Flux Calibration Spectrograph calibration Flux calibration Requirements Test
Flux Calibration
Spectrograph calibration: Flux calibration Requirements : Test the feasibility of flux calibration : Punctual Object Flat Field Specification: - measure relative flux between ≠ λ to 1 % - measure absolu flux to 10 % What means ? Correct flux losses Calibrate flux losses to define the correction function Source Spectrograph Φ(λ) Image calibrated Optical losses: diffraction (mainly), aberrations Flux Correction Treated Image Detector QE, noise, intra-pixel variations Detector Image Φmeasured(λ) Detector calibration Untreated Image
Flux Variations Main causes of flux variations: - optical losses: diffraction, diffusion - detector: noise (thermal, readout), gain of pixel, intra-pixel variations Flux losses depend on: - position on the slicer plane: (x, y) - wavelength 2 methods to correct flux losses: • create a library of reference images at different positions (x, y) and wavelength • calibrate diffraction losses as a function of (x, y, λ). Which means to well-calibrate detector (dark, flat, intra/inter pixel variation).
Flux Correction from library of reference images: simulation Image at (x, y, λ), I 1=kth×I 0 Image at (x, y, λ) Compare the pixels distribution ∕ Method ? Library of reference images at I 0 Image calibrated in flux Selected Reference Image How to calculate k ? How to find the best reference image ? - k = ∫ image / ∫ image ref - Correlation - minimization chi 2 - Minimisation: chi 2
PSF Library creation Creation of library of 100 PSFs on detector at ≠ positions into one pixel (step 1/10 of pixel) : SNAP spectrograph simulation From old design of SNAP spectrograph y one pixel slice n+1 0. 15 ’’ slice n x slice n-1 Conditions -No noise - step of position variations: 1/10 of a pixel= 0, 15’’/10=0. 015” -Initial pixel (x 0, y 0)=(0”, 0”)
Х 2 Minimization Method (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 :
Method of Х 2 Minimization : Summary Si, j =Image subtracted of the noise average Image k x Φ 0 to calibrate Image (p) of library: Φ 0 Determine the ONE reference image pmin the nearest Determine M reference images the nearest Interpolation :
Normalized Image to calibrate Interpolation Х 2 Minimization to find coefficient {ap}0<p<M Normalization cste Solve the M linear equations Minimize Normalized Reference Images
Si, j =Image subtracted of the noise average X 2 minimization without interpolation For each reference image (p), minimize: X 2 minimization with interpolation Goal - Minimize: First step: find the “nearest” reference image A first method of X 2 minimization determines the M reference images the nearest (M=2 by default) The interpolation consists in computing the coefficients ap from normalized images: the method used is the Х 2 Minimization. This method leads us to solve a linear system of M equations (see next slide). After solving the system of equation, we determine the ratio k (δX 2/δk=0) : The one nearest reference image combination of the nearest reference images
Х 2 Minimization Method in practice To compute: We need to well-know the noise B per pixel impossible (random) Hypothesis; B = 0 (first application to check the method): no detector noise, no photonic noise Generate 32 images (without noise) at λ, x given scan along the slice width by step of 0. 003 ’’ (y 0={0. 02 ’’: 0. 113’’}) Source flux= k x source flux of reference images (k=0. 6) Find k(=0. 6) from 2 library of reference images (with different sampling)
Method used: minimization chi 2 Library used: 10 reference images 40 reference images x 0=0’’ fixed, λ=1, 4 µm fixed y 0={0. 001’’: 0, 135”} by step 1/10 of a pixel=0. 015” y 0={0’’: 0, 146”} by step 1/40 of a pixel=0. 00375”
Method used: minimization chi 2 to determine k+ interpolation Library used: 10 reference images 40 reference images x 0=0’’ fixed, λ=1, 4 µm fixed y 0={0. 001’’: 0, 135”} by step 1/10 of a pixel=0. 015” y 0={0’’: 0, 146”} by step 1/40 of a pixel=0. 00375”
λ=0. 5 µm λ=1 µm (visible arm) Erreur augmente au bord de la slice + critique ds le visible: variation de la PSF + rapide λ=1 µm (IR arm) λ=1. 5 µm
Flux variation per slice as a function of source position into the slicer λ=1. 5 µm slice 3 slice side Comprendre l’évolution de la distribution spatiale et du flux sur le détecteur en fonction de la position de la source pour ameliorer l’interpolation et la minimisation slice 4 5 Direction to move 3 0 slice 2 slice 1 slice 5 slice 0
λ=0. 5 µm λ=1 µm (vis arm) Pente + raide ds visible (cf resultat de la minimisation ds vis) λ=1 µm (IR arm) λ=1. 5 µm
Integration on 1 pixel per slice around the maximum slice 3 λ=0. 5 µm slice 2 Integration of 49 pixels per slice around the maximum slice side slice 3 slice 4 slice 2 slice side Integration of 9 pixels per slice around the maximum slice 3 slice 2 slice side slice 4 Au bord de la slice, non seulement le flux varie bcp mais aussi la distribution spatiale: interpolation lineaire suffisante ? slice 0
Variation of spatial distribution into one slice as a function of source position y (around the side of slice) y=0, 065” y=0, 077” y=0, 068” y=0, 080” y=0, 071” y=0, 074” y=0, 083” y=0, 086”
Variation of flux into one slice as a function of source position y (around the side of slice) side of slice
A faire Minimiser non pas les images sur le détecteur mais le flux total de ROI prédefini (1 roi par slice ou 2 roi par slice) Images de référence Image a calibrer flux de la slice 0 A minimiser On s’affranchit d’une variation de la distribution spatiale trop rapide
Calibration with Photonic Noise generated Φ 0=0. 00005 S/Nmax=106 <S/N>=1. 2 Library used: 10 reference images 40 reference images x 0=0’’ fixed, λ=1, 5 µm fixed y 0={0. 001’’: 0, 135”} by step 1/10 of a pixel=0. 015” y 0={0’’: 0, 146”} by step 1/40 of a pixel=0. 00375” λ=1. 5 µm
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- Slides: 21