Читать книгу Optical Engineering Science - Stephen Rolt - Страница 99

The previous chapters have provided a substantial grounding in geometrical optics and aberration theory that will provide the understanding required to tackle many design problems. However, there are two significant omissions.

Firstly all previous analysis, particularly with regard to aberration theory, has assumed the use of spherical surfaces. This, in part, forms part of a historical perspective, in that spherical surfaces are exceptionally easy to manufacture when compared to other forms and enjoy the most widespread use in practical applications. Modern design and manufacturing techniques have permitted the use of more exotic shapes. In particular, conic surfaces are used in a wide variety of modern designs.

The second significant omission is the use of Zernike circle polynomials in describing the mathematical form of wavefront error across a pupil. Zernike polynomials are an orthonormal set of polynomials that are bounded by a circular aperture and, as such, are closely matched to the geometry of a circular pupil. There are, of course, many different sets of orthonormal functions, the most well known being the Fourier series, which, in two dimensions, might be applied to a rectangular aperture. As the wavefront pattern associated with defocus forms one specific Zernike polynomial, the orthonormal property of the series means that all other terms are effectively optimised with respect to defocus. This topic was touched on in Chapter 3 when seeking to minimise the wavefront error associated with spherical aberration by providing balancing defocus. The optimised form that was derived effectively represents a Zernike polynomial.