Mathematics of Zernike polynomials: a review

Monochromatic aberrations of the eye principally originate from the cornea and the crystalline lens. Aberrometers operate via differing principles but function by either analysing the reflected wavefront from the retina or by analysing an image on the retina. Aberrations may be described as lower order or higher order aberrations with Zernike polynomials being the most commonly employed fitting method. The complex mathematical aspects with regards the Zernike polynomial expansion series are detailed in this review. Refractive surgery has been a key clinical application of aberrometers; however, more recently aberrometers have been used in a range of other areas ophthalmology including corneal diseases, cataract and retinal imaging.