Definitions
There are even and odd Zernike polynomials. The even ones are defined as
and the odd ones as
where m and n are nonnegative integers with n≥m, φ is the azimuthal angle, and ρ is the radial distance . Zernike polynomials have the property of being limited to a range of -1 to +1, i.e. . The radial polynomials Rmn are defined as
for n − m even, and are identically 0 for n − m odd.
Read more about this topic: Zernike Polynomials
Famous quotes containing the word definitions:
“What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”
—G.C. (Georg Christoph)
“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)
“The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
—Pamela Patrick Novotny (20th century)