1. Spectrophotometric calibration of the IFU spectrograph
Marie-Hélène AUMEUNIER
LAM/CPPM/CNRS (IN2P3,INSU) FRANCE
Collaboration Meeting SNAP
June 2006

2. Slicer λ SN Slicer Mirror Array Telescope Focal Plane SN
“Slice” image into the telescope focal plane
“Rearrange the slices along the entrance slit of spectro: the row of slit mirror
Row of Pupil Mirrors
Row of Slit Mirrors λ

3. PLAN Objective, Specifications Method
Results obtained from simulated images
Conclusion

4. Objective
Prove the slicer performances for the photometric calibration with an accuracy < 1 %
Error Budget
poisson noise
procedure
margin
The error due to the calibration procedure σcalibration must be lower than 0.33 %

5. Tools Pixel-level simulation of the SNAP IFU spectrograph
Demonstrator equivalent to the SNAP design
(mounted for the end of 2006)

6. Problematic
Undersampled condition  Sensitive to all effects within a pixel: intrapixel variation and diffraction losses variation
Optical throughput in NIR
Optical throughput in visible
Intrapixel variation
100%
100%
slice width
slice width 0% 0%
one pixel
one pixel
one pixel
one pixel
Case 1: the slice is imaged on one pixel
Case 2: the slice is imaged on 2 pixels
The total throughput depends on both the position into the slicer AND the position within a pixel
 The photometric calibration requires to know the position with a precision < pixel size

7. Calibration procedure
Methods
Solution 1:
Calibrate individually each effect damaging the measurement : diffraction losses, intra-pixel variation..
Requires:
To well know the position with an accuracy < pixel size (undersampled condition)
To calibrate the response of each pixel of detector
Calibrated point source
Flux KNOWN Φref (λ)
Discrete position {xi,yi}i€N
Object
Flux UNKNOWN
Φobj(λ) = k×Φref(λ)
Position at (xobj,yobj)
Instrument
Instrument
Library of reference images at {xi,yi}i€N
Image of object
Solution 2: Do not decorrelate the 2 effects
Mapping the global spectrograph response as a function of the position into the slicer {xi,yi} and the wavelength λ
Condition: no detector effect that varies with the time or effect completely corrected
Calibration procedure
Calibration coefficient

8. Summary of calibration procedure
Reference Images
Image to calibrate
X2 Minimization per pixel
The M nearest reference images
Image to calibrate
Interpolation

9. Progress of the calibration procedure
the library of reference image
the calibration procedure

10. Library of reference images
Create many library at different wavelength:
monochromatic images
only the y-coordinate varies with a step of 1/10 of a pixel (sensitive to slit effect)
S/N maximum (close to the saturation) (σstat = 0,14%<1/3 %)
Reference image ↔ one position {xi,yi} & wavelength λi
Reference source: calibrated lamp
Wavelength
one slice λ
Spatial position
Simulated images with SNAP framework when we move the PSF along the spatial direction x

11. Reference position of library slice width = one pixel for the IR
Calibration Procedure
1- Create objects (50):
monochromatic source
generated at different position along the slice width AND without/with noise
k= Object flux / Reference flux = 0. 6
2- Compare images of object with the reference images to find the calibration coefficient k
3- Statiscal analysis
1.4 µm
 edge of slice
K distribution of 50 images
Error on calibration coefficient k
RMS
Reference position of library
1/10 of a pixel
slice width = one pixel for the IR

12. First results

13. Calibration of images generated WITHOUT noise
Calibration of 50 images generated at different wavelength
S/N=380
S/N=540
IN NIR, the calibration is good < 1/3 % (inside the specification )
In visible, the wavelength is higher, the calibration is better because the PSF size increases

14. Calibration of images generated WITH noise
Only Poisson noise
No detector noise
S/N=380
S/N=540
Photonic noise affects slowly the calibration procedure
In visible range = out of specification
 the slit effect is higher for low wavelength!
How to correct slit effect ? Dithering ?

15. Dithering
Random dithering: combination of N images shifted with a random value following a Gaussian distribution with a RMS of 0.03” (pointing accuracy of telescope)
The results of calibration depends on the position into the slicer
The dithering permits to combine many images at different position
How many images to combine to improve the calibration ?
slice i
slice i+1

16. Dithering: a method to minimize the slit effect on calibration ?
Consequence of dithering:
In IR : low gain (inside the specification < 1/3 %)
In visible:
at 0,8 µm, the calibration is improved of a factor 2
at low wavelength (0,7 µm), it is not sufficient to correct completely the high slit effect
 Why ?

17. Slit effect for low wavelength
0.7 µm
High calibration error around this position
1/10 of a pixel
PSF at 0.7 µm on one slice (step 1/10 of a pixel)
The shape and intensity of PSF varies quickly at low wavelength
The dithering minimizes the dispersion of the calibration error
The dithering does not correct a bias in calibration procedure
Sampling of 1/10 of a pixel not sufficient for this area
Optimization of sampling under worked
μ=0,48 %
σ=0,93 %
μ=0,46 %
σ=0,71%

18. Condition on object flux at 1,4 µm
The S/N is higher, the calibration is better: factor 2 between S/N=150 and S/N=530
As in the visible case the gain of the dithering technique is more sensitive for critical case but not sufficient to achieve specification
Object flux ≥ reference flux / 2
S/N of reference image= 690

19. Conclusion
Feasibility of photometric calibration at percent level by comparison of photometric flux from reference images
Condition on object flux
Object flux ≥ reference flux / 2  inside specification
VISIBLE RANGE
NIR RANGE
No dithering
> 0.33 % for the lowest wavelength
(slit effect )
< 0.33 %
With dithering
Minimization of the error dispersion
Optimization of the sampling underworked for low wavelength to correct slit effect
Low gain
Inside specification

20. Spares

21. Summary of calibration procedure
Reference Images
X2 Minimization per pixel
The nearest M reference images
Image to calibrate
Interpolation per ROI
NROI= numbers of measurement areas
{Φj}1<j<NROI=flux per measurement areas for the image to calibrate
Si,j =Image subtracted of the mean of noise
Image to calibrate

22. Х2 Minimization Method For each image (p), find :
(i,j) matrix index (0<i,j<N)
signal and noise of the image to calibrate into pixel (i,j)
Flux error
signal and noise of reference image indexed p (0<p<100) associated with a single position (x,y) & λ into pixel (i,j)
k : Ratio image to calibrate over reference image
For each image (p), find :
Deduce the index pmin of the reference image (the nearest one of the image to calibrate):
Error on parameter k :

23. Solve the linear equations system at M solutions
Interpolation
Reference Images
Flux into pixel (i,j) or total flux into ROI for the image to calibrate (subtracted of noise)
Х2 Minimization to find coefficient {au}1<u<4
Solve the linear equations system at M solutions
Method to find the minimal norm solution : singular value decomposition

24. Calibration procedure
Method
Calibrated punctual source
Flux KNOWN Φref (λ)
Discrete position {xi,yi}i€N
Object
Flux UNKNOWN
Φobj(λ) = k×Φref(λ)
Position at (xobj,yobj)
Solution 1:
Calibrate individually each effect damaging the measurement 
well knowledge of the position into the slicer to evaluate diffraction losses
calibration of each pixel of detector
Instrument
Instrument
Library of reference images at {xi,yi}i€N
Image of object
 Difficult to set up
 Difficult with the demonstrator (intrapixel variation not well known)
Calibration procedure
Solution 2: Do not decorrelate the 2 effects
Mapping the spectrograph response as a function of the position into the slicer {xi,yi} and the wavelength λ
Calibration coefficient

25. 1 pixel slice 1/75 of a pixel PSF @ 1.4 µm 1/10 of a pixel
Max=14 400ADU
Position of reference images
Max= ADU
Position of object
x=0,012” y=0.078”
x=0,0135” y=0.078”
slice
1/75 of a pixel
Max=24 000ADU
Max=23 000ADU
Max= ADU
1.4 µm
x=0,012” y=0.074”
x=0,0135” y=0.074”
x=0,015” y=0.074”
1/10 of a pixel

26. λ=0.5 µm λ=1 µm (vis arm) λ=1 µm (IR arm) λ=1.5 µm
Steep slope for low λ
λ=1 µm (IR arm)
λ=1.5 µm