A flat fielding primer

1. A flat fielding primer Pete Kalajian NEAIC 2010

2. Cataclysmic Variables  Oph Arcturus Exoplanet transits Spectroscopy My interests

3. Part 1 What does a flat do?

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

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

6. Next 5 images courtesy Steve Mazlin

9. No flat

10. After flat Magic!

11. Part 2 The math!

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

13. 1 1.1 pixel value Normalized value = average value 1 0.9 Normalization (Flat frame-dark frame) pixel values Assumes that flat light source is even! 100 110 Average value = 100 90 100 Done automatically in your image processing software!

14. 300 275 ÷ 1 1.1 By normalized flat 331 305 1 0.9 Calibrated frame Applying the normalized flat to your image frame (Raw frame - dark frame) pixel values 300 302 298 305

15. Flat frame-dark frame Subtract dark Average: 100 1 1 1.1 1.09 100 110 Normalized values too low! 1 1 0.91 0.9 90 100 Importance of dark subtraction Assume 10 ADU of dark noise in the flat frame Raw flat frame Average: 110 110 120 100 110 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. 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. 30000 100/30000 100/10000 0.3% uniformity 1% uniformity 100 Histogram of flat (mean 30k ADU) Statistics II • For a given light source, range of values is constant regardless of mean value! 10000 3 x better! 100 Histogram of flat (mean 10k ADU) Standard deviation is a measure of evenness of illumination!

26. Good Statistics Non-linear pixels 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

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 2 2010 • 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= 24271 ADU • Range of values 2 x 3 = 57 ADU • 57/24271 x 100% = 0.23% variation in brightness!

39. Repeatable! Flat quality comparison

40. Spectrum of AA el panels

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

42. 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 DOs DON’Ts

43. Flat -Man XL $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 8 - 12.5” telescopes • Shipping by May 1 • $50 off today and tomorrow