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« Discovering Asteroids: Part 6 - Astrometry Using Unstacked Images | Main | Discovering Asteroids at itelescope.net: Part 8-Near Earth Objects »
Tuesday
Dec042012

Discovering Asteroids at iTelescope Part 7- Discovery Astrometry Using Stacked Images

Astrometry Using Stacked Images 

The Discovery Mission - Asteroids

Go to Part  1 - 2 - 3 - 4 - 5 - 6 - 7 - 8

In this article I will deal with the use of the image stacking technique to detect faint asteroids. This is the technique I use when attempting to discover asteroids and I will use one of my discovery missions as an example. My previous articles dealt with telescope and target selection, the use of dithering, image reduction, position measurement and reporting results to the Minor Planet Center (MPC). All of these techniques come together in this article so you will find it helpful if you are familiar with what has gone before.

Image Stacking-Why it Works

In CCD astronomy, the image that we see is obtained by processing photoelectrons that are generated by:-
1. Photons from the object we are trying to detect.
2. Photons from sky glow / light pollution.
3. Sources other than photons (thermal and electronic).
Item 1 is termed the signal while 2 and 3 jointly can be regarded as noise. 
This image shows an enlarged portion of a single 5-minute exposure of some stars taken using T11. The enlargement is such that you can see the individual pixels that make up the image. The pixels representing the sky vary in brightness from black through various shades of grey to white. This random variation in brightness is the noise referred to above and differs from image to image. 
Here we see the effect of stacking five different 5-minute images. The stacking was carried out using Astrometrica and this software gives you the option of different modes of stacking. I followed their advice and used the Add mode.
The first thing to notice is that the pixels representing the sky are a much more uniform shade of grey than they are in the single image. If for example a given pixel was black in image 1, light grey in image 2, dark grey in image 3…..etc, the stacking process averages out these variations to give a more uniform grey colour. 
The other thing to notice is that in addition to the two stars that were visible in the single image there are some fainter stars appearing.
This image shows what happens when we stack fifteen different 5-minute images. The background sky becomes even more uniform and the faint stars become easier to see. The stars represent the signal while the sky represents the noise and what we are doing when we stack images is to increase the signal to noise ratio.
In should be noted that in order to increase the signal to noise ratio you need to stack different images. 
This image shows what happened when I made five identical copies of the single image shown above and stacked them. As you can see there is no improvement in the signal to noise ratio and the result looks virtually identical to the original single image. What this shows is that when you stack different images, the random variation in the noise is averaged out. When you stack the same image there is no random variation and hence there is no averaging out.

Selecting the Target Area

In Part 4, I described the advantages and limitations of different potential target areas. I carried out this observation on 18 January 2012 which was 9 days after the full moon. My target area was 22 days before opposition and 9 degrees North of the ecliptic.
During the 100 minute imaging session the altitude of the target area ranged from 61 to 78 degrees.

Choosing the Imaging Conditions

I chose telescope T11 because it gives both a large field of view and good sensitivity. The need to detect faint objects also prompted me to select 2 x 2 binning which is the highest level for which itelescope produce darks and flats.
The choice of exposure time for the individual images was more problematical. As we saw in the previous article, if you intend to image an object whose speed is known you can calculate the maximum exposure that will prevent the image from trailing. Obviously in this case I had no way of knowing how fast any previously undiscovered object might be moving so I had to compromise.
On possible option is to take a large number of short-exposure images. This has the advantage that fast moving objects are less likely to trail. Another point in its favour is that with a large number of images you are better placed to overcome the problem of images spoilt by stellar interference, space junk trails and the odd lump of cloud that moves through the field of view.
One obvious disadvantage of collecting large numbers of short-exposure images is the extra time involved in downloading, unzipping and checking each image for quality.
Another less obvious disadvantage is concerned with the relationship between exposure time and image noise. In general the shorter the exposure time of an image the greater the noise level. For this reason there is a school of thought that states “sub-exposures should be sky limited” In other words if you are going to stack individual images, the exposure time of the individual images should be as long as possible bearing in mind that if the sky glow becomes too bright you are no longer winning.   
Taking all these advantages and limitations into consideration, I chose to take 15 images each with a 5-minute exposure time.
The preparation of the observation plan and the evaluation and reduction of the individual images was exactly the same as described in Part 6.

Choosing the Stacking Conditions

In Part 5 of this series I described how Astrometrica allows us to displace each image in a stack so as to compensate for the movement of an asteroid. This compensation is defined in terms of the speed of the asteroid and also the direction in which it is moving.
I have chosen asteroid 15305 as an example in order to show the importance of setting the speed and angle correctly.
This image shows the effect of stacking five images each with a 5 minute exposure. The speed is set to zero and the trailed image of 15305 shows how far it has moved during the 25-minute exposure. The stars of course, being virtually motionless, appear as near-perfect circles.
Using the Object Verification and Object Identification features in Astrometrica I was able to see that the asteroid was moving at 0.49 arcseconds per minute at an angle of 303.4 degrees. This image shows the effect of entering these values and re-stacking.
Astrometrica has compensated for the motion of the asteroid and it now appears as a circular image with the stars trailed. 
In order to show the effect of getting the stacking conditions wrong, I then re-stacked the images using completely different values (0.60 arcseconds per minute at an angle of 250 degrees).
Predictably in this image both the asteroid and the stars are trailed. In the previous article I dealt with the importance of measuring asteroid positions accurately. If we have a good circular asteroid image then Astrometrica will be able to calculate the exact centre of the image with a high degree of accuracy. With a trailed image the measurement will be less accurate but fortunately there is a way around this problem.
The first step is to use Astrometrica to display the speed and direction of all the known asteroids in the immediate vicinity of out target area. We do this by clicking on a point close to the centre of the field of view and then scrolling down the list of asteroids displayed by the Object Identification window. We can then make a rough estimate of the average speed and angle of the first dozen or so asteroids displayed.
I did this for my 18 January 2012 observations and found that the average motion was roughly 0.5 arcseconds per minute at an angle of 300 degrees. I then stacked my 15 images as three sets of five using these values and began searching for undiscovered asteroids. 

How I Search

The first point to make is that what is described here is a method that works for me but I make no claim that it will suit everybody. Depending on your eyesight, your peripheral vision and your level of concentration you may well find a better / faster way of doing things. Please try variations and find the one that suits you best.
The first thing that I do is display the blinked images in negative form using the Invert Display function. I then use the magnify feature to enlarge the image to its maximum size and scroll to the top left-hand corner. 
Earlier in the day I will have updated MPCOrb to ensure that all recently discovered asteroids are included and I now use the Known Object Overlay to display them.
I then examine the portion of the image displayed (the field) for any moving objects. I find that in order to detect a moving object I need to be looking at it directly at the moment that the images blink so starting a the top left hand corner I run my eye down the field slowly enough to be sure of eyeballing each potential moving object at the moment of blinking.
I then repeat this operation systematically searching the screen in vertical strips until I have covered the entire portion of the field displayed.
The next step is to scroll horizontally to reveal the next field of view and repeat the whole exercise. Eventually I reach the right hand side of the image and when this has been searched I scroll back horizontally to my starting point, scroll down vertically to reveal a new field of view and search as before.
Using this method on my computer, a T11 image yields about 80 searchable fields and on average it takes me about a minute to search each one. 
The search as described is carried out using calibrated images without any further adjustment. Once it is complete I use the Background and Range tool in order to optimise the brightness and contrast in order to make faint objects easier to see. Normally this process renders some regions of the image (e.g. close to bright stars) too dark to search so I need to pay special attention to these regions during the initial check. I then repeat the search.
One way of checking your ability to find moving objects is to use the Select Markings option in Astrometrica to hide the Known Object Overlay and then search the image marking all the moving objects you detect. You can then switch the overlay back on and check if you missed anything.  
One important point to note is that you cannot make accurate position measurements on stacked images which have been saved, closed and then re-opened.
The reason for this is that Astrometrica calculates the Universal Time that is included in the report that we send to MPC.  The method of calculation for single images is different for that used for stacked images. If you re-open a saved stacked image and re-process it, Astrometrica treats it a single image and reports an incorrect time.
Any description of the search method would be incomplete without mention of the Moving Object Detection (MOD) option provided by Astrometrica. The method is described in one of their tutorials and I have used it to search sets of single and stacked images.
My own experience of MOD has been mixed: I find it can work quite well for bright moving objects but cannot be relied upon to detect the faint ones. There are a number of parameters you can vary in order to improve the detection limit but the problem then is that you made have to wade through large numbers of suspect objects most of which turn out to be spurious.
However the choice between manual searching versus MOD is not an either / or decision: you can do both and I suggest that you try MOD for yourself. Please note that if you search saved stacked images and find a possible new asteroid you need to record the position, speed and angle and then prepare fresh image stacks which you use for the actual measurement and reporting. 

Dealing With a Potential Discovery

If you are observing using T11 within 10° of the ecliptic and less than 30 days from opposition on a clear dark night and an altitude greater than 60° then your chances of finding one or more potential discoveries are excellent. When all the above apply, I have never failed to find something and my current personal best is six potential discoveries in the same field of view.  
My search on 18th January 2012 resulted in three potential discoveries and I will use one of these as an example of how I report and follow up these objects.
Here you see one of the unidentified moving objects that I detected. My first task was to check that it was real and not an artifact.
In Part 5, I described the way in which hot pixels and chance alignments of noise can mimic the motion of asteroids. I could see that the object was too bright to be due to random noise and a quick check of the motion of hot pixels showed that these were moving in a different direction from the object.
My next step was to measure the position of the object but before reporting it, I needed to measure the speed and angle of motion. I did this by opening the MPC Report File window, copying the three positions for the object that I had named nfxx6 and pasting them into Notepad and saving the resulting text file.
In Part 5, I described how Find_Orb can be used to measure the residuals of a set of observations. I did this for nfxx6 and found that the mean residuals were 0.08. A low value like this is added evidence that I was looking at a real object. 
Another useful feature of Find_Orb is that if you can display the speed and angle of motion of the object. I did this and found it was moving at 0.49 arcseconds per minute at an angle of 323 degrees. This is fairly close to the values I had used when stacking the images (0.5 arcseconds per minute and 300 degrees) but in order to improve the accuracy of my results I re-stacked the images to match the motion of the object.
I then re-measured the position of the object and re-named it nf384 ready for reporting to the MPC. Before reporting however, there was one final check that I carried out and this was to run the coordinates through the MPC Near Earth Object (NEO) checker.
This tool is designed to alert you to objects which the MPC regard as interesting. Most of these will be NEOs but in addition it also flags up a variety of other objects that do not appear to be main belt asteroids.
The check showed that the object was not an NEO and at this point I reported it to the MPC. 

Follow-up

This is the process where we use the measurements we have made to predict the position of an asteroid at some time in the future and then measure its new position
 In Article 4 I dealt with the advantages of obtaining a 60-day observation arc for potential new discoveries that we want to recover in a subsequent opposition. Once we have recovered the object at the second or later opposition it is quite easy to find it during the subsequent oppositions and to make the position measurements required to improve the accuracy of the orbit to a point where the asteroid is numbered.
Asteroids with only a single-night observation and those with an observation arc of only a few days are very easily lost and the trick is to make sufficient observations over the first ten days or so to be certain of being able to locate it and progressively extend the arc to about 60 days. 

The Väisälä Method

In this case I had three position measurements taken over a period of about an hour. A typical main belt asteroid takes about three to five years to complete a single orbit so a one-hour observation arc cannot realistically be expected to give a very accurate definition of the orbit.
Another point to consider is that we are using a two-dimensional computer screen to represent a three-dimensional universe. In other words although we can see an asteroid moving up and down and right and left we cannot measure the motion that corresponds to it moving out of the screen towards us or back into the VDU.
The NEO check that I described earlier might at first sight to be an odd thing to do on an object that appears to be travelling at a fairly modest speed since objects close to the Earth generally appear to be moving much faster than this. However we have to remember the third dimension and for example an object that appears to be barely moving could in fact be going like a bat of out of hell and coming directly towards us (or, less alarmingly, moving directly away from us).
 My measurements lacked two important items of information:-
1. How far the asteroid was from the Sun.
2. Its true motion in three dimensions.
In order to predict the position of an asteroid at some future date we need these two missing items of information and since it is impossible to derive them from the data that we have, we resort to what is termed the Väisälä method which is based on two assumptions.
We assume that the object is at a distance from the Sun that is typical of main belt asteroids and we assume that it is at its closest point to the Sun i.e. at its perihelion. The reason for the perihelion assumption is that at that moment in time the asteroid is maintaining a constant distance from the Sun and the two-dimensional motion displayed on our screen is a reasonable approximation to the asteroid’s three-dimensional motion.
We now have enough information to calculate an orbit and predict future positions but since neither of the assumptions is likely to be correct we will probably end up with an inaccurate orbit. However moving from no-orbit situation to an inaccurate orbit can be regarded as progress and a Väisälä orbit based an observation arc of about an hour is generally good enough for us to predict the position of an asteroid for up to about a week. 
The MPC provide a tool the New Object Ephemeris Generator. All I needed to do was to input my three observations together with the date and time when I planned to make my follow-up observation and the observatory code for Mayhill. The tool then calculates the asteroid position using the Väisälä method.
All that remained to do was to display the target area using SkyMap and to check that there were no bright stars / planets in the vicinity at the planned observation time.
I recovered the asteroid two days later and reported it to MPC as nf 391. A few days later I received the following brief but welcome email from MPC:-  nf384    K12B24F    nf391 (K12B24F  
 
This translates as “The objects you have reported as nf384 and nf 391 are in fact the same. We cannot match this object with anything in our data base and consequently we have given it the provisional designation of 2012 BF24”. 
At this point 2012 BF24 still had a Väisälä orbit but now one based on a 48-hour arc and which was good enough to predict its position for about the next 30 days. Each object with a provisional designation and a Väisälä orbit has its own unique page on the MPC Minor Planet Ephemeris Listings but this does not include any orbital data. You can use this page to calculate the position of the object at any time although the results will become increasingly inaccurate for predictions more than 30 days in the future.
Objects with Väisälä orbits also appear when using the Minor Planet Checker but this listing only lasts for about 100 days. This is consistent with the fact that by then any positions calculated will be totally meaningless. 

The First Orbit

I used the 48-hour Väisälä orbit data to find the asteroid three days later and reported the position as before. The MPC now had positions measured on three nights and an observation arc of five days and this enabled them to dispense with the Väisälä method and calculate the first true orbit. At this point the Minor Planet Ephemeris page was upgraded to include the six elements that define such an orbit. 
Although a five-day orbit is not sufficiently accurate for long-term prediction of position it does enable you to locate an asteroid fairly easily for the next few months.
Some you Win and Some You Lose
When you first find a moving object that does not correspond to any of the known objects displayed by Astrometrica it may eventually be your discovery. However there are a number of other possibilities which include:-
1. It has been observed previously on a single night within the past week. Astrometrica will not display it but the MPC will probably link it to your observation and assign the provisional designation to the other observer.
2. It has been observed previously on two linked nights and has been assigned a provisional designation and a Väisälä orbit. Astrometrica does not display objects with Väisälä orbits but if it was observed less that about 100 days previously it will be findable using the MPC Checker. If it was observed less than 30 days previously, MPC will probably link it to your observation.
3. It has been observed on two or more unlinked single nights during a previous opposition. Astrometrica will not display it and MPC will not link your single night observation. However as you extend the observation arc of your potential new discovery to 10 days or more it becomes increasingly probable that MPC will make the link.
4. It has been observed previously on three or more linked nights and consequently it has a provisional designation, a true orbit and is displayed by Astrometrica. However if for example it has a 10-day arc and was last observed 10 years ago, the point in the sky where Astrometrica displays it will be nowhere near its true position.  Once again as you extend your arc MPC will eventually make the link.
As you work towards your target of a 60-day arc you progressively link with any prior observations in the MPC data base.
My own experience is that by the time I have a 20-day arc I will have linked to any single night observations in the current opposition and most short-arc observations in previous oppositions. My current record for the arc length of an object I subsequently lost is 58 days when my observations were identified with seven previously unlinked single nights spread over three oppositions.

Extending the Arc

There are a couple of advantages in getting the first three nights observations as close together as possible. 
If you are fortunate enough to make more than one potential discovery on the first night then you may be able to adjust the field of view on the second and third nights so that the target asteroids are all included. I find that after about five days, the different speeds and directions of the asteroids causes them to separate to such a degree that you need a different field of view for each one. 
The other advantage is connected with the ability of the MPC to make the linkages that you need to obtain a provisional designation and an orbit. As we have seen above, the first two linkages are based on Väisälä orbits which have limited accuracy.
In theory I could wait five days before obtaining my second night and a further 30 days before my third night. However I would really be pushing my luck since the MPC, understandably, errs on the side of caution when linking observations mainly because it is time consuming for them break incorrect linkages and then check all the de-linked components against other observations in their database.
Now for a couple of tips regarding follow-up: the first is to remember that a follow-up session can also result in discoveries, so after you have recovered your target asteroid, search the image for potential new discoveries. A surprising number of my potential new discoveries have been made during follow-up sessions.
The other tip concerns precovery. An example of this would be where you find a new object during the second night’s observation and then predict where it would have been on the first night. If it turns out that the predicted position is within the field of view and free from stellar interference then a careful search of the region may reveal an object that you missed during your earlier search.  The New Object Ephemeris Generator can predict position in the past as well as the future and the speed and angle of motion it predicts enables you to optimise the stacking of the earlier images.
Once I have the first three nights I normally aim to get another three corresponding to an arc of 10, 30 and 60 days. In the case of 2012 BF 24, I was helped on my way by two night’s observations by one of the professional surveys and in March 2012 I ended up with a 61-day arc. By this time the asteroid was too faint and too close to the Sun for further observation but in August 2012 the MPC reported links to two isolated single night observations, one in 2004 and the other in 2008.
In the first article in this series I summarised the current discovery rules.  These two prior observations were made in different oppositions and consequently I can still regard the asteroid as a potential discovery. It is important to emphasise however that there may still be other observations on the MPC database which will be linked to the asteroid when the orbit is improved further. I plan to make additional observations when the object returns to the night sky in 2013.
For the record the other two potential discoveries I mentioned earlier survived the first opposition without being linked to earlier observations and I hope to recover both in 2013.

What Next?

Now that we can find and follow up main belt asteroids it is time consider what we do if we come across a Near Earth Object. I will deal with this in my next article.