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Strehl ratio is an important performance measure for adaptive-optics systems. Its calculation is more complicated than that of variances. Nevertheless, it is shown below that one can obtain exact expressions for the Strehl ratio for propagation through uncorrected turbulence, and through turbulence for which all modes except tilt have been corrected. Asymptotic expressions are also obtained that apply when the distortion is high.
The effect of anisoplanatism on the Strehl is especially important. Here I consider isoplanatic effects of aperture displacement in space and angle, time delay, and chromatic offsets. A formula is obtained that is a good approximation to the Strehl ratio when it is above 0.2. Fortunately, this is the region of greatest interest in adaptive-optics system design.
For many problems one must revert to numerical techniques to find the Strehl ratio. Normally, this can be done with little difficulty; however, there are cases in which the structure function is a function of position in the aperture. Problems in which one is interested in the Strehl ratio when the tilt is removed generally fall into this category. For these cases a 7-fold integration must be performed. It is only recently that computer speed allows these integrations to be performed on even a reasonably fast computer cluster in less than a day. Examples of these types of problems are given.
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