# Thread: Telescope Optical Quality Analysis Strehl Ratio

1. ## Telescope Optical Quality Analysis Strehl Ratio

The Strehl ratio, named after the German physicist and mathematician Karl Strehl (1864-1940), is a measure for the optical quality of telescopes and other imaging instruments. It is defined as the ratio of the observed peak intensity at the detection plane from a point source compared to the theoretical maximum peak intensity of a perfect imaging system working at the diffraction limit. This is closely related to the sharpness criteria for optics defined by Karl Strehl.[1][2]

Unless stated otherwise, the Strehl ratio is usually defined at the best focus of the imaging system under study. The intensity distribution in the image plane of a point source is generally called the point spread function. Obviously, characterising the form of the point-spread function by a single number, as the Strehl Ratio does, will only be meaningful and sensible if the point-spread function is little distorted from its ideal (aberration-free) form. This is valid for well corrected systems that operate close to the diffraction limit. This includes most telescopes and microscopes, but excludes most photographic systems, for example. The Strehl ratio has been linked via the work of Marechal to an aberration tolerancing theory which is very useful to designers of well corrected optical systems, allowing a meaningful link between the aberrations of geometrical optics and the diffraction theory of physical optics. A significant shortcoming of the Strehl ratio as a method of image assessment is that, although it is relatively easy to calculate for an optical design prescription on paper, it is normally difficult to measure for a real optical system, not least because the theoretical maximum peak intensity is not readily available.

The ratio is commonly used to assess the quality of seeing in the presence of atmospheric turbulence and assess the performance of any adaptive optical correction system. It is also used for the selection of short exposure images in the lucky imaging method.

In industry the Strehl ratio has become a popular way to summarize the performance of an optical design because it gives the performance of a real system, of finite cost and complexity, in terms of a theoretically perfect system which would be infinitely expensive and complex to build and would still have a finite point spread function. Essentially, it's the square of the ratio of the point spread function you've got to the best point spread function money can buy.

It provides a simple method to compare a system with a Strehl ratio of, for example 0.95 is good enough, or whether twice as much should be spent to try to get a Strehl ratio of perhaps 0.97 or 0.98.
Note the measurement of the ratio varies depending on the measuring instrument used, light used, colour and more.

Some similarly measured Strehl values:

Scope Name - Stehl Ratio (1.0 is best)

SkyWatcher
ED100 - 0.98
ED80 - 0.975

William Optics
Wo 66sd - 0.97

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