This book addresses some of the issues in visual optics with a functional analysis of ocular aberrations, especially for the purpose of vision correction. The basis is the analytical representation of ocular aberrations with a set of orthonormal polynomials, such as Zernike polynomials or the Fourier series. Although the aim of this book is the application of wavefront optics to laser vision correction, most of the theories discussed are equally applicable to other methods of vision correction, such as contact lenses and intraocular lenses
1. Introduction. 1.1. Wavefront optics and vision correction -- 1.2. Purpose and structure of the book -- Bibliography -- 2. Fundamentals of ocular wavefront correction -- 2.1. Principle of phase conjugation -- 2.2. Munnerlyn equation -- 2.3. Principle of customized laser vision correction -- 2.4. Principle of Excimer laser ablation of the cornea -- 2.5. Fine-tuning ablation profiles -- Appendix A. Derivation of the Munnerlyn equation -- Appendix B. Derivation of laser energy loss due to reflection -- Bibliography -- 3. Ocular wavefront representation -- 3.1. Orthonormal polynomials and their merits -- 3.2. Geometrical aberrations and power series -- 3.3. Zernike polynomials -- 3.4. Other basis functions for ocular aberrations -- 3.5. Refractive laser profiles -- Appendix A. Orthonormal polynomials and related properties -- Appendix B. Determination of orthonormal polynomials -- Appendix C. Properties of the inner product of polynomials -- Appendix D. Zernike polynomials up to the th order -- Appendix E. Aberration balancing of orthonormal polynomials -- Appendix F. Derivation of Fourier transform of Zernike polynomials -- Appendix G. Examination of the Munnerlyn equation -- Bibliography
4. Ocular wavefront sensing and reconstruction -- 4.1. Wavefront slopes -- 4.2. Ocular wavefront sensing methods -- 4.3. Wavefront reconstruction methods -- 4.4. Non-fourier-based modal reconstruction -- 4.5. Fourier-based modal reconstruction -- Appendix A. Wavefront tilts and image displacement -- Appendix B. Matlab code for zonal reconstruction -- Appendix C. Matlab code for Zernike reconstruction -- Appendix D. Derivation of eq. (4.28) -- Bibliography -- 5. Ocular wavefront conversion -- 5.1. General discussion of wavefront conversion -- 5.2. Conversions of Zernike polynomials and Seidel series -- 5.3. Conversions of Zernike polynomials and Fourier series -- 5.4. Conversions of Taylor monomials and Zernike polynomials -- 5.5. Conversions of Fourier series and Taylor monomials -- Appendix A. Derivation of Eq. (5.3) -- Appendix B. Derivation of Eqs. (5.6) and (5.7) -- Appendix C. Derivation of conversion matrices Cs2z and Cz2s -- Appendix D. Proof of Eq. (5.15) -- Appendix E. Derivation of conversion matrices Ct2z and Cz2t -- Appendix F. Matlab code for conversions of Zernike and Taylor -- Appendix G. Derivation of Qq/p(k,c) -- Bibliography -- 6. Ocular wavefront transformation -- 6.1. Wavefront transformation and iris registration -- 6.2. Wavefront representation for pupil resizing -- 6.3. Wavefront representation for cyclorotation -- 6.4. Wavefront representation for decentration -- 6.5. Wavefront representation for resizing, rotation, and decentration -- Appendix A. Derivation of Eq. (6.19) -- Appendix B. Zernike resizing polynomials -- Appendix C. Derivation of Eq. (6.27) -- Appendix D. Derivation of Eq. (6.28) -- Appendix E. Derivation of eq. (6.32) -- Appendix F. Matlab code for geometrical transformations -- Bibliography
7. Ocular wavefront propagation -- 7.1. Review of some eye models -- 7.2. Classical vertex correction -- 7.3. Propagation of ocular wavefronts -- 7.4. Wavefront propagation of common aberrations -- Appendix A. Proof of eq. (7.23) -- Appendix B. Derivation of eq. (7.39) -- Appendix C. Matlab code for wavefront propagation -- Appendix D. Proof of eq. (7.52) from wavefront propagation -- Bibliography -- 8. Optical metrics of ocular wavefronts -- 8.1. Pupil plane metrics for ocular aberrations -- 8.2. Image plane metrics for ocular aberrations -- 8.3. Visual performance metrics -- 8.4. Simulation of visual outcomes -- Appendix A. Derivation of eq. (8.9) -- Appendix B. Derivation of eq. (8.28) -- Appendix C. Matlab code for calculation of point spread functions -- Bibliography -- 9. Clinical results of wavefront-driven refractive surgery -- 9.1. Statistics of ocular aberrations -- 9.2. Treatment validation -- 9.3. Wavefront-driven myopic correction -- 9.4. Wavefront-driven hyperopic correction -- Bibliography -- Author index -- Subject index
Wavefront optics for vision correction
SPIE Press monograph ; PM179
2008
1 online resource (xvi, 347 p. : ill.)
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Buch
Elektronische Ressource
Englisch
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