Slide 9 of 19

Notes:

• For my third example of "traps for beginners", consider the problem of converting the Zernike polynomials from their native format in polar coordinates to a rectangular coordinate reference frame. To do this you need to define the angle theta. It turns out there are two ways to do this, and both are in common use.

  For example, in Malacara's well-known textbook "Optical Shop Testing", theta is measured clockwise from the vertical. However, this is an awkward convention when it comes time to implement the coordinate transformation because most programming languages adopt the mathematical convention in which angles are measured counter-clockwise from the horizontal.

  So, even if two people agree on a numbering scheme for the Zernike polynomials, they can still get different results if the data are expressed in rectangular coordinates because of the different conventions for specifying the polar angle theta.