Hadamard transform optics

PrefaceAcknowledgmentsChapter 1. An Introduction to Optical Multiplexing Techniques 1.1 Introduction 1.2 Weighing Designs and Optical Multiplexing 1.3 Masks from Hadamard Matrices and S-MatricesChapter 2. A Survey of Multiplexing Spectrometers 2.1 Introduction 2.2 Spectrometers which Use Interference Methods 2.3 Spectrometers which Use Masks 2.4 A Survey of Multiplexing Mask Spectrometers 2.4.1 Simple Masking Spectrometer 2.4.2 Golay's Static Multislit Spectrometer 2.4.3 Golay's Dynamic Multislit Spectrometer 2.4.4 Girard's Grill Spectrometer 2.4.5 Mertz's Mock Interferometer 2.4.6 Hadamard Transform SpectrometersChapter 3. The Basic Theory of Hadamard Transform Spectrometers and Imagers 3.1 Introduction 3.1.1 Comparison of Different Encoding Schemes 3.2 Analysis of a Singly Encoded Spectrometer 3.2.1 The Basic Equation Relating Measurements and Unknowns 3.2.2 Estimating the Spectrum 3.2.3 The Mean Square Error of the Estimates 3.2.4 Hotelling's Bound on the Mean Square Error 3.2.5 Masks with the Largest Determinant 3.2.6 Masks of 0's and 1's; S-Matrices 3.2.7 Cyclic Masks 3.3 Imagers 3.3.1 Definition of an Imager 3.3.2 Hadamard Transform Imager 3.3.3 Folding the Mask Configuration 3.4 Doubly Encoded Spectrometers and Imaging Spectrometers 3.4.1 Imaging Spectrometer 3.4.2 The S-Matrix Grill Spectrometer 3.4.3 A Second Doubly Encoded Spectrometer 3.4.4 If mn measurements are Made 3.5 More Measurements than Unknowns; Generalized Inverses 3.5.1 Moore-Penrose Generalized Inverse 3.5.2 Singly Multiplexed Spectrometer 3.5.3 Doubly Multiplexed Instrument 3.5.4 Realizing a Hadamard Design with Two Detectors 3.6 Comparison with the Michelson Interferometer 3.6.1 Comparison of Singly Encoded Instruments 3.6.2 Comparison of Doubly Encoded Spectrometers with Wide Aperture Interferometers 3.6.3 Mertz's Mock Interferometer 3.6.4 Rotating Grid Collimator 3.6.5 Comparison of Noise in Different Multiplexing MethodsChapter 4. Noise, or When to Multiplex and When to Avoid it 4.1 Observed Gain in Signal-to-Noise Ratio 4.2 Light Losses 4.3 Sources of Noise 4.4 Comparison of Noise in Different InstrumentsChapter 5. Instrumental Considerations 5.1 Optics for Singly Encoded Spectrometers 5.2 Pupils and Stops 5.3 Diffraction 5.4 Aberrations 5.4.1 Spherical Aberration 5.4.2 Coma 5.4.3 Distortion 5.4.4 Curvature of Field 5.4.5 Astigmatism 5.4.6 Chromatic Aberration 5.5 Image Defects occurring in Dispersive Spectrometers 5.5.1 Curvature of Slit Image 5.5.2 Anamorphic Magnification 5.6 Optical Limitations in Practice 5.7 Grating Efficiency 5.8 Doubly Encoded and Imaging Spectrometers 5.9 Operation of a Doubly Encoded Spectrometer as an Imaging Spectrometer 5.10 Design of Imaging Spectrometers 5.11 Electronic System Constraints 5.12 Light Gathering Power of Hadamard and Fourier Transform SpectrometersChapter 6. Systematic Errors 6.1 Introduction 6.2 Description of Instrument and Spectrum: Simplest Case 6.2.1 Description of Instrument 6.2.2 Description of Spectrum 6.2.3 Operation as a Multiplexing Spectrometer 6.2.4 Example 1: No Diffraction 6.2.5 Example 2: Full Diffraction 6.2.6 Operation as a Monochromator 6.2.7 Recovery of Spectrum 6.2.8 Computing the Spectrum. Inverse Matrices 6.3 Errors Occurring with a Mask which is Moved in Steps 6.3.1 Faulty Mask Alignment 6.3.2 Differences between Slit Width and Step Size 6.3.3 Undercutting in the Mask Pattern 6.3.