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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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STScI TIPS – Sep. 16, 2010
linear fit to the first 20 samples
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.
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.
THIS IS THE WEIRD (NON POLYNOMIAL)
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
We can try with the physically more correct expression:
i.e. we modulate the real flux Fc to get F, not viceversa
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!
From the values of c2, c3, an c3 one can derive Fc by solving
Need to use an iterative method:
Same “detector”, i.e. exponential non-linearity term
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