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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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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

linearity is assumed at the beginning of the ramp
Linearity is assumed at the beginning of the ramp

linear fit to the first 20 samples

how we do it now
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.

problems with this approach
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.

a controlled experiment using simulated data
A controlled experiment using simulated data

THIS IS THE WEIRD (NON POLYNOMIAL)

NON-LINEARITY TERM

and derive the correction a la hst
… 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

let s look at the equation
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

method
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!

linearity correction
Linearity correction

From the values of c2, c3, an c3 one can derive Fc by solving

the equation:

Need to use an iterative method:

results
Results

i=0

1

2

4

check different flux rate
Check: different flux rate

Same “detector”, i.e. exponential non-linearity term

conclusion
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