Summary: I attempt to roughly rank the DARM noise contribution from glints seen in photographs taken from the point of view of beam spots on various optics, in order to inform decisions on stray light mitigation. This ranking is based on the assumption that many of the locations that retro-reflect light scattered from a beam spot similarly reflect the camera flash. The glints are weighted according to estimates of the power on the optic, of the coupling of scattered light to DARM at that location, of the fraction of light scattered towards the glint site, given by updated estimates of optic BRDF, estimates of the solid angle of the glint, and estimates of the distance to and motion of the reflector. The highest ranked glint was the glint from the pre-mitigated P-Cal periscope, suggesting that the ranking is reasonable. The next highest rankings were glints from the arm cavity baffles, reduction flanges near the ITM optical levers, BS chamber walls, and possibly certain valve seats. This ranking does not account for beamed light from ghost beams, or light that is scattered at one optic and recombines at another optic.
Introduction
A potential source of scattering noise is light that is scattered from the beam spot on an optic to a moving reflector, which then reflects the light back to the same beam spot where it can recombine with the main beam and produce noise as the phase varies with the optical path length. To inventory potential reflectors, I take what I call beam-spot photos, taken with a camera as near as possible to the beam spot so that the photograph records potential scattered light paths, especially those that would reflect light back to the beam spot. Here I attempt to inform the priorities for stray light mitigation by roughly ranking the glints in the beam-spot photos according to how much noise they might produce in DARM.
I use a small camera that can easily and safely be held right in front of the beam spot position on an optic. The flash on the camera is located right next to the aperture so that the light emitted and the light received are at similar locations near the beam spot. The camera is an underwater camera that can be immersed for cleaning.
Of course, there are several differences between the flash and the light scattered from the beam spot. First, the flash and camera image sensors are broad-band while we care about scattered light at the laser frequency. Thus, the flashes are useful for spotting metal and other broad-band reflectors, but the reflection is reduced for narrow band reflectors like many of our optics. Second, the laser light scattered by the optic has a strong angular dependence, while the camera flash is designed to provide uniform illumination.
The glints are ranked according to a weighting factor. I attempt to account for the difference in the angular distribution of the scattered light from the laser and the camera flash by assuming that the flash is uniform and by estimating the BRDF of the optic and incorporating this and the angle to the glint in the weighting factor. The BRDF value is squared in order to account for scattering from the optic and recombination of the retro-reflected light at the optic. The squared distance to the reflector is included to account for the geometrical attenuation of the light from the beam spot.
The weighting factor also includes a rough estimate of the transfer function of scattered light to DARM for the point at which the scattered light is re-injected. The estimate used here is the value of the transfer function at 100 Hz from figures 1 and 2 of https://dcc.ligo.org/DocDB/0008/P1000002/001/P1000002-v1_MG12_scattered%20light%20control.pdf
In addition, the weighting factor includes weights for the relative power of the beam on the optic, and the solid angle of the glint in the photograph. However, I do not account for saturation in the images and variation between pixels: the power/steradian of all glints identified in the photographs are assumed to be equal. While this is not very accurate, I think it is a reasonable first step, considering that other factors, like the transfer functions, cause many orders of magnitude variation in the weighting factors. Eventually it would be nice to calibrate the relationship between pixel values in the photograph and the power incident on the pixel sensor, but I haven’t done that yet (it might make sense to flash in IR before getting to this stage). Finally, the weighting factor includes a rough estimate of the relative motion of the reflector, and assumes that the motion coupling is in a linear regime.
So, at present the rough weighting factor is:
Weight = BRDF^2 * transfer-to-DARM * relative-power-on-optic * steradians-of-glint * reflector-motion * normalization-factor / distance-optic-to-reflector^2
BRDF estimate used for ITM/ETM and other optics
The objects producing glints in the photos are all in the angular range of optical levers, so I estimate the angular weighting of the glints using BRDF estimates made from the step observed in optical lever signals when the interferometer drops lock. I used values or data from: https://dcc.ligo.org/DocDB/0125/T1600085/001/Diode_PDF.pdf, https://alog.ligo-la.caltech.edu/aLOG/index.php?callRep=28662, and https://alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=30622 . In addition, I include some more recent measurements. By the way, it is interesting that the values from repeated measurements have not changed over the course of more than a year. The plot and model is shown in Figure 1. The model is more weighted to ITM and ETM values because the PRM is not very important for scattering. The BS values are upper limits. The model in Figure 1 is used for all optics, TMs, BS, and CPs being the most important.
Ranking results
Figure 2 shows a table of ranked sites and images of the sites that ranked the highest (worst). The highest weighting factor turned out to be for the glints from the P-Cal periscope (before baffling). This suggests that the ranking is reasonable, since the P-Cal periscope scattering was one of the worst scattering problems during the O2 run at both sites. Peaks from the P-Cal periscope were almost continuously visible in the spectrum at LLO, and, at LHO, were responsible for transient events, such as raven-peck coupling. For this reason, the weighting factor is normalized to give the P-Cal periscope glints a value of 1.
The next highest weighting factor was for the valve seats nearest the ITMs (weighting = 0.95). We have previously suspected that this valve seat might be a problem, but we have shaken it without producing noise. Corey is going to check if the seat is actually visible from the beam spot: it may be visible to the camera but not the beam spot because the camera is a few cm in front of the test mass. The next highest estimates are for linear structure retro-reflections ( https://alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=40454 ) in the internal corners of the arm cavity baffles (weighting factor up to 0.3). These are followed by the remaining “visible” portion of the reduction flange containing the ITM optical levers (weighting = 0.01), and the BS chamber walls (weighting = 0.0015).
The relatively high ranks of the BS chamber and the reduction flange by the ITM optical levers are consistent with these sites being the worst sites (after LLO HAM5-6) for shaking injections (https://alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=39199, https://alog.ligo-la.caltech.edu/aLOG/index.php?callRep=37831 ). We should use HEPI to shake the ACBs, which hang from stage 0.
While I did not get a photo of the Swiss-cheese baffle from the beam spots on the compensation plates and BS before the baffle was removed, an estimate suggests that it’s weighting factor would have been about 5e-5. Since we did have transient noise from the Swiss-cheese baffle at more than 5e-5 of the level of the P-Cal periscope, this may indicate that the baffle noise was produced by reflection of a stray beam originating possibly at the ITM or compensation plates or PR2, rather than by wide-angle scattering from the compensation plates.
This example is a reminder that the ranking here does not account for stray beams. However, the bright reflections in the photos indicate locations where a stray beam would be strongly reflected. A second reminder is that the flash technique probably doesn’t work well for paths that include a couple of narrow-band mirrors such as the P-Cal beam path, a path for which there is some evidence of scattering noise (https://alog.ligo-wa.caltech.edu/aLOG/index.php?callRep=39121 ). A final caveat is that the camera technique does not necessarily detect scattering paths where the light is scattered from one optic and recombines at another optic rather than at the same optic. To investigate such two-optic paths, we would want to flash at one beam spot and photograph at another.
Figure 3 shows the views from many beam spots, ordered roughly from input arm to output arm. Weighting factors are included in some of these, even when they are very low.
Figure 4 is an Excel file giving the calculations.
