Zacarias Malacara

Handbook of Optical Design

Geometrical Optics Principles Wave Nature of Light and Fermats Principle Reflection and Refraction Laws Basic Meridional Ray Tracing Equations Gaussian or First-Order Optics Image Formation Stop, Pupils, and Principal Ray Delanos Relation Optical Sine Theorem Lagrange Invariant Herschel Invariant and Image Magnifications Thin Lenses and Spherical Mirrors Thin Lenses Formulas for Image Formation with Thin Lenses Nodal Points of A Thin Lens Image Formation with Converging Lenses Image Formation with Diverging Lenses Systems of Several Lenses and Thick Lenses Focal Length and Power of A Lens System Image Formation with Thick Lenses or Systems of Lenses Cardinal Points Image Formation with A Tilted or Curved Object Thick Lenses Systems of Thin Lenses The Lagrange Invariant in A System of Thin Lenses Effect of Object or Stop Shifting The Delano y - y Diagram Chromatic Aberrations Introduction Axial Chromatic Aberration Conradys D - d Method of Achromatization Secondary Color Aberration Magnification Chromatic Aberration Spherical Aberration Spherical Aberration Calculation Primary Spherical Aberration Aspherical Surfaces Spherical Aberration of Aspherical Surfaces Surfaces without Spherical Aberration Aberration Polynomial for Spherical Aberration High-Order Spherical Aberration Spherical Aberration Correction with Gradient Index Monochromatic Off-Axis Aberrations Introduction Petzval Curvature Coma Astigmatism Aplanatic Surfaces Distortion Off-Axis Aberrations in Aspherical Surfaces The Symmetrical Principle and the Bow-Sutton Conditions Stop Shift Equations Aberrations of the Pupil Aberration Polynomials and High-Order Aberrations Wavefronts in an Optical System Ray Aberrations and Wavefront Aberrations Wavefront Aberration Polynomial Zernike Polynomials Fitting of Wavefront Deformations to A Polynomial Wavefront Representation by an Array of Gaussians Wavefront Aberrations in Refractive Surfaces Wavefront Aberrations in Reflective Surfaces Aldis Theorem Computer Evaluation of Optical Systems Transverse Aberration Polynomials Transverse Aberrations with H.H. Hopkins, Seidel, and Buchdahl Coefficients Meridional Ray Tracing and Stop Position Analysis Spot Diagram Wavefront Deformation Point and Line Spread Function Optical Transfer Function Tolerance to Aberrations Diffraction in Optical Systems Huygens-Fresnel Theory Fresnel Diffraction Fraunhofer Diffraction Diffraction Images with Aberrations Strehl Ratio Optical Transfer Function Resolution Criteria Gaussian Beams Prisms Tunnel Diagram Deflecting A Light Beam Transforming an Image Deflecting and Transforming Prisms Nondeflecting Transforming Prisms Beam-Splitting Prisms Chromatic Dispersing Prisms Nonimaging Prisms Basic Optical Systems and Simple Photographic Lenses Optical Systems Diversity Magnifiers and Single Imaging Lens Landscape Lenses Periscopic Lens Achromatic Landscape Lens Doublets Laser Light Collimators Spherical and Paraboloidal Mirrors Some Catoptric and Catadioptric Systems F-Theta Lenses Fresnel Lenses and Gabor Plates Complex Photographic Lenses Introduction Asymmetrical Systems Symmetrical Anastigmat Systems Varifocal and Zoom Lenses The Human Eye and Ophthalmic Lenses The Human Eye Ophthalmic Lenses Ophthalmic Lens Design Prismatic Lenses Spherocylindrical Lenses Astronomical Telescopes Resolution and Light-Gathering Power Reflecting Two-Mirror Cameras and Telescopes Catadioptric Cameras Astronomical Telescopes Field Correctors Multiple-Mirror Telescopes Active and Adaptive Optics Visual Systems and Afocal Systems Visual Optical Systems Basic Telescopic System Afocal Systems Visual And Terrestrial Telescopes Telescope Eyepieces Relays and Periscopes Microscopes Compound Microscope Microscope Objectives Microscope Eyepieces Microscope Illuminators Projection Systems Image Projectors Main Projector Components Coherence Effects in Projectors Anamorphic Projection Slide and Movie Projectors Overhead Projectors Profile Projectors Television Projectors LCD Computer and Home Theater Projectors Lens Design Optimization Basic Principles Optimization Methods Glatzel Adaptive Method Constrained Damped Least-Squares Optimization Method Merit Function and Boundary Conditions Modern Trends in Optical Design Flowchart for a Lens Optimization Program Practical Tips for the Use of Lens Evaluation Programs Some Commercial Lens Design Programs Appendices Appendix: Notation and Primary Aberration Coefficients Summary Appendix: Mathematical Representation of Optical Surfaces Appendix: Optical Materials Appendix: Exact Ray Tracing of Skew Rays Appendix: General Bibliography on Lens Design Index Chapters include references.

Design of lenses to project the image of a pupil in optical testing interferometers

When an optical surface or lens in an interferometer (Twyman-Green or Fizeau interferometer) is tested, the wave front at the pupil of the element being tested does not have the same shape as at the observation plane, because this shape changes along its propagation trajectory if the wave front is not flat or spherical. An imaging lens must then be used, as reported many times in the literature, to project the image of the pupil of the system being tested over the observation plane. This lens is especially necessary if the deviation of the wave front from sphericity is large, as in the case of testing paraboloidal or hyperboloidal surfaces. We show that the wave front at both positions does not need to have the same shape. The only condition is that the interferograms at both places be identical, which is a different condition. This leads to some considerations that should be taken into account in the optical design of such lenses.

SUB-NYQUIST NULL ASPHERIC TESTING USING A COMPUTER-STORED COMPENSATOR

A novel method to demodulate undersampled interferograms using a computer-stored undersampled compensator is presented. First, the sine and cosine of the computer-stored wave front is correlated with the interferogram that emerges from the asphere under test. Afterward, these two correlation images are used to find the phase map. The detected phase of the correlation fringes is the estimated phase difference between the software compensator and the frame-grabbed interferogram. The prior information required for this method is a good knowledge of the wave front being tested to a few wavelengths of error. Complying with this prior knowledge, the undersampled interferogram under analysis may be easily demodulated. Given that the proposed method is based on the correlation of the frame-grabbed interferogram and the computer-stored one, the method also withstands noise.

Aberrations of sphero-cylindrical ophthalmic lenses

The authors have presented in two previous articles the graphic solutions resembling Tscherning ellipses, for spherical as well as for aspherical ophthalmic lenses free of astigmatism or power error. These solutions were exact, inasmuch as they were based on exact ray tracing, and not third-order theory as frequently done. In this paper sphero-cylindrical lenses are now analyzed, also using exact ray tracing. The functional dependence of the astigmatism and the power error for these lenses is described extensively.