Detecting
Cosmic Rays in
Infrared Data
Rachel Anderson  Karl Gordon
RIAB Monthly Meeting
5/28/2016
Outline
 The CR Problem
 Linear Fit Algorithm
 CR Detection Methods
 The 2-Point Difference Method
 The Deviation from Fit Method
 The Y-Intercept Method
 Results
RIAB Monthly Meeting
5/28/2016
The CR Problem
 Every 1000 seconds, up to 20% of the field of view of
JWST will be affected by CRs
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Offenberg, J.D., et al. 1999
Rouscher, B., et al. 2000, STScI-NGSTR-0003A
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The CR Problem
 Every 1000 seconds, up to 10% - 20% of the field of view
of JWST will be affected by CRs
+ CR =
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Offenberg, J.D., et al. 1999
Rouscher, B., et al. 2000, STScI-NGSTR-0003A
5/28/2016
The CR Problem (cont.)
 The Question: What is the best we can do, given the noise
in the ramp?
 The How:
 Simulate non-destructive read ramps.
 Add some CRs with various magnitudes and locations.
 Test CR detection methods, then try to find them.
RIAB Monthly Meeting
5/28/2016
Linear Fit Algorithm
We want to solve the equation: Y = AX, with solution: X = [ATC-1A]-1[ATC-1Y]
y1
Y = y2 ,
…
yn
1
A= 1
…
1
x1
x2 ,
…
xn
X=
b
m
σy12
c1,2
…
c1,n
, and C = c2,1
…
σy22
…
c2,n
…
…
…
cn,1
cn,2
…
σyn2
Fixsen, D. J., et al. 2000, PASP, 112, 1350
Gordon, K. D., et al. 2005, PASP, 117, 503
Hogg, D. W. et al. 2010, ArXiv e-prints
RIAB Monthly Meeting
5/28/2016
Linear Fit Algorithm
We want to solve the equation: Y = AX, with solution: X = [ATC-1A]-1[ATC-1Y]
y1
Y = y2 ,
…
yn
1
A= 1
…
1
x1
x2 ,
…
X=
b
m
xn
σy12
c1,2
…
c1,n
, and C = c2,1
…
σy22
…
c2,n
…
…
…
cn,1
cn,2
…
σyn2
It is easiest to think of C as the sum of two matrices: C = R + P
p 12
p12
p 12
…
2
R = r2 I , and P = p1
p 12
p22
p22
…
p22
…
…
…
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…
…
pn
2
Fixsen, D. J., et al. 2000, PASP, 112, 1350
Gordon, K. D., et al. 2005, PASP, 117, 503
Hogg, D. W. et al. 2010, ArXiv e-prints
5/28/2016
CR Detection Methods
 Three methods:
 2- Point Difference
 Deviation from Fit
 Y-Intercept
 For each method:
 Detect CRs (largest first)
 Calculate the slope for the resulting ‘semi-ramps’
 Calculate final slope of entire ramp by taking weighted
average of the slopes of the ‘semi-ramps’
Regan, M. 2007, JWST-STScI-001212
Robberto, M. 2008, JWST-STScI-0001490, SM-12
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5/28/2016
2-Point Difference
| di – μd |
Ratio =
σd
di = yi – yi-1
μd: median of di’s
σd = √2rn2 + pn2
… where pn = √μd
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5/28/2016
Deviation From Fit
yi – fi
devi =
σi
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5/28/2016
Y-Intercept
| b2 – b1 |
Ratio =
σb
σb = √2rn2 + pn2
… where pn = √ m
,
and rn is calculated
from un-correlated
errors in our linear-fit
program.
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5/28/2016
Results:
Fraction Found vs. False Detections
40 Frames, Input Slope: 10.00 DN/s
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5/28/2016
Results:
Fraction Found vs. False Detections
40 Frames, Input Slope: 0.00 DN/s
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5/28/2016
Results: Multiple CR’s
2-Point Difference
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5/28/2016
Conclusions
 To optimize results, our linear fit algorithm must take into
account correlated and un-correlated errors.
 The 2-Point Difference method is simple, fast, consistent,
and best for photon-noise dominated regime.
 The Y-Intercept method is better in read-noise dominated
regime.
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Results: Number of Frames
Slope = 10.0 DN/s
Fraction of False Detections = 0.05
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Results: Various Slopes
2- Point Difference
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5/28/2016
Results: Various Slopes
Deviation from Fit
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Results: Various Slopes
Y-Intercept
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slopecalc / (slope-1)
Linear Fit Algorithm (cont.)
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5/28/2016
Results: Number of Frames
2-Point Difference
Slope = 0.00 DN/s
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Slope = 10.00 DN/s
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Results: Number of Frames
Deviation from Fit
Slope = 0.00 DN/s
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Slope = 10.00 DN/s
5/28/2016
Results: Number of Frames
Y-Intercept
Slope = 0.00 DN/s
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Slope = 10.00 DN/s
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Results: Multiple CR’s
Deviation from Fit
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5/28/2016
MIRI Parameters
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Frame Time (s)
27.7
Slope (SN/s)
10.0
Zero Point (DN)
3,000.0
Number of Frames
40
Gain (e-/DN)
7.0
Dark Current (e-/s)
0.02
Read Noise (e-/sample)
16.0/√8
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Results: Multiple CR’s
Y-Intercept
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5/28/2016