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A flat fielding primer
Pete Kalajian
NEAIC 2010
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My interests
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Exoplanet transits
Oph
Arcturus
Spectroscopy
8
8.5
9
9.5
10
10.5
11
11.5
12
12.5
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0 5 10 15 20 25 30 35 40 45
JD - 2455075
SS CYG V MAG
Cataclysmic Variables
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Part 1
What does a flat do?
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What is a flat field frame?
• Camera/OTA exposed to a uniform illumination source
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CCD review
• Noise (quantum mechanics)
• Pixel-to-pixel variation (manufacturing)
• Vignetting (optics)
• Dust (environment)
Flats take care of the last three!
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Next 5 images courtesy Steve Mazlin
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No flat
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After flat
Magic!
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Part 2
The math!
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CCD calibration math
raw frame - dark frame
( flat frame - dark frame)Final frame =
Remove dark current noise
Very simple equation!
Brightens weak pixels, dims strong pixels
Normalized
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Normalization
110
10090
100 Average value = 100
(Flat frame-dark frame) pixel values
pixel value
average valueNormalized value =
1
0.9
1.1
1
Done automatically in your image processing software!
Assumes that flat light source is even!
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Applying the normalized flat to your image frame
302
305298
300
(Raw frame - dark frame) pixel values
1
0.9
1.1
1
275
305331
300
Calibrated frame
÷By normalized flat
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Importance of dark subtraction
120
110100
1101
0.91
1.09
1
Assume 10 ADU of dark noise in the flat frame
Average: 110Raw flat frame
Overcorrected images!
Flat frame-dark frame
110
10090
100
Average: 100Subtract dark
1
0.9
1.1
1
Normalized values too low!
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Importance of staying in linear regime
• If non-linear, pixel values will read less than actual value
• Normalized flat pixel value too small
• Flatted image pixel value too large: Overcorrected images!
# of photons arriving at detector
ADU values
Non-linear
linear
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Characterizing linearity
• Aim at 6-9th mag star near the zenith• Expose series of images with increasing
exposure length• Measure flux inside aperture• Divide flux by exposure time to get
flux/sec• Will be similar at each exposure length
in the linear regime
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0.95
0.97
0.99
1.01
1.03
1.05
0 5000 10000 15000 20000 25000 30000
Max Pixel Value
5 second
10second
15 second
20 second
30 second
40 second
50 second
60 second
Figure 3. Detector linearity test. The normalized flux rate is linear to 1% up to maximum pixel values of around 23 kADU.
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Noise considerations
• Make master bias/dark (s/n improves as the square root of the # of frames combined)
• Dark OR bias correct flats
• Million photon flats – 106/avg ADU = # of frames = 40 frames!
• No matter what, flats add some noise to final calibrated image
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Part 3
How to get good flats
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Acquisition methods
• All sky flats
• Light box
• Twilight flats
• Dome flat
• Electroluminescent panel
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What makes a good flat?
• Evenness of illumination• ADU values at upper range of
linear regime of CCD detector• Longer than 2 seconds to
eliminate shutter effect• Many dark subtracted sub frames• Repeatable filter wheel
positioning
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The rotation method for evaluating flats
• Expose / rotate 90˚/ expose
• Dark subtract and use second set as flats - “flatted flat”
• Look at histogram
• Analyze standard deviation ()
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Basic statistics
• Poisson distribution of ADU values centered on a mean value
• Width of distribution measured by standard deviation,
• 99.7% of all values lie within 3 of the mean
3
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Statistics II• For a given light source, range of values
is constant regardless of mean value!
10000
100
100/10000
1% uniformity
3 x better!
Histogram of flat (mean 10k ADU)
30000
100
100/300000.3% uniformity
Histogram of flat (mean 30k ADU)
Standard deviation is a measure of evenness of illumination!
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How many ADU is enough?
• Maximum value of any pixel must be in the linear regime of the chip.
• Anti-blooming chips go non-linear somewhere mid-range
• Non-linear pixels in flat will result in incorrect normalization
• Funny artifacts in flatted images
Good Statistics Non-linear pixels
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All sky flats
• Sum lots of images dithered to get enough ADU’s for good stats.
• Can be important for photometry or back illuminated chips because spectral response matches raw images
• Star artifacts difficult to remove completely• Tough with wide field images/big non-linear
stretches
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Light boxes
• Needs proper baffling and reflective illumination
• Careful attention to corner shadows
• Bulky and difficult to use robotically
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Twilight flats
• Racing against the clock• Neutral point in sky is not fixed• Virtually guaranteed to have gradients
in wide field images• Possible star artifacts• Can you get all filters covered in one
twilight?• Quality is not repeatable!
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Twilight flat case study
• April 2 2010
• Average transparency (clear sky clock)
• No visual signs of cirrus
• 12.5” RCOS with ST2000 (identical setup)
• Moon below horizon
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Twilight flatted flat at Galaxy Quest
Standard deviation = 171 ADU
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Dome flats
• Painted section of dome illuminated by light source
• Difficult to eliminate gradients
• Requires careful set up and testing
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Dome flatted flat at SSRO
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Standard deviation = 187 ADU
Data courtesy Jacob Gerritsen, SSRO
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Electroluminescent panels
• Proper design ensures excellent flatness• Easy to diffuse• Compact• Not all panels are broad spectrum• Variation in manufacturing• Stability of power supply• Alnitak Astrosystems!
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Flat-Man XL case study
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A dark subtracted sigma combined master flat
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“Flatted flat”
Standard deviation = 9.5 ADU!
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Flat-Man XL Statistics
• For our test case: mean= 24271 ADU• Range of values 2 x 3 = 57 ADU• 57/24271 x 100% = 0.23% variation in
brightness!
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Flat quality comparison
Flat illumination source Standard deviation
Twilight flat 171 ADU
Dome flat 187 ADU
Flat-Man XL 9.5 ADU !!!
Repeatable!
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Spectrum of AA el panels
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Ha Flats
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Courtesy Doug Baum (Flip-Flat owner) at Nightvision Astronomy
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DOs DON’Ts
• Use even illumination• Master dark/bias
subtract individual flat frames
• Sigma combine lots of calibrated flat frames
• Check your flat quality with the rotation method
• Overexpose into non-linear regime
• Apply noise reduction or smoothing
• Stretch histogram
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Flat -Man XL
$100 off on XL’s today and tomorrow
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Flip-Flat
$50 off today and tomorrow
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• 13” diameter EL panel• Wall or manually
mounted• USB controlled• For 8 - 12.5” telescopes• Shipping by May 1• $50 off today and
tomorrow
Flat-Man L