# A flat fielding primer Pete Kalajian NEAIC 2010.

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A flat fielding primer Pete Kalajian NEAIC 2010

My interests Cataclysmic Variables Exoplanet transits  Oph Arcturus
Spectroscopy Mostly into scientific imaging Almost finished with Masters degree at SAO Partner Alnitak Astrosystems Physics Teacher at Watershed School

Part 1 What does a flat do?

What is a flat field frame?
Camera/OTA exposed to a uniform illumination source What are flats

CCD review  Flats take care of the last three!
Noise (quantum mechanics) Pixel-to-pixel variation (manufacturing) Vignetting (optics) Dust (environment) Flats take care of the last three! Why flats?

Next 5 images courtesy Steve Mazlin
Here we see some vignetting and a funny sicle like imperfection on the flat field image Next 5 images courtesy Steve Mazlin

Close up of the imperfection

No flat

After flat Magic!

Part 2 The math!

CCD calibration math Very simple equation! raw frame - dark frame
Remove dark current noise raw frame - dark frame Final frame = Brightens weak pixels, dims strong pixels ( flat frame - dark frame) Normalized Very simple equation!

Normalization Done automatically in your image processing software!
(Flat frame-dark frame) pixel values Assumes that flat light source is even! 100 110 Average value = 100 1 0.9 1.1 pixel value average value Normalized value = 90 100 Done automatically in your image processing software!

Applying the normalized flat to your image frame
(Raw frame - dark frame) pixel values 300 302 275 305 331 300 Calibrated frame ÷ By normalized flat 1 0.9 1.1 298 305

Importance of dark subtraction
Assume 10 ADU of dark noise in the flat frame Flat frame-dark frame 110 100 90 Average: 100 Raw flat frame Subtract dark Average: 110 110 120 Normalized values too low! 1 0.91 1.09 1 0.9 1.1 100 110 Overcorrected images!

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! linear ADU values Non-linear # of photons arriving at detector

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

Figure 3. Detector linearity test
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 3

Statistics II For a given light source, range of values is constant regardless of mean value! 10000 30000 100 100/30000 0.3% uniformity Histogram of flat (mean 30k ADU) 100/10000 1% uniformity 3 x better! 100 Histogram of flat (mean 10k 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

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 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

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
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

“Flatted flat” Standard deviation = 9.5 ADU!

Flat-Man XL Statistics
For our test case: mean= 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 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 L 13” diameter EL panel Wall or manually mounted
USB controlled For ” telescopes Shipping by May 1 \$50 off today and tomorrow

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