Introduction to Image Reduction

Motivation & background Instrumental Signature Removal Combining multiple images Photometric calibration 

Introduction to Image Reduction 

David Wittman 

University of California, Davis 

2011 Summer School: 

Weak and Strong Gravitational Lensing 

Beijing


Goals 

Everyone believes an experiment except the experimenter; no one 

believes a theory except the theorist. 

So my goals are 

• to give theorists some appreciation of observational difficulties 

• to give potential observers a roadmap


What do you see on a raw image?


What do you see on a raw image? 

Some things can be removed (or at least masked) as part of instrumental 

signature removal: 

• response (“flatfield”) 

variations 

• saturation and bleeding 

• cosmic rays 

• bad columns or areas 

• different amplifier gains 

• fringing (if present) 

Instrumental signature removal “cleans” your images: 

→ 

and allows you to do relative photometry (these are not the same thing!).


Beyond ISR 

ISR is also necessary before you can combine multiple images: 

20x → 

Other effects will be treated later: 

• point-spread function (PSF): the response of the optical 

system to a point source is not a point 

• photometric calibration: comparing with standard stars to 

calibrate sources in terms of Wm −2 s −1 (in the relevant 

bandpass)


Important parameters: 

• quantum efficiency 

How a CCD works 

Amplifier 

• full well and saturation/bleeding 

• charge transfer inefficiency 

One pixel 

• pixel size and (mostly) other variations: flatfield response 

• readnoise and gain (next page)


Noise and S/N 

If electrons accumulate at a rate r, after a time t a pixel will contain rt 

electrons and the Poisson noise will be √ rt. The readout electronics add 

a Gaussian noise σ so that the signal-to-noise ratio is: 

S 

N = 

rt 

√ 

σ + rt 

For long (“sky noise limited”) exposures S 

N ∝ √ t so it’s hard to go deep! 

(Note tradeoff with area.) Be aware short exposures suffer a relatively 

large read noise penalty. 

The amplifier applies a “gain” factor G to obtain a digital number (DN) 

or analog to digital unit (ADU): 

where G is in e − /ADU. 

ADU = rt 

G


Major types of CCDs 

• Front vs back illuminated: Back is best 

for quantum efficiency. 

• Thick (∼ 100µm vs thin ∼ 10µm: thick 

increases red sensitivity and decreases 

fringing 

• type of antireflective coating strongly 

influences red/blue sensitivity 

FRONT 

BACK 

CMOS and infrared sensors are not CCDs because they have an 

amplifier on each pixel and can read nondestructively. 

.


Ground-based vs space-based 

Ground Space 

Background high ∗ 

low 

CR rate low high 

Charge transfer efficiency good degrades with time † 

Photometric stability variable stable 

Angular resolution limited by atmospheric “seeing” can be very good ‡ 

Wavelength limitations some none 

Cost low high 

Typical reduction mode do-it-yourself (software provided) more automated 

∗ most galaxies are much fainter than “blank” sky! 

† result: streaking as shown at right 

‡ depends greatly on observatory parameters


Instrumental signature removal: overview 

• mask: identify bad pixels/areas to eliminate them from the 

following computations 

• overscan: correct for the bias of each row 

• crosstalk: correct for “signals” from nearby amplifiers 

• debias: correct for spatial variation of bias 

• defringe: subtract fringe pattern due to sky lines if present 

• flatfield: correct for nonuniform response


Masking 

• identify 

pixels/areas 

which are always 

bad (eg dark 

column at left) 

• on each image, 

identify unique 

bad areas 

• always take 

multiple shifted 

exposures to fill 

in bad areas


Overscan 

Determines ADU level corresponding to zero light, by reading out virtual 

pixels after the last real pixel in each row. 

Subtract the overscan level from each row.


Bias and dark frames 

Bias (or zero) frames measure how the zero-light ADU level changes 

across each row. Always take multiple frames per night and average them 

for a robust measure. 

Dark frames measure how this level changes with time: usually negligible 

in modern cameras, but you should always check. 

Subtract the bias or dark frame from each data frame.


Defringing 

Fringes have a stable spatial pattern, but amplitude varies in time. 

Make a fringe frame by median-combining your data and high-pass 

filtering the result: 

On each science frame, subtract the fringe frame times the best-fit 

amplitude.


Flatfielding 

Basic idea: make a “uniformly illuminated” image (see below) and divide 

your data frames by it. 

This image shows dust (dark rings) 

and center-to-edge illumination 

gradient (vignetting) . 

Instead of uniformly illuminated, we really want an image illuminated just 

as the science objects are, e.g., vignetted in exactly the same way.


Standard flatfielding options 

• dome flats: most telescopes have a (roughly) uniformly 

illuminated white screen inside the dome 

• twilight flats: the sky itself is roughly uniform (on camera 

scales) at twilight 

• dark-sky flats: median-combine the science frames 

None of these is perfect, for two reasons: 

• sky (and dome) photons can travel through the optical system 

in different ways than object photons! 

• response is a function of color


Beyond Standard Flatfielding 

Ubercal (Padmanabhan et al 2008): use object photometry from multiple 

shifted expsures to solve for a model of required flatfield corrections. 

minstr = mtrue + kA + f (x, y) 

where A is the airmass of each exposure (assuming a photometric night!). 

Solve for k, f (x, y), and mtrue for each star (nuisance parameters). f (x, y) 

should be zero if standard flatfielding has worked. 

Results from Deep Lens Survey: ∼ 0.05 mag variations


Beyond Standard Flatfielding II 

Stubbs et al: calibrate each pixel’s response at each wavelength 

with a tunable laser: 

Pan-STARRS at 901 nm. 

This way the colors of the sources can properly be taken into 

account.


Caution for wide-field cameras 

The pixel size (as projected on the sky) changes from center to 

edge in wide-field cameras, due to optical distortion. 

Pixels at corners subtend less sky and appear fainter on sky flats, 

but do not collect fewer photons from stars and galaxies! 

Model the optical distortion to remove this effect. 

Also account for this effect when repixelizing onto a uniform grid! 

(See, eg, Mosaic data reduction manual for a more detailed 

explanation.)


Why don’t we remove effect of PSF by deconvolving? 

from GREAT08, Bridle et al 

Deconvolution works well only in the high-S/N limit. (Same is true of 

many classical image-processing techniques.) 

Lensers extract lensing-specific corrections from the PSF, or 

forward-model the whole process.


Combining multiple images: overview 

Conceptually, simply “coadd” multiple images of the same field to obtain 

a higher S/N “stacked image.” 

20x → 

This is a form of lossy data compression with (usually) high compression 

and low loss. 

There may be better ways to analyze your dataset (eg comeasurement, 

model fitting), but you usually want a stack at least for reference 

purposes.


Cosmic ray rejection strategies 

• Start by building observatories/cameras with low-radioactivity materials! 

• If you have only one image, you can still identify most CR (at the catalog 

stage) as narrower than the PSF: 

• If you have two unshifted exposures, you can compare and mask. 

• Most often, you have multiple exposures and you can reject CR while 

stacking 

• CR are not the only things that change from image to image: also 

asteroids and satellite trails.


Combining multiple images: prerequisites 

• coordinate transforms between stack and each exposure 

• relative photometric throughput of each exposure 

• relative S/N of each exposure (for weighting) 

• masks for each exposure 

• sky model for each exposure 

• other metadata for each exposure: eg saturation level 

• (ignoring PSF for now)


Combining multiple images: subtleties 

• clipping biases the photometry (eg stars get much peakier in 

good seeing). Best to identify outliers before stacking (eg 

with psf-matched difference imaging) 

• for the same reason, a pixel saturated in any exposure should 

be considered always saturated 

• it’s not clear how to combine exposures with very different 

PSFs. May be best to forward-model everything. 

• track how many input pixels go into each output pixel (and 

their variance)


Photometric calibration 

• on “cloudless” (photometric) nights, image (and reduce, photometer) 

standard star fields several times, at a range of airmass 

• model the effect of airmass (usually linear in mag) and derive a 

photometric zeropoint m0 such that mtrue = minstr + m0 at zero airmass:


Next lecture: 

Turning your image into a catalog of stars and galaxies and 

their properties.

Introduction to Image Reduction

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