Modeling the Digital Output of the Multichannel Astrometric Photometer
**Previous
abstract** **Next
abstract**

**Session 3 -- Instrumentation and Techniques I: Ground Based**
*Display presentation, Monday, June 12, 1995, 9:20am - 6:30pm*

## [3.11] Modeling the Digital Output of the Multichannel Astrometric Photometer

*Joost Kiewiet de Jonge (University of Pittsburgh)*
The periodic variation in the photon counts induced by the
precision Ronchi ruling among the target and field stars imaged
in the focal plane of the Thaw refractor has been and continues
to be analyzed for phase differences in a purely numerical way.
Efforts to develop a theoretical analytical output model for the
MAP have so far been thwarted by the lack of an available,
readily integrable mathematical function accurately representing
the observed extended wing profiles of star images. However, it
is shown that such a function exists in the form of a modified
Bessel function. A complete theory of the instrument can
therefore in principle be constructed.

The derived time dependent output function has one given
parameter (the ruling constant) and four adjustable parameters:
FWHM image diameter (seeing diameter), semi-amplitude of the
star's photon count, the cycle period and the time of zero phase.
For each star first order approximations to these adjustable
parameters (same for all cycles in a given run) are then improved
by the method of differential corrections by solving the
linearized equations of condition in a standard least square
solution. The least square adjustments may extend over a few
cycles or longer, yielding times of zero phase for each star and
ultimately mean phase differences between all stars for a given
run.

Because the analytical model is capable of fitting the digital
output of the MAP with great fidelity and is very flexible (it
can accommodate a very wide variation in seeing and sky
transparency) it is expected that its application to ongoing
astrometric studies will bring about a further increase in the
precision of astrometric observations at Allegheny Observatory.

**Monday
program listing**