1	PHYS 278 Advanced Astronomy
2	Median Filtering
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5	Application of a median filter
6	Median Filtering M87 Original 21x21 Median Filter Subtracted Image
7	Image photometry What do we want to get from this meadian filtered image? Numbers of objects Positions Brightnesses (magnitudes) Rejection of non-stellar objects
8	PSF-Fitting Photometry Ordinary aperture photometry is impossible for crowded fields where stars are overlapping -- e.g. globular cluster One needs to detect and separate the overlapping images --- basically a deconvolution! Relies on CCDs being linear devices Thus, the PSF (dirty beam) can be shifted, scaled, and fit to each overlapping image simultaneously to give its position and brightness Much like CLEAN for radio data --- several packages, e.g. DAOPHOT, DOPHOT
9	Overlapping Images
10	DAOPHOT Procedure Need to know data characteristics (gain, read-noise, etc) (1) Derive the PSF from isolated, bright stars (2) Find stellar objects in the frame --- look for peaks above the local sky level (3) Obtain initial magnitudes for those objects --- simple aperture photometry (4) ‘Shift-and-Scale’ the PSF and fit to each object -- local sky value determined during the fitting
11	Finding Stars Original With found Image objects (TVMARK)
12	The Final Result Original With stars Image fitted and subtracted
13	SuperCOSMOS IAM: image analysis mode
14	Data compression
15	Image Restoration/Deconvolution O(x) = output image (observed) H(x) = blurring function N(x) = noise I(x) = input image -- what we want to find !! Problem: given the observed image O(x) and blurring H(x), what was the original image I(x)? Image Deconvolution
16	Image Blurring For astronomical imaging, the blurring H(x) arises from: -- Earth’s atmosphere (‘seeing’) -- telescope + instrument (imperfect optics) -- detector (e.g. sampling image with CCD pixels) Sum of these = Point Spread Function (PSF) The PSF describes how a point source of light (e.g. a star) is smeared out by all of the above things -- PSF is roughly a (two-dimensional) Gaussian -- Radio astronomy equivalent is ‘Dirty Beam’
17	Image Deconvolution Deconvolution is hard: there are no unique solutions! -- many light distributions will be smeared out into the same output image, within the errors Thus, add some constraints: input image has to be positive, smooth and have right noise properties (Poisson) Deconvolution algorithms are usually iterative, using the known PSF, and starting with an initial guess Have to worry about increased noise, and photometric accuracy
18	Deconvolution Algorithms Van Cittert (1931)! take the output image O(x) as the first approximation to the input image I(x) blur this first approximation and compare with the true output image O(x) the difference between the two is used as a correction to our initial estimate for I(x) Iterate until the model ‘agrees’ with real output image O(x)
19	Deconvolution Algorithms Richardson-Lucy (Richardson 1972, Lucy 1974) -- one of the most commonly used, especially with pre-refurbishment HST images -- also an iterative method, but using Poisson statistics, which also forces input image to be positive Image(n+1) = Image(n) x Original data * Reflect(PSF) Image(n)*PSF
20	Examples
21	Richardson-Lucy Examples
22	One More ...
23	Deconvolution Algorithms Maximum Entropy (Skilling and Brian 1984) -- maximizes the entropy: here this means that the model brightness distribution should be as close as possible to actual brightness distribution on sky -- often used to sharpen radio maps Dithering and Drizzling (Space Telescope, ESO, 1994--) -- extensively used with HST/WFPC2 data -- here shifted images are used to effectively carry out finer sampling of the image -- ‘sharper’ PSF -- more recently MCS deconvolution
24	"MCS Deconvolution" MCS Deconvolution
25	M31 Globular Clusters Image taken with HST/WFPC2 and restored using the MCS algorithm
26	Image processing software A wide variety of image processing software packages are available both as freeware and as sophisticated commercial packages Many have direct application to astronomical images and image processing problems Some are available to the general and amateur community (e,g, MIRA) Professional astronomers make use of a range of software packages developed specifically with astronomical image processing requirements in mind The most common astronomical IP packages come under the umbrella titles of: iraf (developed in USA - very complex, hierarchical extensive library of ip products) Midas (developed for ESO and European astronomers) STARLINK packages (developed in UK) such as KAPPA, PISA, GAIA