CCD Photometry of Comets
This article was originally published in October 1994 issue of International Comet Quarterly (ICQ) and was reproduced here in slightly revised form with kind permission of the ICQ editor - D. W. E. Green.

Authors:
Herman Mikuz (1,2)
Bojan Dintinjana (2)

(1) Crni Vrh Observatory, 5274 Crni Vrh nad Idrijo, Slovenia
(2) Department of Physics, University of Ljubljana, Slovenia

Abstract
1.Introduction
2.Observations
3.Image processing and data reduction
4.Results
5.Conclusions
6.Acknowledgements
7.References
8.Appendix

Abstract
This article is based on our 4-years of experience with the CCD photometry of comets, performed mainly with 20-cm and 36-cm telescopes and two CCDs. Regular observations started in September 1992 at the Crni Vrh Observatory, using the 20-cm, f/2 Baker-Schmidt camera equipped with the ST-6 CCD detector and standard V filter. The image processing and data reduction are performed by the observatory PCs with the PCVISTA, DAOPHOT II and FitsPro packages. They enables a wide variety of routines, including dark subtraction and flat-fielding as well as complete photometric reduction. These procedures and also observational techniques are reviewed in detail. Our present configuration of telescope and CCD detectors enables photometry of comets down to 18th magnitude.
1. Introduction
Until very recently, the visual magnitude estimates of faint comets have been rather tricky, reserved mainly to dedicated observers with large telescopes. According to our experiences, the 14th magnitude comets are barely visible via a 36-cm telescope, even in good conditions. In addition, there is often lack of good reference fields close to the comet - resulting in estimates that are rather uncertain. Thus, the quality of estimates greatly depends on the observer's experience and on physical observing conditions. However, the present availability of commercial CCDs has changed the situation in the field. Thanks to their high sensitivity, accurate photometry can now be performed with fairly small telescopes.
2. Observations
2.1 Instrumentation
A good observing site with dark sky and unobstructed horizons is necessary for comet photometry. Our observations are performed at the Crni Vrh Observatory, located in the woodland region of Western Slovenia, at an altitude of 730m. It has about 120 clear nights/year and fairly dark skies in all directions.
2.1.1 Telescopes
The observatory holds a wide variety of instruments which enable us to follow almost any comet - from very faint up to very bright. The following telescopes + CCDs are in use:
Telescope Range of comet magnitudes covered CCD detector Field (arc min)
36-cm, f/6.8 Schmidt-Cassegrain 13-18 Wright 578 x 385 pixels, 22 um x 22 um pixel size, thinned 16.7 x 10.9
20-cm, f/2 Baker-Schmidt 5-12 ST-6 (TC-241) 375 x 244 pixels, 23 um x 27 um pixel size 72 x 54

Table 1: Our combinations of telescopes + CCDs

Both telescopes are attached on a separate mountings. The 36-cm Schmidt-Cassegrain is completely computerized and operated from the control room. The 20-cm, f/2 Baker-Schmidt camera is mounted on the Byers equatorial mounting. The camera have a special bar cage structure, made of low-expansion Invar alloy that holds the mirrors at a permanent distance. This prevents shifting of the focal planes due to ambient temperature changes and enables us to begin observations without losing time for focusing.

For very bright comets with coma as large as 1 degree (such as Hyakutake or Hale-Bopp), the only way to successfully perform CCD photometry is the use of short-focus lenses. In addition such lenses may cover a field of several degrees and are thus very suitable for imaging of the comet tail. Some combinations of lenses + CCDs that we frequently used are given below:

Camera Lens Range of comet magnitudes covered Useful Field (with the Wright CCD)
180mm f.l. lens brighter than 5m 3.8o x 2.5o
90mm f.l. lens brighter than 5m 7.5o x 5.0o
65mm f.l. lens brighter than 5m 10.4o x 6.9o

Table 2: Our combinations of lenses + CCDs

2.1.2 CCDs
Considering the front-illuminated CCD detectors that are now commonly used in commercial (low cost) CCDs, the main difference among them is in their quantum efficiency (QE). Let us compare the QE data for Kodak KAF-400/1600 chips now widely used and TC-211-255 series used in SBIG ST-4, ST-5 and ST-6. The comparative results are summarized in Tables 3 and 4.
Photometric passband Wavelength (nm) QE (%)
TC-211-255 KAF-0400 KAF-1600(*)
B 450 28 12 12
V 550 45 36 39
R 650 62 35 32

(*) Sources: Texas Instruments CCD Sensor Specifications, Kodak CCD Sensor Specifications

Table 3: Quantum efficiency of some CCD sensors in respect to standard photometric passbands

CCD sensor Relative QE TC/KAF (TC=1)
B V R
TC-211-255 1 1 1
KAF-0400 0.43 0.80 0.56
KAF-1600 0.43 0.87 0.52

Table 4: Relative quantum efficiency of some CCD sensors, used in present commercial CCDs

It is evident from Table 4 that the QE of Kodak KAF series CCDs is only half or less in B,R bands and about 80% in V band when compared to TC-241 (ST- 6) CCD. This detectors are thus less suitable for CCD photometry. If we compare both detectors, we believe the Kodak ones with 9 micron pixels and lower QE are suitable for astrometry where high resolution is more important than sensitivity (filters are not necessary for astrometric work). On the other hand, the TC- based CCDs with higher QE are more suitable for CCD photometry. Furthermore the TC-241 chip have additional advantage due to larger pixels, which are able to collect more photons on a single pixel, resulting in additional improvement of S/N ratio. Indeed, the S/N ratio may be improved even at Kodak chips by the use of binning option although the difference in QE (sensitivity) still remains.
We may therefore conclude that the combination of short focus telescope and large-pixel detector is most suitable for CCD photometry of extended objects like comets.
2.1.3 Filters
CCDs have responses that vary with spectral wavelength; they are predominantly sensitive to longer wavelengths, reaching a peak at red spectral bands. Meanwhile, comparison stars have different surface temperatures and thus differ in color index. In order to measure comparison stars and the comet in the standard Johnson V band, the observers should use V photometric filter. Once having filters, they need to calibrate them (e.g. determine the color transformation coefficients) using some standard sequence. In this way we get information on how well our filters conform to the standard passbands.
Our V filter for coated CCDs was made as proposed by Bessel (1990, 1995). Using standard equatorial sequences (Menzies et. al. 1991), we obtained the V color-transformation coefficient epsilon = 0.069 (Henden and Kaitchuck 1990) for our 20-cm, f/2 camera + V filter. This indicate that our combination of filter and CCD is very close to the standard Johnson V passband.

The molecular carbon and cyanogen emitted by the head are the first spectra to become visible as the comet approaches the sun (Brandt & Chapman 1992, A'Hearn & Festou 1990). The light of fainter comets mainly originates from the emission of diatomic carbon (C2). There are several lines of C2, dominating over the visual wavelengths, forming the so-called Swan bands (Liller 1992). The 515-nm line is often dominant; together with those at 560 nm, the Swan-band lines are well inside the passband of our filter (Figure 1).

Spectres
Figure 1.

The spectral response of our V filter + CCD is compared to the main emission lines of diatomic carbon (C2). The spectral response of dark adapted human eye is also plotted for comparison.

Two additional reasons favour the use of a V-band filter. Due to its sharp cut-off at 480nm (Figure 2), it considerably reduces the contribution of sky background at blue wavelengths. This enables photometry to be performed even in moonlight conditions. Also, the filter drop at 650nm noticeably reduces the emission from artificial sources, mainly due to mercury and sodium streetlights (Wallis & Provin, 1988).
Polut
Figure 2.

The spectral response of our V filter compared to the spectra of light-polluted night sky.

Altogether, the V band filter absorbs the undesirable emission from sky background, transmitting mainly the light of cometary coma. This results in noticeable improvement of signal-to-noise (S/N) ratio of the cometary image.
2.2 Observational method
Our observational procedure is similar to the technique used in differential photometry of variable stars (Henden and Kaitchuck 1990). It consists of successive imaging of the comparison star and the comet. Several sequences are usually obtained. During each observational run, dark and flat-field frames are taken. The dark frame is exposed for the same time as the object frame but with the camera shutter closed. The flat-field frame is taken on illuminated observatory wall.
In order to avoid the influence of atmospheric extinction, we always choose the comparison stars as close to the comet as possible. Furthermore, we avoid observations at more than two air masses, which correspond to elevations less than 30 deg above the horizon. Fortunately, faint comets are generally far from the sun, which enables observations to be performed when they are at large Solar elongations and well placed in the night sky. In rare occasions, when data are urgently needed, observations at lower elevations are performed and the extinction corrections applied.
We mainly use comparison stars from the "Bright Star Catalogue" (Hoffleit, 1982) and "Guide Star Photometric Catalog" (Lasker et al. 1988), as it contains precise V-band photometry for stars down to 7th and 15th magnitude respectively. The secondary source for comparisons is "The AAVSO Variable Star Atlas" (Scovil 1980). In general, we avoid using comparisons from the AAVSO, because they are less accurate.

Our objective is to record as much cometary coma as possible. Since the f/2 camera is fast, we found that a 5 min exposure is long enough to record comets down to 15th magnitude with sufficient S/N ratio. The integration time for the comparison star depends on its brightness and is thus determined individually. Because comparison stars are relatively bright, exposures are short, ranging from a few seconds to one minute. Obviously it is necessary to be careful and avoid the saturation of the stellar as well as comet image.

When the comet is very bright, the images became saturated yet on short exposures. We may avoid this by slightly defocusing the telescope/lens. However, the telescope/lens should remain defocused to the same amount until the whole photometric sequence is completed.
During the final reduction, the comparison-star instrumental magnitude is corrected to the same integration time as the comet and the magnitudes are then compared.

3. Image processing and data reduction
3.1 Image processing
Due to the ST-6 CCD high "dark current", it is necessary to subtract the dark frame immediately after the exposure, using the original software supplied with the camera. In that way, a relatively clear frame is obtained and the presence of comet checked. Since the ST-6 CCD camera software uses its own file format that is not widely supported by other packages, we convert files to FITS, which is the working format for the PCVISTA (Wells et al. 1981, Richmond & Treffers 1989) as well as DAOPHOT II and FitsPro packages.
Next we have to perform flat-field correction on all frames; obviously, it must be done because fast systems have significant vignetting over the frame. The final step is to remove the stellar images that may appear inside the comet's coma. This is a common problem, particularly in dense Milky Way regions, and may significantly affect the measurements. Experiences shows that all background stars must be removed at fainter comets and at least those of 12 mag. and brighter at bright comets (such as Hale-Bopp or Hyakutake).
 
Figure 3.

A 300-s CCD image of P/1994 A1 (Kushida) taken on Jan. 23, 1994 with the 20-cm, f/2 Baker-Schmidt camera and V filter. Note several stars inside the comet coma (left image) and pure coma with stars removed (on the right), using the PCVISTA CLIP procedure. The stars inside the coma added 0.15 mag. to the comet's total V value.

3.2 Data reduction
The data analysis is performed by using the aperture photometry program. First, the positions of comet and comparison-star centroids are found manually and stored in a file. The next step is to inspect both images and carefully determine the radius of star/comet aperture in pixels. The program counts the units inside the specified aperture, subtracts the sky counts - leaving only the star/comet counts - and converts them into instrumental magnitudes.

In this way we obtain instrumental magnitudes of the comet (mc) and comparison star (m*). Since the integration times of the comparison and the comet images are not the same, we must first calculate the magnitude difference (D) between frames by using standard Pogson equation:

D = - 2.5 log (Ec/E*)

where Ec and E* are the integration times of the comet and comparison, respectively. The difference (delta m) between the comparison (m*) and the comet instrumental magnitude (mc) is then calculated by

delta m = mc - m* - D

where m* is the instrumental magnitude given by the aperture-photometry program. The standard V magnitude of the comet Vc may now be calculated from

Vc = V* + delta m

where V* is the standard V magnitude of a comparison star obtained from the catalogue.

When the air mass of the comet (Xc) and that of the comparison star (X*) differ by more than ~0.3, further correction for the atmospheric extinction is deemed necessary. The equations for this are:

delta m' = delta m - k'(Xc - X*)
Vc = V* + delta m'
4. Results
Summary of our observations (Updated November 5, 1998)
Light curves
Images of faint comets
CCD V Photometry of Comet Hale-Bopp
4.1 Estimation of errors in our measurements
4.1.1 Errors induced by photon statistics
We calculated the S/N ratio and corresponding errors in magnitudes for three comets having the V magnitudes between 10 and 15. All frames were taken with the 20-cm, f/2 Baker-Schmidt camera and exposed for 300 seconds. Following Buil (1991), we compared the comet signal (Nc) with the contribution of all noise sources using the formula

where N are signals given in electrons (for our ST-6 CCD we assumed that 1 ADU corresponds to 10e-). In our case, we considered comet, sky, dark frame, and readout noise. The readout noise is induced in every reading of the CCD chip and was multiplied by 3 because it is present on the comet frame, as well as on dark and flat-field frames. The uncertainties estimated from photon statistics are given in Table 5.

Comet V N(e-) (S/N)c Error (mag)
Kushida (1994A1) 10.1 424030 211 0.005
29P/S-W 1 12.3 76000 79 0.014
76P/W-K-I 14.9 7410 18 0.058

Table 5: Uncertainties estimated from photon statistics

4.1.2. Errors induced by other sources
Some errors are introduced by the noise of the comparison star, but given the fact that the star is brighter and more compact source than the comet, this cannot be a dominant source of error. The observer should also take care about the level of saturation of both the comet and comparison star image. Too saturated images may give completely false photometric results.

Finally, the measurements may be influenced due to the bad determination of coma radius before running the aperture photometry program - for instance, when the specified radius of aperture is smaller than the actual radius of the coma. We may avoid this problem through careful reduction.

5. Conclusions
Our recent work on CCD photometry of comets enables us to perform routine V magnitude measurements of comets down to 18th magnitude with precision exceeding those obtained by any visual method.

We conclude that, when using our present equipment, we are able to measure a 18th magnitude comet with the accuracy of ~0.1 magnitude. Better results are achieved for brighter comets. The introduction of this new technique made it possible for us to start a regular observing program.

Another important advantage of using CCD detectors is that a large number of quality observations may be collected on a single night without too much fatigue.

6. Acknowledgements
The authors wish to thank D. W. E. Green of the ICQ for his encouragement in starting our observing program. Thanks are also due to "Javornik Astronomical Society" in Ljubljana, providing us with the ST-6 CCD detector and University of Ljubljana, Department of Physics, enabling us to use the Wright CCD.
7. References
1. A'Hearn, M. F., Festou, M. C. 1990 in Physics and Chemistry of Comets, (W. F. Heubner, Ed.; Springer-Verlag), p. 69
2. Holmes, A. (1995). CCD Astronomy 2, No. 1, p. 14
3. Bessell, M. S. 1990, P.A.S.P. 102, 1181
4. Bessell, M. S. (1995). CCD Astronomy 2, No. 4, p. 20
5. Brandt, J. C., Chapman, R. D. 1992. Rendesvouz in Space: the science of comets (New York: W. H. Freeman and Co.).
6. Buil, C. (1991). CCD Astronomy (Richmond, VA: Willmann-Bell).
7. Henden, A.A.; and R. Kaitchuk (1990). Astronomical Photometry (Willmann-Bell).
8. Hoffleit, D. (1982). The Bright Star Catalogue (Yale University Observatory).
9. Lasker B. M. et al. (1988). ApJ Suppl. 68, 1 (September 1988).
10. Liller, W. (1992). The Cambridge guide to astronomical discovery (Cambridge University Press).
11. Menzies, J. W.; F. Marang; D. J. Laing; I. M. Coulson; and C. A. Engelbrecht (1991). M. N. R. A. S. 248, 642.
12. Richmond, M.; and R. Treffers (1989). PCVISTA, Astronomical Image Display for IBM PC's or Compatibles (University of California, Berkley).
13. Scovil, C. E. (1980). The AAVSO Variable Star Atlas (Sky Publishing Corp.).
14. Treffers, R.; M. Richmond (1989). P.A.S.P. 101, 725.
15. Wallis, B. D.; R. W. Provin (1988). A manual of advanced celestial photography (Cambridge University Press).
16. Wells, D. C.; E. W. Greisen; and R. H. Harten (1981). A.Ap.Suppl. 44, 363.
8. Appendix
Further remarks about the computer programs that we currently use for CCD photometry of comets.

ST6OPS is supplied with ST-6 CCD camera by Santa Barbara Instrument Group and is used for the image acquisition and dark subtraction. The program also enable conversion to FITS file format (Wells et al., 1981). We use 16-bit conversion. In order to transport frames to PCVISTA, the generated files must be divided by 2 and added the constant of 16384.

PCVISTA is an image processing and analysis package, developed at University of California (Richmond & Treffers 1989).

We used the following procedures:
MN - computes mean of the image.
DIV - divides object image with flat image to perform flat-field correction.
CLIP - replaces all pixels in a specified box. It is used to remove stars inside the comet coma by replacing star counts with the nearby sky value.
CURSOR - displays data values at cursor position on the image.
PHOT - performs aperture photometry with specified aperture radii.

The following programs were written by the authors and are available upon request.

XST6 reads the data from the FITS image header and calculates the air mass, X, of the object.
SKYSUB calculates the linear best-fit sky value and subtracts it from the frame; it is used when the comet is near the horizon and the sky gradient differs significantly over the frame.

DAOPHOT II for PCs is a software package for CCD photometry, written by Peter Stetson from Dominion Astrophysical Observatory. It has been recently transfered from main-frame and workstation environments to personal computers running DOS.
FitsPro is an image processing program for MS Windows 3.1; it incorporates various image processing and data reduction options (including aperture photometry) and works with FITS-format files. The program is avilable on-line.

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