Strehl ratio, wavefront power series expansion

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Strehl ratio, wavefront power series expansion
Zernike polynomials expansion in small
aberrated optical systems

• By Sheng Yuan
• OPTI 521
• Fall 2006

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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)

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Wave aberration function
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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.

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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.

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How to calculate Strehl ratio?
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How to calcuate wavefront variance?
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Power series expansion of Aberration function
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What is the problem with power series expansion?
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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!

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Why Use Zernike Polynomials?
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What is the unique properties of Zernike
Polynomials?
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How Zernike Polynomials looks like?
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Zernike Polynomials expansion of Aberration
function (OPD)
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How the variance of the aberration function
looks like now?
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Is Zernike Polynomials Superiorthan Power
Series Expansion?

• Why dont we use Zernike Polynomials always?
• Why dont we abandon the classical power series
  expansion?

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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!!

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Reference