Strehl ratio

Key facts and history

Karl Strehl, a German physicist, mathematician, and astronomer, originally proposed the Strehl ratio at the end of the 19th century.^[1] Strehl's 1895 paper "Aplanatische und fehlerhafte Abbildung im Fernrohr" and his 1902 paper "Über Luftschlieren und Zonenfehler" are foundational works on the topic.^[2] The Strehl ratio is used to express the effect of wavefront aberrations on image quality in both professional and amateur optics.^[1] It is the simplest meaningful way of expressing the effect of wavefront aberrations on image quality.^[1]

The ratio indicates the level of image quality in the presence of wavefront aberrations.^[1] A conventional diffraction-limited level is set at a Strehl ratio of 0.80.^[1] Characterizing the point-spread function by a single number like the Strehl ratio is meaningful only for systems operating close to the diffraction limit.^[4] André Maréchal linked the Strehl ratio to an aberration tolerancing theory useful for designers of well-corrected optical systems.^[4]

A formula from antenna theory, the Ruze formula, allows the Strehl ratio to be approximated using only the root mean square (σ) of the wavefront phase deviation: S ≈ e^{-σ^2}.^[5] Well-corrected systems that operate near the diffraction limit, such as most telescopes and microscopes, are suitable for Strehl ratio analysis, whereas most photographic systems are not.^[4]

What the cited sources add

Sacek's notes on amateur telescope optics state that the Struve ratio is a similar indicator but expresses peak diffraction intensity of an aberrated versus aberration-free line spread function.^[1] Sacek notes that the peak-to-valley nominal aberration only specifies the peak of deviation and tells nothing about its extent over the wavefront area.^[1] For relatively small errors, roughly 0.15 wave RMS and smaller, the RMS wavefront error and resulting Strehl ratio accurately reflect the effect of overall change in energy distribution.^[1] With larger errors, the correlation between RMS error and Strehl vanishes, and larger RMS error can produce higher PSF peak intensity.^[1]

Sacek provides that a 0.90 Strehl indicates about 10% lower energy within the Airy disc.^[1] The Mahajan approximation gives a very close approximation of the Strehl ratio in terms of the RMS wavefront error.^[1]