Eversberg / Vollmann Spectroscopic Instrumentation

Fundamentals and Guidelines for Astronomers
1. Auflage 2014
ISBN: 978-3-662-44535-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 677 Seiten

Reihe: Springer Praxis Books

In order to analyze the light of cosmic objects, particularly at extremely great distances, spectroscopy is the workhorse of astronomy. In the era of very large telescopes, long-term investigations are mainly performed with small professional instruments. Today they can be done using self-designed spectrographs and highly efficient CCD cameras, without the need for large financial investments.This book explains the basic principles of spectroscopy, including the fundamental optical constraints and all mathematical aspects needed to understand the working principles in detail. It covers the complete theoretical and practical design of standard and Echelle spectrographs. Readers are guided through all necessary calculations, enabling them to engage in spectrograph design. The book also examines data acquisition with CCD cameras and fiber optics, as well as the constraints of specific data reduction and possible sources of error. In closing it briefly highlights some main aspects of the research on massive stars and spectropolarimetry as an extension of spectroscopy. The book offers a comprehensive introduction to spectroscopy for students of physics and astronomy, as well as a valuable resource for amateur astronomers interested in learning the principles of spectroscopy and spectrograph design.

Dr. Thomas Eversberg is wireless electrician and astrophysicist. He investigated the winds of massive stars in Germany and Canada by using space and ground based astronomical facilities. Today he manages and supervises the development and design of new optical instruments and space optics for the German Space Agency.Dr. Klaus Vollmann is atmospheric physicist and worked on the time behavior of infrared detectors and models of the higher atmosphere by using space borne instruments. After many years as a financial engineer and risk controller in financial management he now works as technical engineer in machine building industry.Both are spectroscopists by education and astronomers by passion. They still build telescopes, develop optical instruments for their private astronomical observatory and publish in professional and amateur journals. They organize international research campaigns on stellar winds together with professional and amateur astronomers and bring both communities closer together.

Autoren/Hrsg.

Eversberg, Thomas

Vollmann, Klaus

Inhaltsverzeichnis

1;Preface;8
2;Contents;10
3;List of Figures;20
4;List of Tables;34
5;1 Prologue;36
5.1;A Short Story;36
5.2;1.1 Ulysses;37
6;2 Fundamentals of Standard Spectroscopy;43
6.1;A Short Story;43
6.2;2.1 The Law of Diffraction;43
6.3;2.2 On the Geometrical Optics of a Prism;44
6.4;2.3 Principles of Wave Optics;50
6.4.1;2.3.1 Interference Phenomena;51
6.4.2;2.3.2 The Huygens–Fresnel Principle;51
6.4.3;2.3.3 Fraunhofer Diffraction for a Slit and a Pinhole;53
6.4.4;2.3.4 Spectral Resolution and Resolving Power;62
6.5;2.4 The Prism Spectrograph;64
6.5.1;2.4.1 Properties of a Prism Spectrograph;65
6.5.2;2.4.2 The Angular and Linear Dispersion of a Prism;65
6.5.3;2.4.3 Wavelength Dependence of the Refraction Index: Sellmeier Equation;68
6.5.4;2.4.4 The Spectral Resolution of a Prism;69
6.6;2.5 The Grating Spectrograph;70
6.6.1;2.5.1 Fraunhofer Diffraction for a Grating;72
6.6.2;2.5.2 Higher Efficiency with a Blaze Angle;80
6.6.3;2.5.3 The Wavelength of the ``Blaze'' at Arbitrary Angle of Incidence;84
6.6.4;2.5.4 The Angular and Linear Dispersionof a Grating Spectrometer;85
6.6.5;2.5.5 The Maximum Resolving Power of a Grating;87
6.7;2.6 Collimator, Camera and Pixel Size;88
6.7.1;2.6.1 Reproduction Scale and Anamorphic Magnification Factor;88
6.7.2;2.6.2 The Necessity of a Collimator;92
6.7.3;2.6.3 The Spectral Resolution of a Spectrograph;95
6.7.4;2.6.4 Spectrometer Function: The Folding Integral;97
6.7.5;2.6.5 Broadening Processes and the System Function: Multiple Convolution;101
6.7.6;2.6.6 Shannon's Theorem or the Nyquist Criterion;106
6.7.6.1;The Message of Nyquist–Shannon: Sampling with the Cardinal Series;107
6.7.6.2;Consequences for Spectroscopy;109
6.7.6.3;Signal Band Limitations;110
6.7.7;2.6.7 Signal Sampling by Appropriate Interpolation;112
6.7.7.1;Pixel Sampling, Interpolation and Signal-to-Noise Ratio;113
7;3 Remarks About Dioptric Imaging Systems;118
7.1;A Short Story;118
7.2;3.1 Basic Remarks;118
7.3;3.2 Beam Calculation of an Optical System in the Paraxial Area;119
7.4;3.3 Paraxial Image Scale and Focal Length of a Lens System;122
7.5;3.4 The Focal Length of a Single Lens: The Lensmaker Equation;124
7.6;3.5 Monochromatic Seidel Aberrations;127
7.7;3.6 Chromatic Aberrations;133
7.8;3.7 The Calculation of Seidel Image Aberrations;138
7.8.1;3.7.1 The Calculation of the Seidel Sums;143
7.8.2;3.7.2 Discussion of the Different AberrationContributions;145
7.8.2.1;Seidel Coefficient I?: Spherical Aberration;146
7.8.2.2;Seidel Coefficient II?: Coma;147
7.8.2.3;Seidel Coefficient III? and IV?: Meridional and Sagittal Image Curvature;147
7.8.2.4;Seidel Coefficient V?: Distortion;150
7.9;3.8 The Seidel Sums and Their Interpretation;150
7.9.1;3.8.1 Average Image Curvature and Astigmatism;152
7.9.2;3.8.2 Example Calculation for a Simplet;154
7.10;3.9 The Impact of Field Curvature: A Simple Example;156
7.11;3.10 Permitted Deviations from Ideal Focus: The Blurring Circle;159
7.12;3.11 Estimation of the Imaging Performance by Ray-Tracing Methods;160
7.12.1;3.11.1 The Spot Diagram;162
7.12.2;3.11.2 Longitudinal and Transversal Aberrations;165
7.12.3;3.11.3 Field Aberrations;166
7.13;3.12 Possibilities for the Correction of Aberrations;167
7.13.1;3.12.1 Spherical Aberration;168
7.13.2;3.12.2 The Effects of Aperture Position;172
7.13.3;3.12.3 Removal of Petzval Field Curvature Through a Field Flattener;175
7.13.4;3.12.4 An Achromat Is Necessary;178
7.13.5;3.12.5 Example Considerations for a Commercial Spectrograph;182
7.14;3.13 Resume;185
7.15;Suggested Reading;187
8;4 Considerations About the Standard Spectrograph Layout;188
8.1;A Short Story;188
8.2;4.1 Basic Remarks and Requirements;188
8.2.1;4.1.1 Slit Width and Resolving Power;189
8.2.2;4.1.2 Remarks About the Optical Slit;191
8.2.3;4.1.3 Wavelength Calibration with an Artificial L195
8.2.4;4.1.4 The Design of Collimator and Camera Optics;197
8.2.5;4.1.5 Some words on the grating choice;199
8.2.6;4.1.6 Fixing the Total Angle;200
8.3;4.2 Project ``MESSY'' Maximum Efficiency Slit SpectroscopY for f/4 Telescopes;203
8.3.1;4.2.1 Calculating the Parameters of the Spectrograph;205
8.3.2;4.2.2 Optical and Mechanical Design;212
8.3.3;4.2.3 Telescope Guiding;213
8.3.4;4.2.4 Construction and First Results;215
8.3.5;4.2.5 Vignetting in a Lens System;219
8.4;Conclusion;223
8.5;Suggested Readings;224
9;5 Fundamentals of Echelle Spectroscopy;225
9.1;A Short Story;225
9.2;5.1 High Orders;225
9.3;5.2 The Echelle Spectrograph;228
9.4;5.3 The Echelle Grating and Its Dispersion;229
9.5;5.4 The Geometrical Extent of the Echelle Orders;231
9.6;5.5 Central Wavelength and Order Number;233
9.7;5.6 The Spectral Extent of the Echelle Orders;234
9.8;5.7 Tilted Lines;236
9.9;5.8 Curved Orders;241
9.10;5.9 Remarks About the Cross-Disperser;243
9.11;5.10 The Spectral Resolving Power of an Echelle Spectrometer;244
9.12;5.11 The Total Efficiency of the Echelle Spectrograph;248
9.13;5.12 Comparison Between Echelle and Standard Spectrographs;251
9.14;5.13 The Blaze Efficiency of an Echelle Grating;253
9.14.1;5.13.1 The Shadowing;255
9.15;Recommended Readings for Echelle Spectroscopy;259
10;6 Considerations for Designing an Echelle Spectrometer;260
10.1;A Short Story;260
10.2;6.1 General Comments on the Design;260
10.3;6.2 Requirements for the Optical Elements;266
10.3.1;6.2.1 Collimator;267
10.3.2;6.2.2 Camera;273
10.4;6.3 The Choice of the Echelle Grating;275
10.4.1;6.3.1 Effects of Line Density on the Spectrograph Design;276
10.4.2;6.3.2 Effects of the Angle of Incidence on the Order Length;278
10.4.3;6.3.3 The Influence of the Angle of Incidence on the Echelle Efficiency;279
10.5;6.4 The Choice of the Cross-Disperser;284
10.5.1;6.4.1 Grating;284
10.5.2;6.4.2 Prism;286
10.6;6.5 ``SimEchelle'': A Simple Echelle Simulation Program;288
10.7;6.6 Project ``Mini-Echelle'' an Echelle Spectrograph for f/10 Telescopes;289
10.7.1;6.6.1 The Limit of an Achromatic Lens as a Camera for the Mini-Echelle;294
10.7.2;6.6.2 Compensation of Longitudinal Chromatic Aberration by Camera Tilt;298
10.8;6.7 Projekt ``Research-Echelle'': First Tests;299
10.9;6.8 Specific Echelle Design Constraints;306
10.9.1;6.8.1 The ``White Pupil'' Concept;306
10.9.2;6.8.2 Data Reduction;307
10.9.3;6.8.3 Design Implications by Fiber Optics;308
10.10;6.9 Prospect;309
10.11;Recommended Readings for All Spectroscopy Chapters;310
11;7 Reflecting Spectrographs;311
11.1;A Short Story;311
11.2;7.1 Basic Design Considerations;311
11.2.1;7.1.1 Ebert-Fastie Configuration;312
11.2.2;7.1.2 Czerny-Turner Configuration;312
11.3;7.2 The Imaging Equation of a Spherical Mirror;314
11.4;7.3 Aberrations of a Concave Mirror;315
11.4.1;7.3.1 Spherical Aberration;316
11.4.1.1;Longitudinal Spherical Aberration;316
11.4.1.2;Transverse Spherical Aberration;320
11.4.1.3;The Circle of Least Confusion of a Spherical Mirror;321
11.4.1.4;An Example;321
11.5;7.4 Fermat's Principle;323
11.5.1;7.4.1 The Law of Reflection;324
11.5.2;7.4.2 Snell's Law of Refraction;326
11.6;7.5 Seidel Aberrations of a Single Refracting Surface;327
11.6.1;7.5.1 The Connection Between Wave Aberration and Longitudinal and Transverse Aberration;332
11.6.2;7.5.2 The Estimation of the Aberration Coefficients;335
11.6.2.1;Coefficient A0 of y;335
11.6.2.2;Coefficient A1 of y2;336
11.6.2.3;Coefficient A'1 of x2;337
11.6.2.4;Coefficient A2 of y3;337
11.6.2.5;Coefficient A'2 of x2y;338
11.6.2.6;Coefficient A3 of h4;338
11.6.2.7;The Meaning of the Coefficients A1 and A'1: Astigmatism;339
11.7;7.6 Calculation of the Czerny-Turner Spectrometer;341
11.8;7.7 Focusing Gratings;344
11.9;Suggested Readings;349
12;8 Practical Examples;350
12.1;A Short Story;350
12.2;8.1 From Unique Instruments to Mass Production;350
12.3;8.2 Littrow Systems;353
12.3.1;8.2.1 Keyhole Littrow: Good Data for Little Money;353
12.3.2;8.2.2 Mahlmann Littrow: Solid Mechanics;355
12.3.3;8.2.3 Lhires III: A Littrow for All;357
12.3.4;8.2.4 SPIRAL: A Littrow for Large Telescopes;359
12.4;8.3 Classical Systems;361
12.4.1;8.3.1 The Mice Mansion: A Classical Grating Spectrograph;362
12.4.2;8.3.2 Spectrashift: A Czerny–Turner for Exoplanets;363
12.4.3;8.3.3 Boller & Chivens: Work-Horse Spectrographs for Midsize Telescopes;365
12.4.4;8.3.4 Hectospec: Multi-Object Spectroscopy at the MMT;368
12.4.5;8.3.5 MODS: A Multi-Object Double Spectrograph for the LBT;370
12.4.6;8.3.6 COMICS: Ground Based Thermal IR Spectroscopy;374
12.5;8.4 Echelle Systems;375
12.5.1;8.4.1 Stober Echelle: A Physician on New Tracks;377
12.5.2;8.4.2 Feger Echelle: From Mechatronics to Optics;379
12.5.2.1;Feger I;379
12.5.2.2;Feger II;380
12.5.3;8.4.3 eShel: A Stable Off-the-Shelf Fiber Echelle;382
12.5.4;8.4.4 FEROS: An Echelle for Chile;385
12.5.5;8.4.5 HDS: Highest Resolution at the Nasmyth Focus;387
12.5.6;8.4.6 X-Shooter: 20,000 Å in a Single Shot;388
12.6;8.5 Spectrographs with Spherical Convex Gratings;392
12.6.1;8.5.1 FUSE: The Far Ultraviolet Spectroscopic Explorer;392
12.6.2;8.5.2 COS: The Cosmic Origins Spectrograph for HST;395
12.7;Suggested Readings;396
13;9 Image Slicer;397
13.1;A Short Story;397
13.2;9.1 Basic Remarks;397
13.3;9.2 The Bowen Slicer;399
13.4;9.3 Bowen–Walraven Slicer;402
13.5;9.4 FEROS: A Modified Bowen–Walraven Slicer;404
13.6;9.5 X-Shooter Mirror Slicer;406
13.7;9.6 The Waveguide;408
13.8;9.7 CAOS Low Cost Slicer;411
14;10 Some Remarks on CCD Detectors;415
14.1;A Short Story;415
14.2;10.1 High Quantum Efficiencies;415
14.3;10.2 Linear Response: The Gain;417
14.4;10.3 Noise;419
14.4.1;10.3.1 Photon Noise: The Number Is It;419
14.4.2;10.3.2 Dark Noise: Bad Vibrations;420
14.4.3;10.3.3 Read-Out Noise: Electronic Influences;423
14.4.4;10.3.4 Additional Noise: Pixel-to-Pixel Variations;424
14.5;10.4 The Combination Is Crucial;425
14.6;10.5 A Simple Sensor Model;427
14.7;10.6 Measuring the Read-Out Noise and the CCD Gain;428
14.8;10.7 The Signal-to-Noise Ratio and Detection Threshold;433
14.9;Suggested Readings;437
15;11 Remarks on Fiber Optics;438
15.1;A Short Story;438
15.2;11.1 Basic Remarks;438
15.3;11.2 A Few Words About Fiber Types;439
15.3.1;11.2.1 Multimode Fibers;439
15.3.2;11.2.2 Single Mode Fibers;440
15.4;11.3 Step-Index Fundamentals;440
15.5;11.4 Transmission and Attenuation;445
15.6;11.5 Focal-Ratio Degradation (FRD);446
15.7;11.6 Fiber Noise;450
15.8;11.7 Photometric Shift and Scrambling;454
15.9;11.8 Tapered Fibers;455
15.10;11.9 Lenses for the Telescope Link;457
15.10.1;11.9.1 Imaging the Star onto the Fiber Aperture;457
15.10.2;11.9.2 Imaging the Telescope Pupil onto the FiberAperture;459
15.11;11.10 Opto-Mechanical Coupling;462
15.12;11.11 Resume;464
15.13;Suggested Readings;465
16;12 Data Reduction;466
16.1;A Short Story;466
16.2;12.1 Open Tools for Reliable Results;466
16.3;12.2 LINUX and Windows;467
16.4;12.3 CCD Reduction;468
16.4.1;12.3.1 General Mathematical Considerations;469
16.4.2;12.3.2 The Bias Field;470
16.4.3;12.3.3 The Dark Field;470
16.4.4;12.3.4 Saving Time;471
16.4.5;12.3.5 The Flat Field;472
16.4.6;12.3.6 Why Flat Fielding;474
16.4.7;12.3.7 Collapsing the Spectrum;475
16.4.8;12.3.8 Flats for Echelle Spectroscopy;475
16.4.9;12.3.9 Remarks on the Response Function;480
16.5;12.4 The Data Reduction Recipe;481
16.6;12.5 Noise Contribution of Bias and Dark Fields;482
16.7;12.6 The Necessary Flat Field Quality;483
16.8;12.7 Cosmic Rays;485
16.9;12.8 A Quick Exposure Time Estimation;486
16.10;12.9 Wavelength Calibration;486
16.10.1;12.9.1 Standard Light Sources;486
16.10.2;12.9.2 Laser Frequency Combs;488
17;13 Measurement Errors and Statistics;491
17.1;A Short Story;491
17.2;13.1 Basic Remarks;491
17.3;13.2 Systematic Errors;492
17.4;13.3 Drift;493
17.5;13.4 Statistical Errors;494
17.5.1;13.4.1 The Standard Deviation;495
17.5.2;13.4.2 The Standard Deviation of the Average;496
17.5.3;13.4.3 The Average Error of the Function Value;496
17.6;13.5 Statistical Errors of Equivalent Widths;498
17.6.1;13.5.1 The Equivalent Width of Spectral Lines;498
17.6.2;13.5.2 The Error of the Equivalent Width;500
17.7;Suggested Readings;502
18;14 Massive Stars: Example Targets for Spectroscopy;503
18.1;A Short Story;503
18.2;14.1 Some Example Targets;503
18.3;14.2 Dots in the Sky;504
18.4;14.3 The Heavy Weights: Massive Stars;506
18.5;14.4 Winds That Sail on Starlight;511
18.6;14.5 The Velocity Law;512
18.7;14.6 Aspheric Geometries: Be Star Disks as Prototypes;513
18.8;14.7 O Stars: Extreme Radiators, Thin Winds and Rotating Shocks;524
18.8.1;14.7.1 Discrete Absorption Components and Co-rotating Interaction Regions;525
18.8.2;14.7.2 Turbulent Wind Clumps;528
18.9;14.8 Wolf–Rayet Stars: Massive, Small Hot Stars Below Thick Winds;531
18.10;14.9 Clumps as Wind Tracers;539
18.11;14.10 A Short Remark on Evolution;543
18.12;14.11 Dance of the Giants;544
18.13;14.12 So What…?;551
18.14;Suggested Readings;553
19;15 The Next Step: Polarization;555
19.1;A Short Story;555
19.2;15.1 Beyond Spectroscopy;555
19.3;15.2 Polarized Light in Astronomy;556
19.4;15.3 Description of Polarization with the Stokes Parameters;557
19.5;15.4 Properties of Stoke Parameters;559
19.6;15.5 The Mueller Calculus;560
19.7;15.6 The Retarder Matrix;561
19.8;15.7 The Polarizer Matrix;562
19.9;15.8 Spectropolarimetry;563
19.10;15.9 The William–Wehlau Spectropolarimeter;564
19.11;15.10 Polarimetric Investigations of Massive Stars;569
19.11.1;15.10.1 Interstellar Polarization;569
19.11.2;15.10.2 Intrinsic Linear Polarization;570
19.11.2.1;(A) Wavelength Dependence;570
19.11.2.2;(B) Time-Dependence;574
19.11.3;15.10.3 Intrinsic Circular Polarization;574
19.12;Suggested Readings;578
20;16 Epilogue: Small Telescopes Everywhere;579
20.1;A Short Story;579
20.2;16.1 Small versus Big;579
21;17 Acknowledgements;584
21.1;A Short Story;584
22;A The MIDAS Data Reduction;586
22.1;A Short Story;586
22.2;A.1 The MIDAS Environment;586
22.2.1;A.1.1 Nomenclatura;587
22.2.2;A.1.2 Start, Help and End;588
22.2.3;A.1.3 Image Import;588
22.2.4;A.1.4 The Display;591
22.2.5;A.1.5 Image Size Estimation;592
22.2.6;A.1.6 Image Statistics;592
22.2.7;A.1.7 Copies of the Original Image;593
22.2.8;A.1.8 Image Rotation;593
22.2.9;A.1.9 The MIDAS Descriptor;593
22.2.10;A.1.10 Look-Up Tables (LUT);594
22.2.11;A.1.11 Positioning the Graphic Window;594
22.3;A.2 Spectrum Extraction;595
22.3.1;A.2.1 AVERAGE/ROW;595
22.3.2;A.2.2 EXTRACT/AVERAGE;597
22.3.3;A.2.3 EXTRACT/LONG;599
22.4;A.3 Wavelength Calibration;600
22.4.1;A.3.1 Calibration with Two Absorption Lines;600
22.4.2;A.3.2 Many Spectral Absorption Lines;602
22.4.3;A.3.3 Prism Spectra;605
22.4.4;A.3.4 The Use of a Comparison Spectrum;606
22.4.5;A.3.5 Spectral Resolving Power;607
22.5;A.4 Rectification;608
22.6;A.5 Spectral Analysis;609
22.6.1;A.5.1 The Equivalent Width;609
22.6.2;A.5.2 Measuring the Signal-to-Noise Ratio;610
22.6.3;A.5.3 Spectral Co-adding;611
22.6.4;A.5.4 Window Texts;613
22.6.5;A.5.5 Exporting Reduced Spectra: Fits/ASCII/Postscript;614
22.6.6;A.5.6 Postscript;614
22.6.7;A.5.7 Printing;615
23;B Important Functions and Equations;616
23.1;B.1 The Bessel Function;616
23.2;B.2 The Poisson Distribution;617
23.3;B.3 The Fresnel Equations;619
23.4;B.4 The Spline Function;621
23.5;B.5 The Continuous Fourier Transform;625
23.5.1;B.5.1 Rules for the One-Dimensional Fourier Transform;625
23.5.2;B.5.2 Correspondences of the One Dimensional Fourier Transform;625
24;C Diffraction Indices of Various Glasses;626
25;D Transmissivity of Various Glasses;634
26;E Line Catalogues for Calibration Lamps;642
26.1;E.1 Line Catalogue Sources;642
26.2;E.2 Line Catalogue for the Glow Starter RELCO SC480;643
27;F Manufacturers and Distributors;658
27.1;F.1 Spectrographs;658
27.2;F.2 Fiber Optics;659
27.3;F.3 Optical Elements: Laboratory Material;659
27.4;Suggested Reading;660
27.5;A Short Story;660
28;Bibliography;662
29;Index;669