1. A flat fielding primer
Pete Kalajian
NEAIC 2010

2. 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

3. Part 1
What does a flat do?

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

5. 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?

6. 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

7. Close up of the imperfection

9. No flat

10. After flat
Magic!

11. Part 2
The math!

12. 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!

13. 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!

14. 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

15. 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!

16. 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

17. 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

18. 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.

19. 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

20. Part 3
How to get good flats

21. Acquisition methods All sky flats Light box Twilight flats Dome flat
Electroluminescent panel

22. 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

23. 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 ()

24. 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

25. 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!

26. 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

27. 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

28. Light boxes Needs proper baffling and reflective illumination
Careful attention to corner shadows
Bulky and difficult to use robotically

29. 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!

30. 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

31. Twilight flatted flat at Galaxy Quest
Standard deviation = 171 ADU

32. Dome flats Painted section of dome illuminated by light source
Difficult to eliminate gradients
Requires careful set up and testing

33. Dome flatted flat at SSRO
Standard deviation = 187 ADU
Data courtesy Jacob Gerritsen, SSRO

34. 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!

35. Flat-Man XL case study

36. A dark subtracted sigma combined master flat

37. “Flatted flat”
Standard deviation = 9.5 ADU!

38. 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!

39. Flat quality comparison
Flat illumination source
Standard deviation
Twilight flat
171 ADU
Dome flat
187 ADU
Flat-Man XL
9.5 ADU !!!
Repeatable!

40. Spectrum of AA el panels

41. Ha Flats
Courtesy Doug Baum (Flip-Flat owner) at Nightvision Astronomy

42. 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

43. $100 off on XL’s today and tomorrow
Flat -Man XL
I hope I’ve convinced you of the quality and repeatability of electroluminescent panels. Ours are broad spectrum, fully adjustable, and very even!
$100 off on XL’s today and tomorrow

44. Flip-Flat
$50 off today and tomorrow

45. Flat-Man L 13” diameter EL panel Wall or manually mounted
USB controlled
For ” telescopes
Shipping by May 1
$50 off today and tomorrow