T1300403 Wide Angle Scatter from ETM
8-20-12
Displacement noise requirement @ 100 Hz, m/rt Hz
Motion of manifold @ 100 Hz, m/rt Hz
motion of ACB @ 100 Hz, m/rtHz
motion of ISI optical table @ 100 Hz, m/rtHz
Transfer function @ 100 Hz, ITM HR
BRDF of chamber wall, sr^-1
BRDF of oxidized un-polished steel, sr^-1
laser wavelength, m
wave number, m^-1
wide angle hemispherical scattering loss fraction from TM wide, ref: T070089
see T070303 with arm cavity gain = 13000
arm power, W
input laser power, W
arm cavity length, m
The following data comes from ZEMAX sensor data; see /ALIGO/SLC/ACB ETM power summary.xlsx
SCATTER PATH LENGTH
distance from spool 7A2, m
distance from PCal structure, m
distance from BSC bottom, m
distance from BSC front, m
distance from BSC back, m
distance from SUS mid, m
distance from ACB PLATE Top ETM, m
distance from ACB PLATE Bottom ETM, m
distance from ACB PLATE 2 ETM, m
distance from ACB PLATE 3 ETM, m
distance from ACB PLATE 4 ETM, m
distance from ACB PLATE 5 ETM, m
distance from ACB PLATE 6 ETM, m
distance from ACB PLATE 7 ETM, m
distance from peak and cabling, m
distance from ETM to WIDE ANGLE BAF TOP LEDGE ITMX, m
distance from ETM to WIDE ANGLE BAF BOTTOM LEDGE ETM m
distance from WIDE ANGLE BAF SIDE right, m
distance from WIDE ANGLE BAF SIDE left, m
SCATTER ANGLE
angle from spool 7A2, rad
angle from PCal structure, rad
angle from BSC bottom, rad
angle from BSC front, rad
angle from BSC back, rad
angle from SUS mid, rad
angle from ACB PLATE Top ETM, rad
angle from ACB PLATE Bottom ETM, rad
angle from ACB PLATE 2 ETM, rad
angle from ACB PLATE 3 ETM, rad
angle from ACB PLATE 4 ETM, rad
angle from ACB PLATE 5 ETM, rad
angle from ACB PLATE 6 ETM, rad
angle from ACB PLATE 7 ETM, rad
angle from peak and cabling, m
angle from ETM to WIDE ANGLE BAF TOP LEDGE ITMX, rad
angle from ETM to WIDE ANGLE BAF BOTTOM LEDGE ETM, rad
angle from WIDE ANGLE BAF SIDE right, rad
angle from WIDE ANGLE BAF SIDE left, rad
FRACTION of LAMBERTIAN SCATTER FROM COC HITTING SURFACE
fractional power from spool 7A2, W
fractional power hitting PCal structure, W
fractional power passing through hole in ACB, W
fractional power from BSC bottom, W
fractional power from BSC front, W
fractional power from BSC back, W
fractional power from SUS mid, W
fractional power from ACB PLATE Top ETM, W
fractional power from ACB PLATE Bottom ETM, W
fractional power from ACB PLATE 2 ETM, W
fractional power from ACB PLATE 3 ETM, W
fractional power from ACB PLATE 4 ETM, W
fractional power from ACB PLATE 5 ETM, W
fractional power from ACB PLATE 6 ETM, W
fractional power from ACB PLATE 7 ETM, W
fractional power hitting ACB box, W
fractional power from ETM to WIDE ANGLE BAF TOP LEDGE ITMX, W
fractional power from ETM to WIDE ANGLE BAF BOTTOM LEDGE ETM, W
fractional power from WIDE ANGLE BAF SIDE right, W
fractional power from WIDE ANGLE BAF SIDE left, W
fractional power hitting ACB plus wide angle box, W
INCIDENT POWER
incident power from spool 7A2, W
incident power hitting PCal structure, W
incident power from BSC bottom, W
incident power from BSC front, W
incident power from BSC back, W
incident power from SUS mid, W
incident power from ACB PLATE Top ETM, W
incident power from ACB PLATE Bottom ETM, W
incident power from ACB PLATE 2 ETM, W
incident power from ACB PLATE 3 ETM, W
incident power from ACB PLATE 4 ETM, W
incident power from ACB PLATE 5 ETM, W
incident power from ACB PLATE 6 ETM, W
incident power from ACB PLATE 7 ETM, W
incident power from ETM to WIDE ANGLE BAF TOP LEDGE ITMX, W
incident power from ETM to WIDE ANGLE BAF BOTTOM LEDGE ETM, W
incident power from WIDE ANGLE BAF SIDE right, W
incident power from WIDE ANGLE BAF SIDE left, W
POWER SCATTERED INTO IFO MODE
Lambertian scatter function for the TM
differential wide angle scattered light from TM onto adjacent surfaces
total wide angle scattered light from TM onto each adjacent surfaces
ZEMAX power fraction
incident power hitting the adjacent surface is
irradiance of TM by power scattered from adjacent surface, W/m^2
Flanagan-Thorne scattering cross-section
power scattered by TM into IFO mode
incident power hitting the adjacent surface is
combining these equations, we get
spool 7A2, W
PCal structure, W
BSC bottom, W
BSC front, W
BSC back, W
SUS mid, W
ACB PLATE TOP ETM, W
ACB PLATE Bottom ETM, W
ACB PLATE 2 ETM, W
ACB PLATE 3 ETM, W
ACB PLATE 4 ETM, W
ACB PLATE 5 ETM, W
ACB PLATE 6 ETM, W
ACB PLATE 7 ETM, W
WIDE ANGLE BAF TOP LEDGE ITMX, W
WIDE ANGLE BAF BOTTOM LEDGE ETM, W
WIDE ANGLE BAF SIDE right W
WIDE ANGLE BAF SIDE left, W
DIFFUSE SCATTERING FROM PEEK AND CABLING
length of cabling, m
diameter of cabling, m
frontal area of cabling, m^2
diameter of peek end cap, m
number of peek end caps
total area of scattering surfaces, m^2
frontal area of ACB, m^2
Incident Power, W
PEEK AND CABLING, W
Power Scattered into IFO Mode, W
PEEK AND CABLING, W
TOTAL ACB BACK, W
TOTAL ACB BACK AND BOX, W
TOTAL BSC Walls, W
DISPLACEMENT NOISE @ 100 Hz, m/rtHz
Displacement Noise Requirement @ 100 Hz, m/rt Hz
Amplitude spectral density of sine phase fluctuations of the injected field
displacement noise according to Flanagan-Thorne
displacement noise using Smith_Yamamoto formalism
where the factor 1/rt2 was added to correct for the slow phase motion that is below the gravity wave band
The two different approaches give results within < 5%
TOTAL ACB BACK AND BOX
SUS
TOTAL BSC Walls
spool 7A2
PCal structure