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An improved treatment of the linearity correction of IR detectors

An improved treatment of the linearity correction of IR detectors. Massimo Robberto JWST/ NIRCam STScI TIPS – Sep. 16, 2010. Ouverture. IR detectors are non linear. Linearity is assumed at the beginning of the ramp. linear fit to the first 20 samples.

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An improved treatment of the linearity correction of IR detectors

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  1. An improved treatment of the linearity correction of IR detectors Massimo Robberto JWST/NIRCam STScI TIPS – Sep. 16, 2010

  2. Ouverture

  3. IR detectors are non linear

  4. Linearity is assumed at the beginning of the ramp linear fit to the first 20 samples

  5. The “true” slope depends on the range of the assumed linear regime

  6. In fact, the angular coefficient of the true slope is hard to find…

  7. Act 1CURRENT STATUS

  8. How we do it now In the case of NICMOS and WFC3, we apply the following correction Fare the measured counts Fc are the true counts. The calibration process assumes that they are known (fit to the first part of the ramp). Known both F’s, we derive the correction coefficients c2, c3 and c4used for general linearity correction.

  9. Problems with this approach 1) We do not really know what is the real slope of the calibration frame, and our estimate depends on the samples we use. 2) Physically, one has a linear true flux which is converted in a non-linear measured count rate by the detector. This is not what we model! We modulate the observed data to get the real flux; instead, we should modulate the real flux to get the observed data.

  10. A controlled experiment using simulated data THIS IS THE WEIRD (NON POLYNOMIAL) NON-LINEARITY TERM

  11. Let’s plot our baseline…

  12. … and derive the correction “a’la HST” I will assume that we know perfectly the true slope, i.e. problem 1 has been solved. I therefore get the best possible c coefficients. THIS IS THE POLYNOMIAL CORRECTION TERM

  13. The result is:

  14. Residuals

  15. Act 2A different approach

  16. Let’s look at the equation Instead of We can try with the physically more correct expression: i.e. we modulate the real flux Fc to get F, not viceversa

  17. Method In Equation the Fc and c2,c3,c4 values are unknown. I use IDL/curvefit.pro to derive them from the set of known tiand measured Fi: having defined the function: 0.3% error on the slope!

  18. Linearity correction From the values of c2, c3, an c3 one can derive Fc by solving the equation: Need to use an iterative method:

  19. Results i=0 1 2 4

  20. Check: different flux rate Same “detector”, i.e. exponential non-linearity term

  21. Correction: old vs. new method Old New

  22. Conclusion The current strategy we implement to correct for non-linearity seems less than ideal. Problems with the estimate of the coefficients, which depend on the assumed “linearity” region of the detector Problems with the equation, which does not correctly describes the non-linearity effect The new method has two advantages Coefficients are estimated without any assumption on the true, linear flux The correct equation, with an iterative solve, seems to provide a much better estimate of the true linear flux. Check on real data is in progress

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