DRIFT-SCAN
TIMING OF ASTEROID OCCULTATIONS
John
Broughton (Updated 2010-06-22)
Occultations present the opportunity
to remotely investigate shape and dimensions of planetary objects with
orders-of-magnitude gain in resolution over direct imaging. I have in the past
observed visually a spectacular Jupiter occultation of 2.6-magnitude Beta SCO
and measured brief disappearances of a fifth magnitude star by ringlets of
Saturn but until 2003 I had never observed the more common variety of
occultation by an asteroid. Following
on from the development of Dave Herald’s Occult software,
the turning point came with the advent of Steve Preston’s updated predictions,
the accuracy of which made viable a CCD imaging and timing technique I had
under consideration many years earlier. The original inspiration was a trailed
photograph of a Metis occultation taken by Paul Maley in 1979.
CCD
Due to their slow image
transfer rate, most astronomical CCD cameras cannot record short-term
variability on consecutive frames without missing out on most of the action;
hence an occultation is best recorded on a single frame. One technique that has
been particularly useful in recording rapid changes during lunar occultations
is called TDI (time delay integration) where the CCD array is read out line by
line to produce a trailed image. Not many cameras including my own have
operating software supporting this electronic option but any integrating camera
attached to a stationary telescope can take trailed images as a consequence of
Earth’s extremely regular rotation, which just happens to provide a rate of
motion well suited to recording asteroid occultations.
With the advantage of noise
reduction, a cooled CCD camera provides a substantial magnitude gain over
non-integrating video cameras. From a
moderately light-polluted location under otherwise favourable circumstances,
sidereal-rate star trails as faint as magnitude 14 can be acquired with a
telescope of 25cm aperture. A single image provides a convenient record for
analysis, producing in most cases an unambiguously positive or negative result.
Although cloud induced disappearances can mar an observation, they equally
affect all nearby trails, making them easy to differentiate from the real
thing.
Rigorous timing methods
were devised and first employed for the Lutetia occultation of
COORDINATING CCD AND
VIDEO DRIFT-THROUGH OBSERVATIONS
The telescope is
pre-pointed to a fixed position in the sky where by virtue of Earth’s rotation;
the target will drift through the centre of field at the time of occultation.
Because the trail ends of drift scans are used in the timing calculations, the
exposure must begin and end while the star is within the frame boundary,
therefore it is important to employ accurate and fail-safe methods of
coordinating both telescope and camera, especially when the field of view is
small. Originally developed in 2004, ScanTracker now includes three
pre-pointing modes and a printable chart of alignment stars, making it easy to
point all kinds of telescopes whether used for drift scan, video or visual
drift-through observations. The new modes enable an alignment on a naked-eye
star followed by a single-axis offset and no faint-star hopping is required.
Altazimuth mode is especially useful for rapid set up of portable telescopes.
Recent developments include an extension of the charted limiting magnitude from
6 to 12; dispensing with any need to rely on other planetarium software for alignments
in any mode. See help for details.
The camera is preferably
oriented north up to produce left to right drift along rows of the CCD array;
quite straight forward on a polar-aligned equatorial. For an altazimuth SCT,
the east-west line of occultation displayed in ScanTracker will give an idea of
the orientation. Final adjustments can be made with the aid of trial and error
imaging of star trails.
In the drift-scan exposure
section, its length is adjustable from 10 seconds up to a maximum dependant on
field width and declination. An
exposure 20 times longer than duration of the occultation is necessary if you
want to cover the region in which an asteroid satellite could reside. Exceeding
this can be disadvantageous since there is loss of limiting magnitude by sky
glow the longer the exposure lasts. A 200 second exposure for instance may lose
2 magnitudes over one of 20 seconds at a moderately light-polluted site. For
this reason it is good practise to shorten the exposure if circumstances are
unfavourable for obtaining a well recorded image such as might be caused by
bright moonlight or twilight, poor seeing, small magnitude drop, low elevation
or combinations thereof. A minimal
exposure should always be employed when there is threat of obscuration by
cloud. With reference to an updated
prediction, a rule of thumb I use to find minimum exposure is to add the
maximum duration of the occultation to the time uncertainty plus 15 seconds for
some margin of safety. Another reason to use an exposure shorter than the
maximum allowed for your field-width is to avoid an overlap by a trail of
equivalent or brighter magnitude. Such overlaps contain their own
contrast-reducing seeing variations. GUIDE 8 with UCAC stars enabled is my
preferred planetarium software when checking a target’s surroundings for
interfering stars lying within 8 arc seconds of the same declination and within
the intended exposure length in seconds of RA. In general, a drift scan of an
occultation fainter than Magnitude 13.5 in a crowded field is not likely to
produce measurable results.
The simulated drift scan at
the bottom of ScanTracker displays the field of view and estimated limiting
magnitude relevant to the selected telescope-camera combination. The magnitude
represents the faintest star whose occultation is potentially detectable under
favourable moonless conditions. A
2-magnitude loss from the listed limit can be expected when a full moon is present.
MANUAL TIMING OF THE EXPOSURE
In the Windows operating system, the
time listed in image file headers can easily be off by a second, even shortly
after setting the clock and as in my case the exposure length may not be
exactly as commanded, so for timing occultations I disregard this information.
Because computer equipment floods short-wave with static, a digital timer
previously synchronised to WWVH can be visually monitored during the beginning
and end of exposure. If the camera lacks an audible shutter, a cardboard disk
taped to a tennis racket can be used to unblock and block the telescope
aperture (without actually touching the telescope) at the intended times within
an electronic exposure a few seconds longer in duration. If as is preferable
the camera has a mechanical shutter, the times when the shutter is heard to
open and close are written down with the fractional second part estimated.
Either method may be as accurate as 0.2-second, depending on the individual.
RIGOROUS TIMING OF THE MECHANICAL SHUTTER
A
$10 quartz analogue clock provides a low-cost means to derive accurate timing
of the sub-second part, using the ticking sound. The small unit containing the
workings can be removed from the clock and placed in contact with a microphone.
Audio tests on mine revealed an hourly drift rate of only .008 second! The battery can be inserted by trial and
error until the ticking is heard synchronized with short-wave UTC. This is then
recorded on one channel of a stereo tape recorder while UTC is simultaneously
recorded on the other through a second microphone or line-in. This recording is done prior to, or after
the event when computer and camera equipment are not operating and causing
radio interference to the short-wave signal. The microphone that recorded from
the radio is then fastened in contact with the CCD camera to record its shutter
clicks during the occultation. As in the first recording, the clock ticks are
recorded on the other channel, guaranteeing a clear time signal at the critical
time. It’s possible to make the drift-scan observation autonomous in order to
observe the same event from another site. Both ScanTracker and MaxIm DL support
delayed exposures of up to 32768 seconds (9.1 hours). The tape recorder could
be on a power-point timer and an alarm set up to go off at the beginning of a
specific minute and be audible on the clock-tick channel.
Audio software such as GoldWave
is later used to analyse both stereo recordings in deducing the times the
shutter opened and closed relative to UTC, as is shown in the diagram of a
1-second interval between clock ticks. Such timing measurements done within
second intervals are not prone to errors caused by tape stretch. If the
short-wave signal is faint and immersed in static, the clearest part of the
recording can be selected, the volume maximised and noise reduction button
pressed a few times until the UTC second marker stands out more clearly. The
spike in the audio plot repeats every second in the same place relative to the
clock tick. In my experience if the signal can be heard, then its position can
be measured. To correct for propagation, 0.01-second for every 3000 km from the
short-wave transmitter should then be added to the shutter timings.
GPS
More conveniently, the short-wave
time signal and clock can be replaced by a GPS-based timer for simultaneous
recording with the shutter clicks, in which case only a single stereo recording
is necessary and propagation does not apply. Suitable devices are the KIWI system,
the GPS
Clock and the newly developed VNG-uc
GPS Time Signal Generator. This
last one is the only fully self-contained GPS timing device capable of
recreating short-wave UTC signals but is not yet in production.
ELECTRONIC SHUTTERS
Cameras lacking mechanical shutters
give no audible cue we can use to time the exposure, so a different approach is
required. A tie-clip mike can be
attached to the RA drive motor instead of the camera. If sidereal tracking is
turned on for just a second or two near each end of the exposure, a star image
will show up near each end of the trail to become measurement points instead of
the trail ends themselves. From the audio recording of the time signal and
drive motor noise, it is the time of the end of the first short tracking period
and beginning of the second that represent the star image centres on the trail.
The tracking periods are kept short to minimise any degradation of timing
accuracy by periodic error. I’ll later
refer to trails of this type as having star-bump profiles to distinguish them
from normal ones.
IMAGE ANALYSIS
As with any CCD image, the drift
scan should be calibrated with bias, dark and flat field frames to achieve the
highest signal to noise ratio. Contrary
to popular belief, timing resolution of an occultation using a CCD drift image
is not limited by pixel size, except in unlikely events of very short 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
point where the profile crosses a certain brightness level. For best results,
the whole width of the trail needs to be taken into account by averaging X
values over several rows on the Y-axis. In MaxIm
DL this can be achieved automatically using a horizontal box aperture. First though it may be necessary to
precisely level the trail using the edit menu rotate function with the bicubic resample box ticked. Next hold down
the left mouse button to drag a long narrow aperture around the trail starting
at the left edge of the frame, excluding any adjacent trails and as much
background as possible. Then use the view menu line profile function, select
horizontal box and the mean sample option and press the export button to save
it to disk in the form
of a comma-separated-values file.
A normal profile is a stretched
version of a fixed star’s bell-shaped curve and being a time variable image, it
is modified by atmospheric turbulence.
Calculations I did in 2004 showed the end of trail profile to be
stretched 200% compared to that of a fixed-star radius, and the point of origin
to be located exactly midway in height between the trail and background
levels. Measurement levels derived from
the lengths of many rigorously timed trails in 2003 averaged within 1% of the
50% level. Even under the influence of diffraction, the measurement level of
the occulted part was calculated to be at or very close this level so I believe
diffraction to be self-cancelling in the case of sidereal-rate drift scans.
This is different from the measurement level of high-frame-rate video
recordings where diffraction theory indicates should be made at the 25% level.
SCANALYZER
This trail measuring application
includes dynamic vertical scaling, smoothing of scintillation and signal noise,
cancellation of optical distortion effects and calculation of overall timing
accuracy. The LOAD button facilitates loading a profile such as included
example file 050521 Bilkis.csv. The
four measurements on the profile are always made in left to right order.
Clicking the plot produces an expanded view whose width in pixels can be zoomed
in as far as 32 or all the way out using those arrows that appear either side
of the SMOOTH button. Clicking in this expanded view where the levels change
brings about a sub-pixel X measurement displayed in green. A right click
returns the full profile where the next position can be selected. Once the fourth measurement is made, times
for the occultation based on the 50% level are computed and displayed.
Measurements can be re-done by use of the BACK button. Scanalyzer recognises and can measure
star-bump profiles, in which case ‘Star Bump’ replaces the terms ‘Trail Start’
and ‘Trail End’ after the first position is measured.
Since in practice the moving star is
a distribution of light on the CCD two or more pixels wide, sudden changes
caused by an occultation always have a slope and are less abrupt than the rapid
variations due to scintillation and signal noise. The SMOOTH button applies a
gaussian filter to suppress this high-frequency interference and improve
accuracy without biasing the measurements. Smoothing should be applied at least
once and can be done twice in the case of poor seeing conditions. On the third
press, the original raw state is restored. Lights below the button indicate the
level of smoothing and timing results are updated automatically.
When loading a CSV profile file,
Scanalyzer also loads a TXT file of the same name if present in the same
directory. Previously edited in Notepad by the user, this file holds two lines
for trail-end shutter timing followed by one line for accuracy, followed by
four lines of astrometric data used in averting a distortion-induced warp in
timing. If this file is absent, timings
can be manually entered into the white boxes or alternately the file can be
present but omitting the four lines of astrometry. Lacking astrometry,
computations are based on a simple extrapolation of image coordinates to time,
which scarcely matters in the case of telescopes with negligible distortion
such as unmodified SCTs. On the other hand a focal reduced SCT will have a
little distortion while Newtonians and Cassegrains suffer considerably more.
The astrometric data can be measured from any image taken with the same optical
configuration. After calibration to
celestial coordinates using Astrometrica,
four positions are measured near the X and Y image coordinates equivalent to
trail start (alternately star-bump), disappearance, reappearance and trail end
(alternately star-bump). A Ctrl-click
operation enables measurement within a pixel or two of where intended and the X
parameter is displayed to two decimal places in the PSF-Fit box. This figure is
to be manually incorporated into a contiguous object name of the form X468.55
when saving a position. X can be followed by anything up to 4096 but there must
be no spaces. The four lines of data
are then copied from Astrometrica’s MPCReport.txt and added to the timings as
in the example file 050521 Bilkis.txt. These positions show up as red dots in
the Scanalyzer profile plot to indicate astrometric data is loaded and verify
their locations align approximately with the four measurement positions.
Relative scales between these astrometric positions are derived and applied as
corrections to the timings.
Faintly recorded occultations having
depth comparable to the amplitude of seeing irregularities and random noise
might produce what is obviously a bad measurement. A hump or hollow may
interfere where a level is being averaged or could cause the profile slope to
level out temporarily just where X is being interpolated. In such cases the
keyboard Ctrl-up and Ctrl-down arrow keys enable modification of the profile at
the position of the cursor. This is best done after returning the profile to an
unfiltered and unmeasured state via the SMOOTH and BACK buttons. After
adjustments to the problem area, the profile is resmoothed and remeasured. Keep in mind that such modifications
disappear if the profile is again restored to its original state.
Timing accuracy is derived from the
sum of the audio recording measurement uncertainty and profile measurement
uncertainties for both occultation and trail end. The latter calculations involve a simulated drop in light in an
unocculted part of the profile made at a string of consecutive pixel locations
before being averaged. A magenta coloured line represents that region. The
Bilkis drift-scan observation made with a 0.5-m telescope seems to indicate
that for larger apertures, the best events measured in Scanalyzer will approach
0.01-second accuracy once the audio measurement uncertainty is effectively
zeroed with the aid of direct GPS-based timings.
SOFTWARE ScanTracker
3 and Scanalyzer can be freely downloaded here.
See the readme file before running ScanTracker. Once started, press the HELP
button. ScanTracker 4 shown in the image above is currently in development and
should be available soon. My current contact
address is jbroughton2(at)dodo(dot)com(dot)au
ACKNOWLEDGEMENTS The camera used by the author was acquired
following a Planetary Society Gene Shoemaker NEO research grant. Keith Gelling
made diffraction calculations on an example asteroid occultation. I thank the
principal members of IOTA and the RASNZ Occultation Section for recognizing the
value of this work.
LINKS IOTA Euraster
RASNZ Occult Updated Predictions Guide
8 MaxIm DL
Astrometrica GoldWave