### Strehl_Ratio_estimation

```Strehl Ratio estimation
SR from H band images
High Strehl PSF ->fitting with Zernike modes
We suppose:
No relevant loss of energy due to high modes (Z>36)
Amoeba fit with
First 36 Zernikes
Generation
of DL PSF and SR meas as:
Peak fitted / Peak DL
NO DEPENDENCE on
FLUX estimation
Check on
residuals
SR from H band images
Low Strehl PSF: fitting with two gaussian ditributions
Halo energy >> rings energy
Point = meas
Line = fit
Line = residual
Fit with 2 gaussians
Repeated considering
Different IRTC crops
SR
Relativ error on SR
Total flux estimation
flux_im
= (Meas image – fitted bias)
Flux_im thresholded to 0
flux
= total(flux_im)
Line = DL
Line = meas
DL generation and
SR meaurement
IRTC field in pixels
psf DL generated with nominal FWHM and the energy = flux
sr_meas = max(y-R[0])/max(psf_dl)
Estimation from real-time data
2

  2 
2
SR  exp   
  tot
 

 
Marechal approximation:
 tot   res  
2
Wavefront error estimation:
2





2
fit
n mod
Correction residuals:
 res 
2
2


m
 res i
and:
m res  Rs
i 1
!
• The optical gain of the pyramid WFS depends on the size of the PSF.
• Since the reconstructor, R, is usually calibrated with a diffraction-limited
source, the residual WF will be systematically under-estimated through the
vector
m res  Rs
Since the gain (1/R) with high peak PSF is higher, when slopes
resulting from low peak PSF are used with this lower value of R,
the mirror surface error is under-estimated.
Estimation from real-time data
There is another reason that this method underestimates the WF error. The
2
factor sigma(res) only estimates the
due

 to spatial modes whose
 2 error

 WF
2 
SR the
 exp
 tot 
Marechal
approximation:
   of actuators
order
is less than or equal to
number
used. The higher order





 not included
 in the WFS slopes.
modes in the residual error are
 tot   res  
2
Wavefront error estimation:
2
2
fit
n mod
Correction residuals:
 res 
2
2


m
 res i
and:
m res  Rs
i 1
!
• The optical gain of the pyramid WFS depends on the size of the PSF.
• Since the reconstructor, R, is usually calibrated with a diffraction-limited
source, the residual WF will be systematically under-estimated through the
vector
m res  Rs
Comparison
20091005_133216
MAG 8.5
____ Acquired PSF
____ DL Psf with same flux
Closed Loop parameters
Bin = 1 (30x30)
Freq = 1000 Hz
Flux = 232 ph/subap/frame
TT Modulation = +- 2 /D
N modes = 153
Gain = 0.7
H band Strehl Ratios
Expected from simulations = 62 – 80 %
Estimated with mirror positions = 81 %
Estimated on IRTC image = 84+- 8 %
[FWHM on IRTC = 41 mas]
20091005_164935 FP3
MAG 10.7
____ Acquired PSF
____ DL Psf with same flux
Closed Loop parameters
Bin = 2 (15x15)
Freq = 800 Hz
Flux = 140 ph/subap/frame
TT Modulation = +- 3 /D
N modes = 153
Gain = 0.7
H band Strehl Ratios
Expected from simulations = 50 – 62 %
Estimated with mirror positions = 55 %
Estimated on IRTC image = 55 +- 7 %
[FWHM on IRTC = 41 mas]
20091005_173152 FP5
MAG 12.4
____ Acquired PSF
____ DL Psf with same flux
Closed Loop parameters
Bin = 2 (15x15)
Freq = 625 Hz
Flux = 40 ph/subap/frame
TT Modulation = +- 3 /D
N modes = 153
Gain = 0.6
H band Strehl Ratios
Expected from simulations = 42 – 54 %
Estimated with mirror positions = 47 %
Estimated on IRTC image = 45 +- 5 %
[FWHM on IRTC = 42 mas]
```