Heuristic Filter Design applied to Gaia

C.A.L. Bailer-Jones

The design of the Gaia photometric systems is a complex task because it must accommodate numerous different requirements. The filter systems are primarily designed to determine astrophysical parameters (such as effective temperature, surface gravity, abundances) for single stars - the main Gaia target. They must do this across a very wide range of spectral types, thus some of the requirements are inevitably conflicting. Designing a system which is the best compromise between these requirements is a challenge.

To address this problem, I have developed a novel method to design photometric systems using principles of natural selection from evolutionary biology. By parameterizing a filter system and defining an appropriate Figure-of-Merit (FoM) of its performance, this method uses a population-based approach to search the vast space of possible solutions and to converge on an optimum solution.

The figure above shows how the three filter parameters - central wavelength, filter width (HWHM) and fractional integration time - evolve during the successive generations of the procedure. The run shown is for the optimization of a 5-filter system (i.e. a total of 15 free parameters), using a population of 200 individuals (filter systems). Thus at each generation, there are 1000 different values of each of the three parameter types in the population. These are shown as a grey scale density plot, with darker representing more individuals. As the evolution proceeds, one can see how the central wavelength and HWHM distributions are dominated by a restricted set of values, indicating some kind of convergence.

This method, HFD (Heuristic Filter Design), has the advantage that it turns filter design into a quantitative optimization procedure which makes minimal assumptions about the required filter system. The FoM can be adjusted to reflect the scientific goals of the mission, and the performance of the filter systems on the different aspects of the problem can be assessed. The systems designed so far appear to perform at least as well as other proposed Gaia systems, although the HFD method has highlighted potential problems with all of these. Ongoing developments of HFD are targeted at addressing such problems.

More information on HFD can be found in the report Evolutionary design of photometric systems and its application to Gaia.

Return to my homepage.

Coryn Bailer-Jones, calj at mpia-hd.mpg.de
Last modified: 20 February 2004