## Filters

For pure astrometry, the choice of filter is somewhat arbitrary. Roughly, the number of speckles is proportional to the diameter of the telescope aperture and inversely proportional to the wavelength (assuming a not too broad bandwidth):

The speckle size has a wavelength dependence as well as a weaker bandwidth dependence. A speckle is essentially an image of the Airy disk, dominated by the central peak. Equation (10.1) shows the functional form, which is for an infinitesimally narrow bandwidth. If a finite bandwidth is used, each wavelength "bin" creates its own Airy disk, each of a slightly different size. The net effect is to "fuzz out" the Airy disk edges, which makes the speckles bigger, and merges more of them together. In addition, for wide bandwidths, the atmosphere will chromatically split the object light, creating an elongated speckle. This effect is more prominent with larger telescopes and objects at a significant angle down from zenith. A filter with a narrower bandwidth lessens this problem and makes astrometry more precise.

Astronomers mostly use the Johnson UBV11 and Cousins RI12 filter systems. These are fairly wide bandwidth filters. Another system that is frequently used is the Stromgren ubvy13 - see also Crawford and Barnes14. These are quite a bit narrower and may give more precise astrometry. Additional information about astronomical filter systems can be found in the General Catalogue of Photometric Data15 (visit http://obswww.

unige.ch/gcpd/gcpd.html). Again, for pure astrometric work, any filter that produces good, sharp speckles will suffice.

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