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# Understanding Strehl ratio & wavefront error for optical systems

by | Jun 16, 2020 | optics definitions

A Strehl ratio is used to define the quality of an optical system by showing how a real optical system compares to an ideal aberration-free system. The Strehl ratio incorporates the Point Spread Function (PSF) and its relation to wavefront aberration of the optical system.

The ratio compares the value of intensity of central maximum PSF of a real system (real lens elements and tolerances) to the value of intensity of central maximum PSF of an aberration-free system.

The PSF of an aberration-free optical system has a well defined shape described by a Fraunhofer diffraction equation.

The diffraction pattern of a rotational symmetry optical system has an axial symmetrical pattern. The pattern cross section has a central maximum where 83.9 % of total energy is encircled

The radius of the central disc is called “Airy disc” and is defined by

R(airy) =1.22 λ f/#w where λ is working wavelength, f/#w is working F-number.

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When designing an optical system, the Strehl ratio is used to estimate the required correction of wavefront aberrations.

The acceptable level of wavefront aberrations is different for every application but a value of 0.80 Strehl is conventionally used to define an optical system as “Diffraction limited” or ideal. Aberration-free Fraunhofer diffraction pattern 3-D shape Fraunhofer diffraction patterns 2-D intensity map at the image plane.

Below are Zemax PSF plots based on real optical system designs PSF cross section Optical path difference PSF cross section Optical path difference

In the above system, wavefront aberrations correspond to 0.25 λ Peak-to Value-this matches to Rayleigh ¼-wave PV criteria of image quality provided by a “Diffraction limited” system.

MTF plot corresponding to 0.8 Strehl ratio is shown in the final image Polychromatic diffraction MTF