Slide 8 of 19

Notes:

• Next there is the problem of giving names to specific aberration coefficients. In our little project last summer, it was pretty clear that although Ray and I were using the same words, we aren't speaking the same language!

  For example, consider the meaning of the word defocus. In the classical Seidel sense of this word, defocus is the name we give to an aberration which varies in proportion to pupil radius squared. So if W=Kr^2, then K is the magnitude of defocus.

  However, in the Zernike expansion the corresponding term is more complicated. W = Z*(2r^2 - 1). So now we have an ambiguous situation. Do we quote the zernike coefficient itself when reporting defocus? or do we quote the coefficient of r-squared? There is a difference of a factor of 2 plus a constant depending on which of these conventions you adopt.

  Likewise, when we use the term "spherical aberration" in the classical Seidel sense, we are referring to the coefficient of the r^4 term. But the term"spherical aberration" is also used when referring to a Zernike polynomial which includes not only r^4, but also r^2 and a constant. So which is to be reported, Z or the coefficient of just the r^4 term? While the experienced investigator may have a convincing answer to this question, it can baffle the novice needlessly and impede progress.