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 © Springer-Verlag Berlin Heidelberg 2015 This work is subject to copyright. 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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). Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To Anthony F. J. Moffat & Hans-Siegfried Nimmert Teachers, Motivators & Friends 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............................................