Interlaced Stacking

(for detecting faint fast moving objects in crowded star fields)

Introduction

The effect of speed

The effect of many stacked images

When to use interlaced stacking

How to use Interlaced Stacking

Some examples of interlaced stacking

Considerations for taking exposures when interlaced stacking is to be used

Introduction

Arguably the most important processing stage after image acquisition of a NEO is identification of the target object within the images. Interlaced stacking is a technique that helps locate the target in difficult circumstances (when the object is both faint and fast moving and there is some degree of uncertainty in the predicted position). Having used interlaced stacking to locate the object, more normal stacking techniques would then be used to measure a set of astrometric positions.

Finding bright moving objects on a set of images is normally very straightforward, blinking consecutive images using software such as Astrometrica allows the eye to notice a moving object easily. Indeed, with bright objects that can be seen easily on individual images, there may be no need to stack images together to enhance the visibility of the object any further (though stacking will generally allow more precise positions to be measured, even for bright objects).

For fainter objects moving at relatively slow speeds normal stacking techniques work very well. Standard practice is to use all available images to "track and stack" into three equal sets to enhance the strength of the image of the moving object in each set. These stacks can then be used to blink for motion (rather than using the individual images as in the case of bright objects). The stacking strengthens the image of the faint object while keeping it point-like and, depending on the number of images stacked and the speed of the object the stars will appear as trails.

The effect of speed

However, in some circumstances normal stacking techniques may not be enough. For a faint fast mover, if the motion is great enough for the star trails to be stretched so much that instead of solid trails the stars appear as a chain of individual star images, then recognising the moving object is much more difficult, it will appear as a faint point-like star, but so will all the faint stars in the image as well.

20 images@0.5"/min	20 images@5"/min	20 images@50"/min	20 images@100"/min
Here the same set of 20 images are re-stacked with different speeds of motion. The number of dots in the image that might be confused with a target object increases dramatically as the speed passes the threshold where the gaps between successive exposures can be seen. In this case each exposure was 4 seconds with a 3 second gap between exposures. At a speed of 5"/min the stars are solid trails, at 50"/min the individual exposures can just be detected but are not too distracting but at 100"/min there are many individual star images visible that might make it difficult to notice a target object amongst them.

The effect of many stacked images

Once the speed of the object has reached the point where the star images can be seen as individual dots rather than trails, then with traditional stacking both the speed of the object and the faintness make identification much more difficult. To combat faintness, more images need to be stacked together, but more images mean more individual star images cluttering up the stacks. More images also implies that the fast moving object will be found in very different parts of the field of view in sequential stacked images used for blinking, very difficult to pick out amongst the stars.

1 image	5 images@50"/min	10 images@50"/min	50 images@50"/min
In this crowded star field, with a single image there is still plenty of space between individual stars. However, as more and more exposures are stacked to reveal a faint and fast moving object the star trails lengthen and the amount of space between stars decreases. With 50 images stacked together the majority of the image is covered in faint star images, making it very difficult to find the target.

Interlaced stacking is a simple track & stack technique that gets around these issues and can help reveal a fast moving NEO in a crowded star field with remarkable ease and certainty by reducing the distance an object appears to move when blinking two sets of images.

When to use interlaced stacking

• The speed of the object needs to be great enough for there to be noticeable difference in position between consecutive images (say a minimum of 2-3 pixels). As well as the apparent motion of the object, image transfer time from the CCD is a factor here, the longer the transfer time, the longer the interval between consecutive exposures and therefore more motion will be apparent, so comparatively slower moving objects will respond to interlaced stacking if a CCD with slow readout time is being used ... and ...

• The object is too faint to be seen on individual images. Use traditional stacking (or just blinking of unstacked images) to identify brighter objects.

How to use Interlaced Stacking

The examples below have been made from a set of 20 four second exposures of fast moving NEO 2006 JE from 01 May 2006 when it was about magnitude +18.4 and moving at 94"/min. All 20 images have been stacked together and annotated (left hand) and on the right hand side two halves of the images have been stacked together and blinked to reveal the motion of the object. The first example shows traditional stacking, the second example shows interlaced stacking. Note that with interlaced stacking the object appears to move much less between frames. The method is most benefit in more crowded star fields, or when more exposures need to be stacked together (and therefore more star images are scattered throughout the images).
Traditional Track & Stack	Example
In a traditional track & stack consecutive images are stacked together to form sets (in this case images 1 -10 and 11-20 are stacked to form two stacks to be blinked). The amount the target moves between stacks depends on how far the object moves between the start of the first exposures in each stack, i.e. images 1 and 11.
Interlaced Stacking	Example
With interlaced stacking, instead of stacking consecutive images, alternate images are combined (normally just two sets), e.g. all the odd numbered images and all the even numbered images, so in the example above, images 1,3,5,7,9,11,13,15,17 & 19 are stacked together and images 2,4,6,8,10,12,14,16,18 & 20 are stacked together. Note that the amount the target moves between stacks again depends on how far the object moves between the start of the first exposures in each stack but this time the first exposures in each stack are images 1 & 2. This greatly reduces the change in position of the target between stacks and makes it much easier to locate a faint fast moving target in a crowded star field. Because the apparent movement of the target object using interlaced stacking depends on the interval between images 1 & 2 (or one interval of motion), the movement of any suspect must be half the distance between adjacent star images. The star trails consist of images 1,3,5 etc and 2,4,6 etc and so are separated by 2 units of the expected targets motion. Once the object has been located by interlaced stacking, the images would then be re-stacked, preferably into three (traditional) sets, the object carefully re-located and measured. If real, it should appear in all three stacks.

Some examples of interlaced stacking

• Artificial satellite IMP-8 moving at 66"/min.

• NEO 2004 LA₁₀ moving at 17"/min through an extremely rich starfield in Aquila, as it appeared in Bill Allen's 05 July 2004 edition of Major News About Minor Objects. Due to the density of stars this took extra effort to determine which of the images needed to be left out when the NEO was too close to the background stars. 

• NEO 2007 EH moving at 1249"/min during a very close approach to Earth on 11 March 2007

Considerations for taking exposures when interlaced stacking is to be used

The time interval between consecutive exposures needs to be as constant as possible

If the times are irregular, then when blinking the images there will be a great deal of movement presented to the eye because stars will not be in the same place in each of the stacked images. Irregular start times may be caused by other processes running during image download, slowing the computer down, or manual or semi-automatic triggering of exposures etc.

The target may be obscured by a star

It is always possible that the target may have moved in front of a background star during the run of exposures. In that case, there may only be a single image of the target visible during the blinking of interlaced stacked images. The measurer should be aware of  isolated single potential target images and try re-stacking the interlaced images again but excluding the frames where a star may be involved.