Strehl ratio, wavefront power series expansion & Zernike polynomials expansion in small aberrated optical systems By Sheng Yuan OPTI 521 Fall 2006

Introduction The wave aberration function(OPD), W(x,y), is defined as the distance, in optical path length, from the reference sphere to the wavefront in the exit pupil measured along the ray as a function of the transverse coordinates (x,y) of the ray intersection with a reference sphere centered on the ideal image point. It is not the wavefront itself but it is the departure of the wavefront from the reference spherical wavefront (OPD)

Wave aberration function

Strehl Ratio Strehl ratio is a very important figure of merit in system with small aberration, i.e., astronomy system where aberration is almost always “well” corrected, thus a good understand of the relationship between Strehl ratio and aberration variance is absolutely necessary.

Defination of Strehl Ratio For small aberrations, the Strehl ratio is defined as the ratio of the intensity at the Gaussian image point (the origin of the reference sphere is the point of maximum intensity in the observation plane) in the presence of aberration, divided by the intensity that would be obtained if no aberration were present.

How to calculate Strehl ratio?

How to calcuate wavefront variance?

Power series expansion of Aberration function

What is the problem with power series expansion?

How can we solve this coupling problem? If we can expand the aberration function (OPD) in a form that each term is orthogonal to one another!! Zernike Polynomial in the orthogonal choice!

Why Use Zernike Polynomials?

What is the unique properties of Zernike Polynomials?

How Zernike Polynomials looks like?

Zernike Polynomials expansion of Aberration function (OPD)

How the variance of the aberration function looks like now?

Is Zernike Polynomials Superior than Power Series Expansion? Why don’t we use Zernike Polynomials always? Why don’t we abandon the classical power series expansion?

Comparison of both expansion Zernike Polynomials can only be useful in circular pupil!! Power series expansion is an expansion of function, have nth to do with the shape of pupil, thus it is always useful!!

Reference