Nonimaging Optics: Solar and Illumination System Methods, Design, and Performance
Nonimaging Optical Systems and Their UsesNonimaging CollectorsFailure of Imaging OpticsDefinition of the Concentration Ratio; the Theoretical MaximumUses of ConcentratorsUses of IlluminatorsReferencesSome Basic Ideas in Geometrical OpticsThe Concepts of Geometrical OpticsFormulation of the Ray-TracingElementary Properties of Image-Forming Optical SystemsAberrations in Image-Forming Optical SystemsThe Effect of Aberrations in an Image-Forming System on the Concentration RatioThe Optical Path Length and Fermat’s PrincipleThe Optical LagrangianThe Fermi Vector MethodThe Generalized Étendue or Lagrange Invariant and the Phase Space ConceptThe Skew InvariantDifferent Versions of the Concentration RatioReferencesSome Designs of Image-Forming ConcentratorsIntroductionSome General Properties of Ideal Image-Forming ConcentratorsCan an Ideal Image-Forming Concentrator Be Designed?Media with Continuously Varying Refractive IndicesAnother System of Spherical SymmetryImage-Forming Mirror SystemsConclusions on Classical Image-Forming ConcentratorsReferencesNonimaging Optical SystemsLimits to ConcentrationImaging Devices and Their LimitationsNonimaging ConcentratorsThe Edge-Ray Principle or “String” MethodLight ConesThe Compound Parabolic ConcentratorProperties of the Compound Parabolic ConcentratorThe Equation of the CPCThe Normal to the SurfaceTransmission-Angle Curves for CPCsCones and Paraboloids as ConcentratorsReferencesDevelopments and Modifications of the Compound Parabolic ConcentratorIntroductionThe Dielectric-Filled CPC with Total Internal ReflectionThe CPC with Exit Angle Less Than π/2The Concentrator for a Source at a Finite DistanceThe Two-Stage CPCThe CPC Designed for Skew RaysThe Truncated CPCThe Lens-Mirror CPCD Collection in GeneralExtension of the Edge-Ray PrincipleSome ExamplesThe Differential Equation for the Concentrator ProfileMechanical Construction for 2D Concentrator ProfilesA General Design Method for a 2D Concentrator with Lateral ReflectorsA Constructive Design Principle for Optimal ConcentratorsReferencesThe Flowline Method for Nonimaging Optical DesignsThe Concept of the FlowlineLines of Flow from Lambertian Radiators: 2D ExamplesD ExampleA Simplified Method for Calculating Lines of FlowProperties of the Lines of FlowApplication to Concentrator DesignThe Hyperboloid of Revolution as a ConcentratorElaborations of the Hyperboloid: The Truncated HyperboloidThe Hyperboloid Combined with a LensThe Hyperboloid Combined with Two LensesGeneralized Flowline Concentrators with Refractive ComponentsReferencesSupporting Quadric Method (SQM)Precise Statement of the FFR ProblemRelaxed Formulation, SQM, and Freeform SurfacesReflectors and Radial FunctionsFocal FunctionGeneralized Reflector MapWeak SolutionsWeak Solutions to the FFR Problem and Its Semi-Discrete VersionDerivation of the Semi-Discrete FFR ProblemSolution to Equation (8.25)Numerics and SQMBrief Related and Historical CommentsReferencesVariational ApproachThe FFR Problem as an Optimization ProblemDiscrete Maximization ProblemConnection with Optimal Mass TransportComputed Reflector for FFR Problem—Point SourceType B ReflectorsWhen Does the Variational Approach Not Apply?Strong Solutions of the FFR ProblemAcknowledgmentReferencesA Paradigm for a Wave Description of Optical MeasurementsIntroductionThe van Cittert–Zernike TheoremMeasuring RadianceNear-Field and Far-Field LimitsA Wave Description of MeasurementFocusing and the Instrument OperatorMeasurement by Focusing the Camera on the SourceExperimental Test of FocusingConclusionReferencesAppendix A: Derivation and Explanation of the Étendue Invariant, Including the Dynamical Analogy; Derivation of the Skew InvariantAppendix B: The Luneburg LensReferencesAppendix C: The Geometry of the Basic Compound Parabolic ConcentratorAppendix D: The θi/θo ConcentratorAppendix E: The Truncated Compound Parabolic ConcentratorAppendix F: Skew Rays in a Hyperboloidal ConcentratorAppendix G: Sine Relation for Hyperboloidal/Lens Concentrator
