This book is Part III of a series of books on Optical Imaging and Aberrations. Part I on Ray Geometrical Optics and Part II on Wave Diffraction Optics were published earlier. Part III is on Wavefront Analysis, which is an integral part of optical design, fabrication, and testing. In optical design, rays are traced to determine the wavefront and thereby the quality of a design. In optical testing, the fabrication errors and, therefore, the associated aberrations are measured by way of interferometry. In both cases, the quality of the wavefront is determined from the aberrations obtained at an array of points. The aberrations thus obtained are used to calculate the mean, the peak-to-valley, and the standard deviation values. While such statistical measures of the wavefront are part of wavefront analysis, the purpose of this book is to determine the content of the wavefront by decomposing the ray-traced or test-measured data in terms of polynomials that are orthogonal over the expected domain of the data. These polynomials must include the basic aberrations of wavefront defocus and tilt, and represent balanced classical aberrations.
We start Part III with an outline of optical imaging in the presence of aberrations in Chapter 1, i.e., on how to obtain the point-spread and optical transfer functions of an imaging system with an arbitrary shaped pupil. The Strehl ratio of a system as a measure of image quality is introduced in this chapter, and shown to be dependent only on the aberration variance when the aberration is small. It is followed in Chapter 2 with a brief discussion of the wavefronts and aberrations. This chapter introduces the nomenclature of aberrations. How to obtain the orthogonal polynomials over a certain domain from those over another is discussed in Chapter 3. For systems with a circular pupil, the Zernike circle polynomials are well known for wavefront analysis. They are discussed at length in Chapter 4. These polynomials are orthogonalized over an annular pupil in Chapter 5, and over a Gaussian pupil in Chapter 6. They are obtained similarly for systems with hexagonal, elliptical, rectangular, square, and slit pupils in the succeeding chapters. For each pupil, the polynomials are given in their orthonormal form so that an expansion coefficient (with the exception of piston) represents the standard deviation of the corresponding polynomial aberration term. The standard deviation of a Seidel aberration with and without aberration balancing is also discussed in these chapters.
Since the Zernike circle polynomials form a complete set, a wavefront over any domain can be expanded in terms of them. However, the pitfalls of their use over a domain other than circular and resulting from the lack of their orthogonality over the chosen domain are discussed in Chapter 12. Finally, the aberrations of anamorphic systems are discussed, and polynomials suitable for their aberration analysis are given in Chapter 13 for both rectangular and circular pupils. The use of the orthonormal polyonomials for determining the content of a wavefront is demonstrated in Chapter 14 by computer simulations of circular wavefronts. The determination of the aberrations coefffcients from the wavefront slope data, as in a Shack-Hartmann sensor, is also discussed in this chapter.
Virendra N. Mahajan
El Segundo, California