[Keita, Koji, Yuta] (written by Yuta, poted by Koji)

ETMY green transmissivity and reflectivity were measured to be T=31.6 +/- 0.2(stat.) % and R=67.8 +/- 0.3(stat.) %
at the incident angle of 0.4 +/- 0.1(sys.) deg.

From the incident angle dependence measurement, the trasmissivity at 0 deg was estimated to be T=31.4 +/- 0.4(stat.) %.

[Motivation]
We wanted to check the transmissivity and reflectivity of ETMY at 532nm since ETMX has lower transmissivity than designed.

[Method]
1. Injected the green beam of the Prometheus laser from the HR side of ETMY at the quad stand.
Measured the incident, reflected, and transmitted power levels with the OHIR power meter configured for the wavelength of 532nm.
Performed three sets of the measurements at the spots at the top part of the mirror horizontally separated by 1 inch
around the horizontal center of the mirror. The horizontal shift of the spots were

The incident angle was assessed by measuring the beam separation at reflection.
The beam separation was 0.5 +/- 0.1 inch at 36 +/- 1 inch away from the HR surface. The incident power was ~50 mW.

2. Rotate ETMY and measured the transmitted power and the beam separation at reflection. Repeat the measurement with different incident angle.

During the measurement, ETMY was kept inside the clean booth at the end Y station. The beam spot on ETMY was ~2 inch blow the top edge of the mirror.

[Result]
1. At the incident angle of 0.4 +/- 0.1(sys.) deg;

T = 31.6 +/- 0.2(stat.) %
R = 67.8 +/- 0.3(stat.) %

2. ETMYtrans.png shows the transmissivity dependence on the incident angle. By fitting the measured data with a quadratic curve, we get

T = 31.4 +/- 0.4(stat.) %

at the incident angle of 0 deg. The incident angle dependence was

k = -0.25 +/- 0.09(stat.) %/deg^2


[Wavelength dependence]
We can estimate the wavelength dependence of the transmissivity from the incident angle dependence.
The wavelength dependence can be expressed by

T = T0 + dT/dlambda * dlambda

When the incident beam has some incident angle, the effective thickness of the coating changes. Thus,

dlambda = lambda/cos(theta) - lambda = theta^2/2*lambda

where theta is the refraction angle incide the coating and

theta = theta_{in}/n_eff

when theta << 1. n_eff is the effective refractive index of the coating.

So,

T = T0 + dT/dlambda (theta_{in}/n_eff)^2/2*lambda
  = T0 + k*theta_{in}^2

From the measurement of k,

dT/dlambda = 2*k*n_eff^2/lambda = -9 +/- 3(stat.) %/nm

Here, we assumed n_eff=1.7.