Transcript An improved treatment of the linearity correction of IR detectors Massimo Robberto JWST/NIRCam STScI TIPS – Sep.

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
The “true” slope depends on the range
of the assumed linear regime
In fact, the angular coefficient of the
true slope is hard to find…
ACT 1
CURRENT STATUS
How we do it now
In the case of NICMOS and WFC3, we apply the following correction
F are 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 c4 used for general linearity correction.
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
THIS IS THE WEIRD
(NON POLYNOMIAL)
NON-LINEARITY
TERM
Let’s plot our baseline…
… 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
The result is:
Residuals
ACT 2
A DIFFERENT APPROACH
Let’s look at the equation
Instead of

Fc  F  1  c2  F  c3  F  c4  F
2
3

We can try with the physically more correct expression:

Fc  1  c2  Fc  c3  F  c4  F
2
c
i.e. we modulate the real flux Fc to get F, not viceversa
3
c
 F
Method
In Equation


Fc  1  c2  Fc  c3  Fc2  c4  Fc3  F
the Fc and c2,c3,c4 values are unknown. I use IDL/curvefit.pro
to derive them from the set of known ti and measured Fi:
having defined the function:
0.3% error on the slope!
Linearity correction
From the values of c2, c3, an c3 one can derive Fc by solving
the equation:
Fc 

F
1  c2  Fc  c3  Fc2  c4  Fc3
Need to use an iterative method:

Results
i=0
1
2
4
Check: different flux rate
Same “detector”, i.e. exponential non-linearity term
Correction: old vs. new method
Old
New
Conclusion
The current strategy we implement to correct for non-linearity
seems less than ideal.
1) Problems with the estimate of the coefficients, which
depend on the assumed “linearity” region of the detector
2) Problems with the equation, which does not correctly
describes the non-linearity effect
The new method has two advantages
1) Coefficients are estimated without any assumption on the
true, linear flux
2) 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