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Strehl ratio and modulation transfer function for segmented mirror telescopes as functions of segment phase error.

G Chanan¹, M Troy

¹Department of Physics and Astronomy, University of California, Irvine, Irvine, California 92697, USA. gchanan@galaxy.ps.uci.edu

|March 8, 2008

Summary

We developed a formula for the Strehl ratio of segmented mirror telescopes, considering mirror errors and wavelength. This helps determine precise phasing needs for telescopes like Keck.

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Area of Science:

Optical astronomy
Telescope engineering

Background:

Segmented mirror telescopes offer advantages in size and cost.
Accurate phasing of mirror segments is critical for optimal image quality.

Purpose of the Study:

To derive the Strehl ratio for segmented mirror telescopes.
To analyze the impact of segment phase errors and wavelength on telescope performance.
To provide a framework for determining telescope phasing requirements.

Main Methods:

Derivation of analytical expressions for Strehl ratio.
Inclusion of atmospheric effects in the analysis.
Calculation of modulation transfer functions.

Main Results:

A simple analytical expression for the atmosphere-free Strehl ratio was obtained.
The Strehl ratio was quantified as a function of rms segment phase error and observing wavelength.
Modulation transfer functions were derived.

Conclusions:

The derived formulas are adaptable to various segmented mirror designs.
Results aid in specifying the required phasing accuracy for segmented mirror telescopes.
This work is crucial for optimizing image quality in astronomical observations.