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

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

PLAN Objective, Specifications Method Results obtained from simulated images Conclusion

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 %

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

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

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

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

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

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

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

First results

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

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 ?

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

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 ?

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%

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

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

Spares

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

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 :

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

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

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=13 600 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=21 100 ADU PSF @ 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

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