Trials to fit the mode content of the carrier at the dark port are starting to look more promising. The fit is based on the intensity image of the carrier obtained with the PC observing the B1p beam.

1. The basis is chosen by an astigmatic Gaussian fit to the carrier at MICH = 0.1 (dominated by the TEM00 mode, similar results if recombined is used instead of MICH = 0.1). The coordinates of the data points obtained are x_ini and y_ini.

2. The mode content is then fitted minimizing the function

|intensity_image -|sum_lm p_lm E_lm(x,y)|^2|^2,

where the basis is allowed to be slightly adjusted to make the fit

x = (cos(theta)*x_ini+sin(theta)*y_ini)*scaling,
y = (cos(theta)*y_ini-sin(theta)*x_ini)*scaling.

E_lm(x,y) are the amplitudes of the HOM modes.

The parameters p_lm are complex to absorb the phase offset between the modes.

The scaling and the angle of the basis are

theta =  1.12,
scaling =  0.77.

The scaling parameter seems from experience with simulated input rather sensitive to mode content and is probably not capturing actual size changes between the two ifo states (to be further investigated).

The fit uses HG modes with n+m = 0,1,2,8. Preliminary relative power in the fitted modes are:

(l,m) has strength |p_lm|^2/sum(|p_lm|^2)

(0,0) has strength 9.83E-01
(8,0) has strength 6.85E-10
(0,8) has strength 6.15E-11
(4,4) has strength 2.35E-07
(2,6) has strength 2.56E-08
(6,2) has strength 1.57E-07
(1,7) has strength 2.75E-08
(7,1) has strength 1.27E-08
(3,5) has strength 5.74E-07
(5,3) has strength 6.50E-09
(1,0) has strength 4.38E-03
(0,1) has strength 3.16E-03
(2,0) has strength 4.27E-03
(0,2) has strength 5.22E-03
(1,1) has strength 1.31E-04
power in n+m =  8 modes  is 1.04E-06

Next we will check robustness.

Attached is a figure with the fitting result for gpstime =1219540768.

work in progress...