To Stack or not to Stack?
In Part 5 of this series I described how we can use image stacking to enable us to produce long-exposure images of moving objects. The advantage of image stacking is that it allows us to see objects that would be too faint to detect using unstacked images. One disadvantage is that astrometry using stacked images is more complex than working with unstacked images. It is for this reason that I intend to deal with stacked image astrometry in a later article. In this article I will describe how to use unstacked images to measure the position of relatively bright asteroids and report our findings to the Minor Planet Center (MPC).
If I have a choice I always use unstacked images the reasons being:-
I have more images to choose from so I can reject those where the object is close to a star, where the seeing degrades or where a cloud moves across the field of view.
All image processing brings with it the risk of degrading the accuracy of the measurements so I only use image stacking if it is really necessary.
Stacking images reduces the observation arc i.e. time interval between the first and the last image. As a general rule, the longer the observation arc, the more useful it is in predicting the position of the object at some future date.
How Good do our Measurements Need to be?
The iTelescope observatories have all been assigned observatory codes by the MPC and this means that we can log on to a telescope, measure the position of an asteroid and report its position to them.
The MPC accepts measurements from both professionals and amateurs but their requirements for both are exactly the same. They emphasise the importance of both accuracy and consistency. In the case of accuracy they are expecting us to produce measurements that are accurate to within 1 arcsecond.
If either of the residuals in a RA-Dec measurement are greater than or equal to 1.5 arcseconds then the MPC will not include that particular data point when calculating an orbit. For any given night the MPC require at least two RA-Dec data points on an object so if I were to submit three data points and two of them had a residual greater than or equal to 1.5 arcseconds then all three data points would be excluded from the orbit solution. This is significant because the lost night’s observations might have included a discovery observation.
In the case of consistency the MPC would like our measurements to vary by no more than a few tenths of an arcsecond.
The difference between accuracy and consistency can be shown by the arcsecond residuals obtained when four different observers each make six different measurements:-
A: 0.0, 0.2, 1.6, 0.9, 0.1, 1.3
B: 0.0, 0.4, 0.1, 0.5, 0.1, 0.9
C: 0.6, 0.6, 0.8, 0.7, 0.7, 0.6
D. 0.1, 0.3 0.1, 0.2, 0.3, 0.0
Observer A is neither accurate nor consistent. Their residuals are basically all over the place ranging from 0.0 (spot on) to 1.6 (not good enough for linking).
Observer B is accurate insomuch as all the residuals are less than 1 but not very consistent since their residuals range between 0.0 and 0.9.
Observer C is less accurate that Observer B since all of their residuals are greater than 0.5 but they are much more consistent with the spread of residuals only ranging from 0.6 to 0.8.
Observer D is up to professional standard with results that are both accurate and consistent.
The MPC value night-to-night consistency and would probably prefer the consistent observations of C to those of the slightly more accurate but less consistent values supplied by B.
What I aim now is to show you what needs to be done in order to produce results which meet the MPC accuracy and consistency requirements. I will be using various items of software but I will not be going into their operational details. The reason for this omission is partly because to do otherwise would make this a very long article but mainly because the authors of the software do a really good job in explaining how to use their products.
In order to establish how good my measurements were I needed to choose an asteroid whose position is known very accurately and which is within an acceptable magnitude range. The MPC advise that asteroids with numbers between 400 and 40,000 meet these requirements.
In Part 3 of this series, I dealt with telescope selection and had my observations been limited to an accuracy check using a relatively bright asteroid, I could have used any of the seven telescopes suitable for asteroid observation in the Northern Hemisphere (Siding Spring observatory was still under construction at this time). However, I wanted to combine the check with a follow-up observation on one of my potential discoveries at magnitude 21.7 and this prompted me to choose T11.
I carried out the observation in March 2012 and, using SkyMap, I found that the earliest date when the weather conditions were acceptable and the telescope was available was March 30th. I displayed the first 40,000 numbered asteroids in my target area at midnight on that day and selected a number of possible candidates.
I then used the MPC Ephemeris page to eliminate those that were moving at more than 1 arcseconds per minute. Anything faster than that would have been more difficult to measure accurately. My final choice was 34997 1978 OP. On March 30th 2012, the asteroid was at magnitude 18.3 and was moving at 0.1 arcseconds per minute.
The timing of the observation was a compromise between avoiding lunar interference while keeping the asteroid as high in the sky as possible. I chose a start time of 00 30 hrs Mountain Daylight Time which meant that the asteroid’s elevation ranged from 55 to 33 degrees.
Time is of the Essence
Asteroid observation means having to work with up to three different time zones:-
1. Observatory Local Time which is used for planning the observation and reserving the telescope.
2. Universal Time (UT) which is used when reporting results to the MPC.
3. Observer Local Time which you need to know if you want to be at your computer watching while the observations take place.
Intercontinental time conversions are complicated by the fact that different time zones may have daylight saving times that change on different days (and at different times of day). In addition the conversion may result in a date change.
I find this time zone converter useful:-
and using it I found that 00 30 hours Mountain Daylight Time in New Mexico converted to 07 30 hours British Summer Time in England and to 06 30 hours UT. The date remained March 30th in each case.
I used the MPC Ephemeris page to obtain the exact position of 34997 at the start of observation but in order to do this I had to express the UT date and time in a decimal form.
The calculation of decimal UT involves converting UT to seconds and then dividing it by the 86,400 seconds in a day. In this case, 06 30 hours UT on March 30th converts to 30.27083 decimal UT.
The coordinates of the asteroid at this time were: - R A 09 16 47.7, Dec +28 40 32
Choosing the Binning
Reference to the T11 information page showed that for optimum results I had a choice between 1 x 1 and 2 x 2 binning and a check of the calibration images currently available revealed that I could use either of these options. I chose 2 x 2 binning which as we saw in Part 3 gives higher sensitivity at the expense of reduced accuracy. Had I not had also been trying to follow up a magnitude 21.7 asteroid I would have gone for the more accurate option.
Choosing the Exposure Time
The points I needed to take into account were that the exposure time needed to be:-
long enough to give a detectable image of the asteroid.
short enough to prevent the image trailing
a time interval for which iTelescope produced flats and darks calibration images.
The 2 x 2 binning level gives a resolution of 1.62 arcseconds per pixel and if we want to avoid trailing we need an exposure time short enough to prevent the asteroid moving more than 1 pixel i.e. more than 1.62 arcseconds. As we saw earlier, 34997 on the planned observation day would be moving at 0.1 arcseconds per minute so the longest exposure that keeps the motion to less than 1.62 arcseconds can be calculated by dividing the resolution by the speed i.e. 1.62 / 0.1 = 16.2 minutes which is 972 seconds.
If we log on to T11 and navigate to the telescope information page we see that exposure times greater than 600 seconds require guiding. I decided to avoid the need to guide by selecting a shorter exposure time and reference to the general T11 information page showed that the longest guide-free time recommended was 300 seconds. On this basis I opted for a 300 second exposure.
Choosing the Number of Exposures
The MPC recommend that the observation arc should be at least 30 minutes and preferably between one and two hours. They ask that the arc should be made up of between three and five positions. Single positions are rejected while more than five on a single night do not add significantly to the accuracy of the arc.
With this in mind I decide to obtain 15 images each with a 300 second exposure. I know from experience that, allowing for the download time of each image, this will give me an unstacked observation arc of about 1 hour 45 minutes. If I stacked the images as 3 sets of five, the arc reduces to about one hour.
Choosing the Filter
Depending on which telescope you select you will find that it is fitted with either a clear or a luminance filter. T11 comes with a luminance filter and this is the one I selected.
Preparing the Observation Plan
I used the ACP Planner to produce the plan that would control the telescope during the imaging session. iTelescope use a customised version of ACP Observatory Control Software and this is described here:- https://go.itelescope.net/downloads/itn-acp-directives.pdf
In Part 5 of this series, I recommended the use of dithering in order to prevent confusing artifacts with real asteroids and my plan incorporates the multiple re-targeting that I detailed therein.
This is the plan I produced:-
; This plan was generated by ACP Planner 3.2.2
; For: Norman
; Targets: 3
; NOTE: Timing features are disabled
; Autofocus at start of run.
; === Target 34997a ===
34997a 09:16:50.00 28° 40' 30.0"
; === Target 34997b ===
34997b 09:17:00.00 28° 41' 00.0"
; === Target 34997c ===
34997c 09:17:00.00 28° 40' 00.0"
#shutdown ; Shut down the observatory
; END OF PLAN
After the initial focussing command, there are instructions to collect three sets each of five images. The exposure time, filter and binning are the same throughout but the target coordinates are dithered.
Setting up for Image Processing
I use Astrometrica and I suggest that if you are unfamiliar with this software you start by reading through the tutorials in the Help section. The next step is to set up the six screens that control the way in which the program processes the data and reports the results. You will find details of how to do this in the Help section under Dialog Boxes – Program Settings.
Evaluating the Images
The sky conditions were not ideal when I obtained my 15 images. The cloud meter read minus 20 and the seeing ranges averaged around 2.8 arcseconds. After downloading I opened each image in turn to check that the tracking was good and faint stars were detectable. In fact all the images looked OK so the next step was to select one of them and carry out a reduction.
If you have no difficulty in reducing images you can skip the following section but when I first used Astrometrica I did experience problems with images which stubbornly resisted reduction. This is the method that I used to overcome the problem.
I refer to T11 throughout but the method is the same for any of the iTelescope scopes.
The first thing I do is to display the target area using SkyMap with a CCD frame set to show the T11 field of view. I do this so that North is up and West is to the right. I then compare this with my image. Hopefully the pattern of stars in SkyMap and the image is identical but if not my next step is open the Program Setting-CCD window and change the settings of the Flip Horizontal and Flip Vertical tick boxes (if they are both ticked, un-tick them and vice versa). Closing and reopening the image should display it inverted both laterally and vertically.
If the images still does not match SkyMap it is possible that there is a targeting error or that the CCD is not mounted in a North-South vertical: East-West horizontal orientation.
I can generally spot any targeting error by adjusting SkyMap to give a wider field of view and then trying to match the image star pattern both before and after inversion. If this does not work I log on to T11 and open up the appropriate log file.
In order to locate the target area, the telescope software will have carried out an image reduction and this information is recorded in the log. If you scroll down to the point where the first image is recorded and then look a few lines above you will find the following lines:-
True focal length is ……
Imager sky position angle is ….
In this case my log showed the focal length as 226.0 cm and the sky position angle as 192.5 degrees.
I then enter these values into the Astrometrica CCD window. Astrometrica allows you to choose between Automatic and Manual reduction. I favour Manual because it allows me to see what is going on. I can set Astrometrica to Manual by opening the Astrometrica Program window and setting Reference Star Matching-Number of Stars to zero. This image shows the result of my attempted reduction. I have displayed it in negative form for clarity
As you can see there is a problem. The red circles show where Astrometrica thinks the stars should be and black dots show where they actually are. In fact what has happened is that the 192.5 degree angle recorded in the log refers to a reduction carried out on an inverted image. All we have to do is to subtract (or add) 180 degrees which gives us an angle of 12.5 degrees.
This image shows the result of a reduction carried out after re-setting the sky position angle to 12.5 degrees, Although we still do not have an alignment you can see that if we were to shift the red circles slightly to the left and very slightly upwards the stars and the circles would align. In practice I find it helps if I reduce the magnitude until only the circles representing the brightest stars are displayed.
This image shows the circles and stars aligned and if I now click on OK, the image will reduce.
The last refinement you can carry out is open the Astrometrica log file and note the focal length and rotation. I do this and feed the values back into the CCD window. Another piece of useful information in the log is the RA-Dec Center Coordinates i.e. the true image centre. If there is a significant pointing error (which can happen when the sky conditions are poor) then it can save time to enter these values just before carrying out the reduction. If you do this it minimises the time you have to spend aligning the circles and stars.
When you reduce an image, Astrometrica displays a Data Reduction Results window and this includes the dRa and dDec residuals. I find that with a good reduction these values are less than 0.3 arcseconds.
Evaluating the Images
I find a good way of evaluating image quality is to reduce the image and then check both the residuals and the total number of stars detected. If the sky condition worsens during an imaging session the number of stars detected is reduced and the residuals are increased.
I reduced all 15 images at the same time and discarded one with poor residuals and a low star count. I then used Known Object Overlay to identify the asteroid and blinked the images in order to check if there was any stellar interference. Finally I select five of the images which were of good quality and gave the longest observation arc.
I loaded the five selected images, reduced then and then added the know object overlay. I then blinked the images and centered 34997 in the field of view at maximum magnification.
I measured each image in turn by stopping the blink option and then positioning the cursor as close as possible to the centre of the asteroid and then clicking. In the Help section of Astrometrica there are details of other measurement options involving the use of the Control and Shift keys which you may find useful.
Whichever method I use, I always check (using the Object Verification Window) that the asteroid is centred correctly within the locating circle. The diameter of this circle is controlled by the Aperture Radius setting which is located in Program Setting window. I sometimes have problems centering an object within the locating circle and I find that making the Aperture Radius larger or smaller usually overcomes this problem.
Having centered the asteroid correctly I then gave it what the MPC term an Observer Assigned Temporary Designation which is basically my reference number. The MPC favour the method followed by the professionals whereby each object observed on any given night is assigned its own unique Observer Assigned Temporary Designation. The designation can be a maximum of six characters but should not be in a form that could be confused with the designations formats used by MPC i.e. numbers only (34997), unpacked provisional designation, (1978 OP) and packed provisional designation (currently a letter followed by four digits). I suggest that you adopt a system based on your initials (case dependent) followed by a number. I called this object nf458.
I used the same method and designation for the remaining four images.
Reporting to MPC
Astrometrica prepares a report in the approved MPC format so all I had to do was to check that I had five readings all with the same designation and then click the send button.
MPC has a well-automated system for dealing with reported positions and the first email I received was their standard autoack message which said:-
The receipt of a message (probably containing observations) is hereby
The formatting code returned the following statistics:
Number of header lines read = 8
Number of observation lines read = 5
I normally get one of these within a few minutes of sending a report but at busy times it can take longer. If you don’t get one within 24 hours the send it again but include RESEND in the subject line.
The next message I usually get is information regarding their designation of the object I have reported. This autodes message is very brief and in this case of 34997 simply read nf458 (34997.
It means “we have identified to object you call nf458 as the numbered asteroid 34997”. The bracket is highly significant to those hoping to discover new asteroids because if it is absent it means that the MPC has not been able to identify it with a known object.
How Good were my Measurements?
In order to check the accuracy of my results all I had to do was to use the MPC Ephemeris page to display the residuals for 34997
If you have reported an object for which the MPC has rated observations as Desirable or Highly Desirable then they normally report your residuals within a day or so. However well observed-objects like 34997 are rated as No Observations Needed at this Time. What this means in practice is that for MPC this is a low priority matter and they normally wait until the end of the lunar month before including the results in the residuals section.
The residuals for the five positions I reported were:
There is a lot credit due here to iTelescope for enabling me to produce residuals of this accuracy bearing in mind that the sky conditions were not ideal. In order to achieve this accuracy you need perfectly aligned optics, spot-on tracking and a clock which is constantly synchronised with Universal Time.
Now that we have demonstrated that the equipment can produce accurate results, we are ready for our first discovery mission. This will be the subject of my next article.