Spectroscopic Instrumentation Fundamentals and Guidelines for Astronomers More information about this series at http://www.springer.com/series/4175 Thomas Eversberg • Klaus Vollmann

Spectroscopic Instrumentation Fundamentals and Guidelines for Astronomers

123 Thomas Eversberg Klaus Vollmann Schnörringen Telescope Science Institute Schnörringen Telescope Science Institute Waldbrol,R Germany Waldbrol,R Germany

SPRINGER-PRAXIS BOOKS IN SPACE EXPLORATION

ISBN 978-3-662-44534-1 ISBN 978-3-662-44535-8 (eBook) DOI 10.1007/978-3-662-44535-8 Springer Heidelberg New York Dordrecht London

Library of Congress Control Number: 2014953769

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Cover illustration: Larger image: This illustration shows the three spectra produced simultaneously by the new efficient X-shooter instrument on ESO’s Very Large Telescope. X-shooter can record the entire spectrum of a celestial object (in this example a distant lensed quasar) in one shot – from the ultraviolet to the near-infrared– with great sensitivity and spectral resolution. This unique new instrument will be particularly useful for the study of distant exploding objects called gamma-ray bursts, among the most energetic events in the Universe, which fade rapidly in brightness in matter of hours after their appearance. The rainbow colours applied to the spectra indicate X-shooter’s wide spectral coverage and are meant for illustrative purposes only. The majority of the wavelengths covered are in fact invisible to the human eye. Credit: ESO. Smaller image: The X-shooter NIR spectrograph optical layout (Vernet et al. 2011, reproduced with permission c ESO).

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Preface

To design spectroscopic instruments for astronomy, one needs appropriate tools. However, the necessary skills are not sufficiently aggregated in the literature so far. This is confirmed by repeated discussions with scientists and engineers. We wanted to meet this gap with an extensive summary and analysis. For the entire under- standing this includes, inter alia, wave and imaging optics, fiber optics, detectors, and considerations about appropriate data reduction and analysis. In particular, we will highlight the parameters for the two most common fundamental spectroscopic systems in astronomy—standard long-slit and echelle spectrographs. We do this in complete mathematical detail and perform all necessary calculations by example. We attempt to avoid the unfortunately common phrase “As you can easily see!” Therefore, the book can be used as an introduction to spectroscopy in appropriate university lectures and seminars. Thus we will not only appeal to design engineers for optical instruments but also professional astronomers and their students as well as advanced amateur astronomers. However, we emphasize that our text is really nothing more than a collection and organized combination of already existing publications. On the other hand, we have also tried to work through mathematical and physical approaches for the reader to make the understanding as easy as possible. We do not claim to be the first who present the appropriate theoretical and practical methods. Therefore, it is important to take this opportunity to recognize the many pioneers of instrument development, on whose shoulders we stand. We explicitly point out that our book represents only an introduction to the topic. In particular, our considerations on refractive lenses and their aberrations, which may play a central role for spectroscopy at relatively small telescopes, provide only a first insight into the calculation strategies and consequences for the interpretation of lenses. The reader is especially here urged to consult further and much more extensive works. This is also more or less true for all other considerations, which we discuss in various chapters. Apart from the theoretical data reduction methods, the practical aspects (software and hardware) are today particularly subject to rapid changes. Appropriate texts are quickly aging. One can capture the enormous depth of the spectroscopic world by only going beyond our introductory discussions.

vii viii Preface

For the sake of completeness we also show potential spectroscopic astrophysical applications. Of course, our outline of the spectroscopy of massive stars is only a field of many, and we have chosen this topic only because of our own expertise. Nevertheless, we believe that after reading the book, a transfer to observation targets other than point sources (sun, nebulae, galaxies) is easily possible. With our considerations, the reader should be able to fully calculate, design, and build a spectrograph for his/her own purposes. We will repeatedly indicate that the instrumental choice always depends on the corresponding applications or targets. The ultimate selection must be done by the observer.

Waldbröl, Germany Thomas Eversberg July 2014 Klaus Vollmann Contents

1 Prologue ...... 1 1.1 Ulysses ...... 2 2 Fundamentals of Standard Spectroscopy ...... 9 2.1 TheLawofDiffraction ...... 9 2.2 OntheGeometricalOpticsofa Prism ...... 10 2.3 PrinciplesofWaveOptics...... 16 2.3.1 InterferencePhenomena...... 17 2.3.2 The Huygens–Fresnel Principle ...... 17 2.3.3 Fraunhofer Diffraction for a Slit and a Pinhole...... 19 2.3.4 SpectralResolutionandResolvingPower...... 28 2.4 ThePrismSpectrograph...... 30 2.4.1 Propertiesofa PrismSpectrograph...... 31 2.4.2 The Angular and Linear Dispersion of a Prism ...... 31 2.4.3 Wavelength Dependence of the Refraction Index:SellmeierEquation ...... 34 2.4.4 TheSpectralResolutionofa Prism...... 35 2.5 TheGratingSpectrograph...... 36 2.5.1 Fraunhofer Diffraction for a Grating...... 38 2.5.2 HigherEfficiencywitha BlazeAngle ...... 46 2.5.3 The Wavelength of the “Blaze” at Arbitrary AngleofIncidence...... 50 2.5.4 The Angular and Linear Dispersion ofa GratingSpectrometer...... 51 2.5.5 TheMaximumResolvingPowerofa Grating...... 53 2.6 Collimator, Camera and Pixel Size...... 54 2.6.1 Reproduction Scale and Anamorphic MagnificationFactor...... 54 2.6.2 The Necessity of a Collimator...... 58 2.6.3 TheSpectralResolutionofa Spectrograph...... 61 2.6.4 SpectrometerFunction:TheFoldingIntegral ...... 63 ix x Contents

2.6.5 Broadening Processes and the System Function: Multiple Convolution...... 67 2.6.6 Shannon’s Theorem or the Nyquist Criterion ...... 72 2.6.7 SignalSamplingbyAppropriateInterpolation...... 78 3 Remarks About Dioptric Imaging Systems ...... 85 3.1 BasicRemarks ...... 85 3.2 BeamCalculationofanOpticalSystemintheParaxialArea .... 86 3.3 ParaxialImageScaleandFocalLengthofa LensSystem...... 89 3.4 The Focal Length of a Single Lens: The Lensmaker Equation ... 91 3.5 Monochromatic Seidel Aberrations ...... 94 3.6 ChromaticAberrations...... 100 3.7 TheCalculationofSeidelImageAberrations ...... 105 3.7.1 TheCalculationoftheSeidelSums...... 110 3.7.2 Discussion of the Different Aberration Contributions...... 112 3.8 TheSeidelSumsandTheirInterpretation...... 117 3.8.1 AverageImageCurvatureandAstigmatism...... 119 3.8.2 ExampleCalculationfora Simplet ...... 121 3.9 TheImpactofFieldCurvature:A SimpleExample...... 123 3.10 Permitted Deviations from Ideal Focus: The Blurring Circle ..... 126 3.11 Estimation of the Imaging Performance by Ray-Tracing Methods ...... 127 3.11.1 TheSpotDiagram ...... 129 3.11.2 LongitudinalandTransversalAberrations...... 132 3.11.3 FieldAberrations ...... 133 3.12 Possibilities for the Correction of Aberrations ...... 134 3.12.1 SphericalAberration...... 135 3.12.2 The Effects of Aperture Position ...... 139 3.12.3 Removal of Petzval Field Curvature Through a Field Flattener...... 142 3.12.4 AnAchromatIsNecessary...... 145 3.12.5 Example Considerations for a Commercial Spectrograph...... 149 3.13 Resume...... 152 Suggested Reading...... 154 4 Considerations About the Standard Spectrograph Layout ...... 155 4.1 BasicRemarksandRequirements...... 155 4.1.1 SlitWidthandResolvingPower ...... 156 4.1.2 Remarks About the Optical Slit ...... 158 4.1.3 WavelengthCalibrationwithanArtificialLamp...... 162 4.1.4 The Design of Collimator and Camera Optics ...... 164 4.1.5 Somewordsonthegratingchoice ...... 166 4.1.6 FixingtheTotalAngle...... 167 Contents xi

4.2 Project “MESSY” Maximum Efficiency Slit SpectroscopYforf/4Telescopes...... 170 4.2.1 CalculatingtheParametersoftheSpectrograph...... 172 4.2.2 OpticalandMechanicalDesign...... 179 4.2.3 TelescopeGuiding...... 180 4.2.4 ConstructionandFirstResults ...... 182 4.2.5 Vignetting in a Lens System...... 186 Conclusion ...... 190 Suggested Readings...... 191 5 Fundamentals of Echelle Spectroscopy ...... 193 5.1 HighOrders ...... 193 5.2 TheEchelleSpectrograph ...... 196 5.3 TheEchelleGratingandItsDispersion...... 197 5.4 TheGeometricalExtentoftheEchelleOrders...... 199 5.5 CentralWavelengthandOrderNumber ...... 201 5.6 TheSpectralExtentoftheEchelleOrders...... 202 5.7 Tilted Lines ...... 204 5.8 CurvedOrders...... 209 5.9 Remarks About the Cross-Disperser ...... 211 5.10 TheSpectralResolvingPowerofanEchelleSpectrometer...... 212 5.11 TheTotalEfficiencyoftheEchelleSpectrograph...... 216 5.12 ComparisonBetweenEchelleandStandardSpectrographs ...... 219 5.13 TheBlazeEfficiencyofanEchelleGrating ...... 221 5.13.1 TheShadowing ...... 223 RecommendedReadingsforEchelleSpectroscopy...... 227 6 Considerations for Designing an Echelle Spectrometer ...... 229 6.1 GeneralCommentsontheDesign ...... 229 6.2 RequirementsfortheOpticalElements...... 235 6.2.1 Collimator ...... 236 6.2.2 Camera ...... 242 6.3 TheChoiceoftheEchelleGrating...... 244 6.3.1 Effects of Line Density on the Spectrograph Design... 245 6.3.2 Effects of the Angle of Incidence ontheOrderLength ...... 247 6.3.3 The Influence of the Angle of Incidence ontheEchelleEfficiency...... 248 6.4 TheChoiceoftheCross-Disperser...... 253 6.4.1 Grating ...... 253 6.4.2 Prism ...... 255 6.5 “SimEchelle”:A SimpleEchelleSimulationProgram...... 257 6.6 Project “Mini-Echelle” an Echelle Spectrograph forf/10Telescopes...... 258 6.6.1 The Limit of an Achromatic Lens asa CamerafortheMini-Echelle...... 263 xii Contents

6.6.2 Compensation of Longitudinal Chromatic AberrationbyCameraTilt...... 267 6.7 Projekt“Research-Echelle”:FirstTests...... 268 6.8 SpecificEchelleDesignConstraints ...... 275 6.8.1 The“WhitePupil”Concept ...... 275 6.8.2 DataReduction...... 276 6.8.3 DesignImplicationsbyFiberOptics...... 277 6.9 Prospect ...... 278 RecommendedReadingsforAllSpectroscopyChapters...... 279 7 Reflecting Spectrographs ...... 281 7.1 BasicDesignConsiderations...... 281 7.1.1 Ebert-FastieConfiguration ...... 282 7.1.2 Czerny-TurnerConfiguration...... 282 7.2 TheImagingEquationofa SphericalMirror...... 284 7.3 Aberrationsofa ConcaveMirror...... 285 7.3.1 SphericalAberration...... 286 7.4 Fermat’sPrinciple...... 293 7.4.1 TheLawofReflection...... 294 7.4.2 Snell’sLawofRefraction ...... 296 7.5 SeidelAberrationsofa SingleRefractingSurface...... 297 7.5.1 The Connection Between Wave Aberration andLongitudinalandTransverseAberration...... 302 7.5.2 TheEstimationoftheAberrationCoefficients...... 305 7.6 CalculationoftheCzerny-TurnerSpectrometer...... 311 7.7 FocusingGratings...... 314 Suggested Readings...... 319 8 Practical Examples ...... 321 8.1 From Unique Instruments to Mass Production ...... 321 8.2 Littrow Systems ...... 324 8.2.1 Keyhole Littrow: Good Data for Little Money ...... 324 8.2.2 Mahlmann Littrow: Solid Mechanics ...... 326 8.2.3 Lhires III: A Littrow for All ...... 328 8.2.4 SPIRAL: A Littrow for Large Telescopes ...... 330 8.3 ClassicalSystems...... 332 8.3.1 The Mice Mansion: A Classical Grating Spectrograph...... 333 8.3.2 Spectrashift: A Czerny–Turner for Exoplanets ...... 334 8.3.3 Boller & Chivens: Work-Horse SpectrographsforMidsizeTelescopes...... 337 8.3.4 Hectospec: Multi-Object Spectroscopy attheMMT...... 339 8.3.5 MODS: A Multi-Object Double SpectrographfortheLBT ...... 342 8.3.6 COMICS: Ground Based Thermal IR Spectroscopy ... 345 Contents xiii

8.4 EchelleSystems...... 347 8.4.1 StoberEchelle:A PhysicianonNewTracks ...... 348 8.4.2 FegerEchelle:FromMechatronicstoOptics...... 350 8.4.3 eShel:A StableOff-the-ShelfFiberEchelle...... 353 8.4.4 FEROS:AnEchelleforChile...... 356 8.4.5 HDS:HighestResolutionattheNasmythFocus...... 358 8.4.6 X-Shooter: 20,000 Å in a Single Shot ...... 360 8.5 SpectrographswithSphericalConvexGratings...... 363 8.5.1 FUSE: The Far Ultraviolet Spectroscopic Explorer .... 363 8.5.2 COS:TheCosmicOriginsSpectrographforHST ..... 366 Suggested Readings...... 367 9 Image Slicer ...... 369 9.1 BasicRemarks ...... 369 9.2 TheBowenSlicer...... 371 9.3 Bowen–WalravenSlicer ...... 374 9.4 FEROS:A ModifiedBowen–WalravenSlicer...... 376 9.5 X-Shooter Mirror Slicer ...... 378 9.6 TheWaveguide...... 380 9.7 CAOSLowCostSlicer...... 383 10 Some Remarks on CCD Detectors ...... 387 10.1 HighQuantumEfficiencies...... 387 10.2 Linear Response: The Gain...... 389 10.3 Noise...... 391 10.3.1 PhotonNoise:TheNumberIsIt ...... 391 10.3.2 DarkNoise:BadVibrations...... 392 10.3.3 Read-OutNoise:ElectronicInfluences...... 395 10.3.4 AdditionalNoise:Pixel-to-PixelVariations ...... 396 10.4 TheCombinationIsCrucial...... 397 10.5 A SimpleSensorModel ...... 399 10.6 MeasuringtheRead-OutNoiseandtheCCDGain ...... 400 10.7 TheSignal-to-NoiseRatioandDetectionThreshold...... 405 Suggested Readings...... 409 11 Remarks on Fiber Optics ...... 411 11.1 BasicRemarks ...... 411 11.2 A Few Words About Fiber Types ...... 412 11.2.1 Multimode Fibers ...... 412 11.2.2 SingleModeFibers...... 413 11.3 Step-Index Fundamentals...... 413 11.4 TransmissionandAttenuation...... 418 11.5 Focal-RatioDegradation(FRD)...... 419 11.6 FiberNoise...... 423 11.7 PhotometricShiftandScrambling ...... 427 11.8 TaperedFibers ...... 428 xiv Contents

11.9 LensesfortheTelescopeLink...... 430 11.9.1 ImagingtheStarontotheFiberAperture...... 430 11.9.2 Imaging the Telescope Pupil onto the Fiber Aperture...... 432 11.10 Opto-MechanicalCoupling...... 435 11.11 Resume...... 437 Suggested Readings...... 438 12 Data Reduction ...... 439 12.1 OpenToolsforReliableResults ...... 439 12.2 LINUXandWindows...... 440 12.3 CCDReduction ...... 441 12.3.1 GeneralMathematicalConsiderations...... 442 12.3.2 TheBiasField...... 443 12.3.3 TheDarkField...... 443 12.3.4 SavingTime...... 444 12.3.5 TheFlatField ...... 445 12.3.6 WhyFlatFielding...... 447 12.3.7 CollapsingtheSpectrum ...... 448 12.3.8 FlatsforEchelleSpectroscopy...... 448 12.3.9 Remarks on the Response Function...... 453 12.4 TheDataReductionRecipe ...... 454 12.5 NoiseContributionofBiasandDarkFields...... 455 12.6 The Necessary Flat Field Quality ...... 456 12.7 CosmicRays ...... 458 12.8 A Quick Exposure Time Estimation ...... 459 12.9 WavelengthCalibration...... 459 12.9.1 StandardLightSources...... 459 12.9.2 LaserFrequencyCombs...... 461 13 Measurement Errors and Statistics...... 465 13.1 BasicRemarks ...... 465 13.2 SystematicErrors ...... 466 13.3 Drift...... 467 13.4 StatisticalErrors ...... 468 13.4.1 TheStandardDeviation ...... 469 13.4.2 TheStandardDeviationoftheAverage...... 470 13.4.3 TheAverageErroroftheFunctionValue...... 470 13.5 StatisticalErrorsofEquivalentWidths ...... 472 13.5.1 TheEquivalentWidthofSpectralLines...... 472 13.5.2 TheErroroftheEquivalentWidth...... 474 Suggested Readings...... 476 14 Massive Stars: Example Targets for Spectroscopy...... 477 14.1 SomeExampleTargets ...... 477 14.2 DotsintheSky...... 478 Contents xv

14.3 TheHeavyWeights:MassiveStars ...... 480 14.4 WindsThatSailonStarlight ...... 485 14.5 TheVelocityLaw...... 486 14.6 AsphericGeometries:BeStarDisksasPrototypes ...... 487 14.7 O Stars: Extreme Radiators, Thin Winds and Rotating Shocks... 498 14.7.1 Discrete Absorption Components andCo-rotatingInteractionRegions...... 499 14.7.2 TurbulentWindClumps...... 502 14.8 Wolf–Rayet Stars: Massive, Small Hot Stars Below ThickWinds...... 505 14.9 Clumps as Wind Tracers...... 513 14.10 A ShortRemarkonEvolution...... 517 14.11 DanceoftheGiants...... 518 14.12 SoWhat...?...... 525 Suggested Readings...... 527 15 The Next Step: Polarization ...... 529 15.1 Beyond Spectroscopy ...... 529 15.2 Polarized Light in Astronomy ...... 530 15.3 DescriptionofPolarizationwiththeStokesParameters ...... 531 15.4 PropertiesofStokeParameters...... 533 15.5 TheMuellerCalculus...... 534 15.6 TheRetarderMatrix ...... 535 15.7 ThePolarizerMatrix...... 536 15.8 Spectropolarimetry...... 537 15.9 The William–Wehlau Spectropolarimeter ...... 538 15.10 PolarimetricInvestigationsofMassiveStars ...... 543 15.10.1 InterstellarPolarization...... 543 15.10.2 IntrinsicLinearPolarization...... 544 15.10.3 IntrinsicCircularPolarization...... 548 Suggested Readings...... 552 16 Epilogue: Small Telescopes Everywhere ...... 553 16.1 SmallversusBig...... 553 17 Acknowledgements ...... 559

A The MIDAS Data Reduction ...... 561 A.1 TheMIDASEnvironment...... 561 A.1.1 Nomenclatura...... 562 A.1.2 Start,HelpandEnd...... 563 A.1.3 ImageImport...... 563 A.1.4 TheDisplay ...... 566 A.1.5 ImageSizeEstimation...... 567 A.1.6 ImageStatistics ...... 567 A.1.7 CopiesoftheOriginalImage...... 568 A.1.8 ImageRotation...... 568 xvi Contents

A.1.9 TheMIDASDescriptor...... 568 A.1.10 Look-Up Tables (LUT) ...... 569 A.1.11 PositioningtheGraphicWindow...... 569 A.2 SpectrumExtraction...... 570 A.2.1 AVERAGE/ROW...... 570 A.2.2 EXTRACT/AVERAGE...... 572 A.2.3 EXTRACT/LONG...... 574 A.3 WavelengthCalibration...... 575 A.3.1 CalibrationwithTwoAbsorptionLines ...... 575 A.3.2 ManySpectralAbsorptionLines...... 577 A.3.3 PrismSpectra ...... 580 A.3.4 TheUseofa ComparisonSpectrum...... 581 A.3.5 SpectralResolvingPower ...... 582 A.4 Rectification...... 583 A.5 SpectralAnalysis...... 584 A.5.1 TheEquivalentWidth...... 584 A.5.2 MeasuringtheSignal-to-NoiseRatio...... 585 A.5.3 SpectralCo-adding ...... 586 A.5.4 WindowTexts...... 588 A.5.5 Exporting Reduced Spectra: Fits/ASCII/Postscript .... 589 A.5.6 Postscript...... 589 A.5.7 Printing...... 590

B Important Functions and Equations ...... 591 B.1 TheBesselFunction ...... 591 B.2 ThePoissonDistribution ...... 592 B.3 TheFresnelEquations...... 594 B.4 TheSplineFunction ...... 596 B.5 The Continuous Fourier Transform ...... 600 B.5.1 RulesfortheOne-DimensionalFourierTransform.... 600 B.5.2 Correspondences of the One Dimensional FourierTransform ...... 600

C Diffraction Indices of Various Glasses ...... 601

D Transmissivity of Various Glasses ...... 609

E Line Catalogues for Calibration Lamps ...... 617 E.1 Line Catalogue Sources...... 617 E.2 Line Catalogue for the Glow Starter RELCO SC480 ...... 618 Contents xvii

F Manufacturers and Distributors ...... 633 F.1 Spectrographs...... 633 F.2 FiberOptics ...... 634 F.3 OpticalElements:LaboratoryMaterial...... 634 Suggested Readings...... 635

Bibliography ...... 637

Index ...... 645

List of Figures

Fig. 1.1 ThesolarorbitiftheUlyssesprobe...... 2 Fig. 1.2 ObservationsmadebytheUlyssesprobe...... 3 Fig. 1.3 Joseph v. Fraunhofer/Robert Bunsen/Gustav Kirchhoff ...... 4 Fig. 1.4 CCD exposure of M 51 and a historical photo...... 5 Fig. 1.5 CombinedwebcamimagesofMars...... 6 Fig. 2.1 Refractionoflightattheborderbetweentwomedia...... 10 Fig. 2.2 Refractionoflightina planeparallelplate ...... 11 Fig. 2.3 Effectofa planeparallelplateatvariouswavelengths ...... 12 Fig. 2.4 Diffractionoflightina prism...... 12 Fig. 2.5 Deflectionangleovertheangleofincidencefora prism...... 14 Fig. 2.6 Newtonianringsasanexampleforinterferencepatterns...... 17 Fig. 2.7 Pictorialofa planewavefrontfora starata largedistance...... 18 Fig. 2.8 Diffractionata diaphragm...... 21 Fig. 2.9 Diffraction at an optical slit...... 24 Fig. 2.10 Diffraction pattern of a rectangular diaphragm ...... 26 Fig. 2.11 Diffractionpatternofa pointsourceina telescope...... 26 Fig. 2.12 Definition of the Rayleigh criterion ...... 29 Fig. 2.13 Airydiskofa binaryfortheRayleighcriterion...... 29 Fig. 2.14 PresentationoftheRayleighcriterion...... 29 Fig. 2.15 Prismspectrographprinciple ...... 30 Fig. 2.16 The prism as diffraction limiting element ...... 32 Fig. 2.17 Non-linear refraction index of different prisms versus wavelength...... 33 Fig. 2.18 RefractiveindexanddispersionforBK7...... 34 Fig. 2.19 Principle of the grating spectrograph with mirrors as collimator and camera...... 36 Fig. 2.20 Beamgeometryata diffractiongrating...... 37 Fig. 2.21 Derivation of the grating equation from geometrical conditionsatthegrating...... 38 Fig. 2.22 Descriptionofthegratingintensityfunction...... 42 xix xx List of Figures

Fig. 2.23 Possible optical arrangements for transmission and reflectiongratings...... 45 Fig. 2.24 Grating with blaze angle ‚ ...... 47 Fig. 2.25 Example efficiency curve of a blazed grating...... 47 Fig. 2.26 Comparisonofcomputedandmeasuredblazeefficiency...... 50 Fig. 2.27 Imaging geometry at the grating with the anamorphic magnificationfactor...... 58 Fig. 2.28 Diffractionangleversusangleofincidence...... 60 Fig. 2.29 Dependence of the beam angle on the f-ratio...... 61 Fig. 2.30 Principleofa gratingspectrograph...... 62 Fig. 2.31 Convolving of two rectangular functions...... 65 Fig. 2.32 Sequence of six normal distributions and their output distributions...... 69 Fig. 2.33 Thealiaseffectfora harmonicsignal...... 73 Fig. 2.34 Representation of a single sinc function for a specially selectedsamplingpoint...... 74 Fig. 2.35 Illustrationoftherecoveryalgorithm...... 75 Fig. 2.36 Samplingofa sinewave...... 76 Fig. 2.37 BoxcarfunctionanditsFouriertransform...... 78 Fig. 2.38 Sampling of a noise-free sine function...... 80 Fig. 2.39 Samplingofa slightlynoisyGaussiansignal...... 80 Fig. 2.40 Maximum signal of a Gaussian function with sampling noise. ... 81 Fig. 2.41 Maximumsignalofa Gaussianfunctionwithspectralnoise...... 82 Fig. 3.1 Diffracting spherical surface...... 87 Fig. 3.2 Two diffracting spherical surfaces and their distance...... 88 Fig. 3.3 Geometricinterpretationoftheparaxialimagescale...... 89 Fig. 3.4 Geometric situation for the derivation of the lensmakerEquation...... 91 Fig. 3.5 Principleplanesandintersectionpoints...... 95 Fig. 3.6 Sphericalaberration...... 96 Fig. 3.7 Coma...... 97 Fig. 3.8 Theformationofanastigmaticimageanditscausticlines...... 98 Fig. 3.9 Distortion...... 99 Fig. 3.10 Chromaticaberrationofa lens...... 101 Fig. 3.11 Chromatic aberration of a Fraunhofer achromat...... 103 Fig. 3.12 Relativepartialdispersionasa functionoftheAbbenumber..... 104 Fig. 3.13 Chromatic aberration of a two-lens apochromat out of FK54andLaK10...... 105 Fig. 3.14 Chromatic aberration of an apochromat out of BaF52, KzFSN4andSK4...... 105 Fig. 3.15 Variables for the position of an inclined ray...... 107 Fig. 3.16 Relative contributions of the Seidel cross aberrations of3rdorder...... 110 Fig. 3.17 Theemergenceofcoma...... 115 List of Figures xxi

0 0 Fig. 3.18 Connections of the variables .yk/mer,.yk/sag and 0 0 .sk/mean, .sk/ast...... 117 Fig. 3.19 Different position possibilities for the meridional, sagittal and Petzval fields...... 120 Fig. 3.20 Originandgeometryofimagecurvature...... 124 Fig. 3.21 DistanceofthePetzvalspheretotheCCDplane...... 126 Fig. 3.22 Thecircleofconfusion...... 126 Fig. 3.23 Cross aberration presented by a spot diagram for two objectangles...... 130 Fig. 3.24 Spot diagrams of the best-form biconvex lens versus “defocus”...... 130 Fig. 3.25 Spotdiagramsforthebestformbiconvexlens...... 131 Fig. 3.26 Transverseaberrationfortwoobjectangles...... 133 Fig. 3.27 DepictionofthefieldaberrationsinWinLens3D...... 134 Fig. 3.28 Sphericalaberrationina converginganda diverginglens...... 135 Fig. 3.29 Spherical aberration of collective lenses of equal powerbutdifferentshape...... 136 Fig. 3.30 Correction of the spherical aberration by two lenses of opposite power...... 137 Fig. 3.31 Effects of lens splitting on spherical aberration...... 138 Fig. 3.32 Dependence of coma on the position of the stop...... 140 Fig. 3.33 Spotdiagramofa bi-convexlensmadeofBK7...... 141 Fig. 3.34 As in Fig. 3.33 now with aberration elimination by the stopposition...... 141 Fig. 3.35 Effects of different aperture positions on a plano-convexlensspotdiagram...... 143 Fig. 3.36 Effects of the aperture position on the spot diagram...... 143 Fig. 3.37 Spotdiagramoftheplano-convexlensshowninFig.3.35...... 144 Fig. 3.38 CorrectionofthePetzvalfieldcurvature...... 145 Fig. 3.39 CurvedimageplaneoftheKeplerspacetelescope...... 145 Fig. 3.40 Spot diagrams of a plano-convex lens for three differentwavelengths...... 146 Fig. 3.41 Spot diagrams of an f=10 achromat with 100 mm focallength...... 147 Fig. 3.42 Spotdiagramsofanachromaticlensanda Cooketriplet...... 148 Fig. 3.43 NeoncalibrationspectrumtakenwithLhires...... 149 Fig. 3.44 Spot diagrams of the Edmunds achromat #47-471-INK...... 150 Fig. 3.45 Spotdiagramsoftheachromatforthreewavelengths...... 152 Fig. 3.46 Optical path in a simple f=10Cooke triplet with 100 mmfocallength...... 153 Fig. 3.47 Classification of different lens types for different f-ratios and object angles...... 153 Fig. 4.1 Comparison of a high-resolution with a low-resolution spectrum ...... 158 Fig. 4.2 As Fig. 4.1, now for the O-supergiant Pup...... 159 xxii List of Figures

Fig. 4.3 AsFig.4.1butnowfortheWolf–RayetstarWR185...... 160 Fig. 4.4 Theopticalslitdefinesthespectralresolution...... 161 Fig. 4.5 Moffat function with ˇ D 2:5...... 161 Fig. 4.6 Thelow-costglowstarterRELCOSC480 ...... 163 Fig. 4.7 Geometricalsituationinsidethespectrograph...... 165 Fig. 4.8 TheechellegratingforPEPSI ...... 167 Fig. 4.9 Typical efficiencies of a grating blazed at 500 nm with 1,200lines/mm...... 168 Fig. 4.10 As Fig. 4.9 but for a grating blazed at 750 nm ...... 168 Fig. 4.11 Monochromatic laser diffraction patterns of a transmissiongrating...... 169 Fig. 4.12 Anglesina classicalspectrograph...... 169 Fig. 4.13 Overallviewofthespectrograph...... 174 Fig. 4.14 OurpolishedopticalZeissslit ...... 179 Fig. 4.15 Reflexiongratingwith638linespermm...... 180 Fig. 4.16 10 m slitimagedbytheguider...... 182 Fig. 4.17 950 m slitimagedbytheguider...... 182 Fig. 4.18 Overallviewoftheopenspectrograph...... 183 Fig. 4.19 Thefeedingoptics(the“vulcano”)...... 184 Fig. 4.20 The grating mount with micrometer screw...... 184 Fig. 4.21 Thegratingwith638lines/mmonthemounting ...... 185 Fig. 4.22 ThefinishedspectrographwithattachedMegaTEK-CCD...... 186 Fig. 4.23 ThefirstNeonspectrum...... 187 Fig. 4.24 The star Vega on the polished and illuminated slit...... 187 Fig. 4.25 Raw spectrum of Regulus with 60 s exposure time ...... 188 Fig. 4.26 Contrast-enhancedimageofthetwilightsky ...... 189 Fig. 5.1 Definition of the angles in the general grating equation ...... 194 Fig. 5.2 Qualitative description of wavelength intervals in differentorders ...... 195 Fig. 5.3 Exampledesignofanechellespectrograph...... 197 Fig. 5.4 Blazegratinginhighorder...... 198 Fig. 5.5 Echellewitha centralbeam...... 199 Fig. 5.6 Tiltoftheslitimageoratomiclines...... 205 Fig. 5.7 Tilt of the slit image, depending on the blaze angle ‚B ...... 206 Fig. 5.8 Principle depiction of the slit image tilt ...... 207 Fig. 5.9 Distortionofthespectralimageofa fiberaperture...... 209 Fig. 5.10 Orientationoftheechelledispersiondirection...... 210 Fig. 5.11 Orderorientationwitha prismcross-disperser ...... 212 Fig. 5.12 Orientationofechelleorderswitha gratingcross-disperser ...... 212 Fig. 5.13 Diffractionfactorforechelleandstandardgrating ...... 219 Fig. 5.14 Efficiency comparison between a holographic, blazed andechellegrating ...... 222 Fig. 5.15 Efficiencies in two adjacent orders ...... 222 List of Figures xxiii

Fig. 5.16 Effective blaze surface as a function of the incident beamangle...... 223 Fig. 5.17 Comparison of two normalized blaze functions dependingonthetotalangle...... 226 Fig. 6.1 Layout of an echelle spectrograph ...... 230 Fig. 6.2 Geometricconditionsinthespectrometer...... 232 Fig. 6.3 Central wavelength for echelle orders 27–58 ...... 233 Fig. 6.4 Free spectral range and geometric length of the echelle orders ... 234 Fig. 6.5 Centralwavelengthspacingandorderseparation ...... 234 Fig. 6.6 Divergence of the collimated beam at a finite seeing disk...... 236 Fig. 6.7 Impact of the angle of incidence on the spectral resolvingpower...... 237 Fig. 6.8 Spotdiagramsofa 250mm/40mmachromat ...... 240 Fig. 6.9 Spotdiagramsofthe250mm/40mmachromatatf/6.25...... 241 Fig. 6.10 Paraxial longitudinal chromatic aberration of a 250 mm/40mmachromat...... 241 Fig. 6.11 Binning dependent imaging depth vs. fcam ...... 243 Fig. 6.12 The depth of focus in dependence on the distance to theechellecamera...... 244 Fig. 6.13 Influence of the angle of incidence on the spectral lengthofanechelleorder...... 248 Fig. 6.14 Positiveandnegativeoperationofanechellegrating ...... 251 Fig. 6.15 Microscopicimageofa Thorlabs31.6l/mmR2grating...... 252 Fig. 6.16 Relative blaze peak intensity vs. angle of incidence in degree .... 252 Fig. 6.17 Blazefunctionsfortwodifferentanglesofincidence...... 253 Fig. 6.18 Comparisonoflineardispersionsatgratingandprism...... 256 Fig. 6.19 Geometry at the CCD chip with respect to the camera aperture ...... 262 Fig. 6.20 Spotdiagramsofanachromat31.5mm/120mm...... 264  3 Fig. 6.21 Increase of the maximum spot diameter with col ...... 266 Fig. 6.22 Spectral resolving power vs. collimator focal length with 50 mslit ...... 266 Fig. 6.23 Spectral resolving power vs. collimator focal length with 75 m slit...... 267 Fig. 6.24 Paraxialchromaticaberrationofanachromat ...... 268 Fig. 6.25 The mechanical camera adjustment of the research spectrograph...... 268 Fig. 6.26 FirstsetupoftheOPTIMAechellespectrograph...... 269 Fig. 6.27 Simple set-up for determining the grating constant of theechellegrating...... 270 Fig. 6.28 Photo of the prism cross-disperser with imaged echellespectrum...... 270 Fig. 6.29 Firstattemptwitha Nikonlens...... 271 Fig. 6.30 WhiteLEDechellespectrumobtainedwithanachromat...... 272 xxiv List of Figures

Fig. 6.31 As Fig. 6.30 now with a f D 300 mm f/4 medium formatlens...... 272 Fig. 6.32 Aberrationsofa Qiopticsachromat ...... 273 Fig. 6.33 SolarspectrumtakenwiththePentacon300mm...... 273 Fig. 6.34 Ordercross-sectionatthecentralwavelengths ...... 274 Fig. 6.35 Section of a Neon calibration spectrum and the half-widthofa line...... 275 Fig. 6.36 Schematicsketchofthe“WhitePupil”concept ...... 276 Fig. 6.37 Superimposed echelle orders behind the echelle gratingbeforeseparation...... 276 Fig. 6.38 Raw spectrum of P Cygni obtained with the Shelyak “Eshel” .... 278 Fig. 6.39 Section through the orders of the P-Cygni spectrum ...... 278 Fig. 7.1 OriginalsketchoftheEbertspectrograph...... 282 Fig. 7.2 Czerny-Turner spectrograph as monochromator ...... 283 Fig. 7.3 Czerny-Turnerdesign ...... 283 Fig. 7.4 Czerny-Turnerdesign ...... 284 Fig. 7.5 Entranceslitanditsimagefora Czerny-Turnerspectrograph .... 284 Fig. 7.6 Thegeometricalconditionsatthesphericalmirror...... 285 Fig. 7.7 Thegeometricconditionsata concavemirror...... 286 Fig. 7.8 Definition of the transverse spherical aberration...... 290 Fig. 7.9 Die Entstehung des circle of least confusion...... 292 Fig. 7.10 Theopticalpathata concavemirror ...... 293 Fig. 7.11 Geometricalconditionsforthereflectionlaw...... 295 Fig. 7.12 GeometricconditionsforSnell’slawofrefraction ...... 296 Fig. 7.13 The general geometric conditions for a refracting surface (Schroeder 1987) ...... 298 Fig. 7.14 Theeffectsofthedistortedwavefront...... 303 Fig. 7.15 Wavefront,transverseandlongitudinalerror ...... 303 Fig. 7.16 ThegeometryoftheCzerny-Turnerspectrometer...... 311 Fig. 7.17 Spot diagrams for Ebert Fastie and Czerny-Turner configurations...... 315 Fig. 7.18 Sketchofa concavediffractiongrating ...... 316 Fig. 7.19 Rowlandcircleprinciple...... 316 Fig. 7.20 About the calculation of the situation on the Rowland circle ..... 316 Fig. 7.21 ConstructionoftheRowlandcircle...... 317 Fig. 7.22 Examplesofspectrographswithconcavegratings...... 318 Fig. 8.1 Spectrograph at the Danish 0.5 m telescope at La Silla ...... 323 Fig. 8.2 Design of the Reinecke Keyhole spectrograph...... 325 Fig. 8.3 The Keyhole spectrograph at the telescope ...... 325 Fig. 8.4 Details of the Mahlmann Littrow ...... 326 Fig. 8.5 Details of the Mahlmann Littrow adjustment unit ...... 327 Fig. 8.6 OpticaldesignoftheLhiresIIIspectrograph...... 329 Fig. 8.7 InsidetheLhiresIIIspectrograph ...... 329 Fig. 8.8 LhiresIIIattheCelestronC14focus...... 330 List of Figures xxv

Fig. 8.9 H˛ emission of the LBV supergiant P Cygni ...... 330 Fig. 8.10 TheSPIRALlensarrayandthefiberconnection...... 331 Fig. 8.11 TheSPIRALfiberslitpattern...... 331 Fig. 8.12 Optical setup of the SPIRAL Littrow spectrograph ...... 332 Fig. 8.13 The MICE MANSION froma petshop...... 333 Fig. 8.14 The MICE MANSION withinternaloptics...... 333 Fig. 8.15 Double peak of the H˛ inthespectrumofMizar...... 334 Fig. 8.16 Time series of  Aurigae in the interval around the H˛ line ...... 335 Fig. 8.17 TheSpectrashiftCzerny-Turnerinstallation ...... 335 Fig. 8.18 Viewoftheparabolamirrors...... 336 Fig. 8.19 Schematc picture of the bundle of seven single fibers ...... 336 Fig. 8.20 Combined phase data points for a single orbit of  Bootis...... 336 Fig. 8.21 LargeBoller& Chivensspectrograph...... 337 Fig. 8.22 OpticalconfigurationoftheOMMspectrograph...... 338 Fig. 8.23 BonetteofHectospecinthefocalplane...... 339 Fig. 8.24 IsometricviewofHectospec...... 340 Fig. 8.25 TheHectospecfibersintheguidechain...... 341 Fig. 8.26 Thermal-BrakeconceptforHectospec...... 341 Fig. 8.27 BeamsintheredandblueMODSchannels...... 343 Fig. 8.28 MODS optical layout...... 344 Fig. 8.29 First Multi-Object Spectrum: Galaxy Cluster Abell 1689...... 344 Fig. 8.30 Images and Long-Slit Spectra of the Crab Nebula...... 345 Fig. 8.31 Optical layout of the COMICS spectrograph ...... 346 Fig. 8.32 Sketchofthecryovacuumchamber...... 346 Fig. 8.33 COMICSattachedtotheCassegrainfocus ...... 347 Fig. 8.34 Wooden layout of the Stober echelle ...... 348 Fig. 8.35 RealizationoftheStoberspectrograph...... 348 Fig. 8.36 Echelle spectrum of the H˛ line of Aurigae...... 349 Fig. 8.37 Echelle spectrum of Aurigae ...... 349 Fig. 8.38 PrinciplesketchoftheFegerechellespectrograph...... 350 Fig. 8.39 Cross-disperserandcameraopticsoftheFegerechelle...... 350 Fig. 8.40 TheFegerechellewiththefocusfeedingmimic ...... 351 Fig. 8.41 Components of the Feger spectrograph ...... 351 Fig. 8.42 Camera and cross-disperser mount of the Feger echelle ...... 352 Fig. 8.43 3DschematicsoftheeShelspectrograph ...... 353 Fig. 8.44 3DsideschematicsoftheeShelspectrograph...... 353 Fig. 8.45 TheeShelspectrographusedatTeideIAC80telescope...... 354 Fig. 8.46 The eShel guiding unit in the focus of the Teide IAC80telescope...... 354 Fig. 8.47 SpectrumofWR134obtainedwiththeeShelspectrograph...... 355 Fig. 8.48 Spectrum of Vega around Hˇ ...... 355 Fig. 8.49 TheFEROSdesign...... 356 Fig. 8.50 FEROS raw spectrum of P Cygni...... 357 Fig. 8.51 HDSinthelab...... 359 Fig. 8.52 The optical layout of HDS ...... 359 xxvi List of Figures

Fig. 8.53 Schematic overview of X-shooter ...... 361 Fig. 8.54 The X-shooter UVB spectrograph optical layout ...... 361 Fig. 8.55 The X-shooter NIR spectrograph optical layout ...... 362 Fig. 8.56 A view of X-shooter at the Cassegrain focus ...... 363 Fig. 8.57 TheFUSEUVchannels...... 364 Fig. 8.58 TheFUSEinstrument...... 365 Fig. 8.59 Optical layout for COS...... 367 Fig. 9.1 Slicerprinciplebylightrefraction...... 370 Fig. 9.2 The two shifted slicer input parts after being sliced ...... 371 Fig. 9.3 TheoriginalBowenconceptforanimageslicer...... 372 Fig. 9.4 Glassplateletsfora Bowenimageslicer...... 373 Fig. 9.5 Sideperspectiveviewoftheslicerconstruction...... 373 Fig. 9.6 Theworkingprincipleofa Bowen-Walravenimageslicer...... 374 Fig. 9.7 Bowen-Walraven image slicer for the 1.52 m OHP Telescope .... 375 Fig. 9.8 TheBowen-WalravenimageslicerforESPaDOnS...... 376 Fig. 9.9 Comparison of the Bowen-Walraven and FEROS imageslicers...... 377 Fig. 9.10 Pictures of the sliced seeing disk in the FEROS slicer prototype...... 378 Fig. 9.11 Sketch of the X-shooter IFU ...... 379 Fig. 9.12 Re-positioning of the image field by the X-shooter slicer ...... 379 Fig. 9.13 Lightinjectionintoa Waveguideslicer ...... 380 Fig. 9.14 Front,sideandtopviewofa Waveguideimageslicer...... 381 Fig. 9.15 Schematicviewofa singleWaveguideplatelet...... 381 Fig. 9.16 Layout of the LBT Waveguide image slicer ...... 382 Fig. 9.17 Waveguide prototype for PEPSI under a microscope...... 382 Fig. 9.18 WorkingprincipleoftheCAOSslicer...... 383 Fig. 9.19 Geometrydeterminationfora two-sliceimageslicer ...... 384 Fig. 9.20 Detailedviewofthemirrorseparation...... 385 Fig. 9.21 3Ddrawing ...... 385 Fig. 9.22 Laboratorysetup...... 385 Fig. 9.23 Input and output slicer image ...... 386 Fig. 9.24 EchellespectrumobtainedwiththeFegerslicer...... 386 Fig. 10.1 Quantum efficiency of a Tektronix TK 1024 CCD chip ...... 388 Fig. 10.2 Quantum efficiency of a Kodak 1603ME CCD chip ...... 389 Fig. 10.3 ADU dependence on the exposure time for a 12-bit CCD ...... 390 Fig. 10.4 Dark current in electrons per pixel and second versus temperature...... 394 Fig. 10.5 Dark Noise versus exposure time for an AlphaMaxi camera...... 395 Fig. 10.6 Noise caused by pixel-to-pixel variations compared to photon noise ...... 396 Fig. 10.7 Raw spectrum of a Be star taken with a Tektronix TK 1024 chip ...... 397 Fig. 10.8 As Fig. 10.7 but for a Kodak KAF 1603ME Chip ...... 397 List of Figures xxvii

Fig. 10.9 Signal and standard deviation of the bias of a Megatek camera ...... 398 Fig. 10.10 Signalandstandarddeviationofthebiasofa Sigmacamera..... 398 Fig. 10.11 read-out noise and the conversion factor for the Megatekcamera...... 401 Fig. 10.12 Bias field of an Apogee AP8P camera with a Tektronix 1024  1024 CCD (Source: Magnus Schneide,HamburgerSternwarte)...... 403 Fig. 10.13 FlatfieldimageobtainedwithanAlphaMaxicamera...... 404 Fig. 10.14 Difference of two flat fields obtained with the same CCDcamera...... 404 Fig. 10.15 Gainandread-outnoiseofanAlphaMaxicamera...... 405 Fig. 10.16 Synthetic emission-line with background noise ...... 406 Fig. 11.1 Beampathinfiberopticsformeridionalrays ...... 414 Fig. 11.2 Lightpathinfiberoptics...... 415 Fig. 11.3 Skewraysfroma parallelincomingbeam ...... 415 Fig. 11.4 Projectedcircularpatterncreatedbyskewrays...... 416 Fig. 11.5 Reflectioncharacteristicsfordifferentaluminumcoatings...... 417 Fig. 11.6 Beampathinfiberoptics...... 417 Fig. 11.7 Totaltransmissionoftwodifferent10m fiberoptics...... 419 Fig. 11.8 Totaltransmissionoftwodifferent26m fiberoptics...... 419 Fig. 11.9 DegradationoftheF-numberbybendingfiberoptics...... 420 Fig. 11.10 EfficiencyfordifferentF-numbersoftheincidentbeam...... 421 Fig. 11.11 Normalized relative efficiency for a 200 mfiber...... 421 Fig. 11.12 Normalized relative efficiency for a 200 m fiber with strongbending...... 422 Fig. 11.13 Image of a 100 m octagonal core fiber and a 200  200 msquarecorefiber ...... 423 Fig. 11.14 F-number at the fiber output as a function of the F-number at the input ...... 423 Fig. 11.15 Speckle distribution of monochromatic light of a 660 nm-HeNelaser...... 424 Fig. 11.16 Setupfortheobservationoffiberspecklesinthefarfield...... 425 Fig. 11.17 Setup for the observation of fiber speckles by an imaginglens ...... 425 Fig. 11.18 Theoretical S/N according to photon statistics and measuredS/N...... 426 Fig. 11.19 Setupfortheobservationoffiberspecklesinthefarfield ...... 426 Fig. 11.20 Photometricshift ...... 427 Fig. 11.21 Sketchofa taperedfiberandthreelightrays ...... 428 Fig. 11.22 Imaginga starona fiberwitha singlelens ...... 430 Fig. 11.23 Best coupling between telescope and fiber for a real stellarimage ...... 431 Fig. 11.24 TheFerosfiberlink ...... 432 xxviii List of Figures

Fig. 11.25 Coupling a telescope to a fiber by projecting the pupil onthefibreend...... 433 Fig. 11.26 Two apertures under the microscope ...... 434 Fig. 11.27 Typicalopto-mechanicalfibercouplingwithguidingoptics...... 435 Fig. 11.28 Simple fiber coupler and guiding unit ...... 436 Fig. 11.29 Optomechanical fiber coupling with beam splitter ...... 436 Fig. 12.1 Spectrum obtained with the echelle spectrographs at theMMTtelescope...... 450 Fig. 12.2 2D-sketchofanintegrationsphere ...... 450 Fig. 12.3 Intensity in an integration sphere seen by a normal andoff-normalobserver...... 451 Fig. 12.4 NIRSpecradiometriccalibrationspectralsource...... 452 Fig. 12.5 NIRSpeccalibrationsphere...... 452 Fig. 12.6 1D calibration spectrum of a neon lamp between 5,800and7,500Å...... 460 Fig. 12.7 2DcalibrationspectrumoftheThArNevlampofFEROS...... 461 Fig. 12.8 Instrumental setup of the LFC test system at ESO-HARPSspectrograph ...... 462 Fig. 12.9 Comparison of LFC and thorium emissions with ESO-HARPS ...... 462 Fig. 13.1 A spectrum of the Be star  Tauri around H˛ ...... 466 Fig. 13.2 Continuous stellar spectrum ...... 468 Fig. 13.3 TheGaussiannormaldistribution ...... 468 Fig. 13.4 The definition of the equivalent width...... 472 Fig. 13.5 Syntheticemissionlinewithanintensityof1.5 ...... 473 Fig. 13.6 Syntheticemissionlinewithanintensityof1:1.05...... 475 Fig. 14.1 Subsequently colored solar spectrum from Fraunhofer...... 478 Fig. 14.2 Red or blue line shiftduetostellarrotation...... 479 Fig. 14.3 Absorptionlinebroadeningbystellarrotation...... 479 Fig. 14.4 Spectralradiationfluxofa G5VstarandanO4Vstar ...... 480 Fig. 14.5 Spectra of the WRCObinary Velorum and the O4If-star  Puppis ...... 481 Fig. 14.6 Hydrogen emission of the star P-Cygni ...... 482 Fig. 14.7 Isowavelength-shiftcontoursfora Keplerianrotatingdisc...... 484 Fig. 14.8 Isowavelength-shift contours for a disc velocity being purelyinexpansion...... 484 Fig. 14.9 How to produce a P-Cygni profile ...... 486 Fig. 14.10 Thevelocitylawforstellarwinds ...... 487 Fig. 14.11 H˛ lines of ˇ Cas and  Cas...... 488 Fig. 14.12 Artist’ssketchofa Bestar ...... 489 Fig. 14.13 The H˛ lineofa Bestaratdifferentinclinations...... 490 Fig. 14.14 Comparison of the H˛ line of the Be star  Cas with a Gaussian ...... 491 List of Figures xxix

Fig. 14.15 Long-term V/R, H˛ emission strength of  Tau ...... 492 Fig. 14.16 Observations of V/R variations in Hˇ and their simplisticinterpretation...... 492 Fig. 14.17 The rotationally induced severely flattened Be star ˛ Eridani .... 493 Fig. 14.18 Orbital trajectories of particles in the wind of a fast rotatingBestar ...... 494 Fig. 14.19 Equatorial disk material density of a Be star for various velocities ...... 495 Fig. 14.20 Gravity darkening for a hot B star and different rotational velocities...... 495 Fig. 14.21 Radiativeforcefroma fastrotatingstar...... 496 Fig. 14.22 Different regions of the Be star  Cas at different wavelengths... 497 Fig. 14.23 Interaction between a magnetic flare and the disk in  Cas...... 497 Fig. 14.24 The Pleiades and the H˛ linesofthesevenbrightestBestars .... 498 Fig. 14.25 HeII line of the O4If supergiant  Puppis ...... 499 Fig. 14.26 Si IV at 1,394 and 1,402 Å of PerseiobservedwithIUE...... 500 Fig. 14.27 Hydrodynamic simulation of DACs ...... 501 Fig. 14.28 SketchoffourCorotatingInteractionRegions...... 502 Fig. 14.29 Residuals for  Puppis during a single observing night ...... 504 Fig. 14.30 The wind geometry of  Pup derived from various observations ...... 505 Fig. 14.31 Broadbandemission-linespectrumofWR136...... 506 Fig. 14.32 Mean spectrum of the WRCO binaryWR140 ...... 507 Fig. 14.33 Approximationofanemissionlineprofile...... 508 Fig. 14.34 Principle of multiple scattering ...... 509 Fig. 14.35 The nebula M1-67 in H-alpha around the WN8 star WR 124 ..... 510 Fig. 14.36 CIII residuals of a single observing night in  Velorum...... 511 Fig. 14.37 The effect of a sinusoidal velocity perturbation in a stellarwind ...... 512 Fig. 14.38 Velocity and density behaviour leading to turbulence inthestellarwind ...... 512 Fig. 14.39 Time stack of residuals for the HeII 4686 line of  Puppis...... 514 Fig. 14.40 Radial acceleration vs. radial velocity for individual clumps in  Puppis ...... 515 Fig. 14.41 Radial acceleration vs. radial velocity for individual clumpsinWR140...... 516 Fig. 14.42 Randomly generated isotropic clumps ...... 516 Fig. 14.43 Artist’s impression of WR 140...... 518 Fig. 14.44 Density simulation of the WR 140 system and its shock-cone .... 519 Fig. 14.45 ThedustspiralofWR112 ...... 519 Fig. 14.46 SchematicviewoftheLührs’shock-conemodel...... 520 Fig. 14.47 CIIIlineat5,696Å oftheWolf-RayetstarWR79...... 521 Fig. 14.48 The CIII 5696 line profiles of WR 42 and WR 79 ...... 522 Fig. 14.49 FitofsyntheticLührsconeprofilestoWR42andWR79 ...... 523 xxx List of Figures

Fig. 14.50 The CIII 5696 excess emission of WR 140 as a functionoforbitalphase ...... 524 Fig. 14.51 Fit of the radial velocity and width of the CIII 5696 excessemission...... 524 Fig. 14.52 HST image of the Bubble nebula NGC 7635 ...... 525 Fig. 14.53 MolecularHydrogeninaninterstellarwindfilament...... 526 Fig. 14.54 Large-scale winds from star burst regions in NGC 3079 ...... 527 Fig. 15.1 Parametersdefiningthepolarizationofa simplewave...... 532 Fig. 15.2 Theelectronscatteringprocess...... 534 Fig. 15.3 Beam-splitting analyzers ...... 537 Fig. 15.4 Simple sketch of the William-Wehlau Spectropolarimeter ...... 538 Fig. 15.5 View of the William-Wehlau Spectropolarimeter in thelab ...... 539 Fig. 15.6 One of the two /4retarders ...... 539 Fig. 15.7 The two /4 plates and their stepping motors in the polarimeterunit ...... 540 Fig. 15.8 Wavelengthdependenceofinterstellarlinearpolarization...... 544 Fig. 15.9 Sources of spectropolarimetric observations ...... 545 Fig. 15.10 Spectropolarimetric measurements of EZ CMa ...... 546 Fig. 15.11 Cartoondepictinga steady-state“disk”...... 547 Fig. 15.12 Polarizationfromaxisymmetric“clumps”...... 548 Fig. 15.13 Wavelength dependence of emergent intensity and polarization ...... 550 Fig. 15.14 Fluxandcircularpolarizationprofiles...... 551 Fig. 15.15 Magneticspotsandcircularpolarization...... 552 Fig. 16.1 Variability of lines of Puppis ...... 554 Fig. 16.2 The K 7699 line behaviour of epsilon Aur ...... 555 Fig. A.1 MIDASstartingwindow...... 563 Fig. A.2 Spectrumofa star ...... 565 Fig. A.3 Darkfield ...... 565 Fig. A.4 Example of an image descriptor for the exposure time ...... 565 Fig. A.5 Ourflatfield ...... 566 Fig. A.6 Exampleimagedescriptor ...... 567 Fig. A.7 Exampleimagedescriptorfortheimagesize...... 567 Fig. A.8 Imagestatistics ...... 567 Fig. A.9 Cursoroutput...... 568 Fig. A.10 TheMIDASdescriptor...... 569 Fig. A.11 Image statistics for the region [2,2:770,40] ...... 570 Fig. A.12 Image statistics for the region [2,2:770,40] ...... 570 Fig. A.13 Columnplotperpendiculartothedispersiondirection...... 571 Fig. A.14 Collapsed1Dspectrum ...... 571 Fig. A.15 FlippedimageofFig.A.14 ...... 572 List of Figures xxxi

Fig. A.16 Plotofthetwoimagecolumnsno.5 and500...... 573 Fig. A.17 Stellar spectrum, background reduced with EXTRACT/AVERAGE ...... 573 Fig. A.18 Skyreducedimages...... 574 Fig. A.19 RawspectrumofSirius ...... 575 Fig. A.20 EstimatedpixelpositionswithCENTER/GAUSS...... 576 Fig. A.21 Calibrated spectrum lhs1 ...... 577 Fig. A.22 Lineidentificationwitha linetable...... 578 Fig. A.23 Lineidentificationwiththecurser...... 579 Fig. A.24 LinecalibrationwithCALIBRATE/LONG...... 579 Fig. A.25 LinecalibrationwithREBIN ...... 579 Fig. A.26 SpectraofRigelandRegulus...... 580 Fig. A.27 Detection of catalogue calibration lines ...... 581 Fig. A.28 Line positions found with the cursor ...... 581 Fig. A.29 Collapsedcalibrationspectrum...... 582 Fig. A.30 CalibrationrelationcalculatedwithCALIBRATE/LONG...... 582 Fig. A.31 200Å intervalofa neoncalibrationlamp...... 583 Fig. A.32 Continuum fit for consecutive rectification ...... 584 Fig. A.33 Rectifiedspectrum...... 584 Fig. A.34 Estimationofthelineequivalentwidth ...... 585 Fig. A.35 Estimationofthelineequivalentwidth ...... 585 Fig. A.36 Estimationofthelineequivalentwidth ...... 586 Fig. A.37 Fitting parameters ...... 586 Fig. A.38 Wavelengthoverlapoftwospectra...... 587 Fig. A.39 Aftermergingthetwospectra ...... 587 Fig. A.40 Labeling within the MIDAS graphic window. Co-addingthetwospectra ...... 588 Fig. A.41 Outputforpostscriptformat ...... 590

Fig. B.1 Several Bessel functions Jn.x/ ...... 592 Fig. B.2 SeveralPoissondistributions ...... 594 Fig. B.3 Classical interpolation with a 3rd degree polynomial ...... 599 Fig. B.4 Interpolationwitha cubicspline...... 599 Fig. C.1 Graph of the refraction indices of all available Schott glasstypes ...... 602 Fig. D.1 Graph of the transmissivity of all available Schott glass types.... 610 Fig. E.1 SQUES echelle orders 28–37 of the RELCO SC480 glowstarter...... 619 Fig. E.2 SQUES echelle orders 38–47 of the RELCO SC480 glowstarter...... 620 Fig. E.3 SQUES echelle orders 48–57 of the RELCO SC480 glowstarter...... 621 Fig. E.4 SQUES echelle spectrum of the glowstarter RELCO SC480 (orders 28–32) ...... 622 xxxii List of Figures

Fig. E.5 SQUES echelle spectrum of the glowstarter RELCO SC480 (orders 33–37) ...... 623 Fig. E.6 SQUES echelle spectrum of the glowstarter RELCO SC480 (orders 38–42) ...... 624 Fig. E.7 SQUES echelle spectrum of the glowstarter RELCO SC480 (orders 43–47) ...... 625 Fig. E.8 SQUES echelle spectrum of the glowstarter RELCO SC480 (orders 48–52) ...... 626 Fig. E.9 SQUES echelle spectrum of the glowstarter RELCO SC480 (orders 53–57) ...... 627 List of Tables

Table 3.1 Wavelength-dependentintersectionlengths ...... 100 Table 3.2 CoefficientsoftheSeidelaberrations...... 108 Table 3.3 Auxiliary parameters for a thin biconvex lens ...... 122 Table 3.4 Specific Seidel coefficient corresponding to Table 3.3 ...... 122 Table 3.5 OpticalDesignSoftware...... 128 Table 3.6 WinLens Seidel table for the Edmunds achromat #47-741-INK...... 150 Table 4.1 Typicaltargetandsystemparametersatdifferenttelescopes..... 157 Table 5.1 Overlapofthefirst9 ordersfora grating...... 195 Table 5.2 Resolvingpowerofanechelle ...... 215 Table 6.1 Input and output parameters of the simulation program“SimEchelle”...... 258 Table 6.2 Modelingthe“Mini-Echelle” ...... 261 Table 6.2 (continued) ...... 262 Table 6.3 Necessary camera aperture dcam and its f-ratio and cameraspotsize...... 263 Table 6.4 Illumination of the camera aperture with increasing collimator focal length ...... 265 Table 6.5 ModelingofthemodifiedOPTIMAwith“SimEchelle”...... 271 Table 10.1 Gain, average and standard deviation for a Megatek anda Sigmacamera...... 399 Table 10.2 Parametersfora simplesensormodel...... 400 Table 10.3 Device specifications from the SITe Tk 1024  1024 CCDdatasheet...... 402 Table 11.1 Efficiencies depending for a 600–200m taperedfiber...... 429 Table 11.2 Efficiencies for a 400–100 mtaperedfiber...... 430

xxxiii xxxiv List of Tables

Table 13.1 Correction factor k forthestandarddeviationoftheaverage..... 470 Table C.1 Refraction indices for all Schott glasses (8,521–5,893 Å) ...... 603 Table C.2 Refraction indices for all Schott glasses (8,521–5,893 Å) ...... 604 Table C.3 Refraction indices for all Schott glasses (8,521–5,893 Å)...... 605 Table C.4 Refraction indices for all Schott glasses (5,876–4,047 Å) ...... 606 Table C.5 Refraction indices for all Schott glasses (5,876–4,047 Å)...... 607 Table C.6 Refraction indices for all Schott glasses (5,876–4,047 Å) ...... 608 Table D.1 Transmissivity for all Schott glasses (10,600–5,460 Å)...... 611 Table D.2 Transmissivity for all Schott glasses (10,600–5,460 Å)...... 612 Table D.3 Transmissivity for all Schott glasses (10,600–5,460 Å)...... 613 Table D.4 Transmissivity for all Schott glasses (5,000–4,000 Å) ...... 614 Table D.5 Transmissivity for all Schott glasses (5,000–4,000 Å) ...... 615 Table D.6 Transmissivity for all Schott glasses (5,000–4,000 Å) ...... 616 Table E.1 RELCO SC480 glowstarter line catalogue 8,136.406–6,483.082 Å ...... 628 Table E.2 RELCO SC480 glowstarter line catalogue 6,416.307–5,562.766 Å ...... 629 Table E.3 RELCO SC480 glow-starter line catalogue 5,558.702–4,596.097 Å...... 630 Table E.4 RELCO SC480 glowstarter line catalogue 4,589.898–4,198.317 Å ...... 631 Table E.5 RELCO SC480 glowstarter line catalogue 4,181.884–3,888.65 Å ...... 632