STAR-SUBTRACTION AND ASTEROID TRACK/STACK
Bruce L. Gary, 2007.02.12

Introduction

Asteroid astrometry can be thought of as belonging to one of three categories: 1) bright asteroid with few background stars, 2) faint asteroid with few background stars, and 3) faint asteroid with too many background stars. The best procedure for processing images will differ for these three categories. For the first category it is sufficient to use PinPoint to perform the entire analysis procedure. For the second category it is adequate to merely perform a track/stack (no star subtraction). It's the challenge of the third category that this web page is meant to address.

When dealing with faint asteroids in a crowded star field it may be worth the effort to perform a labor-intensive analysis that greatly fades the star field while retaining the asteroid's brightness. The procedure on this web page is recommended for only those people who love image analysis. The payoffs are not dramatic enough for the casual user. For example, when an initial set of 12 images is used the final image affords a limiting magnitude improvement of only 0.6 magnitude (SNR greater by 1.7) compared to a single image. This may sound like a losing endeavor, and it would be if there were no background stars. But since stars are always present there may be times when this procedure is useful. I'll consider a case of 12 images taken 16 minutes apart of a NEO (near Earth asteroid) field. (For a typical NEO, which moves fast, it would be better to take images spaced ~ 5 minutes apart.)

The loss of SNR is compensated by a 9 magnitude reduction in star intensities while preserving the asteroid's brightness. Provided the asteroid passes close to only unsaturated stars this objective procedure promises to make use of the asteroid's "information" in each image, which makes the procedure "objective." This procedure is NOT recommended when the star field is uncrowded or when the asteroids are bright enough to be seen in each image.

Case Study of Star-Subtract and Asteroid Track-Stack Procedure

The present set of 12 images were made with a 32-inch Ritchey-Chretien telescope owned and operated by my neighbor Dave Healy (Junk BOnd Observatory, MPC Code 701). Each exposure was unfiltered and 3 minutes long, spaced 16 minutes apart (for fast-moving NEOs I recommend as close a spacing as possible). The NEO has a predicted V-mag = 21.6 and movement of 2.04 "arc/minute at pa = 252 degrees. The images were calibrated using a dark frame at a quite different temperature, which caused an abundance of pixel artifacts. The next two figures show a single raw image and the final image based on the star subtraction procedure using 12 images.

raw image

Figure 1. Raw image #1. FOV = 27 x 18 'arc. FWHM = 3.7 "arc. [Exposure 180 seconds, unfiltered, unguided, Junk BOnd Observatory, 2007.01.16 UT]

Final image showing the asteroid

Figure 2. After star subtraction and median combining (using a reference dot that was pixel edited into each image at a location that moved at the asteroid's rate). The asteroid has SNR = 15 and CV = 21.0. The residual "noise" associated with star features has CV ~21.  [Exposure 180 seconds, unfiltered, unguided, Junk BOnd Observatory, 2007.01.16 UT]

The star subtraction and asteroid track and stack procedure will now be described.

STAR-SUBTRACT AND ASTEROID TRACK/STACK PROCEDURE
    12 images for 3-coordinate result , BLG, 2007.01.17

1) Calibrate 12 images. Save w/ names 1, 2, 3, ... a, b, c.

2) Plate solve the following 3 images: 1, 5, 9.

3) Acquire NEO rate of motion ("arc/min) & direction (pa). Convert to dx/dt and dy/dt (pixels/minute).

4) Note times of all images. Hopefully they’re uniformly spaced with delta-t = constant.

5) Median combine (star-align) all 12 images. Call it ALLSTAR_mc. Select a star (unsaturated, near UL corner) that we’ll refer to as the “reference star.” Read the FWHM of the reference star.  Create sharpened and smoothed versions, and use the FWHM of the reference star to record these images as ALLSTAR_45 (for FWHM = 4.5 “arc), etc. Do this for a range of FWHM (such as 4.2 to 5.5 “arc).  

6) Unload all images; then load images 1, 2, 3 & 4. Star-align them (1 will retain astrometry)

7) Note the reference star’s x,y centroid in image 1. 

8) Make table (or use Excel) to calculate time offsets for images 3, 4 & 5 with respect to the first one. Using dt2, dt3 & dt4 (time offsets w.r.t. image #1), calc dx,dy pixel offsets for the “asteroid offset dot” for all images (including a starting offset of +20 pixels for the 1st image).

9) Pixel edit the "dot" in each image. Save as 1d, 2d, 3d, 4d. 

10) Read FWHM of a specific star (it could be the “reference star”) for images 1d, 2d, 3d & 4d.

11) Load the ALLSTAR_?? images that have similar FWHM readings as 1d, 2d, 3d & 4d. 

12) Run the “align” tool and copy 1d to the process window, then copy the most similar ALLSTAR_?? image to the process window. Complete the align.

13) Highlight image 1d and run the Pixel Math tool. Notice that Image A has “1d” selected. Make sure it’s set to 100%. Click the Subtract operation. For Image B select the ALLSTAR_?? image to be used for subtraction. Make sure 100% is selected for Image B (you could be clever and set it to a more optimum value, but not now). Set Add Constant to 4000. Click OK. The new image has stars greatly diminished in intensity. Don’t worry about rings and dark central spots for the brightest stars. Save this image as 1dss. 

14) Repeat above two step for images 2d, 3d & 4d. This will produce images 2dss, 3dss and 4dss.

15) Median combine the 4 dss-images using the “dot” for alignment (be sure 1dss is at the top of the list). This image will have the stars even fainter. Save this image as A(1234). 

16) As an extra feature you can place a pixel edited symbol (such as an X) at a specific RA/Dec location (near the UL corner). This might be useful when doing an animation in which \you want the RA/Dec coordinates to be fixed to see if you can see an asteroid moving).

17) Repeat steps 6 thru 16 for images 5, 6, 7 & 8. This will produce image B(4567). 

18) Finally, repeat steps 6 thru 16 for images 9, a, b & c. This will produce C(9abc).

19) Median combine A, B & C, using the alignment dot, to produce image ABC. This image should have almost no star signatures while the asteroid’s brightness should remain unchanged but with much greater contrast (SNR) than for any individual unprocessed image. Astrometry for image ABC will correspond to the start time for image 1, so add “exposure time / 2” to ABC’s  time tag and read the RA/Dec of any asteroid that is present. 

Comment: If the asteroid is bright enough to be identified in each of images A, B & C, then you can read its RA/Dec in each of those images & apply a time tag correction to these readings. This will give a 3-epoch astrometry set, suitable for MPC submission. It may be necessary to identify the asteroid in image ABC before noticing that it is also present in A, B & C. To verify that an asteroid candidate is probably true, view animations using first the “dot” for alignment (positioning the cursor at the suggested asteroid’s location to see if it’s present in all images) and second using the RA?Dec “X” symbol for alignment to see the asteroid move while the (invisible) star field remains fixed.


Related Links

    Minor Planet Bulletin article "Image Subtraction Procedure for Observing Faint Asteroids"
    30-image combining for greater SNR improvement
    Tutorial on Asteroid Alignment Dot Stacking
    AstroPhotos - my astronomy home page

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This site opened:  January 2, 2007.  Last Update:  February 12, 2007