Virgo Logbook

We estimated the expected changes in the finesse of the arm cavities due to the etalon effect of the input mirrors.

According to the formula at pag 54 of Bondu's HDR, the FInesse F (without the etalon effect) is related to the finesse F' (with the etalon effect) by

F'=F*(1-r_AR*cos(b)*(2*chi^2 chi-1)/chi) where chi = (-r1 r2*(1-P1))/(1-r1*r2)

we used the following values

r_AR = sqrt (R_AR) with R_AR = 32 ppm reported in VIR-0544A-14

r1 = sqrt (1-T1) with T1 = 1.377e-2 reported in VIR-0544A-14

r2 = sqrt (1-T2) with T2 = 4 ppm reported in VIR-269A-15

P1 (arm losses) = 75 ppm

F = pi*sqrt(r1*r2)/(1-r1*r2) = 453 ± 2

We found F'_min = F'(b = 0) = 448 and F'_max (b =pi) = 458

r_AR = sqrt (R_AR) with R_AR = 58 ppm reported in VIR-0543A-14

r1 = sqrt (1-T1) with T1 = 1.375e-2 reported in VIR-0543A-14

r2 = sqrt (1-T2) with T2 = 4.3 ppm reported in VIR-0270A-15

P1 (arm losses) = 75 ppm

F = pi*sqrt(r1*r2)/(1-r1*r2) = 453.7 ± 2.3

We found F'_min = F'(b = 0) = 446.9 and F'_max (b =pi) = 460.5

In the attached plot these values are compared with the finesse measured from the ringing effect for the noth cavity (see entry 33795).