E O D2q

where O is the solid angle of the field of view, D is the diameter of the telescope, and q is the total throughput quantum efficiency of the instrument assuming that the seeing disk is resolved. One can see that the time needed for completion of a survey to a given brightness limit depends inversely on e.

Using wide-field CCD imagers leads to the inevitable result that new issues of calibration and data reduction must be developed. For example, when the field of view of a large-area CCD (whether a single large CCD

with a wide-field of view or an array of chips) approaches ~ 0.5° in size, differential refraction of the images across the field of view of the CCD begins to become important. Color terms therefore propagate across the CCD image and must be corrected for to properly determine and obtain correct photometric information contained in the data.

CCD observations that occur through uniform thin clouds or differential measures essentially independent of clouds are often assumed to be valid, as it is believed that clouds are grey absorbers and that any cloud cover that is present will cover the entire CCD frame. Thus flux corrections (from, say, previous photometric images of the same field) can be applied to the nonphotometric CCD data, making it usable. Large-field CCD imaging can not make such claims. A one or more square degree field of view has a high potential of not being uniformly covered by clouds, leading to unknown flux variations across the CCD image.

Observations of large spatial areas using CCD mosaics also necessitate greater effort and expense in producing larger filters, larger dewar windows, and larger correction optics. Variations of the quality and color dependence of large optical components across the field of view are noticeable and their optical aberrations will cause point-spread function (PSF) changes and other effects over the large areas imaged with wide-field CCDs. Production of large, high quality optical components is a challenge as well. For example, recent estimates for the cost of a single 16 to 20-inch square astronomical quality glass filter are in the range of $50000-200000.

The use of large-format CCDs or CCD mosaics on Schmidt telescopes is increasing and such an imager provides a good example of the type of PSF changes that occur across the field of view (see Figure 4.11). Coma and chromatic aberrations are easily seen upon detailed inspection of the PSFs, especially near the corners or for very red or blue objects whose peak flux lies outside of the color range for which the optics were designed. Thus, for wide-field applications, such as that represented in Figures 4.8-4.10, the typical assumption that all the PSFs will be identical at all locations within the field of view must be abandoned.

A more subtle effect to deal with in wide-field imaging is that of the changing image scale between images taken of astronomical objects and those obtained for calibration purposes. For example, a dome flat field image taken for calibration purposes will not have exactly the same image scale per pixel over the entire CCD image as an object frame taken with the same CCD camera, but of an astronomical scene. Also, how one maps the light collected per (non-equal area) pixel in the camera to a stored image in say RA and DEC is a tessellation problem to be solved.

PSF Variation across the Field of View n n-1 n-2

Fig. 4.11. PSF variations for a star imaged at nine locations within the field of view of a large mosaic CCD camera placed at the focal plane of a Schmidt telescope. Only the center of the field has a circular, symmetric PSF while the other positions show extended tails due to optical abberations and chromatic effects. The three PSFs at the bottom of the figure are column sums of the PSFs vertically above them. From Howell et al. (1996).

As with previous new advances in CCD imaging, wide-field imaging has issues that must be ironed out. However, this exciting new field of research is still in its infancy and those of you reading this book who are involved in such work are the ones who must help determine the proper data collection and reduction procedures to use.

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4.6.4 CCD drift scanning and time-delay integration

The standard method of CCD imaging is to point the telescope at a particular place in the sky, track the telescope at the sidereal rate, and integrate with the detector for a specified amount of time. Once the desired integration time is obtained, the shutter is closed and the CCD is readout. For telescopes incapable of tracking on the sky or to obtain large areal sky coverage without the need for complex CCD mosaics, the techniques of CCD drift scanning and time-delay integration were developed (McGraw, Angel, & Sargent, 1980; Wright & Mackay, 1981).

Drift scanning consists of reading the exposed CCD at a slow rate while simultaneously mechanically moving the CCD itself to avoid image smear. The readout rate and mechanical movement are chosen to provide the desired exposure time. Each imaged object is thus sampled by every pixel in the column thereby being detected with the mean efficiency of all pixels in the column. Nonuniformities between the pixels in a given column are thus eliminated as each final pixel is, in essence, a sum of many short integrations at each pixel within the column. Cross column efficiency differences are still present but the final image can now be corrected with a one-dimensional flat field. Drift scanning also has the additional advantage of providing an ideal color match to background noise contributions, unavailable with dome flats. Very good flat fielding of a traditional image might reach 0.5 or so percent, while a good drift scanned CCD image can be flattened to near 0.1 percent or better (Tyson & Seitzer, 1988). Drift scanning has even been accomplished with IR arrays (Gorjian, Wright, & Mclean, 1997).

Time-delay integration or TDI is a variant on the drift scanning technique. In TDI, the CCD does not move at all but is readout at exactly the sidereal rate. This type of CCD imaging is necessary if astronomical telescopes such as transit instruments (McGraw, Angel, & Sargent, 1980) or liquid mirror telescopes (Gibson, 1991) are to be used. The same flat fielding advantages apply here as in drift scanning but the integration time per object is limited by the size of the CCD (i.e., the time it takes an object to cross the CCD field of view). For a 2048 x 2048 CCD with 0.7 arcsec pixels, the integration time would be only 96 seconds at the celestial equator. Rescanning the same area could be performed and co-added to previous scans as a method of increasing the exposure time, but time sampling suffers.

TDI is mechanically simple, as nothing moves but the electrons in the CCD. This charge movement has been termed electro-optical tracking. Large sky regions can be surveyed, albeit to shallow magnitude limits, very quickly using TDI. Overhead time costs for TDI only consist of the "ramp up" time, that is, the time needed for the first objects to cross the entire field, and the scan time. Using our same 2048 x 2048 CCD as in the example above, we find that a 23 arcsec by 3 degree long strip of the sky at the celestial equator can be scanned in about 2-3 minutes compared with the nearly 25 minutes required if pointed observations of equivalent integration are used.

Although drift scanning and TDI are seemingly great solutions to flat fielding issues and offer the collection of large datasets, drift scanning requires the CCD to move during the integration with very precise and repeatable steps. This is quite a mechanical challenge and will increase the cost of such an instrument over that of a simple CCD imager. In addition, both techniques suffer two potential drawbacks (Gibson & Hickson, 1992). Images obtained by drift scanning and TDI techniques have elongated PSFs in the east-west direction. This is due to the fact that the rows of the CCD are shifted discretely while the actual image movement is continuous. We note here that objects seperated by even small declination differences (i.e., one CCD field of view) do not have the same rate of motion. The resulting images are elongated east-west and are a convolution of the seeing with the CCD pixel sampling.

TDI imagery contains an additional distortion in the north-south direction due to the cuvature of an object's path across the face of the CCD (if imaging away from the celestial equator). This type of distortion is usually avoided in drift scan applications as the telescope and CCD tracking are designed to eliminate this image smearing. This sort of mechanical correction can not be applied to TDI imaging.

These image deformations have been studied in detail (Gibson & Hickson, 1992) and are seen to increase in magnitude for larger format CCDs or declinations further from the celestial equator. For example, at a declination of ±30°, a 1 arcsec per pixel CCD will show an image smear of about 6 pixels. One solution to this large image smear is to continuously reorient the CCD through rotations and translations, such that imaging scans are conducted along great circles on the sky rather than a polar circle or at constant declination. Such a mechanically complex device has been built and used for drift scanning on the 1-m Las Campanas telescope (Zaritsky, Shectman, & Bredthauer, 1996). Another solution is the development of a multilens optical corrector that compensates for the image distortions by tilting and decentering the component lenses (Hickson & Richardson, 1998).

A few telescopes have made good use of the technique of drift scanning or TDI, providing very good astronomical results. Probably the first such project was the Spacewatch telescope (Gehrels et al., 1986) built to discover and provide astrometry for small bodies within the solar system. Other notable examples are the 2-m transit telescope previously operated on Kitt Peak (McGraw, Angel, & Sargent, 1980) and a 2.7-m liquid mirror telescope currently running at the University of British Columbia (Hickson et al., 1994). This latter telescope contains a rotating mercury mirror and images a 21-arcminute strip of the zenith with an effective integration time of 130 seconds. Using TDI, a typical integration with this liquid mirror telescope reaches near 21st magnitude in R and continuous readout of the CCD produces about 2 Gb of data per night.

Present-day examples of telescopes employing drift scanning and TDI techniques are the QUEST telescope (Sabby, Coppi, & Oemler, 1998), the Palomar QUEST imager (see Table 4.2) and the Sloan digital sky survey (Gunn et al., 1998). The QUasar Equatorial Survey Team (QUEST) telescope is a 1-m Schmidt telescope that will provide UBV photometry of nearly 4000 square degrees of the sky to a limiting magnitude of near 19. The focal plane will contain sixteen 2048 x 2048 Loral CCDs arranged in a 4 x 4 array. The telescope is parked and the CCDs are positioned such that the clocking (column) direction is east-west and the readout occurs at the apparent sidereal rate. Each object imaged passes across four CCDs covered, in turn, with a broadband V, U, B, and V filter. The effective integration time (i.e., crossing time) is 140 seconds, providing nearly simultaneous photometry in U, B, and V.

As we have seen above, a problem with drift scanning is that the paths of objects that drift across the imager are not straight and they can cross the wide-field of view with different drift rates. We have discussed a few solutions to these issues, and in the QUEST project (Sabby, Coppi, & Oemler, 1998) we find another. The CCDs are fixed, in groups of four, to long pads lying in the north-south direction. These pads can pivot independently such that they align perpendicular to the direction of the stellar paths. The CCDs are also able to be clocked at different rates, with each being readout at the apparent sidereal rate appropriate for its declination.

The Sloan digital sky survey (SDSS) is a large-format mosaic CCD camera consisting of a photometric array of thirty 2048 x 2048 SITe CCDs and an astrometric array of twenty four 400 x 2048 CCDs (see Figure 4.12). The photometric CCDs are arranged in six columns of five CCDs each, providing essentially simultaneous five-color photometry of each image object. The astrometric CCDs are mounted in the focal plane above and below the main array and will be used to provide precise positional information needed for the follow-up multi-fiber spectroscopy. The SDSS uses a 2.5-m telescope located in New Mexico to image one quarter of the entire sky down to a limiting magnitude of near 23.

Fig. 4.12. The optical layout within the dewar of the Sloan digital sky survey CCD imager. The right side of the figure labels the CCDs as to their function; 1-15 are photometric CCDs, 16-21 are astrometric CCDs, and 22 (top and bottom) are focus CCDs. The left side gives the dimensions of the array. The labels r'-g' denote the five separate intermediate band filters, each a single piece of glass covering all six horizontal CCDs. The scan direction is upward causing objects to traverse the array from top to bottom. From Gunn et al. (1998).

Fig. 4.12. The optical layout within the dewar of the Sloan digital sky survey CCD imager. The right side of the figure labels the CCDs as to their function; 1-15 are photometric CCDs, 16-21 are astrometric CCDs, and 22 (top and bottom) are focus CCDs. The left side gives the dimensions of the array. The labels r'-g' denote the five separate intermediate band filters, each a single piece of glass covering all six horizontal CCDs. The scan direction is upward causing objects to traverse the array from top to bottom. From Gunn et al. (1998).

TDI scans along great circles are used by the SDSS to image a region of the sky 2.5° wide. Using five intermediate band filters, covering 3550 A to 9130 A, scanning at the sidereal rate provides an effective integration per color of 54 seconds with a time delay of 72 seconds between colors caused by CCD crossing time and chip spacing. Complete details of the SDSS, too lengthy for presentation here, can be found in Gunn et al. (1998). Other projects of a similar nature are discussed in Boulade et al. (1998), Gunn et al. (1998), and Miyazaki et al. (1998). The SDSS prime survey is complete and much of the data are already available (see Appendix B).

4.7 Exercises

1. Derive the first two equations of Chapter 4.

2. What focal length (/-ratio) of telescope is best if your observational requirements need a plate scale of about one tenth of an arcsec/pixel? How does your answer depend on the type of CCD used? What is the /-ratio of a typical present-day large reflecting telescope?

3. Design an experiment to obtain a good flat field image, that is, one that will allow you to measure the pixel-to-pixel variations to 1%. How might your experiment differ if you were to make the measurements in the red? In the blue? Of the night sky?

4. What are the differences between a sky flat and a dome flat? Which is easier to obtain? Which provides the better flat field?

5. What are the flat fielding requirements needed for point source photometry? For extended object spectroscopy? For extended object imaging? How might you accomplish each of these?

6. Using the method outlined in Section 4.3, determine the gain and read noise for a CCD you work with.

7. Using the equations presented in Section 4.4, calculate the individual noise contribution per pixel from read noise, sky background, and dark current given the following conditions. You are using an E2V CCD at operating temperature (as described in Table 3.2) and have obtained a 1200 second exposure on a full moon night using a Johnson V filter. (Note: You will have to estimate the sky brightness (see an observatory website for such details), plate scale, and band-pass of your observation.) Plot your results. Which noise source is the greatest? How might you eliminate it?

8. Derive the signal-to-noise equation.

9. Describe an observational setup for which a 15th magnitude galaxy is a bright source. Do the same for a faint source.

10. Work through the example S/N calculation given in Section 4.4.

11. Answer the question posed in the footnote on page 76.

12. Derive the expression for the integration time needed to achieve a specific S/N as given at the end of Section 4.4.

13. Produce a flow chart of a typical reduction procedure for CCD imaging observations. Clearly show which types of calibration images are needed and when they enter into the reduction process.

14. Why do you divide object frames by a flat field calibration image instead of multiplying by it?

15. Look at Figure 4.4. If the doughnuts are due to out-of-focus dust, how might you be able to use their size or shape to tell if that dust was on the dewar window or on a filter high above the CCD dewar?

16. Using information on the wavelengths and strengths of night sky emission lines (see e.g., Broadfoot and Kendall, 1968, Pecker, 1970, or observatory websites), discuss which broad-band Johnson filters are likely to be affected by these lines. How might one design an observational program that uses these filters but lessens the effect of the night sky lines?

17. Using the physical principles of Newton's Rings, quantitatively describe CCD fringing providing a relationship between the CCD thickness and the wavelength observed.

18. Discuss how OTCCDs can provide tip-tilt corrections over an arbitrary field of view. Why can mechanical tip-tilt systems not do this?

19. Using the expression given for the efficiency of a large area survey, calculate the efficiency for each imaging program listed in Table 4.2. How does the LSST project compare to the rest? How do your values compare with a survey using a 4-m f/1.5 telescope able to image onto a 14 x 14 inch photographic plate?

20. Design an observational experiment to map galaxy clusters using a CCD system that operates in drift scanning mode. Discuss the details of observational strategy, integration times, instrument design, and calibration. Where would you locate your survey telescope and why is this important? How does this type of observation program compare with a similar one that uses a conventional point-and-shoot CCD system?

21. Read the description of the Sloan survey given in Gunn et al. (1998). Discuss why this survey is important to astronomy. Can you think of any improvements you would make to the methods used if you were designing the survey?

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