2 HR ghost beams.
2.1.4 HAM SCRAPER BAFFLE
The HAM Scraper Baffle behind the SR2 AR side catches some of the SR2 AR ghost beams, and
the reverse-path main IFO beam reflected by SRM that transmits through the SR2 AR surface. It
also catches the 1064nm light that reflects from the dichroic filter in the Hartmann beam path.
2.1.5
SRM AR BAFFLE
The SRM AR Baffle catches the reflected beam from the OFI TGG crystal
2.2 ZEMAX LAYOUT
2.2.1 H1 & L1 IFO ZEMAX LAYOUT
The H1 and L1 IFO ZEMAX layout of HAM4 is shown in Figure 1.
10
LIGO
LIGO- T1100445
–v5
HAM Scaper
Baffle
HAM Scraper Baffle
(SR2 AR Baffle)
Dichroic filter
SR2
Dichroic filter
SR2 Scraper Baffle
HAM Scaper
Baffle
Figure 1: H1 & L1 HAM4: SR2 Scraper Baffle, SR2 AR Baffle, HAM Scraper Baffle
A Solid Works Model layout of the HAM 4 table is shown in Figure 2.
11
LIGO
LIGO- T1100445
–v5
Figure 2: HAM4 SW top view layout
12
LIGO
LIGO- T1100445
–v5
Figure 3: SR2 Scraper Baffle, Clamping Detail
A cross section view through the SR2 scraper baffle shown the extender table attached to the HAM
ISI.
13
LIGO
LIGO- T1100445
–v5
Figure 4: HAM4 SW cross section view, showing extender table and SR2 scraper baffle
The H1 and L1 IFO ZEMAX layout of HAM5 is shown in Figure 5.
14
LIGO
LIGO- T1100445
–v5
SR3 HR Baffle
SR3
SRM
SR3 AR Baffle
SRM AR Baffle
OFI
Figure 5: H1& L1 HAM5: SR3 HR Baffle, SR3 AR Baffle, SRM AR Baffle
15
LIGO
LIGO- T1100445
–v5
Figure 6: HAM5 Elevation View
2.2.2 H2 IFO ZEMAX LAYOUT
The H2 IFO ZEMAX layout of HAM10 is shown in Figure 7.
16
LIGO
LIGO- T1100445
–v5
HAM Scraper
Baffle
SR2 Scraper Baffle
Dichroic filter
SR2
HAM Scraper Baffle
(SR2 AR Baffle)
Dichroic filter
HAM Scraper
Baffle
Figure 7: H2 HAM10: SR2 Scraper Baffle, SR2 AR Baffle, HAM Scraper Baffle
The H2 IFO ZEMAX layout of HAM11 is shown in Figure 8.
17
LIGO
LIGO- T1100445
–v5
OFI
SR3 AR Baffle
SRM AR Baffle
SRM
SR3
SR3 HR Baffle
Figure 8: H2 HAM11: SR3 HR Baffle, SR3 AR Baffle, SRM AR Baffle
2.3 BEAM SIZES
2.3.1 H1/L1 BEAM SIZES IN SIGNAL RECYCLING CAVITY
2.3.1.1 H1/L1 ZEMAX PHYSICAL OPTICS PROPAGATION MODEL
The beam sizes in the signal recycling cavity were calculated using the ZEMAX physical optics
program; a Gaussian beam with a 12mm waist located a distance 1835000m away from the ITM
HR surface (approximately at the middle of the arm) was propagated down the signal recycling
cavity optical train. The ZEMAX layout is shown in Figure 9.
18
LIGO
LIGO- T1100445
–v5
Y
X
Z
3D Layout
9/28/2011
H1_signal recycling cavity.ZMX
Configuration 1 of 1
Figure 9: 3D Layout, H1/L1 Physical Optics Propagation
The x (vertical) and y (horizontal) beam profiles at various surfaces within the signal recycling
cavity optical train are shown in the following figures.
19
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+0
1E-1
1E-2
1E-3
1E-4
1E-5
-529.1
-423.3
-317.5
-211.7
-105.8
0
105.8
211.7
317.5
423.3
529.1
Y coordinate value
Irradiance Y-Cross section surface 10 SR3
9/28/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, X = 0.0000E+000
Peak Irradiance = 9.8391E-001 Watts/Millimeters^2, Total Power = 4.5269E+003 Watts
Pilot: Size= 5.4126E+001, Waist= 1.1416E-001, Pos= 1.8242E+004, Rayleigh= 3.8473E+001
Figure 10: H1/L1 SR3, Horizontal Beam Profile
20
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+0
1E-1
1E-2
1E-3
1E-4
1E-5
-528.7
-423
-317.2
-211.5
-105.7
0
105.7
211.5
317.2
423
528.7
X coordinate value
Irradiance X-Cross section surface 10 SR3
9/28/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, Y = 0.0000E+000
Peak Irradiance = 9.8391E-001 Watts/Millimeters^2, Total Power = 4.5269E+003 Watts
Pilot: Size= 5.4126E+001, Waist= 1.1416E-001, Pos= 1.8242E+004, Rayleigh= 3.8473E+001
Figure 11: H1/L1 SR3, Vertical Beam Profile
21
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+1
1E+0
1E-1
1E-2
1E-3
1E-4
-48.68
-38.95
-29.21
-19.47
-9.737
0
9.737
19.47
29.21
38.95
48.68
Y coordinate value
Irradiance Y-Cross section surface 12 SR2 SCRAPER BAFFLE
9/28/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, X = 0.0000E+000
Peak Irradiance = 1.0167E+000 Watts/Millimeters^2, Total Power = 1.5844E+002 Watts
Pilot: Size= 9.9608E+000, Waist= 1.1416E-001, Pos= 3.3568E+003, Rayleigh= 3.8473E+001
Figure 12: : H1/L1 SR2 Scraper Baffle, Horizontal Beam Profile
22
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+1
1E+0
1E-1
1E-2
1E-3
1E-4
-48.64
-38.92
-29.19
-19.46
-9.729
0
9.729
19.46
29.19
38.92
48.64
X coordinate value
Irradiance X-Cross section surface 12 SR2 SCRAPER BAFFLE
9/28/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, Y = 0.0000E+000
Peak Irradiance = 1.0167E+000 Watts/Millimeters^2, Total Power = 1.5844E+002 Watts
Pilot: Size= 9.9608E+000, Waist= 1.1416E-001, Pos= 3.3568E+003, Rayleigh= 3.8473E+001
Figure 13: H1/L1 SR2 Scraper Baffle, Vertical Beam Profile
23
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+1
1E+0
1E-1
1E-2
1E-3
1E-4
-24.69
-19.76
-14.82
-9.878
-4.939
0
4.939
9.878
14.82
19.76
24.69
Y coordinate value
Irradiance Y-Cross section surface 15 SR2 AR baffle
9/29/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, X = 0.0000E+000
Peak Irradiance = 1.0143E+000 Watts/Millimeters^2, Total Power = 4.0709E+001 Watts
Pilot: Size= 5.0551E+000, Waist= 9.5585E-002, Pos= 1.4263E+003, Rayleigh= 2.6974E+001
Figure 14: H1/L1 HAM Scraper Baffle (SR2 AR Baffle), Horizontal Beam Profile
24
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+1
1E+0
1E-1
1E-2
1E-3
1E-4
-24.67
-19.74
-14.8
-9.869
-4.935
0
4.935
9.869
14.8
19.74
24.67
X coordinate value
Irradiance X-Cross section surface 15 SR2 AR baffle
9/29/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, Y = 0.0000E+000
Peak Irradiance = 1.0160E+000 Watts/Millimeters^2, Total Power = 4.0743E+001 Watts
Pilot: Size= 5.0531E+000, Waist= 9.5621E-002, Pos= 1.4263E+003, Rayleigh= 2.6994E+001
Figure 15: H1/L1 HAM Scraper Baffle (SR2 AR Baffle), Vertical Beam Profile
25
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+1
1E+0
1E-1
1E-2
1E-3
1E-4
-9.196
-7.357
-5.518
-3.679
-1.839
0
1.839
3.679
5.518
7.357
9.196
Y coordinate value
Irradiance Y-Cross section surface 17 SRM
9/28/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, X = 0.0000E+000
Peak Irradiance = 1.0214E+000 Watts/Millimeters^2, Total Power = 6.7848E+000 Watts
Pilot: Size= 2.0528E+000, Waist= 8.6681E-001, Pos= -4.7620E+003, Rayleigh= 2.2183E+003
Figure 16: H1/L1 SRM, Horizontal Beam Profile
26
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+1
1E+0
1E-1
1E-2
1E-3
1E-4
-9.187
-7.35
-5.512
-3.675
-1.837
0
1.837
3.675
5.512
7.35
9.187
X coordinate value
Irradiance X-Cross section surface 17 SRM
9/28/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, Y = 0.0000E+000
Peak Irradiance = 1.0232E+000 Watts/Millimeters^2, Total Power = 6.7904E+000 Watts
Pilot: Size= 2.0520E+000, Waist= 8.6695E-001, Pos= -4.7603E+003, Rayleigh= 2.2190E+003
Figure 17: H1/L1 SRM, Vertical Beam Profile
2.3.2 H2 BEAM SIZES IN SIGNAL RECYCLING CAVITY
2.3.2.1 H2 ZEMAX PHYSICAL OPTICS PROPAGATION MODEL
The beam sizes in the signal recycling cavity were calculated using the ZEMAX physical optics
program; a Gaussian beam with a 12mm waist located a distance 1835000m away from the ITM
HR surface (approximately at the middle of the arm) was propagated down the signal recycling
cavity optical train. The ZEMAX layout is shown in Figure 18.
27
LIGO
LIGO- T1100445
–v5
Figure 18: 3D Layout, H2 Physical Optics Propagation
3D Layout
28
LIGO
LIGO- T1100445
–v5
The x (vertical) and y (horizontal) beam profiles at various surfaces within the signal recycling
cavity optical train are shown in the following figures.
Irradiance (Watts per sq Millimeter)
1E+0
1E-1
1E-2
1E-3
1E-4
1E-5
-265.4
-212.3
-159.2
-106.2
-53.08
0
53.08
106.2
159.2
212.3
265.4
Y coordinate value
Irradiance Y-Cross section surface 13 SR3
9/27/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, X = 0.0000E+000
Peak Irradiance = 9.7781E-001 Watts/Millimeters^2, Total Power = 4.5307E+003 Watts
Pilot: Size= 5.4317E+001, Waist= 1.1375E-001, Pos= -1.8241E+004, Rayleigh= 3.8199E+001
Figure 19: H2 SR3, Horizontal Beam Profile
29
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+0
1E-1
1E-2
1E-3
1E-4
1E-5
-265.4
-212.3
-159.2
-106.2
-53.08
0
53.08
106.2
159.2
212.3
265.4
X coordinate value
Irradiance X-Cross section surface 13 SR3
9/27/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, Y = 0.0000E+000
Peak Irradiance = 9.7781E-001 Watts/Millimeters^2, Total Power = 4.5307E+003 Watts
Pilot: Size= 5.4317E+001, Waist= 1.1375E-001, Pos= -1.8241E+004, Rayleigh= 3.8199E+001
Figure 20: H2 SR3, Vertical Beam Profile
30
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+0
1E-1
1E-2
1E-3
1E-4
1E-5
-42.38
-33.9
-25.43
-16.95
-8.476
0
8.476
16.95
25.43
33.9
42.38
Y coordinate value
Irradiance Y-Cross section surface 15 SR2 SCRAPER BAFFLE
9/27/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, X = 0.0000E+000
Peak Irradiance = 9.5848E-001 Watts/Millimeters^2, Total Power = 1.1327E+002 Watts
Pilot: Size= 8.6742E+000, Waist= 1.1375E-001, Pos= -2.9127E+003, Rayleigh= 3.8199E+001
Figure 21: : H2 SR2 Scraper Baffle, Horizontal Beam Profile
31
LIGO
LIGO- T1100445
–v5
1E+0
Irradiance (Watts per sq Millimeter)
1E-1
1E-2
1E-3
1E-4
1E-5
1E-6
1E-7
1E-8
1E-9
1E-10
-42.38
-33.9
-25.43
-16.95
-8.476
0
8.476
16.95
25.43
33.9
42.38
X coordinate value
Irradiance X-Cross section surface 15 SR2 SCRAPER BAFFLE
9/27/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, Y = 0.0000E+000
Peak Irradiance = 8.6263E-001 Watts/Millimeters^2, Total Power = 1.0194E+002 Watts
Pilot: Size= 8.6742E+000, Waist= 1.1375E-001, Pos= -2.9127E+003, Rayleigh= 3.8199E+001
Figure 22: H2 SR2 Scraper Baffle, Vertical Beam Profile
32
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+1
1E+0
1E-1
1E-2
1E-3
1E-4
-16.68
-13.34
-10.01
-6.67
-3.335
0
3.335
6.67
10.01
13.34
16.68
Y coordinate value
Irradiance Y-Cross section surface 18 SR2 AR baffle
9/29/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, X = 0.0000E+000
Peak Irradiance = 1.0395E+000 Watts/Millimeters^2, Total Power = 1.9029E+001 Watts
Pilot: Size= 3.4141E+000, Waist= 9.4371E-002, Pos= -9.5087E+002, Rayleigh= 2.6293E+001
Figure 23: H2 HAM Scraper Baffle (SR2 AR Baffle), Horizontal Beam Profile
33
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+1
1E+0
1E-1
1E-2
1E-3
1E-4
-16.68
-13.34
-10.01
-6.67
-3.335
0
3.335
6.67
10.01
13.34
16.68
X coordinate value
Irradiance X-Cross section surface 18 SR2 AR baffle
9/29/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, Y = 0.0000E+000
Peak Irradiance = 1.0395E+000 Watts/Millimeters^2, Total Power = 1.9029E+001 Watts
Pilot: Size= 3.4141E+000, Waist= 9.4371E-002, Pos= -9.5087E+002, Rayleigh= 2.6293E+001
Figure 24: H2 HAM Scraper Baffle (SR2 AR Baffle), Vertical Beam Profile
34
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+0
1E-1
1E-2
1E-3
1E-4
1E-5
-11.63
-9.302
-6.977
-4.651
-2.326
0
2.326
4.651
6.977
9.302
11.63
Y coordinate value
Irradiance Y-Cross section surface 20 SRM
9/27/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, X = 0.0000E+000
Peak Irradiance = 9.4657E-001 Watts/Millimeters^2, Total Power = 1.0647E+001 Watts
Pilot: Size= 2.6676E+000, Waist= 1.2548E+000, Pos= 8.7208E+003, Rayleigh= 4.6487E+003
Figure 25: H2 SRM, Horizontal Beam Profile
35
LIGO
LIGO- T1100445
–v5
Irradiance (Watts per sq Millimeter)
1E+0
1E-1
1E-2
1E-3
1E-4
1E-5
-11.63
-9.302
-6.977
-4.651
-2.326
0
2.326
4.651
6.977
9.302
11.63
X coordinate value
Irradiance X-Cross section surface 20 SRM
9/27/2011
Wavelength 1.06410 µm in index 1.00000 at 0.0000, 0.0000 (deg)
Center, Y = 0.0000E+000
Peak Irradiance = 9.4657E-001 Watts/Millimeters^2, Total Power = 1.0647E+001 Watts
Pilot: Size= 2.6676E+000, Waist= 1.2548E+000, Pos= 8.7208E+003, Rayleigh= 4.6487E+003
Figure 26: H2 SRM, Vertical Beam Profile
3 DESCRIPTIONS OF SIGNAL RECYCLING CAVITY BAFFLES
3.1 SR3 HR BAFFLE
A model of the SR3 HR Baffle is shown in Figure 27.
The hole diameter was chosen equal to the SR3 mirror diameter to minimize attenuation of the
Hartmann X beam that reflects from the BS AR surface
36
LIGO
LIGO- T1100445
–v5
Figure 27: SR3 HR Baffle
3.1.1 SR3 HR BAFFLE Characteristics
The characteristics of the SR3 HR BAFFLE are shown in Table 1.
Table 1: SR3 HR BAFFLE Characteristics
Parameter
Value
Location
HAM4 and HAM10
37
LIGO
LIGO- T1100445
–v5
Parameter
Value
Suspension
none
Aperture diameter (perpendicular to ITM HR)
See Table 6: Heights and Sizes of SR Baffles
Material
Oxidized polished stainless steel
BRDF
<0.03 sr^-1
Weight
15 lbs (TBD)
3.2 SR3 AR BAFFLE
A model of the SR3 AR Baffle is shown in Figure 28. The baffle catches all beams that transmit
through the AR surface of the SR3 mirror.
38
LIGO
LIGO- T1100445
–v5
Figure 28: SR3 AR Baffle
3.2.1 SR3 AR BAFFLE Characteristics
The characteristics of the SR3 AR BAFFLE are shown in Table 1.
Table 2: SR3 AR BAFFLE Characteristics
Parameter
Value
Location
HAM4 and HAM10
39
LIGO
LIGO- T1100445
–v5
Parameter
Value
Suspension
none
Aperture diameter (perpendicular to ITM HR)
none
Material
Oxidized polished stainless steel
BRDF
<0.03 sr^-1
Weight
15 lbs (TBD)
3.3 SR2 SCRAPER BAFFLE
A model of the SR2 Scraper Baffle is shown in Figure 29. The recycling cavity beams pass through
the hole on the right in the figure; the Hartmann pick-off beam from the BS AR surface passes
through the hole in the left. The positions of the holes were determined from the ZEMAX layout.
The 36 mm minimum radius of the left hole in the baffle was determined by a diffraction analysis
to cause a negligible vignetting of the Hartmann beam. (TBD see TCS reference); the hole radius
was increased to 42mm to allow for misalignment of the baffle. The elliptical size of the right hole
in the baffle allows passage of the incident and reflected signal recycling main beam without
vignetting causing a signal recycling power loss > 10 ppm.
The results of the FEA model show that the lowest internal mode frequency of the baffle is > 150
Hz TBD.
The baffle hangs over the edge of the HAM table, and is supported by a table extension shown in
Figure 30.
40
LIGO
LIGO- T1100445
–v5
Figure 29: SR2 Scraper Baffle, H2
41
LIGO
LIGO- T1100445
–v5
Figure 30: SR2 Scraper Baffle with HAM Table Extension
3.3.1 SR2 Scraper Baffle Characteristics
The characteristics of the SR2 Scraper Baffle are shown in Table 1.
Table 3: SR2 Scraper Baffle Characteristics
Parameter
Value
Location
HAM4 and HAM10
Suspension
none
Aperture diameter
See Table 6: Heights and Sizes of SR Baffles
Material
Oxidized polished stainless steel
BRDF
<0.03 sr^-1
42
LIGO
LIGO- T1100445
–v5
Parameter
Value
Weight
66 lbs (TBD)
3.4 HAM SCRAPER BAFFLE
A model of the original one-sided HAM Scraper Baffle is shown in Figure 31.
The design will be revised to provide a double-sided baffle, as shown in Figure 32. The front side
of the baffle catches ghost beams from the SR2 AR mirror. The back side catches the 1064nm light
that reflects from the dichroic filter in the Hartmann beam path.
The locations of the IFO beams and the Hartmann beam that traverse the HAM Scraper Baffle were
determined from the ZEMAX layout.
The 30 mm minimum radius of the hole in the baffle meets the Hartmann beam aperture
requirement. The actual radius of the hole will be set to 30 + 6 = 36 mm to allow for alignment
tolerance of 6 mm when the baffle is positioned on the HAM table.
43
LIGO
LIGO- T1100445
–v5
Figure 31: One-sided HAM Scraper Baffle
44
LIGO
LIGO- T1100445
–v5
Figure 32: Revised, double-sided HAM Scraper Baffle
The baffle is mounted directly to the HAM ISI table and must meet the requirement that the lowest
internal frequency be > 150 Hz.
The results of the FEA model show that the lowest internal mode frequency of the baffle is
approximately 167 Hz, as shown in Figure 33, and meets the design requirement.
45
LIGO
LIGO- T1100445
–v5
Figure 33: Internal Frequencies of HAM Scraper Baffle Assembly
3.4.1 HAM Scraper Baffle Characteristics
The characteristics of the HAM Scraper Baffle are shown in Table 1.
Table 4: HAM Scraper Baffle Characteristics
Parameter
Value
Location
HAM4 and HAM10
Suspension
none
Aperture diameter
See Table 6: Heights and Sizes of SR Baffles
Material
Oxidized polished stainless steel
46
LIGO
LIGO- T1100445
–v5
Parameter
Value
BRDF
<0.03 sr^-1
Weight
7 lbs
3.5 SRM AR BAFFLE
A model of the SRM AR Baffle is shown in Figure 34. The height of the IFO beams was
determined from the ZEMAX layout.
The hole in the baffle is 25mm diameter, which is larger than the 20mm limiting aperture of the
OFI.
Figure 34: SRM AR Baffle
3.5.1 SRM AR Baffle Characteristics
The characteristics of the SRM AR Baffle are shown in Table 1.
47
LIGO
LIGO- T1100445
–v5
Table 5: SRM AR Baffle Characteristics
Parameter
Value
Location
HAM4 and HAM10
Suspension
none
Aperture diameter
See Table 6: Heights and Sizes of SR Baffles
Material
Oxidized polished stainless steel
BRDF
<0.03 sr^-1
Weight
11 lbs (TBD)
3.6 BAFFLE HEIGHTS
The heights of the signal recycling cavity baffles above the HAM ISI table and the hole dimensions
are shown in Table 6.
3.7 OPTICAL INTERFACES
The locations of the IFO beams and the Hartmann beams that traverse the SR Baffle were
determined from the ZEMAX layout, D0901920 H1 Zemax layout, D0902345 H2 Zemax Layout,
and D0902216 L1 Zemax layout.
A sequential ZEMAX model was made for the signal recycling cavities of H2, H1, and L1 IFOs,
and the physical optics propagation program was used to determine the diffraction beam profiles at
the locations of the baffles.
The holes in the SR3 HR baffle, SR2 Scraper baffle, SR2 AR baffle, and SRM HR baffle are larger
than the 1E-3 radius of the diffraction beam profile that propagates through the signal recycling
cavity optical train and will not vignette the beam appreciably; in addition, the holes are large
enough to allow passage of the diffracted Hartmann probe beams from the ITMX and ITMY mirror
surfaces; see Table 6.
Table 6: Heights and Sizes of SR Baffles
IFO
Baffle
1/e^2
radius,
mm
10ppm
radius,
mm
Hartmann beam
radius
requirement,
mm
54.15
116.2
132.5
7.99
18.4
Baffle hole
radius,
mm
Height above
table,
mm
H2
SR3 HR baffle
SR2 HR scraper
baffle main
132.5
211.0
52.5 H, 42 V
193.2
48
LIGO
IFO
LIGO- T1100445
Baffle
1/e^2
radius,
mm
10ppm
radius,
mm
–v5
Hartmann beam
radius
requirement,
mm
Baffle hole
radius,
mm
Height above
table,
mm
beam
SR2 HR scraper
baffle pick-off
beam
36.0
42
HAM (SR2 AR)
scraper
baffle
4.22
10.1
30.0
30
187.4
HAM
(Hartmann)
Scraper
baffle
4.22
10.1
30.0
30
187.4
HAM-BD
HWSX1
186
HAM-BD
HWSX2
230
HAM-BD HWSY1
193.2
HAM-BD HWSY2
224.2
SRM HR baffle
2.05
5.9
14
176.2
SR3 HR baffle
54.30
118.6
132.5
132.5
230.2
SR2 HR scraper
baffle
9.59
21.3
36.0
42
239.7
HAM (SR2 AR)
scraper
baffle
5.06
12.1
30
30
232.5
HAM
(Hartmann)
Scraper
baffle
5.06
12.1
30
30
232.5
L1
HAM-BD
HWSX1
240.2
HAM-BD
HWSX2
224.2
HAM-BD HWSY1
230.8
49
LIGO
IFO
LIGO- T1100445
Baffle
1/e^2
radius,
mm
10ppm
radius,
mm
–v5
Hartmann beam
radius
requirement,
mm
Baffle hole
radius,
mm
HAM-BD HWSY2
Height above
table,
mm
230.8
SRM HR baffle
2.1
4.5
14
230.1
SR3 HR baffle
54.2
116.2
132.5
132.5
230.2
SR2 HR scraper
baffle
9.6
20.6
36.0
42
220.9
HAM
(HartmannX) scraper
baffle
6.9
14.8
30
30
220.0
HAM (SR2 AR)
scraper
baffle
5.6
11.9
30
30
220.0
HAM
(HartmannY) Scraper
baffle
3.0
6.4
30
30
220.0
H1
HAM-BD
HWSX1
221.2
HAM-BD
HWSX2
224.2
HAM-BD HWSY1
215
HAM-BD HWSY2
230.8
SRM AR baffle
2.1
4.4
12.5
210.9
In every instance, the hole radius is 8mm greater than the 10ppm radius of the signal recycling
cavity beam; therefore, the horizontal and vertical tolerance in placement of the baffles is +/- 8mm.
This meets the clear aperture requirement.
4 SCATTERED LIGHT DISPLACEMENT NOISE
4.1
Scattered Light Requirement
A DARM signal is obtained when the differential arm length is modulated as a result of a gravity
wave strain. The DARM signal was calculated in reference, T060073-00 Transfer Functions of
Injected Noise, and is defined by the following expression:
50
LIGO
LIGO- T1100445
–v5
Vsignal DARMLhSRD P0
Where L is the arm length, hSRD is the minimum SRD gravity wave strain spectral density
requirement, P0 is the input laser power into the IFO, and DARM is the signal transfer function.
In a similar manner, an apparent signal (scattered light noise) occurs when a scattered light field
with a phase shift is injected into the IFO at some particular location, e.g. through the back of the
ETM mirror. The scattered light noise is defined by the following expression:
Vnoise SNXXX SN  PSNi
PSNi is the scattered light power injected into the IFO mode, δSN is the phase shift of the injected
field, and SNXXX is the noise transfer function for that particular injection location.
The phase shift spectral density of the injected field due to the motion of the scattering surface is
given by
4   x
 SNi 
s

where xs is the spectral density of the longitudinal motion of the scattering surface.
In general, the different scattering sources are not coherent and must be added in quadrature. The
requirement for total scattered light displacement noise can be stated with the following inequality:
n

i 1
2
 SNXXX 4  xs PSNi 
1



LhSRD
 DARM 

P0
10


The SNXXX/DARM scattered light noise transfer function ratios for various injection locations
within the IFO are shown in Figure 35: Scattered Light Noise Transfer Functions.
51
LIGO
LIGO- T1100445
Transfer Fcn Ratio [m]
10
10
10
10
10
–v5
-8
ETM
ITM HR
ITM AR
PRM
SRM
BS FROM PR
BS FROM SR
BS FROM ITM
-10
-12
-14
-16
10
1
10
2
10
3
10
4
Frequency [Hz]
Figure 35: Scattered Light Noise Transfer Functions
4.1.1 Scattered Light Parameters
The arm cavity power was taken from T070303 with an arm cavity gain of 13000 referenced to the
PSL input power of 125 W.
52
LIGO
LIGO- T1100445
–v5
 10
Motion of HEPI @ 200 Hz, m/rt Hz
xhepi  2 10
Motion of HAM table @ 100 Hz, m/rt Hz
xham  1.3 10
Motion of HAM flange @ 100 Hz, m/rt Hz
xhamflange  1.7 10
laser wavelength, m
  1.064 10
wave number, m^-1
k  2
IFO waist size, m
wifo  0.012
solid angle of IFO mode, sr
 ifo    
Transfer function @ 100 Hz, ITM AR
TFitmar  3.16 10
Transfer function @ 100 Hz, BS from SR
TFsrbs  4.46 10
 11
 11
6

6
k  5.905  10


  wifo 



2
9
 ifo  2.502  10
 11
 11
Ref. T070247
Transmissivity of ITM HR
Titmhr  0.014
Transmissivity of ETM HR
Tetm  5 10
ETM transmitted power, W
Petmtr  4.4
input laser power, W
Ppsl  125
arm cavity gain
Gac  13000
arm cavity power, W
Pa 
power in power recycling cavity both
W
arm, arms,
W
Prca
rc 
Gaussian power parameter
in recycling cavity
P0rc  Prca
Power recycling cavity gain
reflport
as
output
transmissivity
power
portafter
in
signal
signal
signal
signal
SRM,
power,
ratio
of
ratio
recycling
SRM
W WHRcavity, W
6
Ppsl
2
 Gac
2P
Pa Titmhr
44
2 Prca
Grc 
PPsrm
Psrc  psl
G
P
Tas

0.001080
PT

0.0010
Gsrmhr
G
Pas
refl
sc
srm
srmhr
psl
as0.200
psl
5
Pa  8.125  10
3
Prc 5.688
 10 3
rca 2.844  10
3
P0rc  2.844  10
Grc  45.5
Psrc
sc 0.135
53
LIGO
LIGO- T1100445
–v5
reflectivity of BS HR
Rbshr  0.50
reflectivity of BS AR
Rbsar  50 10
Reflectivity of ITM HR
Ritmhr  0.9860
Reflectivity of ITM AR
Ritmar  50 10
reflectivity of AS septum port
Rsp  0.0025
reflectivity of PR3 HR
Rpr3hr  0.9999
reflectivity of SR3
transmissivity
PR3
PR2
PRM
of SR3
PR3
PR2
PRM
AR
HR
HRHR
AR
AR
HR
AR
T
Rpr2hr
R
1
0.9999
10.212
10
RR
Tpr2ar
 T
50
50
10
pr3hr 
pr3hr
sr3hr
prmhr
pr3hr
pr3ar
pr2hr
prmar
prmhr
prmar
pr3ar
pr2ar
6
6
66
54
5
T
Rprmar
110.788
 10
pr3hr
prmhr
pr3ar  10
pr2ar
pr2hr
sr3hr
LIGO
LIGO- T1100445
–v5
5
reflectivity of SR3 AR
Rsr3ar  Rpr3ar
Rsr3ar  5  10
transmissivity of SR3 AR
Tsr3ar  Tpr3ar
Tsr3ar  1
reflectivity of SR2 HR
Rsr2hr  Rpr2hr
Rsr2hr  1
transmissivity of SR2 HR
Tsr2hr  Tpr2hr
Tsr2hr  10  10
reflectivity of SR2 AR
Rsr2ar  Rpr2ar
Rsr2ar  5  10
transmissivity of SR2 AR
Tsr2ar  Tpr2ar
Tsr2ar  0.99995
transmissivity of SRM HR
Tsrmhr  0.200
reflectivity of SRM HR
Rsrmhr  1  Tsrmhr
reflectivity of SRM AR
Rsrmar  50 10
transmissivity of SRM AR
Tsrmar  1  Rsrmar
Reflectivity of dichroic DCBS1
RDCBS1  0.99
Transmissivity of dichroic DCBS1
TDCBS1  1  RDCBS1
Reflectivity of viewport
Rvp  0.0025
Reflectivity of HWS mirrors
BRDF of dichroic
plate beam
chamber
viewport
mirror
DCBS1
wall,
dump,
sr^-1sr^-1
R
BRDF
0.005
0.1

0.005
0.01
0.05
HWSplatebd
mirror
DCBS1
wall
vp0.99
5
5
Rsrmhr  0.8
6
Tsrmar  1
55
LIGO
LIGO- T1100445
–v5
BRDF of lens
BRDFlens  1
Beam Waist after H2 SR3
wsr30  0.114 10
Beam waist after H2 SR2
wsr20  0.094 10
Beam waist after H2 VAC LENSX
wvaclensx0  0.42 10
Beam waist after H2 VAC LENSY
wvaclensy0  2.739 10
Beam Waist after H1 SR3
wsr30  0.114 10
Beam waist after H1 SR2
wsr20  0.096 10
Beam waist after H1 VAC LENSX
wvaclensx0  0.523 10
Beam waist after H1 VAC LENSY
wvaclensy0  0.152 10
reflectivity of FM HR
RFMhr  Rpr3hr
reflectivity of BS AR
Rbsar  5  10
Reflectivity of SR3
RSR3  0.9999
Reflectivity of dichroic DCBS1
RDCBS1  0.99
Transmissivity of dichroic DCBS1
TDCBS1  1  RDCBS1
Transmissivity
Reflectivity
transmissivity
of HWS
viewport
of
ofSR2
lens
mirrors
HR
R
Tvp
0.0025

0.99
0.005
 110
10
lens
HWS
sr2hr
3
3
3
3
3
3
3
3
RFMhr  1
5
5
56
Tlens  0.995
LIGO
LIGO- T1100445
–v5
4.1.2 BRDF of Baffle Surfaces
The baffle surfaces are oxidized polished stainless steel, with a measured BRDF < 0.03 sr^-1 @ > 5
deg incidence angle.
4.1.3 HAM ISI Seismic Motion
The seismic motion of the HAM ISI optical table at LLO and the HAM chamber viewport motions
are shown below in Figure 36.
57
LIGO
LIGO- T1100445
–v5
-8
10
L1HAMISI z
HAM6Flange
-9
10
-10
Displacement [m/rtHz]
10
-11
10
-12
10
-13
10
-14
10
-15
10
1
10
2
3
10
10
4
10
Frequency [Hz]
Figure 36: HAM optics table Seismic Motion, m/rtHz
4.1.4 Naming Convention for Wedged Optics
58
LIGO
LIGO- T1100445
–v5
Figure 37: Wedged Core Optic ghost beam naming convention
Figure 38: BS ghost beam naming convention
59
LIGO
LIGO- T1100445
–v5
4.1.5 SR3 HR Baffle Scatter
The SR3 HR Baffle catches ghost beams of order GB4 and higher, and the scattered light
displacement noise from these beams is negligible.
The scatter from the non-polished edge of the baffle hole is negligible, and the edge does not need
to be beveled.
4.1.6 SR3 AR Baffle Scatter
The SR3 AR Baffle catches 1) the transmission of the main through the SR3 AR surface and
scatters light back toward the BS, and 2) the SR3 GBAR3 ghost beam.
The scattered light displacement noise caused by scattering from the SR3 AR Baffle is calculated
below.
4.1.6.1 Transmission of Signal Recycling Cavity Main Beam through SR3 HR
The signal recycling cavity has two counter propagating beams that strike the SR3 HR surface.
power incident on SR3 AR Baffle
(forward and backward beams), W
Psr3arbaf  2Psrc Tsr3hr  Tsr3ar
4
Psr3arbaf  1.35  10
The beam incident from the BS is scattered by the SR3 AR Baffle back toward the BS, directly into
the mode of the IFO.
power scattered from SR3 AR Baffle toward BS, W
Psr3arbafbss 
Psr3arbaf
 BRDFbd   ifo Tsr3hr  Tsr3ar
2
 19
Psr3arbafbss  8.445  10
The beam incident from SR2 is scattered by the SR3 AR Baffle back toward SR2, into the mode of
the beam waist created by the SR3 mirror curvature.
power scattered from SR3 AR Baffle toward SR2 W
Psr3arbafsr2s 
Psr3arbaf
2
 BRDFbd   ifo 
wifo
2
2
 Tsr3hr  Tsr3ar
wsr30
 15
Psr3arbafsr2s  9.357  10
60
LIGO
LIGO- T1100445
–v5
The total power scattered is given by
power scattered from SR3 AR Baffle, W
Psr3arbafs  Psr3arbafbss  Psr3arbafsr2s
This scattered light from the signal recycling cavity enters the IFO mode through the BS; the
displacement noise is given by
0.5
 Psr3arbafs 
DNsr3arbaf  TFsrbs  
  xham 2 k
 Ppsl 
displacement noise @ 100 Hz, m/rtHz
 25
DNsr3arbaf  1.139  10
4.1.6.2 SR3 GBAR3 Ghost Beam
The SR3 GBAR3 ghost beams from the two counter propagating signal recycling cavity beams are
caught on the SR3 AR Baffle.
The scattered light displacement noise caused by scattering from the SR3 AR Baffle is calculated
below.
power incident on GBAR3 AR Baffle
(forward and backward beams), W
Psr3gbar3  2 Psrc Tsr3hr  Rsr3ar  Rsr3hr  Tsr3ar
9
Psr3gbar3  6.749  10
The GBAR3 beam incident from the BS is scattered back toward the BS, directly into the mode of
the IFO.
power scattered from SR3 AR Baffle toward BS, W
Psr3gbar3bss 
Psr3gbar3
2
 BRDFbd   ifo Tsr3hr  Rsr3ar  Rsr3hr  Tsr3ar
 27
Psr3gbar3bss  2.111  10
The other GBAR3 beam, incident from the SR2, scatters back toward SR2 into the mode of the
beam waist created by the SR3 mirror curvature.
61
LIGO
LIGO- T1100445
–v5
power scattered from SR3 AR Baffle toward SR2, W
Psr3gbar3sr2s 
Psr3gbar3
2
 BRDFbd   ifo 
wifo
2
2
 Tsr3hr  Rsr3ar  Rsr3hr  Tsr3ar
wsr30
 23
Psr3gbar3sr2s  2.339  10
The
total
power
scattered is given by:
total power scattered from SR3 AR Baffle, W
Psr3gbar3s  Psr3gbar3bss  Psr3gbar3sr2s
 23
Psr3gbar3s  2.339  10
This scattered light from the signal recycling cavity enters the IFO mode through the BS; the
displacement noise is given by
0.5
displacement noise @ 100 Hz, m/rtHz
 Psr3gbar3s 
DNsr3gbar3  TFsrbs  
  xham 2 k
Ppsl


 30
DNsr3gbar3  5.697  10
4.1.6.3 SR3 GBHR3 Ghost Beam
The SR3 GBHR3 ghost beams from the two counter propagating signal recycling cavity beams will
hit the mode cleaner tube wall and scatter back toward the signal recycling cavity.
power incident on SR3 GBHR3
(forward and backward beams), W
Psr3gbhr3  2 Psrc Tsr3hr  Rsr3ar  Tsr3hr
 13
Psr3gbhr3  6.75  10
The GBHR3 beam incident from the BS is scattered back toward the BS, directly into the mode of
the IFO.
62
LIGO
LIGO- T1100445
–v5
power scattered from SR3 GBHR3 toward BS, W
Psr3gbhr3
Psr3gbhr3bss 
2
 BRDFwall  ifo Tsr3hr  Rsr3ar  Tsr3hr
 35
Psr3gbhr3bss  4.223  10
The other GBHR3 beam, incident from the SR2, scatters back toward SR2 into the mode of the
beam waist created by the SR3 mirror curvature.
power scattered from SR3 GBHR3 toward SR2 W
Psr3gbhr3sr2s 
Psr3gbhr3
2
 BRDFwall  ifo 
wifo
2
2

 Tsr3hr  Rsr3ar  Tsr3hr

wsr30
 31
Psr3gbhr3sr2s  4.679  10
The total scattered power is given by
total power scattered from SR3 GBHR3
Psr3gbhr3s  Psr3gbhr3bss  Psr3gbhr3sr2s
 31
Psr3gbhr3s  4.68  10
This scattered light from the signal recycling cavity enters the IFO mode through the BS; the
displacement noise is given by
0.5
displacement noise @ 100 Hz, m/rtHz
 Psr3gbhr3s 
DNsr3gbhr3  TFsrbs  
  xhamflange 2 k
 Ppsl 
 31
DNsr3gbhr3  5.479  10
4.1.7 SR2 Scraper Baffle Scatter
The SR2 scraper baffles on HAM4, and HAM10 traps half of the ghost beams from the ITM, CP,
and BS; the other half of the ghost beams is trapped by the PR2 scraper baffles located on HAM3
and HAM9.
63
LIGO
LIGO- T1100445
–v5
The scatter from the non-polished edge of the baffle hole is negligible, and the edge does not need
to be beveled.
The scattered light displacement noise caused by scattering of the ghost beams from the SR2
Scraper Baffle is calculated below.
4.1.7.1 ITM Ghosts Beams
The X and Y ITM ghost beams are coherent but may have different phase. For the worst case, we
will assume that the fields add in phase.
ITM_GBAR1 H1
Pitmar1bd  Prc Rbshr  Ritmar
Power incident on SR2 Scraper Baffle from
both arms, W
Pitmar1bd  0.142
both ITM AR1 BD scattered power into BS
from SR2 Scraper baffle, W
wifo
Pitmar1bds  Pitmar1bd  BRDFbd 
2
0
2
  ifo  Rbshr  Ritmar
wsr30
 12
Pitmar1bds  9.857  10
0.5
 Pitmar1bds 
DNitmar1bd  TFsrbs  
  xham 2 k
Ppsl


displacement noise @ 100 Hz, m/rtHz
 24
DNitmar1bd  3.698  10
ITM_GBAR3 H1
power incident on SR2 Scraper Baffle from
both arms, W

2
Pitmar3bd  Prc Rbshr  Ritmhr  Ritmar  1  Ritmar
2
Pitmar3bd  0.1382
power scattered from SR2 Scraper Baffle, W
Pitmar3bds  Pitmar3bd  BRDFbd 
wifo
2
0
2
2

  ifo  Rbshr  Ritmhr  Ritmar  1  Ritmar
2
wsr30
 11
Pitmar3bds  1.009  10
64
LIGO
LIGO- T1100445
–v5
0.5
 Pitmar3bds 
DNitmar3bd  TFsrbs  
  xham 2 k
Ppsl


displacement noise @ 100 Hz, m/rtHz
 24
DNitmar3bd  3.595  10
4.1.7.2 BS Ghosts Beam
The beam splitter ghost beams from both arms are almost anti-resonant and the wave fronts
overlap; therefore, their coherent sum is reduced by the square of the asymmetry coefficient for
common mode field rejection.
BS_GBAR3P H1






Pbsar3sr2baf  Prc  1  Rbsar  Rbshr  1  Rbshr  Rbsar  Rbshr  1  Rbsar  Cassy


2
Pbsar3sr2baf  0.169
power scattered from SR2 Scraper Baffle, W
Pbsar3sr2bafs  Pbsar3sr2baf  BRDFbd 
wifo
2
2
wsr30






  ifo  1  Rbsar  Rbshr  Rbsar   1  Rbshr  Rbshr  1  Rbsar 


 12
Pbsar3sr2bafs  5.848  10
0.5
 Pbsar3sr2bafs 
displacement noise @ 100 Hz, m/rtHz DNbsar3sr2baf  TFitmar  
  xham 2 k
Ppsl


 24
DNbsar3sr2baf  2.018  10
4.1.7.3 CP Ghosts Beam
The X and Y CP ghost beams are coherent but may have different phase. For the worst case, we
will assume that the fields add in phase.
65
LIGO
LIGO- T1100445
–v5
4.1.7.3.1 CP_GBAR1 H1
power incident on SR2 Scraper Baffle from
both arms, W
Pcpar1sr2baf  Prc Rbshr  Rcpar
Pcpar1sr2baf  0.142
power scattered from SR2 Scraper Baffle, W
Pcpar1sr2bafs  Pcpar1sr2baf  BRDFbd 
wifo
2
0
2
  ifo  Rbshr  Rcpar
wsr30
 12
Pcpar1sr2bafs  9.857  10
0.5
displacement noise @ 100 Hz,
m/rtHz
 Pcpar1sr2bafs 
DNcpar1sr2baf  TFitmar  
  xham 2 k
Ppsl


 24
DNcpar1sr2baf  2.62  10
4.1.7.3.1.1 CP_GBAR3 H1
power incident on SR2 Scraper Baffle from
both arms, W
Pcpar3sr2baf  0.14
Pcpar3sr2baf  Prc Rbshr  Ritmhr  Rcpar
power scattered from SR2 Scraper Baffle, W
Pcpar3sr2bafs  Pcpar3sr2baf  BRDFbd 
wifo
2
0
 R
 Ritmhr  Rcpar
2 ifo bshr
wsr30
 12
Pcpar3sr2bafs  9.583  10
displacement noise @ 100 Hz, m/rtHz
66
LIGO
LIGO- T1100445
–v5
0.5
 Pcpar3sr2bafs 
DNcpar3sr2baf  TFitmar  
  xham 2 k
 24 Ppsl

DNcpar3sr2baf  2.583  10
4.1.7.4 Summary SR2 Scraper Baffle Scatter
-16
10
Thermal Noise
AOS Req
ITM GBAR1 SR2 Scraper Baf
ITM GBAR3 SR2 Scraper Baf
CP GBAR1 SR2 Scraper Baf
CP GBAR3 SR2 Scraper Baf
BS GBAR3P SR2 Scraper Baf
-18
Displacement [m/rtHz]
10
-20
10
-22
10
-24
10
1
2
10
3
10
Frequency [Hz]
10
Figure 39: SR2 Scraper Baffle Scatter
4.1.7.5 SRM GBAR3 Ghost Beam
The SRM GBAR3 ghost beam is caught on the input baffle of the Output Faraday; it will scatter
from the baffle toward the SRM and enter the signal recycling cavity.
power incident on SRM AR Baffle, W
Psrmarbaf  Psrm Rsrmar  Rsrmhr  Tsrmar
6
The GBAR3 beam is scattered Psrmarbaf  5.4  10
of the beam waist created by the SRM mirror transmission.
back toward SRM, into the mode
67
LIGO
LIGO- T1100445
–v5
power scattered from SRM AR Baffle, W
Psrmarbafs  Psrmarbaf  BRDFbd 
wifo
2
2
  ifo  Rsrmar  Rsrmhr  Tsrmar
wsrm0
 18
Psrmarbafs  5.502  10
The scattered light enters the IFO mode through SRM; the displacement noise is given by
0.5
 Psrmarbafs 
DNsrmarbafs  TFsrm 
  xham 2 k
 Ppsl 
displacement noise @ 100 Hz, m/rtHz
 26
DNsrmarbafs  2.614  10
4.1.7.6 SRM GBHR3 Ghost Beam
The SRM GBHR3 ghost beam is caught on the Mode Cleaner Tube Baffle; it will scatter from the
baffle back toward the SRM and enter the signal recycling cavity.
power of SRM GBHR3, W
Psrmhr3  Psrm Rsrmar  Tsrmhr
6
Psrmhr3  1.35  10
The SRM GBHR3 beam is scattered back toward SRM, into the mode of the beam waist created by
transmission through the SRM.
power scattered from SRM GBHR3 Mode Cleaner Tube
Baffle, W
Psrmhr3bafs  Psrmhr3 BRDFbd 
wifo
2
2
  ifo  Rsrmar  Tsrmhr
wsrm0
 19
Psrmhr3bafs  3.439  10
The scattered light enters the IFO mode through SRM; the displacement noise is given by
displacement noise @ 100 Hz, m/rtHz
68
LIGO
LIGO- T1100445
–v5
0.5
 Psrmhr3bafs 
DNsrmhr3bafs  TFsrm 
  xham 2 k
 Ppsl 
 27
DNsrmhr3bafs  6.536  10
4.1.7.7 Summary SR3, SR2, SRM Ghost
Beam Scatter
AOS Req
SRM GBAR3
SRM GBHR3
SR2 GBAR3
SR2 GBHR3
SR3 GBAR3
SR3 GBHR3
SR3 AR Baffle
-20
Displacement [m/rtHz]
10
-25
10
-30
10
-35
10
1
2
10
3
10
10
4
10
Frequency [Hz]
Figure 40: Summary of SR Ghost Beam Scatter
4.1.8 H2 Hartmann Y Scatter
The 1064nm power recycling cavity beam from the Y-arm follows the Hartmann Y path: 1)
reflection from the BS AR, 2) reflection from mirror HWSYM1, 3) reflection from mirror
HWSYM2, 4) reflection from HWSYM3, 5) transmission through dichroic filter DCBS1Y, 6) and
transmission through VAC LENSY; see Figure 7. The scattered light enters the IFO mode through
the ITMY AR surface.
4.1.8.1 Scattered Light Displacement Noise from H2 HWSYM1
The Hartmann Y beam will scatter from the HWSYM1 mirror back toward the ITM AR, into the
mode of the beam waist created by the SR3 mirror.
69
LIGO
LIGO- T1100445
–v5
H2 HWSY M1
power incident on HWSY M1, W
Phwsym1  Rbsar  Prca
Phwsym1  0.142
power scattered from HWSY M1, W
wifo
Phwsym1s  Rbsar  Phwsym1 BRDFmirror 
2
2
  ifo
wh2sr30
 13
Phwsym1s  9.857  10
The scattered light enters the IFO mode through the ITM AR side; the displacement noise is given
by
displacement noise @ 100 Hz, m/rtHz
0.5
 Phwsym1s 
DNhwsym1sifo  TFitmar  
  xham 2 k
Ppsl


 24
DNhwsym1sifo  1.226  10
The scattered light displacement noise caused by scatter from the HWSYM1 mirror is marginally
acceptable with an assumed BRDF = 0.005 sr^-1.
4.1.8.2 Scattered Light Displacement Noise from H2 HWSYM2
The Hartmann Y beam will scatter from the HWSYM2 mirror back toward the ITM AR into the
mode of the beam waist created by the SR3 mirror.
H2 HWSY M2
power incident on HWSY M2, W
Phwsym2  RHWS Rbsar  Prca
Phwsym2  0.141
power scattered
from HWSY M2, W
70
LIGO
LIGO- T1100445
–v5
Phwsym2s  RHWS Rbsar  Phwsym2 BRDFmirror 
wifo
2
2
  ifo
wh2sr30
 13
Phwsym2s  9.66  10
The scattered light enters the IFO mode through the ITM AR side; the displacement noise is given
by
displacement noise @ 100 Hz, m/rtHz
0.5
 Phwsym2s 
DNhwsym2sifo  TFitmar  
  xham 2 k
Ppsl


 24
DNhwsym2sifo  1.214  10
4.1.8.3 Scattered Light Displacement Noise from H2 HWSYM3
The Hartmann Y beam will scatter from the H2 HWSYM3 mirror back toward the ITM AR into
the mode of the beam waist created by the SR3 mirror.
power incident on HWSY M3, W
Phwsym3  RHWS RHWS Rbsar  Prca
Phwsym3  0.139
power scattered from HWSY M3, W
Phwsym3s  RHWS RHWS Rbsar  Phwsym3 BRDFmirror 
wifo
2
2
  ifo
wh2sr30
 13
Phwsym3s  9.468  10
71
LIGO
LIGO- T1100445
–v5
The scattered light enters the IFO mode through the ITM AR side; the displacement noise is given
by
displacement noise @ 100 Hz, m/rtHz
0.5
 Phwsym3s 
DNhwsym3sifo  TFitmar  
  xham 2 k
 Ppsl 
 24
DNhwsym3sifo  1.202  10
4.1.8.4 Scattered Light Displacement Noise from H2 DCBS1Y
The Hartmann Y beam will scatter from the H2 DCBS1Y filter back toward the ITM AR into the
mode of the beam waist created by the SR3 mirror.
H2 DCBS1Y
power incident on DCBS1Y, W
Pdcbs1y  RHWS RHWS RHWS Rbsar  Prca
Pdcbs1y  0.138
power scattered from DCBS1Y, W
Pdcbs1ys  RHWS RHWS RHWS Rbsar  Pdcbs1y  BRDFDCBS1
wifo
2
2
  ifo
wh2sr30
 12
Pdcbs1ys  1.856  10
The scattered light enters the IFO mode through the ITM AR side; the displacement noise is given
by
displacement noise @ 100 Hz, m/rtHz
0.5
 Pdcbs1ys 
DNdcbs1ysifo  TFitmar  
  xham 2 k
Ppsl


 24
DNdcbs1ysifo  1.19  10
72
LIGO
LIGO- T1100445
–v5
4.1.8.5 Scattered Light Displacement Noise from H2 VAC LENSY
The Hartmann Y beam will scatter from the H2 DCBS1Y filter back toward the ITM AR into the
mode of the beam waist created by the SR3 mirror.
H2 VAC LENSY
power incident on H2 VAC LENSY, W
Ph2vaclensy  TDCBS1 RHWS RHWS RHWS Rbsar  Prca
3
Ph2vaclensy  1.38  10
power scattered from VAC LENSY, W
Ph2vaclensys  TDCBS1 RHWS RHWS RHWS Rbsar  Ph2vaclensy  BRDFlens 
wifo
2
2
  ifo
wh2sr30
 14
Ph2vaclensys  1.856  10
The scattered light enters the IFO mode through the ITM AR side; the displacement noise is given
by
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph2vaclensys 
DNh2vaclensysifo  TFitmar  
  xham 2 k
Ppsl


 25
DNh2vaclensysifo  1.683  10
The lens should be tilted to avoid a direct specular reflection back toward the incident beam. A near
normal incidence BRDF = 1 sr^-1 was assumed for the calculation, which will probably require an
incidence angle > 0.5 deg. A low-scattering lens surface finish and AR coating should be used to
minimize the scattering.
4.1.8.6 H2 Hartmann Y Viewport Scatter
The Hartmann Y beam will scatter from the HAM chamber viewport back toward the ITM AR
surface, into the mode of the beam waist created by the H2 VAC LENSY.
73
LIGO
LIGO- T1100445
–v5
H2 Hartmann Y viewport scatter
power incident on Hartmann X viewport, W


Ph2hyvp  Tlens  TDCBS1 RHWS RHWS RHWS Rbsar  Prca
3
Ph2hyvp  1.373  10
power scattered from Hartmann Y viewport, W
Ph2hyvps  Tlens  TDCBS1 RHWS RHWS RHWS Rbsar  Ph2hyvp  BRDFvp 
wifo
2
2
  ifo
wh2vaclensy0
 19
Ph2hyvps  1.592  10
The scattered light enters the IFO mode through the ITM AR side; the displacement noise is given
by
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph2hyvps 
DNh2hyvpsifo  TFitmar  
  xhamflange 2 k
 Ppsl 
 25
DNh2hyvpsifo  2.264  10
4.1.8.7 H2 Hartmann Y Viewport Reflection, HAM Chamber Scatter
Part of the Hartmann Y beam will reflect from the HAM chamber viewport and scatter from the
chamber wall back toward the ITM AR surface into the mode of the beam waist created by the H2
VAC LENSY mirror.
The scattered light enters the IFO mode through the ITM AR side; the displacement noise is given
by
74
LIGO
LIGO- T1100445
–v5
H2 Hartmann Y viewport reflected wall scatter
power incident on Hartmann X viewport reflected wall, W
Prc
Ph2hyvprwall  Rvp Tlens  TDCBS1 RHWS RHWS RHWS Rbsar 
2
6
Ph2hyvprwall  3.432  10
power scattered from Hartmann Y viewport
reflected wall, W
Ph2hyvprwalls  Rvp  Tlens  TDCBS1 RHWS RHWS RHWS Rbsar  Ph2hyvprwall  BRDFwall
wifo
2
2
  ifo
wh2vaclensy0
 23
Ph2hyvprwalls  1.989  10
The scattered light enters the IFO mode through the ITM AR side; the displacement noise is given
by
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph2hyvprwalls 
DNh2hyvprwallsifo  TFitmar  
  xhamflange 2 k
Ppsl


 27
DNh2hyvprwallsifo  2.531  10
The scattered light from the viewport reflection is negligible, and therefore no reflected viewport
beam dumps are needed!
4.1.8.8 Summary of H2 Hartmann Y Scatter
75
LIGO
LIGO- T1100445
–v5
-18
10
SRD Req
AOS Req
H2 HWSY M1
H2 HWSY M2
H2 HWSY M3
H2 DCBSY
H2 VACLENSY
H2 HartmannY VP
H2 HartmannY VP REFL
-20
10
-22
Displacement [m/rtHz]
10
-24
10
-26
10
-28
10
-30
10
1
2
10
3
10
10
4
10
Frequency [Hz]
Figure 41: Summary of H2 Hartmann Y Surfaces Scatter
4.1.9 H2 Hartmann X Scatter
The 1064nm signal recycling cavity beam transmitted through the BS from the X-arm follows the
Hartmann X path 1) transmission through the SR2 AR, 2) reflection from mirror H2 HWSXM1, 3)
transmission through dichroic filter H2 DCBS1X, 4) transmission through H2 VAC LENSX, 5)
reflection from mirror H2 HWSXM2, and 6) reflection from mirror H2 HWSXM3.
4.1.9.1 Scattered Light Displacement Noise from H2 HWSXM1
The Hartmann X beam will scatter from the HWSXM1 mirror back toward the BS, into the mode
of the beam waist created by the SR2 mirror.
76
LIGO
LIGO- T1100445
–v5
H2 HWSX M1
power incident on H2 HWSX M1, W
Ph2hwsxm1  Tsr2hr  Psrc
5
Ph2hwsxm1  6.75  10
power scattered from H2 HWSX M1, W
Ph2hwsxm1s  Tsr2hr  Ph2hwsxm1 BRDFmirror 
wifo
2
2
  ifo
wh2sr20
The scattered light enters the IFO mode from the signal recycling cavity through the BS AR side;
the displacement noise is given by
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph2hwsxm1s 
DNh2hwsxm1sifo  TFsrbs  
  xham 2 k
Ppsl


 26
DNh2hwsxm1sifo  6.467  10
The scattered light displacement noise caused by scatter from the HWSYM1 mirror is acceptable
with an assumed BRDF = 0.005 sr^-1.
4.1.9.2 Scattered Light Displacement Noise from H2 DCBS1X
The Hartmann X beam will scatter from the H2 DCBS1X filter back toward the BS, into the mode
of the beam waist created by the SR2 mirror.
H2 DCBS1X
power incident on H2DCBS1X, W
Ph2dcbs1x  RHWS Tsr2hr  Psrc
77
LIGO
LIGO- T1100445
–v5
5
Ph2dcbs1x  6.682  10
power scattered from DCBS1X, W
Ph2dcbs1xs  RHWS Tsr2hr  Psrc Ph2dcbs1x BRDFDCBS1
wifo
2
2
  ifo
wh2sr20
 15
Ph2dcbs1xs  1.821  10
The scattered light enters the IFO mode from the signal recycling cavity through the BS AR side;
the displacement noise is given by
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph2dcbs1xs 
DNh2dcbs1xsifo  TFsrbs  
  xham 2 k
Ppsl


 26
DNh2dcbs1xsifo  5.26  10
4.1.9.3 Scattered Light Displacement Noise from H2 VAC LENSX
The Hartmann Y beam will scatter from the H2 VAC LENSX lens back toward the ITM AR into
the mode of the beam waist created by the SR3 mirror.
78
LIGO
LIGO- T1100445
–v5
H2 VAC LENSX
power incident on H2 VAC LENSX, W
Ph2vaclensx  TDCBS1 RHWS Tsr2hr  Psrc
7
Ph2vaclensx  6.682  10
power scattered from VAC LENSX, W
Ph2vaclensxs  TDCBS1 RHWS Tsr2hr  Ph2vaclensx BRDFlens 
wifo
2
2
  ifo
wh2sr20
 17
Ph2vaclensxs  2.698  10
The scattered light enters the IFO mode from the signal recycling cavity through the BS AR side;
the displacement noise is given by
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph2vaclensxs 
DNh2vaclensxsifo  TFsrbs  
  xham 2 k
Ppsl


 27
DNh2vaclensxsifo  9.055  10
The lens should be tilted to avoid a direct specular reflection back toward the incident beam. A near
normal incidence BRDF = 1 sr^-1 was assumed for the calculation, which will probably require an
incidence angle > 0.5 deg. A low-scattering lens surface finish and AR coating should be used to
minimize the scattering.
4.1.9.4 Scattered Light Displacement Noise from H2 HWSXM2
The Hartmann X beam will scatter from the HWSXM2 mirror back toward the BS, into the mode
of the beam waist created by the H2 VAC LENSX.
79
LIGO
LIGO- T1100445
–v5
H2 HWSX M2
Ph2hwsxm2  Tlens  TDCBS1 RHWS Tsr2hr  Psrc
power incident on H2 HWSX M2, W
7
Ph2hwsxm2  6.649  10
power scattered from H2 HWSX M2, W
Ph2hwsxm2s  Tlens  TDCBS1 RHWS Tsr2hr  Ph2hwsxm2 BRDFmirror 
wifo
2
2
  ifo
wh2vaclensx0
 21
Ph2hwsxm2s  6.69  10
The scattered light enters the IFO mode from the signal recycling cavity through the BS AR side;
the displacement noise is given by
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph2hwsxm2s 
DNh2hwsxm2sifo  TFsrbs  
  xham 2 k
Ppsl


 28
DNh2hwsxm2sifo  1.426  10
A laser quality mirror with a BRDF < 5E-3 sr^-1 will suffice.
4.1.9.5 H2 Scattered Light Displacement Noise from H2 HWSXM3
The Hartmann X beam will scatter from the H2 HWSXM2 mirror back toward the BS, into the
mode of the beam waist created by the H2 VAC LENSX.
80
LIGO
LIGO- T1100445
–v5
H2 HWSX M3
power incident on H2 HWSX M3, W
Ph2hwsxm3  RHWS Tlens  TDCBS1 RHWS Tsr2hr  Psrc
7
Ph2hwsxm3  6.583  10
power scattered from H2 HWSX M3, W
Ph2hwsxm3s  RHWS Tlens  TDCBS1 RHWS Tsr2hr  Ph2hwsxm3 BRDFmirror 
wifo
2
2
  ifo
wh2vaclensx0
 21
Ph2hwsxm3s  6.557  10
The scattered light enters the IFO mode from the signal recycling cavity through the BS AR side;
the displacement noise is given by
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph2hwsxm3s 
DNh2hwsxm3sifo  TFsrbs  
  xham 2 k
Ppsl


 28
DNh2hwsxm3sifo  1.412  10
A laser quality mirror with a BRDF < 5E-3 sr^-1 will suffice.
4.1.9.6 H2 Hartmann X Viewport Scatter
The Hartmann X beam will scatter from the HAM chamber viewport back toward the BS, into the
mode of the beam waist created by the H2 VAC LENSX.
81
LIGO
LIGO- T1100445
–v5
H2 Hartmann X viewport scatter
power incident on H2 Hartmann X viewport, W
Ph2hxvp  RHWS RHWS Tlens  TDCBS1 RHWS Tsr2hr  Psrc
7
Ph2hxvp  6.517  10
power scattered from Hartmann X viewport, W
Ph2hxvps  RHWS RHWS Tlens  TDCBS1 RHWS Tsr2hr  Ph2hxvp  BRDFvp 
wifo
2
2
  ifo
wh2vaclensx0
 21
Ph2hxvps  6.426  10
The scattered light enters the IFO mode from the signal recycling cavity through the BS AR side;
the displacement noise is given by
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph2hxvps 
DNh2hxvpsifo  TFsrbs  
  xhamflange 2 k
Ppsl


 26
DNh2hxvpsifo  6.421  10
4.1.9.7 H2 Hartmann X Viewport Reflection, HAM Chamber Scatter
Part of the Hartmann X beam will reflect from the HAM chamber viewport and scatter from the
chamber wall back toward the BS, into the mode of the beam waist created by the H2 VAC
LENSX.
82
LIGO
LIGO- T1100445
–v5
Hartmann X viewport reflected wall scatter
power incident on Hartmann X viewport reflected wall, W
Ph2hxvprwall  Rvp RHWS RHWS Tlens  TDCBS1 RHWS Tsr2hr  Psrc
9
Ph2hxvprwall  1.629  10
power scattered from Hartmann X viewport
reflected wall, W
Ph2hxvprwalls  Rvp  RHWS RHWS Tlens  TDCBS1 RHWS Tsr2hr  Ph2hxvprwall  BRDFwall
wifo
2
2
  ifo
wh2vaclensx0
 25
Ph2hxvprwalls  8.033  10
The scattered light enters the IFO mode from the signal recycling cavity through the BS AR side;
the displacement noise is given by
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph2hxvprwalls 
DNh2hxvprwallsifo  TFsrbs  
  xhamflange 2 k
Ppsl


 28
DNh2hxvprwallsifo  7.179  10
The scattered light from the viewport reflection is negligible, and therefore no reflected viewport
beam dumps are needed!
4.1.9.8 Summary of H2 Hartmann X Scatter
83
LIGO
LIGO- T1100445
–v5
-18
10
SRD Req
AOS Req
H2 HWSX M1
H2 DCBS1X
H2 VACLENSX
H2 HWSX M2
H2 HWSX M3
H2 HartmannX VP
H2 HartmannX VP REFL
-20
10
-22
Displacement [m/rtHz]
10
-24
10
-26
10
-28
10
-30
10
1
10
2
3
10
10
4
10
Frequency [Hz]
Figure 42: Summary of H2 Hartmann X Surfaces Scatter
4.1.10 H1 & L1 Hartmann Beam Scatter
The scattered light displacement noise calculations for H1, and L1 are similar to those presented for
H2. The results of the calculations will be presented in the following.
4.1.10.1 H1 & L1 Hartmann X Arm
The 1064nm power recycling cavity beam from the X-arm follows the Hartmann X path: 1)
reflection from the BS AR, 2) reflection from mirror HWSXM1, 3) reflection from mirror
HWSXM2, 4) 4) reflection from HWSXM3, 5) transmission through dichroic filter DCBS1X, 6)
and transmission through VAC LENSX; see Figure 7. The scattered light enters the IFO mode
through the ITMX AR surface.
84
LIGO
LIGO- T1100445
–v5
H1 HWSX M1
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1hwsxm1s 
DNh1hwsxm1sifo  TFitmar  
  xham 2 k
Ppsl


 24
DNh1hwsxm1sifo  1.226  10
H1 HWSX M2
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1hwsxm2s 
DNh1hwsxm2sifo  TFitmar  
  xham 2 k
Ppsl


 24
DNh1hwsxm2sifo  1.214  10
H1 HWSX M3
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1hwsxm3s 
DNh1hwsxm3sifo  TFitmar  
  xham 2 k
Ppsl


 24
DNh1hwsxm3sifo  1.202  10
H1 DCBS1X
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1dcbs1xs 
DNh1dcbs1xsifo  TFitmar  
  xham 2 k
 Ppsl 
 24
DNh1dcbs1xsifo  1.683  10
The scattered light displacement noise
85
LIGO
LIGO- T1100445
–v5
caused by scatter from the HWSYM1, 2, and 3 mirrors and the H1 DCBS1X filter is acceptable
with an assumed BRDF = 0.005 sr^-1.
H1 VAC LENSX
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1vaclensxs 
DNh1vaclensxsifo  TFitmar  
  xham 2 k
Ppsl


 25
DNh1vaclensxsifo  1.683  10
The lens should be tilted to avoid a direct specular reflection back toward the incident beam. A near
normal incidence BRDF = 1 sr^-1 was assumed for the calculation, which will probably require an
incidence angle > 0.5 deg. A low-scattering lens surface finish and AR coating should be used to
minimize the scattering.
H1 Hartmann X viewport scatter
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1hxvps 
DNh1hxvpsifo  TFitmar  
  xhamflange 2 k
Ppsl


 24
DNh1hxvpsifo  1.186  10
H1 Hartmann X viewport reflected wall scatter
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1hxvprwalls 
DNh1hxvprwallsifo  TFitmar  
  xhamflange 2 k
Ppsl


 26
DNh1hxvprwallsifo  1.326  10
The scatter from the viewport and the reflected wall scatter is negligible.
86
LIGO
LIGO- T1100445
–v5
4.1.10.2 Summary of H1 & L1 Hartmann X Scatter
-18
10
SRD Req
AOS Req
H1 HWSX M1
H1 HWSXM2
H1 HWSXM3
H1 DCBS1X
H1 VACLENSX
H1 HartmannX VP
HartmannX VP REFL
-20
10
-22
Displacement [m/rtHz]
10
-24
10
-26
10
-28
10
-30
10
1
10
2
3
10
10
4
10
Frequency [Hz]
Figure 43: Summary of H1 & L1 Hartmann X
4.1.10.3 H1 & L1 Hartmann Y Arm
The 1064nm signal recycling cavity beam transmitted through the BS from the Y-arm follows the
Hartmann Y path 1) transmission through the SR2 AR, 2) reflection from mirror H2 HWSYM1, 3)
reflection from mirror H2 HWSYM2, 4) transmission through dichroic filter H2 DCBS1Y, 5)
transmission through H2 VAC LENSY, and 6) reflection from mirror H2 HWSYM3, as seen in
Figure 1. The scattered light enters the IFO mode through the BS AR from the signal recycling
cavity side.
87
LIGO
LIGO- T1100445
–v5
H1 HWSY M1
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1hwsym1s 
DNh1hwsym1sifo  TFsrbs  
  xham 2 k
Ppsl


 26
DNh1hwsym1sifo  6.333  10
H1 HWSY M2
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1hwsym2s 
DNh1hwsym2sifo  TFsrbs  
  xham 2 k
Ppsl


 26
DNh1hwsym2sifo  6.269  10
H1 DCBS1Y
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1dcbs1ys 
DNh1dcbs1ysifo  TFsrbs  
  xham 2 k
Ppsl


 26
DNh1dcbs1ysifo  7.211  10
The scattered light displacement noise caused by scatter from the HWSYM1, 2 mirrors and the H1
DCBS1Y filter is acceptable with an assumed BRDF = 0.005 sr^-1.
H1 VAC LENSY
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1vaclensys 
DNh1vaclensysifo  TFsrbs  
  xham 2 k
Ppsl


 27
DNh1vaclensysifo  8.777  10
88
LIGO
LIGO- T1100445
–v5
The lens should be tilted to avoid a direct specular reflection back toward the incident beam. A near
normal incidence BRDF = 1 sr^-1 was assumed for the calculation, which will probably require an
incidence angle > 0.5 deg. A low-scattering lens surface finish and AR coating should be used to
minimize the scattering.
H1 HWSY M3
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1hwsym3s 
DNh1hwsym3sifo  TFsrbs  
  xham 2 k
Ppsl


 28
DNh1hwsym3sifo  3.9  10
A laser quality mirror with a BRDF < 5E-3 sr^-1 will suffice.
H1 Hartmann Y viewport scatter
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1hyvps 
DNh1hyvpsifo  TFsrbs  
  xhamflange 2 k
 Ppsl 
 25
DNh1hyvpsifo  1.774  10
H1 Hartmann Y viewport reflected wall scatter
displacement noise @ 100 Hz, m/rtHz
0.5
 Ph1hyvprwalls 
DNh1hyvprwallsifo  TFsrbs  
  xhamflange 2 k
Ppsl


 27
DNh1hyvprwallsifo  1.984  10
Hartmann viewport scatter, and Hartmann viewport reflected wall scatter are negligible because the
incident power has been attenuated by the dichroic filter and the AR surface of the viewport.
4.1.10.4 Summary of H1 & L1 Hartmann Y Scatter
89
LIGO
LIGO- T1100445
–v5
-18
10
SRD Req
AOS Req
H1 HWSYM1
H1 HWSYM2
H1 DCBS1Y
H1 VACLENSY
H1 HWSYM3
H1 HartmannY VP
H1 HartmannY VP REFL
-20
10
-22
Displacement [m/rtHz]
10
-24
10
-26
10
-28
10
-30
10
1
10
2
3
10
10
4
10
Frequency [Hz]
Figure 44: Summary of H1 & L1 Hartmann Y Scatter
5 INTERFACE CONTROL DOCUMENT
The mechanical and optical interfaces of the Signal Recycling Cavity Baffles are described in
E1100xxx TBD Signal Recycling Cavity Baffle Interface Control Document.
90