The observation of planetary occultations of stars using modest equipment presents the opportunity to investigate the shape and dimensions of distant objects in great detail as if using an immensely powerful telescope. In 1971 I was privileged to witness the spectacular sight of Beta SCO apparently passing through stratified cloud layers in the atmosphere of Jupiter and in 1989, timed occultations by narrow components of Saturn's rings but until recently I had never observed the more common variety of occultation by a minor planet. The turning point has come through the availability of reliable predictions made possible by highly accurate star catalogs generated from space based observations.

CCD

In 1995 after obtaining a CCD camera, I pondered how to record such short term variability with an imager that while much more sensitive to light than video, had too slow a frame rate to consider taking multiple frames. After first considering the idea of using small scope movements to record lines of images on a single frame, I realised that I only had to turn off the drive to let the star drift across the field, leaving a continuous line which would contain a measurable gap if an occultation had taken place and the smoothness of tracking would only be limited by the seeing quality. The Earth's rotation has after all such a vanishingly small amount of mechanical error!

An image revealed star trails to magnitude 14.0, however crossing the field in a minute it seemed unlikely that an occultation could be recorded without a reliable prediction and astronomy magazines by then were no longer listing predictions for locations outside North America. In 2002 I chanced upon Steve Preston's web page of updated predictions, the accuracy of which suddenly made short duration drift-scan observations a viable method of observation. Weather interfered to stymie some attempts to capture an image and I was outside the path for others until the night of June 28, 2003 when an 11th magnitude star was occulted by 709 Fringilla. Results of this and further CCD timings can be found on the RASNZ Occultation Section's page of recent occultation results.

CCD ADVANTAGES

There seems to be a 3 or 4 magnitude gain over video, principally due to noise reduction through thermoelectric cooling. Tables of visual occultation results rarely list events fainter than the 11th magnitude whereas a cooled CCD camera on a 10" telescope brings 13th magnitude occultations within range, depending on magnitude drop and seeing quality. Small magnitude drops on 11th magnitude stars should be detectable that otherwise could only be recorded using a photoelectric detector. False disappearances due to cloud affect all star trails within the image so are easily distinguished from real occultations. The occultation can be accurately timed and a single image provides a permanent and undeniable record of the event.

INSTRUMENTATION

A thermoelectrically cooled CCD camera with mechanical shutter is required. A large format camera such as the Apogee AP6 used by the author is by no means mandatory. For example, a trail length of 15 arc minutes at the celestial equator represents transit times of 1 minute which in most cases should be sufficient to encompass the period of occultation since the uncertainty ellipses of recent updated predictions are on the order of 10 or 20 seconds. A larger field of view than this however facilitates less stringent telescope pointing or a longer scan that could potentially reveal an asteroidal satellite.

The exposure must be coordinated to begin and end while the star is within the frame boundary because the ends of the trail are used in the timing calculations. In the case of a camera having the relatively inexpensive KAF-0401 chip, here are some viable telescope combinations and the time of transit across 85% of the field at the celestial equator:

8" f/6.3 SCT......................... 63 seconds
10" f/10 SCT + F/3.3 focal reducer... 96 seconds  
12" f/10 SCT + F/3.3 focal reducer... 80 seconds
12" F/4.5 Newtonian + coma corrector..59 seconds

Away from the celestial equator, longer maximum exposure times are arrived at after dividing by the cosine of the declination.

OPTICAL CONSIDERATIONS

One needs to consider the effect of optical distortion on timing accuracy. Schmidt Cassegrains are highly corrected and have an image scale across the field so even that distortion related timing errors for drift-scan images should not exceed 0.01 second. The addition of a focal reducer however will degrade the timing accuracy by several hundredths. Newtonians require a coma corrector to improve off-axis sharpness, in which case there is a 1% difference in image scale between the edge of a 30' diameter field and the centre and can result in errors of several tenths of a second. Distortion related timing errors can be eliminated using a non-trailed image taken near the time of occultation without any shift in focus or declination. As detailed later, this image is astrometrically calibrated for reference in converting from image coordinates to RA and then to time.

PRE-PLANNING

Find the time of mid-occultation for your location using an updated prediction. One should check for brighter stars of equal declination that could cause an overlap, especially for targets lying at low galactic latitudes. Such a hazard may be avoided by reducing the exposure duration. Interfering trails fainter than the target shouldn't cause a problem except in the unlikely circumstance of one end coinciding closely with one of the measurement locations.

IMAGING PROCEDURE USING A TELESCOPE ON A STATIONARY ALTAZIMUTH MOUNT

Determine the celestial coordinates of an alignment point west of the target star at the same declination. For Dobsonians without position encoders, use an observable star of known position to align on instead. Multiply the RA difference by 0.99727 to find the amount of time before mid-occultation for this alignment to take place. Before the occultation image is taken, adjust focus and orient the camera north up until test images show stars trailing left to right parallel with the X axis, without bumping the scope out of its carefully aligned position. The drift-scan exposure on time delay is coordinated to start half the exposure length prior to the time of mid-occultation. As discussed later, the observer can then concentrate on timing the shutter operations.

IMAGING PROCEDURE USING AN EQUATORIAL MOUNT

The author uses a 10" LX200 on a permanent equatorial mount. The camera has been carefully oriented north up and is bolted to the back of a home made housing containing a sliding mirror and eyepiece used for aligning on reference stars, focusing and visual observations. The faceplate carrying the eyepiece can be removed for insertion of additional optics ahead of the mirror without needing to remove the camera. Commercially available flip mirrors cannot fit between the camera and F/3.3 focal reducer that was previously used in conjunction with a small format camera. Apart from the inconvenience of needing to interpose a lens unsuitable for visual observations, the disadvantage of using a focal reducer is that focusing is more critical and image sharpness reduced. The author now uses a large format Apogee AP6 camera without focal reduction for exposures that can exceed 160 seconds for these type of observations.

The telescope is first aligned and focused on a nearby reference star before slewing to the target which is then imaged for pointing verification. If required, the same image can be used later in the astrometric reduction calculation applying to the distortion free timing of long trails. The telescope is then slewed 5' RA west of the target. The RA drive is switched off 5 minutes prior to the time of mid-occultation, ensuring that the target will cross the centre of the frame at the right time. The drift-scan exposure on time delay is coordinated to start half the exposure length prior to the time of mid-occultation. If using ASCOM compliant hardware such as a LX200 telescope and MaxIm CCD camera operating software, the star trail image can be acquired automatically by use of a script.

TIMING THE EXPOSURE

The time listed in image file headers is too inaccurate to be used. Because computer and telescope equipment floods shortwave with static, a digital clock which had previously been syncronised to WWVH was monitored during the beginning and end of the exposure. The times when the shutter was heard to open and close were written down with the fractional second part estimated. This method may be as good as 0.2 seconds depending on the individual.

RIGOROUS TIMING

For accurate determination of the fractional second part, a quartz analog clock was rigged with a toggle so that it could be switched off and on until its ticking is heard syncronised with WWVH beeps. Audio tests of the clock rate revealed any shift relative to WWVH to be less than 0.01 seconds per hour so no adjustment for this was necessary. A microphone touching the clock records the ticking on one channel of a tape recorder while WWVH is simultaneously recorded on the other. A second recording during the occultation records the clock and shutter operations, guaranteeing a clear time signal at the critical time. Audio software such as GoldWave (available here) is later used to analyse both recordings in deducing the times the shutter opened and closed relative to WWVH as is shown in the diagram of a 1 second interval between clock ticks. One can select the clearest part of the clock/WWVH recording, maximise the volume and press the noise reduction button a few times to make the UT second marker stand out clearly.

To correct for propagation, 0.01 seconds for every 3000 km from the shortwave transmitter is then added to the timings. More conveniently, WWVH and clock could potentially be replaced by a GPS-beeper unit (such as the GPS/KIWI system) for simultaneous recording with the shutter sounds, in which case only a single recording is necessary and propagation does not apply.

MEASURING THE IMAGE

Contrary to popular belief, the accuracy of timing an occultation using a drift-scan image is not limited by pixel size, except in atypical events of eye blink duration. Trail ends can be measured at the sub-pixel scale by interpolation of the values contained in adjacent pixels, in effect joining the dots to find the place where the profile crosses a certain brightness level. For best results in analysing the profile, the whole width of the trail needs to be taken into account by averaging X values over 3 or 4 rows on the Y axis. In MaxIm DL one can create such a profile using a horizontal box aperture. For valid X values, the aperture should begin at X = 0 and encompass the whole trail in both coordinates. A CSV file containing the averaged X values can then be saved to disk. The profile is mesa shaped with ends having the same gaussian curve as a non-trailed star and being a time variable image, it is roughened by atmospheric turbulence. Comparisons using accurately measured trail lengths and durations show the measurement points are located 49% up from the mean lower to the mean upper level. Individually calculated levels should be used for each of the measurement locations.

These are the measured coordinates and timings for the 2003, August 24 Lutetia occultation:

X 074.47  Start of trail  09 02 35.52 UT  measured time shutter opening
X 468.63  Disappearance   09 03 49.32 UT  simple interpolation
X 489.36  Reappearance    09 03 53.20 UT  simple interpolation
X 936.90  End of trail    09 05 16.80 UT  measured time shutter closing

DISTORTION FREE CONVERSION

The non-trailed image can be calibrated to celestial coordinates using Astrometrica. Since the image was taken at the same declination as that of the drift-scan, the same Y coordinate as for the occulted trail is the row where the measurements apply. A star or even the background can be clicked either side of the relevant X positions to obtain accurate RA conversions as in the example:

X 056.80 = RA 15 01 03.02
X 074.47 = RA 15 00 59.70  Interpolated RA relevant to start of trail 
X 093.12 = RA 15 00 56.20

Doing this for the 4 measurement locations gives:

X 074.47 = RA 15 00 59.70 or 000.00 sidereal seconds for start of trail
X 468.63 = RA 14 59 45.74 or 073.96 sidereal seconds for disappearance
X 489.36 = RA 14 59 41.85 or 077.85 sidereal seconds for reappearance
X 935.90 = RA 14 58 18.07 or 161.63 sidereal seconds for end of trail

Multiply by 0.99727 for conversion to time and add to start of exposure:

000.00 = 09 02 35.52 UT  measured time of start of exposure
073.76 = 09 03 49.28 UT  derived time of disappearance
077.64 = 09 03 53.16 UT  derived time of reappearance
161.19 = 09 05 16.71 UT  derived time of end of exposure 

Due mainly to atmospheric variations, the derived time of end of exposure is out by several hundredths of a second. The timings for disappearance and reappearance are then shifted by half the mismatch so that the error contribution is shared at both ends of the exposure.

Started Observing : 09 02 35.52 UT  measured time of start of exposure
Disappearance At  : 09 03 49.32 UT  derived time of disappearance
Reappearance  At  : 09 03 53.20 UT  derived time of reappearance
Stopped Observing : 09 05 16.80 UT  measured time of end of exposure

Despite this being a long trail, the simple conversion agrees to better than 0.01 seconds with the distortion free conversion because a SCT without additional optics was used. For optical systems not covered here, such comparisons are an indicator of whether the short calculation is adequate. To avoid the tedium and potential calculation errors involved with the longer calculation, software has now been written to do them using input of the shutter timings, 4 approximate measurement locations, the profile file from MaxIm DL and astrometry from Astrometrica. The output can then be pasted directly into an occultation report form.

TIMING UNCERTAINTIES

A reliable method was developed to measure the uncertainty directly from the variations along the unocculted part of the star trail. In excellent seeing conditions, the mean uncertainty along a trail of magnitude 10.0 or brighter having a large magnitude drop is only 0.02 seconds but since there is a 1 in 3 chance the uncertainty of a particular measurement could be greater, I adopted a more conservative approach whereby the odds of this happening is reduced to 1 in 10 which increases the derived uncertainty figure to 0.03. For faint trails or those with small magnitude drops where the change in brightness is smaller than the amplitude of the variations, the relevant timing uncertainty can be as large as 0.6 seconds. In the table of timing uncertainties, the trail magnitude headings refer to the combined brightness of star and asteroid using a 10" telescope under various moonless circumstances.

          MAGNITUDE <=10.0     MAGNITUDE 11.0       MAGNITUDE 12.0
          ----------------     ---------------      ---------------
 MAG      SEEING QUALITY       SEEING QUALITY       SEEING QUALITY     
 DROP     EXC  FAIR  POOR      EXC  FAIR  POOR      EXC  FAIR  POOR
 ------------------------------------------------------------------
 3.0     .03   .05   .08      .04   .07   .12      .07   .10   .20
 2.0     .04   .06   .09      .05   .08   .15      .08   .12   .40
 1.0     .05   .07   .13      .07   .12   .20      .12   .25   .60
 0.8     .06   .09   .18      .08   .20   .40      .18   .40   .60
 0.6     .07   .15   .40      .12   .40   .60      .30   .60   .60
 0.4     .10   .30   .60      .40   .60   .60      .60   .60   .60
 0.2     .40   .60   .60      .60   .60   .60      .60   .60   .60

ACKNOWLEDGEMENT

The camera used by the author was acquired following a 2002 Planetary Society Shoemaker NEO research grant, largely for the purpose of NEO follow-up observations and a modest southern sky survey program.

Contact John Broughton (reedycrk@bigpond.com) for further information.

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