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In my final two lectures I will discuss the general subject of Stellar Photometry with CCDs, and will talk in particular about ways in which statistics contribute to the subject - especially the sort of statistics that you can't find in cookbooks. But first of all let me deal with some more general, astronomical questions. Why do we do Stellar Photometry with CCDs in the first place? I'm not going to consider that part of the question which is "Why do we do stellar photometry?" - since we all know that stellar photometry is one of the very most exciting and important tasks of modern astrophysics - but I do want to answer that part of the question which is "Why do we do it with CCDs?"

As you know, "CCD" stands for "charge-coupled device." These are small, solid-state arrays of silicon photodetectors which, when put at the focus of a telescope, enable us to obtain a digitized representation of a small portion of the sky. Fig. 4-1 is one of the best arguments I can present for why it's worthwhile to use these little dealybobbers for stellar photometry. The figure shows three different color-magnitude diagrams for the globular cluster 47 Tucanae. All three were constructed by the same astronomers using the same telescope, but with three different generations of image-detector technology. (The top parts of the three color-magnitude diagrams, that is, the cluster's giant and horizontal branches, are the same data in all three panels. What I want you to notice just now is the evolution with time of the bottom part of the diagram - the cluster's main sequence.) Rest assured that, in its day, each of these color-magnitude diagrams was considered one of the best and deepest that had ever been made. The left-hand panel is based on the "classical" technique of photographic photometry, where images of the cluster were recorded on photographic plates, and then a device called an iris photometer was used to measure the diameter and the blackness of each star image on those plates (Hesser and Hartwick 1977). Since photographic plates are rather non-linear recorders of relative intensity, these diameter and blackness measurements come out in some arbitrary units and on a varying scale. Thus, they can only be related to legitimate stellar magnitudes through measuring a number of stars on each plate whose brightnesses had previously been determined by photoelectric techniques. A example of such a calibration curve, from Stetson and Harris (1977), is shown in Fig. 4-2. Largely because of the extreme difficulty of obtaining adequate photoelectric observations for faint stars, photographic photometry was seldom reliable much below about 20th magnitude (and more recent work with CCDs has found serious systematic errors in a number of famous old studies at even brighter levels than this).

Figure 4-1
Figure 4-1.

Figure 4-2
Figure 4-2.

The middle color-magnitude diagram in Fig. 4-1 was based on data obtained with a SIT Vidicon camera (Harris, Hesser, and Atwood 1983a, b). This device used standard, commercial television technology to obtain a digital image of a small area of sky. One of the great things about the Vidicon was that it combined the quantum efficiency of a photocathode (~ 20%, as compared to ltapprox 1% for most photographic emulsions) with the plate's ability to record two-dimensional images. But also - perhaps even more important - to a reasonably good approximation the Vidicon was photometrically linear, which means that the signal produced by the detector was directly proportional to the brightness of the source:

magnitude = constant - 2.5 logI.

This meant that the conversion from data numbers to instrumental magnitudes did not require a full calibration curve, the way it did with photographic plates; all you needed was a single zero-point constant, which could be obtained from just the brightest stars in the frame, or even from standard stars in other parts of the sky if the night was photometric. For both of these reasons (sensitivity and linearity) the SIT Vidicon enabled astronomers to make color-magnitude diagrams extending one to two magnitudes fainter than was practical with photographic/photoelectric techniques. And they could do it in less time, in part because of the combination of sensitivity with multiplex advantage, but also because they no longer had to combine two observing techniques (and two or more observing runs) to get their color-magnitude diagram: they could do it all at once.

Still, Vidicon cameras enjoyed only a very brief day in the sun (so to speak), because they were almost immediately supplanted by something even better: CCDs. An early (astronomically speaking) CCD made the rightmost color-magnitude diagram in Fig. 4-1. As I said before, CCDs are image detectors based upon solid-state silicon semiconductor technology. They can be somewhat bigger than Vidicons, having photosensitive areas ranging from 1.2 cm on a side to gtapprox 3 cm, as compared to about 1 cm; they can be more sensitive than Vidicons, reaching peak quantum efficiencies in the neighborhood of 70%, as compared to ~ 20%; and finally, they can be much more stable than Vidicons, because they consist of physical patterns permanently imbedded in a chunk of silicon, while the TV cameras rely on a scanning electron beam, with its propensity for being bent by stray magnetic fields or even by the electronic image which has built up on the target. This makes observations made with CCDs much more repeatable and easy to calibrate. You can easily see in Fig. 4-1 how the greater sensitivity and stability of the CCD have enabled the astronomers (Hesser, Harris, VandenBerg, Allwright, Shott, and Stetson 1987) to produce a main sequence for 47 Tucanae which is both much deeper and much narrower than was possible with either of the two previous technologies. What a difference a decade makes! It is because the CCD is in almost every way the best existing detector for obtaining optical images in astronomy (5) that I call these two lectures "Stellar Photometry with CCDs," even though most of the things I will have to say would apply equally well to photometry obtained from other types of photometricaily linear two-dimensional images.

Before I go deeply into the subject of exactly how we do stellar photometry with CCDs, let me just briefly mention who does stellar photometry with CCDs. Here is a list of the most famous existing packages for photometry from two-dimensional digital images (I include only packages which are designed to deal with crowded-field conditions, where stellar images may overlap each other).

RICHFLD Tody 1981
ROMAFOT Buonanno, et al. 1983
WOLF Lupton and Gunn 1986
STARMAN Penny and Dickens 1986
DAOPHOT Stetson 1987

In most ways, for most typical applications, and as far as I know, these programs are roughly comparable in accuracy, convenience, and power. Any particular program may be less convenient or less accurate in some applications, while the same program may offer distinct advantages for other tasks. I do not intend to present any value judgments. Instead I will spend my time talking about DAOPHOT because that is the program I am most familiar with. You should not take this to mean that I think that DAOPHOT is much better (or much worse) than any of the other programs - I have many opinions on this subject, but I'm not planning to present any of them here and now.

There are numerous tasks which a computer program or ensemble of programs must perform, in order to get from the digital image to a data table containing standard magnitudes and colors for a large number of stars. Today I will discuss the first half of the problem: the path from a single data frame to a list of positions and stellar magnitudes for the stars contained in that frame. Tomorrow I will discuss the second half of the problem: the path from a number of lists of positions and relative magnitudes obtained from a number of frames, to a single list of calibrated magnitudes and colors for the stars in the field. I will not discuss the problems of image-rectification: questions of bias levels, dark signal, flat-fielding and the like. Unfortunately, there have not yet been enough studies done and papers published in these areas, and I do not know of a good, comprehensive, current, essentially correct cookbook for dealing with everything that can go wrong. Understanding this subject seems to be still a matter of picking up a snatch of information from this paper, hearing a good idea from that astronomer over a glass of beer, and figuring it out for yourself. However, there's not enough time left to do everything, so I'm leaving this stuff out. Ask me over a glass of beer someday (you buy), and I'll tell you what little I know of the subject.

So, here is today's list of data-reduction tasks to consider. I present them in the DAOPHOT nomenclature.

(1) FIND

First you must FIND the stellar-appearing objects in the frame. Each program has its own method - sometimes several methods - of performing this, but the basic idea is to produce an initial list of approximate centroid positions for all stars that can be distinguished in the two dimensional data array. The star finder must have at least some ability to tell the difference between a single star, a blended clump of stars, and a noise spike in the data. It's a good idea to get a crude estimate of each star's apparent brightness at the same time. [For cognoscenti, this step combines DAOPHOT's FIND and PHOTOMETRY routines; these are discussed separately below.]

(2) PSF - The Point-Spread-Function

Next, the program must measure, encode, and store the two-dimensional intensity profile of a typical star image in the frame. Again, each package does this in a different way, but the one basic idea which is common to all packages is that the shape of the profile is assumed to be independent of the brightness of the star. Therefore, the profile shape can be determined from one or more bright, isolated stars, and then this profile is fitted by means of least squares to other program stars (which may or may not overlap with each other) pretty much as we did it in the second lecture.

(3) FIT

So, obviously, step 3 is to fit the model profile obtained in step 2 to the images of the stars found in step 1. Assuming that the shape of the profile of each star is now known, we must use nonlinear least squares to shift that profile in x and y and determine the local background intensity - which is the local diffuse sky brightness - and the intensity amplitude of the profile - which gives the relative brightness of the star - to best match the actual observed intensity data within the star image. Since this is a nonlinear problem, you need to have starting guesses at the fitting parameters to get the iterated least squares going; these come from step 1 above. In real images of astronomical starfields, the profiles of several stars will sometimes (often? almost always?) overlap by a bit. The reduction procedure must be able to recognize this situation and determine the positions and brightnesses of blended stars simultaneously.

The next two generic tasks are not necessarily part of the "photometric reduction" procedure in the strictest possible sense of the phrase, but they are so essential to evaluating the results and demonstrating their quality to other people, that any right-thinking reduction package includes them.


Once you have fit model profiles to all the stars in some two-dimensional digital frame, you want to subtract out these model profiles, so that you can examine the fitting residuals by eye and/or software. This enables you to recognize problems, such as stars that the star-finding routine has missed, and galaxies or image flaws that have been found and reduced as though they were stars.

(5) ADD

Finally, once the model stellar profile has been determined, it is extremely handy to be able to add it back into the image at various locations and with various intensity amplitudes. This process creates images of additional "stars" whose positions and relative brightnesses are known a priori. By running this new frame through the same reduction procedure as the original one, the effectiveness and accuracy of the star-finding and profile-fitting routines can be checked with full quantitative rigor, under the precise seeing, sampling, and crowding conditions relevant to your study.

I wrote a computer program - DAOPHOT by name - which performs all of the steps outlined above. Let me tell you something how it does them, and why. (I would like to repeat: this discussion is intended to exemplify ways in which least squares and other statistical methods can be employed in the field of stellar photometry with CCDs, using a software package that I am personally familiar with. If I don't give equal time to your favorite package, tough.)

5 One obvious exception is large-area survey work, such as with Schmidt telescopes for example, where the enormous size of photographic plates (up to 50 cm square, in current astronomical applications) compensates for the loss of quantum efficiency not to mention the much greater ease of transporting and displaying the data. Back.

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