bxy9 Dither Pattern Analysis

An Analysis of Dithering on NIRC-2

Data:

There were three sets of bxy9 patterns used:

narrow camera, high elevation (three sets of "bxy9 3" patterns)
wide camera, high elevation (three sets of "bxy9 5" patterns)
narrow camera, low elevations (two sets of "bxy9 3" patterns)

Analysis:

These were analyzed in three ways:

By using the average (x,y) values for each dither position as the expected position.
By calculating the dither position based on the central measured (x,y) of the first set and calculating subsequent (x,y) values using the known dither length and an assumed scale factor (arcsec/pixel).
By leaving the initial position and the camera scale as free parameters.

A bit of thought shows that the first technique has 18 parameters [(x,y) for each of 9 dither positions], the second has two [the initial (x,y) pair], and the third has three [initial (x,y) pair and a scale]. The standard deviations quoted below have been adjusted for these values.

Note that a more sophisticated analysis may have included a potential rotation of coordinate frames between the bxy9 commands and the actual detector pixels. This has not been performed.

Results:

Method one (called the "relative" method):

Data Set	Standard Deviation
narrow	0.62 px (= 6.2 masec)
wide	0.18 px (= 7.2 masec)
narrow, low-el	1.06 px (= 10.6 masec)

Method two:

Data Set	Standard Deviation
narrow	2.38 px (= 23.8 masec)
wide	1.04 px (= 41.6 masec)
narrow, low-el	2.56 px (= 25.6 masec)

Method three (called the "absolute" method):

Data Set	Standard Deviation
narrow	1.53 px (= 15.3 masec)
wide	0.60 px (= 24.0 masec)
narrow, low-el	1.57 px (= 15.7 masec)

Note that the scales that were determined in method three are consistent with measurements from other sources. The third column below contains the scale estimated during laboratory I&T.

Data Set	Fitted Scale	Lab I & T Scale
narrow	9.926	9.942
wide	39.686	39.686
narrow, low-el	9.922	9.942

Figures:

Four figures are provided: two for method one ("relative") and two for method three ("relative"). For each of these methods separate figures are provided for the narrow camera data and the wide camera data.

Note that the gridlines represent 10 milliarcsec, or one pixel in the narrow camera.

Figure 1. Method one, showing the repeatability of a given dither position, but ignoring the separation between the positions. Note that there may be some slight tendency for "narrow 1," the first bxy9 pattern, to be offset from the other two. This could, for example, be a residual from imperfect DAR (differential atmospheric refraction) correction.

Figure 2. Method one with the wide camera. The scatter is similar to that in the narrow camera.

Figure 3. Method three with the narrow camera. This method includes any deviations between the expected dither positions and the measured positions. Such deviations may occur because of (1) distortions within the camera, (2) errors in the mapping of arcsec on the sky to field steering mirror (FSM) coordinates, or (3) a rotational error in mapping arcsec on the sky to NIRC-2 pixel coordinates.

Figure 4. Method three with the wide camera.