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 value Normalized 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 302 305298 300 (Raw frame - dark frame) pixel values 1 0.9 1.1 1 275 305331 300 Calibrated frame ÷ By normalized flat
Importance of dark subtraction 120 110100 110 1 0.91 1.09 1 Assume 10 ADU of dark noise in the flat frame Average: 110 Raw flat frame Overcorrected images! Flat frame-dark frame 110 10090 100 Average: 100 Subtract 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
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 –10 6 /avg ADU = # of frames = 40 frames! No matter what, flats add some noise to final calibrated image
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 100 100/10000 1% uniformity 3 x better! Histogram of flat (mean 10k ADU) 30000 100 100/30000 0.3% 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 StatisticsNon-linear pixels
All sky flats Sum lots of images dithered to get enough ADUs 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 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 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!
Ha Flats Courtesy Doug Baum (Flip-Flat owner) at Nightvision Astronomy
DOs DONTs 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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