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In the past three to four decades, adaptive optics has evolved from a technology solely for compensating atmospheric turbulence in astronomy to a promising technology with additional applications in the military, vision correction, and laser propagation. A key component of an adaptive optics system is the wavefront sensor, which measures the aberrations of an optical system in real time. Wavefront technology is thus a major component in the research and development of many optical system applications.
The application of wavefront technology in vision was pioneered in the early 1990s by Prof. Josef F. Bille and Dr. Junzhong Liang, then Bille’s PhD student, at the University of Heidelberg. They built the world’s first aberrometer for measuring the low- and high-order aberrations of human eyes. The application of wavefront sensing and adaptive optics in vision science expanded rapidly after Dr. Liang, with colleagues in Prof. David R. Williams’ lab at the University of Rochester, built the world’s first adaptive optics system for retinal imaging. At the same time, laser vision correction was growing rapidly. In the early years of the new century, several manufacturers had obtained FDA approval for wavefront-guided LASIK procedures in the US. Active research in ocular wavefront technology has expanded to include many ophthalmologists, optometrists, vision scientists, optical scientists, and refractive laser engineers.
Along with the development of the wavefront-driven refractive surgical techniques, a new field of research that studies the optics of ocular wavefronts with a consistent mathematical treatment has also emerged. The key to this mathematical approach is the use of orthonormal basis functions, namely Zernike polynomials. Other sets of orthonormal basis functions (e.g., Fourier series) and sets of nonorthonormal basis functions (e.g., Taylor monomials and Seidel series) can also be used. With this consistent mathematical approach in mind, I have arranged this book to answer the following questions: How is the ocular wavefront represented? How is it obtained with wavefront sensing and reconstruction? How are the coefficients of different representing basis functions converted to each other? How do the coefficients change when an ocular wavefront changes due to pupil constriction, cyclorotation, or decentration? How do the coefficients change when the wavefront propagates? How is the ocular wavefront evaluated? What is the clinical impact of the ocular wavefront?
Over the course of my research during the past 15 years, several individuals have influenced me and deserve special appreciation. My first thanks go to Prof. Arne Arderberg, who introduced me to the field of astronomy and adaptive optics. Together with Prof. Mette Owner-Peterson, I enjoyed reading Robert J. Noll’s famous paper on Zernike polynomials and atmospheric turbulence. His paper took me a long time to fully understand, but the result is my increased interest in mathematics and optics. I was lucky enough to work for Prof. David R. Williams at the University of Rochester and Dr. Junzhong Liang at Visx (now Advanced Medical Optics)—two important figures in the development of adaptive optics in vision science. During the past couple of years, I have had a very fruitful collaboration with Dr. Virendra N. Mahajan during our spare time. Our published papers on orthonormal polynomials lay the foundation for the representation of ocular aberrations.
This book would not have been possible without the generous support of my employer, Advanced Medical Optics (AMO). I am very grateful to Leonard Borrmann, Tom Shoup, and Carol Harner for their executive support. During my employment with AMO and while writing this book, I have enjoyed working with some of the world’s leading refractive surgeons: Noel Alpins, Eric Donnenfeld, Ken Greenberg, Jack Holladay, Bruce Jackson, Douglas Koch, Martin Mainster, Marguerite Mc-Donald, Marc Odrich, Luis Ruiz, Steve Schallhorn, Kerry Solomon, Julian Stevens, Gustavo Tamayo, and Steve Trokel. I am indebted to Profs. David A. Atchison and Jim Schwiegerling for reviewing the entire manuscript on a tight schedule and for their valuable suggestions. Drs. Linda Lundström and Sverker Norrby carefully read every chapter and provided me with detailed comments. Many of my colleagues at AMO provided helpful comments and suggestions. Of course, I am responsible for any error or omissions still remaining in the book. It has been a pleasure to work with the SPIE Press staff, in particular Scott Schrum and Tim Lamkins, due to their professionalism and enjoyable cooperation.
Last but not least, I am extremely grateful to my lovely family—my wife Wendy and my sons Percy and Perry—for their understanding and support during my career and, in particular, during the nights and weekends over the past year while this book was being written.
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