[Shimasue, Takano, Michimura]

BS transmission and reflectivity were measured to be:

Ts=51.9 +/- 0.2 for s-pol
Rs=47.7 +/- 0.2 for s-pol
Tp=77.7 +/- 0.6 for p-pol
Rp=21.8 +/- 0.2 for p-pol

BS transmission for s-pol is a bit too high, which might be because BS is not aligned (it is now in SAFE state).
We might need to measure them again once BS and ITMs are aligned.

What we did:
 - Followed the procedure in klog 29275 for measuring the BS transmission.
 - For BS reflection, we opened an ICF203 flange labeled HY-2-1 (Attachment #1) so that we can stick the power meter (Thorlabs S310C) from the hole (Attachment #2).

Results:
 - The table below summarizes the results

 - By calculating T = (BS transmitted power) / (incident power) and R = (BS reflected power) / (incident power), transmission and reflectivity were estimated.

Discussions:
 - We noticed that the beam reflected by BS is not going through the viewport at the gate valve. We then realized that BS is not in ALIGNED state, but in SAFE state.
 - This means that the incident angle to the BS might be off by 50 mrad (~15 cm over 3.3 m distance).
 - The measurent tells that AR reflectivity is small enough compared with the measurement uncertainties.

Next steps:
 - Estimate the effect of incident angle from the wavelength dependence from the design.
 - Re-do the measurements with BS and ITMs aligned.

Systematic uncertainties on BS transmission and reflectivity measurements were estimated.
Updated results are:

Ts=51.9 +/- 0.2 (stat.) +/- 0.2 (sys.) % for s-pol
Rs=47.7 +/- 0.2 (stat.) +/- 0.2 (sys.) % for s-pol
Tp=77.7 +/- 0.6 (stat.) +/- 0.2 (sys.) % for p-pol
Rp=21.8 +/- 0.2 (stat.) +/- 0.2 (sys.) % for p-pol

Here, uncertainties from the incident angle and the polarization angle are considered.
It seems that they are not responsible for Rs being to low and Rp being too high, compared with the design.

Incident angle error:
 - BS and the incident beam was not aligned perfectly to have the incident angle of 45 deg. BS was in SAFE state.
 - BS reflected beam was not going though the viewport at the gate valve between BS and ITMY. The beam spot was off by ~15 cm over 3.3 m distance. From this, we have estimated that the incident angle error is about 50 mrad (3 deg).
 - Left panel of Attachment #1 is the reflectivity from the coating design, extracted from JGW-T1503347. The middle panel is the zoomed plot around 1064 nm.
 - From this, we can estimate the incident angle dependence as follows.
 - Reflectivity can be written as

R = R0 + dR/dtheta * dtheta

where theta = theta_in/n_eff is the incident angle inside the coating with an refractive index of n_eff (we used n_eff=1.7).
Slight change in theta_in introduces effective coating thickness change, which is equivalent to the laser wavelength change of

dlambda = lambda/cos(theta+dtheta) - lambda/cos(theta)
 = lambda/cos^2(theta)*sin(theta)*dtheta
 
 Therefore,

dR/dtheta_in = dR/dlambda*dlambda/dtheta*dtheta/dtheta_in
 = dR/dlambda*lambda*1/cos^2(theta)*sin(theta)*1/n_eff

 - From the coating design, dR/dlambda is -7e-3 %/nm for s-pol and -3e-4 %/nm for p-pol.
 - From the equations above, this gives dR/dtheta is -4e-2 %/deg for s-pol and -2e-3 %/deg for p-pol (Right panel of Attachment #1).
 - 50 mrad gives dR of 0.1% for s-pol and 0.006% for p-pol.

Polarization angle error:
 - When the polarization angle from s-pol is phi, the measured R will be

R = Rs*cos(phi)**2 + Rp*sin(phi)**2

 - If phi had an error of 5 deg, dR will be 0.2% for s-pol and p-pol.
 - It is hard to explain Rs being too low by ~2%, just from the polarization angle error.

Discussions:
 - Combined systematic uncertainties are 0.2% for all.
 - Rs seems to be too low and Rp seems to be too high, compared with the design.
 - The other source of error could be from the offset of the power measurements from the ambient light.
 - We could also try aligning the polarization angle by maximizing (for s-pol) or minimizing (for p-pol) BS transmission.