A flat fielding primer

Pete Kalajian

NEAIC 2010

My interests

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Exoplanet transits

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Arcturus

Spectroscopy

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Cataclysmic Variables

Part 1

What does a flat do?

What is a flat field frame?

• Camera/OTA exposed to a uniform illumination source

CCD review

• Noise (quantum mechanics)

• Pixel-to-pixel variation (manufacturing)

• Vignetting (optics)

• Dust (environment)

Flats take care of the last three!

Next 5 images courtesy Steve Mazlin

No flat

After flat

Magic!

Part 2

The math!

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

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!

Applying the normalized flat to your image frame

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(Raw frame - dark frame) pixel values

1

0.9

1.1

1

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305331

300

Calibrated frame

÷By normalized flat

Importance of dark subtraction

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110100

1101

0.91

1.09

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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!

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

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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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.

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

Part 3

How to get good flats

Acquisition methods

• All sky flats

• Light box

• Twilight flats

• Dome flat

• Electroluminescent panel

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

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 ()

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

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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!

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

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

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!

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

Twilight flatted flat at Galaxy Quest

Standard deviation = 171 ADU

Dome flats

• Painted section of dome illuminated by light source

• Difficult to eliminate gradients

• Requires careful set up and testing

Dome flatted flat at SSRO

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Standard deviation = 187 ADU

Data courtesy Jacob Gerritsen, SSRO

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!

Flat-Man XL case study

A dark subtracted sigma combined master flat

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“Flatted flat”

Standard deviation = 9.5 ADU!

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!

Flat quality comparison

Flat illumination source Standard deviation

Twilight flat 171 ADU

Dome flat 187 ADU

Flat-Man XL 9.5 ADU !!!

Repeatable!

Spectrum of AA el panels

Ha Flats

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Courtesy Doug Baum (Flip-Flat owner) at Nightvision Astronomy

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

• 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