1. CCD Calibrations Eliminating noise and other sources of error

2. Types of CCD calibration data Additive systematic noise (bais, dark) Multiplicative systematic noise (flat)  fig 9.1 Bias or zero image : obtain by resetting the charges on a CCD and then immediately reading it out with the shutter closed Readout noise : simply by measuring the standard deviation of the pixel values in a bias image. Bias offset voltage fluctuates over a small range during a night and from night to night.  taking frequent bias images.  use the overscan region of a CCD image (overscan line contains information on the value of the bias offset voltage at the time it was read out – no information on bias variations across a line).  prepare a “master bias” from many bias images to correct the bias pattern & the overscan region gives the instantaneous value of the offset for each line

5. Dark image Dark image obtained with the CCD shutter closed. – charges are collected for exp times : thermal agitation of the silicon crystal lattice (unless cooled less than -80 C) Temperature stable ; many dark images  master dark images Night sky emission lines produce fringes on a CCD image; also additive noise ; usually in near IR I band :observe the sparse field with the same exp of the targets. (fig 9.3)

7. Pixel to pixel QE variations Multiplocative(or scaling) noise : due to pixel to pixel QE variations & non-uniform illumination QE curve of CCD : average fro all the pixels on the chip Mirrors, lenses, filters & the CCD window  non-uniform illumination  flat correction

8. Flats 1. twilight sky ; most accessible source of uniform illumination, While large brightness gradient, but have a point with very small gradient  after sunset about 20 deg from the zenith, opposite the Sun : reverse is the case just before sun rise.  careful preparation : rapidly changing sky brightness & different transmissions of the filters S/N of flat greater than that of the best science image Requre more than 1 flat image per filter Sometimes stars in flat image when the twilight brightness is low  1. tele sidereal drive is turned on ;star image remain fixed on the same pixels. Move tele for next flat image. Then normalizing and combineing the flat images with a median or mode 2. turn off drive. Cause trails of stars on each image. The combine the same way, most of the trails removed (some trails overlapped, so not so effetive as the first one) 2. Dome flat : can obtain any time, no stars, but not quite uniform, photometry not better than 1% with a dome screen 3. night sky flat : combine with mode ; remove stars. But low S/N so rarely used in optical, but used in the Infrared.

9. Calibrating the Science Data Correct all data for the bias offset ;subtracting the master bias from the dark, flat, target and fringe image Correct dark (scaled) : flat, target, & fringe images Correct fringe for target, flat images Divide target images by the Normalized flat image Data on CCD : two-D array of numbers B[x,y], D[x,y], F l [x,y], Fr l [x,y] & S l [x,y] Bias, dark, flat, fringe, science data

10. Neglecting fringing Normalized flat : F l n [x,y] =( F l [x,y] –B[x,y])/MODE(F l [x,y] – B[x,y]) Reduced science image S l * [x,y] = (S l [x,y]-(t s /t d )D[x,y] – B[x,y])/F l n [x,y] t s, t d ;exp time of science and dark

11. Characteriszing CCD Random noise : read noise & poison or shot noise Gain of CCD: array of counts (analog-to-digital Unit) ADUs or Data numbers =DNs Gain = the numbers of detected photons(=number of photoelectrons or electrons) corresponding to one count A/D converter ;discreet steps  digitization ;a type of noise The greater number of bits in an A/D converter, the less important this noise source becomes. Professional ; 16 bits (65 536 levels) cost speed & cost, many sys : 12 bits(4096) or 14bits(16 384 level) Digitization noise ;related to the value of the gain In units of electron s dig = [(g 2 -1)/12] 1/2

12. Full Well Capacity Gain set that the dynamic range of each pixel matches the count range of the A/D converter : FQC =200 000 A/D =16bits  gain = 3 electrons For faint target ;gain low For high count ;gain set high Smaller A/D converter for given full well, require high gain  greater digitization noise

13. Poisson noise Variance corresponding to N counts s poiss 2 = gN Total random noise = poisson + read noise s 2 = gN + s R Gain & read noise : Two bias B1, B2, and two flat F1, F2 : obtained close in time = eliminate the sys noise Form two difference images from the pair of biases and flats  variance on each difference image obtained with standard statistical methods, (ie width of the histogram of the counts of an image = variance) Variance of the flat difference image = sum of the poisson and read noise variances g 2 s F1-F2 2 = g 2 s poiss 2 + g 2 s B1-B2 2 g 2 s poiss 2 = g [F2 +F1] – (B1 + B2)] :average over all pixels on each images g 2 s B1-B2 2 = g 2 (s B1 2 +s B2 2 ) = 2g 2 s B1 2 = 2g 2 s B2 2 =2s R 2

14. s 2 count = N count /g + s R 2 /g 2 Log s count = ½ log (N count /g + s R 2 /g 2)