Bruce L. Gary, Hereford Arizona Observatory (G95)
Last updated 2005.01.04

SE = standard error uncertainty; the orthogonal sum of SEs and SEc; SE = SQRT (SEs2 + SEc2)
SEs = stochastic SE; SEs = 1 / SNR in magnitude units (when SNR > 10).
SEc = calibration SE; usually estimated. Check stars offer quick estimate of lower limit to SEc, as do multiple measurements of a single star. For faint asteroids SEs > SEc.
Photometer signal circle = the circular aperture containing star light to be measured
Sky background reference annulus = the outermost annulus, with a gap annulus between it and the signal circle, used to determine an average level for subtracting from the signal circle readings
Intensity = sum of counts above background level; sum is performed within a circular photometry aperture; background level is established using an annulus (outside a gap annulus)

Good Observing Practices

Median Combining

It is a good practice to work with images that are a median combine of 3 or more images (that have been dark frame and flat field calibrated). This usually is not done for asteroid search programs since triplets (or quadruplets) of images are taken of a specific star field, each image >20 minutes after the preceding one, and this image set is used to search for moving targets. Photometrists median combine before doing photometry because this process removes cosmic ray artifacts. Fortunately, it is still possible to remove the effect of cosmic ray artifacts using a set of 3 or more images of an asteroid. This can be done by median combining using the asteroid for image alignment. In such an image the background stars disappear leaving only an asteroid feature. There are two advantages for doing this: 1) the asteroid feature has improved SNR, and 2) nearby stars are much less likely to interfere with photometry since they are removed by the median combining process. Combining images can also be done by averaging, but in this case you actually increase the chances of having nearby stars interfere with photometry. Here's an example comparing averaging and median combining (using the asteroid for alignment in both cases).

 Median combine aligning w/ asteroid

Figure 1. Two versions of combining 14 images of asteroid 2004 MN4 (V-mag = 16.88 +/- 0.15 SE). Left panel shows averaging (using the asteroid for aligning), and the right panel shows median combining (also using the asteroid for alignment).  [Celestron 14-inch, prime focus f/1.86, SBIG ST-8XE, red filter, total of 14 60-second exposures, unfiltered; 2005.01.08; Hereford, AZ]

Median combining may incur a ~15% SNR penalty, but it removes cosmic ray defects and it reduces the brightness of star tracks due to the asteroid's motion. Notice that a cosmic ray is visible in the upper-left region of the left panel. The reduction of star track brightness can be an advantage when doing photometry with a large sky reference annulus.

Pixel Editing

Professionals would be "horrified" to learn that someone was suggesting "pixel editing" to recover an image for photometric analysis. But that's what I'm going to do. Here's the situation where I recommend it.

 Animation (26 frames)

 Figure 2. Animation of Asteroid 12753 passing by a bright star. This 26-frame sequence shows motion during a 5-hour period (2004.12.31).

Notice that about 1/3 of the way through the sequence the asteroid appears to fade. This set of observations was made for the purpose of establishing a rotation light curve. But what can be done to minimize the effects of the bright interfering star? Should this data be rejected simply because it would spoil the signal aperture reading, or spoil the sky background reference annulus reading? Here's the problem, using Frame #10 as an example.

problem star

Figure 3. Frame 10 (enlarged) from the above sequence, showing the "problem star" east of the asteroid (at center of aperture circles).

The solutionis to "pixel edit" the problem star away.


Figure 4. Pixel editing was used to "remove" the problem star, permitting the use of a better quality "sky background reference annulus."

The final rotation light curve appears to be unaffected by this problem star and a few other fainter ones that were dealt with in the same manner, as the following graph shows.

Rotation light curve

Figure 5. The red squares are from the 26-frame sequence from 2004.12.31, using an R-filter. Only one frame could not be "rescued" from the effects of nearby stars. The pixel editing example in the previous figure led to the data point at UT = 4.1 hours. The 2004.11.11 data (green circles) are V-filter observations and they have been adjusted by -1.6 magnitudes to achieve agreement with the R-filter rotation light curve. A full rotation occurs each 12.85 hours.

The rescue work appears to have been successful since the rotation light curve is consistent with data from a month before and a year before that. I therefore recommend pixel editing for the rcovery of images that are affected by nearby interfering stars.

additional work planned

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This site opened:  January 1, 2005 Last Update:  January 2, 2005