Strehl ratios

The Strehl ratio is a measure of the quality of optical image formation, originally proposed by Karl Strehl, after whom the term is named. Used variously in situations where optical resolution is compromised due to lens aberrations or due to imaging through the turbulent atmosphere, the Strehl ratio has a value between 0 and 1, with an unaberrated optical system attaining the value of unity.

The Strehl ratio ${\displaystyle S}$ is frequently defined as the ratio of the peak aberrated image intensity from a point source compared to the maximum attainable intensity using an ideal optical system limited only by diffraction over the system's aperture. It is also often expressed in terms not of the peak intensity but the intensity at the image center (intersection of the optical axis with the focal plane) due to an on-axis source; in most important cases these definitions result in a very similar figure (or identical figure, when the point of peak intensity must be exactly at the center due to symmetry). Using the latter definition, the Strehl ratio ${\displaystyle S}$ can be computed in terms of ${\displaystyle \delta (x,y)}$, the offset of the wavefront due to an on-axis point source, compared to that produced by an ideal focusing system over the aperture A(x,y). Using Fraunhofer diffraction theory, one computes the wave amplitude using the Fourier transform of the aberrated pupil function evaluated at 0,0 (center of the image plane) where the phase factors of the Fourier transform formula are reduced to unity. Since the Strehl ratio refers to intensity, it is found from the squared magnitude of that amplitude:

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