[1][2] 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 a hypothetical, perfectly unaberrated optical system having a Strehl ratio of 1.
: 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: where i is the imaginary unit,
Due to diffraction, even a focusing system which is perfect according to geometrical optics will have a limited spatial resolution.
An imperfect optical system using the same physical aperture will generally produce a broader PSF in which the peak intensity is reduced according to the factor given by the Strehl ratio.
An optical system with only minor imperfections in this sense may be referred to as "diffraction limited" as its PSF closely resembles the Airy disk; a Strehl ratio of greater than .8 is frequently cited as a criterion for the use of that designation.
Typically, as wavelength is increased, an imperfect optical system will have a broader PSF with a decreased peak intensity.
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, relative to a theoretically perfect system, which would be infinitely expensive and complex to build and would still have a finite point spread function.
Characterizing the form of the point-spread function by a single number, as the Strehl Ratio does, will be meaningful and sensible only if the point-spread function is little distorted from its ideal (aberration-free) form, which will be true for a well-corrected system that operates close to the diffraction limit.
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.