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Track & Stack
is a technique mentioned on the Methods page
that effectively strengthens the signal from an object by stacking many
images together. If the target object is moving, then adjustment is
automatically made to compensate for its motion, keeping the object in the same place
and causing the stars to be trailed.
The software program Astrometrica
includes powerful functionality to automatically track & stack multiple
images of the same field of view very accurately and is an essential tool at
Great Shefford, part of every observing session.
As an example of track
& stack in action, images
taken of the Amor minor planet 2004 SS early on 2004 September 19th demonstrate
the basics. At the time the object was magnitude +18.1
and moving at 6.7"/minute in p.a. 21° (up and to the left). Each image was
taken binned 2x2, has been enlarged by a factor of x2 and is 5' x5' in size with
North up.
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a. Individual Image
Single 28 second exposure with 2004 SS in the centre of frame. Note that
it is of similar brightness to several other nearby stars. |
b. Stacking
21 x 28 second exposures stacked together but without taking into account
the motion of 2004 SS.
Note the minor planet now appears as a faint streak
towards the bright star at top of frame, how the stars in a. of similar
brightness are now much stronger and how stars too faint to show on a. are
now easily visible |
c. Track & Stack
Same 21 exposures used in b. but tracked on the motion of 2004 SS, keeping
the minor planet in the same place at the centre of the frame and causing
the stars to trail.
Note that the faintest stars visible in b. are now
smeared out so much that they are no longer visible, while 2004 SS is
strongly recorded. |
The 'Track' part of
Track & Stack relies on
knowing the motion of the object (i.e. the speed and direction it is moving in)
reasonably precisely, even when the actual position of the object may not be
that well known. This is almost always the case, even with newly discovered
objects with only preliminary orbits calculated from just a few precise
astrometric positions, the general speed and direction is often well determined even
when the predicted RA & Dec coordinates may have large uncertainties..
Track & Stack
allows many individual images of a moving object to be aligned so that each
image is offset from the last by the precise motion of the moving object, this
makes the background stars appear to trail and keeps the object as a point
source, building up its strength (see image c. above). The more images that are
stacked together the fainter the target object that can be recorded. For faint
minor planets, often the object is not visible at all on individual frames
(unlike 2004 SS in image a above) and is only revealed when many images are
stacked together.
To obtain astrometric
positions of a minor planet, normal procedure would be to take a number of images
and simply stack them into three sets, so that three precise positions can be
derived from the resulting digitally strengthened images.
However, there are occasions when variations on the normal method
may help to locate faint fast moving objects more readily.
General techniques (for
any faint object with large positional uncertainty)
NEOCP
Uncertainty Maps & Variant Orbits
Searching
using NEOCP Variant Orbits (using the NEOCP to full effect for unconfirmed
fast movers)
Interlaced stacking
(finding faint fast moving objects in rich star fields more easily)
General
Techniques
Take plenty of images.
- To recognise an unconfirmed object with large positional uncertainty it
needs to be made as obvious as possible, so the more total exposure time the better.
- The magnitude listed on early search ephemerides may be incorrect
by one or more magnitudes, so if there is time, take more exposures than
might be thought necessary for the quoted brightness to make sure the object is recorded.
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Stack all available images into
one big stack as well as three separate stacks.
- When blinking the four sets together, the enhanced strength of image in
the one big stack will often lead the eye to notice the object, which may
subsequently be able to be made out faintly on the three 'normal' stacks
that are used to identify the object by its motion.
- A 'real' object should be in the same place on the
stack of all images as it is in the smaller stack of images that
starts with image 1. So, if 30 images are taken and stacked into four
sets, set (a) being images 1-10, (b) images 11-20, (c) images 21-30 and
(d) all images 1-30, then when blinking all four sets, look for any
possible objects that are in the same place in stack (a) 1-10
and in stack (d) 1-30. If any are found then make sure they are also
in stacks (b) and (c) in the appropriate positions. Finding an object
in the 'all image stack (d) as well as stack (a) is NOT proof the
object exists, it just gives a short cut to where to look for movement
on the stacks (a), (b) and (c).
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Be sure to
match the exposure length
to the expected speed of the object and your CCD's pixel size.
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Even if you can't initially locate a faint object with a large
positional uncertainty someone else may find it, allowing you to later re-examine your images and obtain useful astrometry.
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Too long an exposure
for a fast moving object may lead to image trailing and cause poor
astrometry, too short an exposure may mean the object is not recorded as
strongly as possible, leading to either the object not being identified at
all,
or the signal/noise ratio being so low that astrometry measured may be
quite inaccurate. (A fast and bright unconfirmed object may be
revealed by exposing relatively long exposures so that the object is
identified by trailing during the exposure. However, for fainter
objects this is not an option and identification will need to be done
via stacking so exposures need to be kept short enough to stop
significant trailing).
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When using
different NEOCP variant orbits be sure to adjust exposure length
according to the orbit being used - they can vary substantially. See
the NEOCP Uncertainty Maps & Variant Orbits page.
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