Spectroscopic Instrumentation (eBook)

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.

Preface 8
Contents 10
List of Figures 20
List of Tables 34
1 Prologue 36
A Short Story 36
1.1 Ulysses 37
2 Fundamentals of Standard Spectroscopy 43
A Short Story 43
2.1 The Law of Diffraction 43
2.2 On the Geometrical Optics of a Prism 44
2.3 Principles of Wave Optics 50
2.3.1 Interference Phenomena 51
2.3.2 The Huygens–Fresnel Principle 51
2.3.3 Fraunhofer Diffraction for a Slit and a Pinhole 53
2.3.4 Spectral Resolution and Resolving Power 62
2.4 The Prism Spectrograph 64
2.4.1 Properties of a Prism Spectrograph 65
2.4.2 The Angular and Linear Dispersion of a Prism 65
2.4.3 Wavelength Dependence of the Refraction Index: Sellmeier Equation 68
2.4.4 The Spectral Resolution of a Prism 69
2.5 The Grating Spectrograph 70
2.5.1 Fraunhofer Diffraction for a Grating 72
2.5.2 Higher Efficiency with a Blaze Angle 80
2.5.3 The Wavelength of the ``Blaze'' at Arbitrary Angle of Incidence 84
2.5.4 The Angular and Linear Dispersionof a Grating Spectrometer 85
2.5.5 The Maximum Resolving Power of a Grating 87
2.6 Collimator, Camera and Pixel Size 88
2.6.1 Reproduction Scale and Anamorphic Magnification Factor 88
2.6.2 The Necessity of a Collimator 92
2.6.3 The Spectral Resolution of a Spectrograph 95
2.6.4 Spectrometer Function: The Folding Integral 97
2.6.5 Broadening Processes and the System Function: Multiple Convolution 101
2.6.6 Shannon's Theorem or the Nyquist Criterion 106
The Message of Nyquist–Shannon: Sampling with the Cardinal Series 107
Consequences for Spectroscopy 109
Signal Band Limitations 110
2.6.7 Signal Sampling by Appropriate Interpolation 112
Pixel Sampling, Interpolation and Signal-to-Noise Ratio 113
3 Remarks About Dioptric Imaging Systems 118
A Short Story 118
3.1 Basic Remarks 118
3.2 Beam Calculation of an Optical System in the Paraxial Area 119
3.3 Paraxial Image Scale and Focal Length of a Lens System 122
3.4 The Focal Length of a Single Lens: The Lensmaker Equation 124
3.5 Monochromatic Seidel Aberrations 127
3.6 Chromatic Aberrations 133
3.7 The Calculation of Seidel Image Aberrations 138
3.7.1 The Calculation of the Seidel Sums 143
3.7.2 Discussion of the Different AberrationContributions 145
Seidel Coefficient I?: Spherical Aberration 146
Seidel Coefficient II?: Coma 147
Seidel Coefficient III? and IV?: Meridional and Sagittal Image Curvature 147
Seidel Coefficient V?: Distortion 150
3.8 The Seidel Sums and Their Interpretation 150
3.8.1 Average Image Curvature and Astigmatism 152
3.8.2 Example Calculation for a Simplet 154
3.9 The Impact of Field Curvature: A Simple Example 156
3.10 Permitted Deviations from Ideal Focus: The Blurring Circle 159
3.11 Estimation of the Imaging Performance by Ray-Tracing Methods 160
3.11.1 The Spot Diagram 162
3.11.2 Longitudinal and Transversal Aberrations 165
3.11.3 Field Aberrations 166
3.12 Possibilities for the Correction of Aberrations 167
3.12.1 Spherical Aberration 168
3.12.2 The Effects of Aperture Position 172
3.12.3 Removal of Petzval Field Curvature Through a Field Flattener 175
3.12.4 An Achromat Is Necessary 178
3.12.5 Example Considerations for a Commercial Spectrograph 182
3.13 Resume 185
Suggested Reading 187
4 Considerations About the Standard Spectrograph Layout 188
A Short Story 188
4.1 Basic Remarks and Requirements 188
4.1.1 Slit Width and Resolving Power 189
4.1.2 Remarks About the Optical Slit 191
4.1.3 Wavelength Calibration with an Artificial Lamp 195
4.1.4 The Design of Collimator and Camera Optics 197
4.1.5 Some words on the grating choice 199
4.1.6 Fixing the Total Angle 200
4.2 Project ``MESSY'' Maximum Efficiency Slit SpectroscopY for f/4 Telescopes 203
4.2.1 Calculating the Parameters of the Spectrograph 205
4.2.2 Optical and Mechanical Design 212
4.2.3 Telescope Guiding 213
4.2.4 Construction and First Results 215
4.2.5 Vignetting in a Lens System 219
Conclusion 223
Suggested Readings 224
5 Fundamentals of Echelle Spectroscopy 225
A Short Story 225
5.1 High Orders 225
5.2 The Echelle Spectrograph 228
5.3 The Echelle Grating and Its Dispersion 229
5.4 The Geometrical Extent of the Echelle Orders 231
5.5 Central Wavelength and Order Number 233
5.6 The Spectral Extent of the Echelle Orders 234
5.7 Tilted Lines 236
5.8 Curved Orders 241
5.9 Remarks About the Cross-Disperser 243
5.10 The Spectral Resolving Power of an Echelle Spectrometer 244
5.11 The Total Efficiency of the Echelle Spectrograph 248
5.12 Comparison Between Echelle and Standard Spectrographs 251
5.13 The Blaze Efficiency of an Echelle Grating 253
5.13.1 The Shadowing 255
Recommended Readings for Echelle Spectroscopy 259
6 Considerations for Designing an Echelle Spectrometer 260
A Short Story 260
6.1 General Comments on the Design 260
6.2 Requirements for the Optical Elements 266
6.2.1 Collimator 267
6.2.2 Camera 273
6.3 The Choice of the Echelle Grating 275
6.3.1 Effects of Line Density on the Spectrograph Design 276
6.3.2 Effects of the Angle of Incidence on the Order Length 278
6.3.3 The Influence of the Angle of Incidence on the Echelle Efficiency 279
6.4 The Choice of the Cross-Disperser 284
6.4.1 Grating 284
6.4.2 Prism 286
6.5 ``SimEchelle'': A Simple Echelle Simulation Program 288
6.6 Project ``Mini-Echelle'' an Echelle Spectrograph for f/10 Telescopes 289
6.6.1 The Limit of an Achromatic Lens as a Camera for the Mini-Echelle 294
6.6.2 Compensation of Longitudinal Chromatic Aberration by Camera Tilt 298
6.7 Projekt ``Research-Echelle'': First Tests 299
6.8 Specific Echelle Design Constraints 306
6.8.1 The ``White Pupil'' Concept 306
6.8.2 Data Reduction 307
6.8.3 Design Implications by Fiber Optics 308
6.9 Prospect 309
Recommended Readings for All Spectroscopy Chapters 310
7 Reflecting Spectrographs 311
A Short Story 311
7.1 Basic Design Considerations 311
7.1.1 Ebert-Fastie Configuration 312
7.1.2 Czerny-Turner Configuration 312
7.2 The Imaging Equation of a Spherical Mirror 314
7.3 Aberrations of a Concave Mirror 315
7.3.1 Spherical Aberration 316
Longitudinal Spherical Aberration 316
Transverse Spherical Aberration 320
The Circle of Least Confusion of a Spherical Mirror 321
An Example 321
7.4 Fermat's Principle 323
7.4.1 The Law of Reflection 324
7.4.2 Snell's Law of Refraction 326
7.5 Seidel Aberrations of a Single Refracting Surface 327
7.5.1 The Connection Between Wave Aberration and Longitudinal and Transverse Aberration 332
7.5.2 The Estimation of the Aberration Coefficients 335
Coefficient A0 of y 335
Coefficient A1 of y2 336
Coefficient A'1 of x2 337
Coefficient A2 of y3 337
Coefficient A'2 of x2y 338
Coefficient A3 of h4 338
The Meaning of the Coefficients A1 and A'1: Astigmatism 339
7.6 Calculation of the Czerny-Turner Spectrometer 341
7.7 Focusing Gratings 344
Suggested Readings 349
8 Practical Examples 350
A Short Story 350
8.1 From Unique Instruments to Mass Production 350
8.2 Littrow Systems 353
8.2.1 Keyhole Littrow: Good Data for Little Money 353
8.2.2 Mahlmann Littrow: Solid Mechanics 355
8.2.3 Lhires III: A Littrow for All 357
8.2.4 SPIRAL: A Littrow for Large Telescopes 359
8.3 Classical Systems 361
8.3.1 The Mice Mansion: A Classical Grating Spectrograph 362
8.3.2 Spectrashift: A Czerny–Turner for Exoplanets 363
8.3.3 Boller & Chivens: Work-Horse Spectrographs for Midsize Telescopes
8.3.4 Hectospec: Multi-Object Spectroscopy at the MMT 368
8.3.5 MODS: A Multi-Object Double Spectrograph for the LBT 370
8.3.6 COMICS: Ground Based Thermal IR Spectroscopy 374
8.4 Echelle Systems 375
8.4.1 Stober Echelle: A Physician on New Tracks 377
8.4.2 Feger Echelle: From Mechatronics to Optics 379
Feger I 379
Feger II 380
8.4.3 eShel: A Stable Off-the-Shelf Fiber Echelle 382
8.4.4 FEROS: An Echelle for Chile 385
8.4.5 HDS: Highest Resolution at the Nasmyth Focus 387
8.4.6 X-Shooter: 20,000 Å in a Single Shot 388
8.5 Spectrographs with Spherical Convex Gratings 392
8.5.1 FUSE: The Far Ultraviolet Spectroscopic Explorer 392
8.5.2 COS: The Cosmic Origins Spectrograph for HST 395
Suggested Readings 396
9 Image Slicer 397
A Short Story 397
9.1 Basic Remarks 397
9.2 The Bowen Slicer 399
9.3 Bowen–Walraven Slicer 402
9.4 FEROS: A Modified Bowen–Walraven Slicer 404
9.5 X-Shooter Mirror Slicer 406
9.6 The Waveguide 408
9.7 CAOS Low Cost Slicer 411
10 Some Remarks on CCD Detectors 415
A Short Story 415
10.1 High Quantum Efficiencies 415
10.2 Linear Response: The Gain 417
10.3 Noise 419
10.3.1 Photon Noise: The Number Is It 419
10.3.2 Dark Noise: Bad Vibrations 420
10.3.3 Read-Out Noise: Electronic Influences 423
10.3.4 Additional Noise: Pixel-to-Pixel Variations 424
10.4 The Combination Is Crucial 425
10.5 A Simple Sensor Model 427
10.6 Measuring the Read-Out Noise and the CCD Gain 428
10.7 The Signal-to-Noise Ratio and Detection Threshold 433
Suggested Readings 437
11 Remarks on Fiber Optics 438
A Short Story 438
11.1 Basic Remarks 438
11.2 A Few Words About Fiber Types 439
11.2.1 Multimode Fibers 439
11.2.2 Single Mode Fibers 440
11.3 Step-Index Fundamentals 440
11.4 Transmission and Attenuation 445
11.5 Focal-Ratio Degradation (FRD) 446
11.6 Fiber Noise 450
11.7 Photometric Shift and Scrambling 454
11.8 Tapered Fibers 455
11.9 Lenses for the Telescope Link 457
11.9.1 Imaging the Star onto the Fiber Aperture 457
11.9.2 Imaging the Telescope Pupil onto the FiberAperture 459
11.10 Opto-Mechanical Coupling 462
11.11 Resume 464
Suggested Readings 465
12 Data Reduction 466
A Short Story 466
12.1 Open Tools for Reliable Results 466
12.2 LINUX and Windows 467
12.3 CCD Reduction 468
12.3.1 General Mathematical Considerations 469
12.3.2 The Bias Field 470
12.3.3 The Dark Field 470
12.3.4 Saving Time 471
12.3.5 The Flat Field 472
12.3.6 Why Flat Fielding 474
12.3.7 Collapsing the Spectrum 475
12.3.8 Flats for Echelle Spectroscopy 475
12.3.9 Remarks on the Response Function 480
12.4 The Data Reduction Recipe 481
12.5 Noise Contribution of Bias and Dark Fields 482
12.6 The Necessary Flat Field Quality 483
12.7 Cosmic Rays 485
12.8 A Quick Exposure Time Estimation 486
12.9 Wavelength Calibration 486
12.9.1 Standard Light Sources 486
12.9.2 Laser Frequency Combs 488
13 Measurement Errors and Statistics 491
A Short Story 491
13.1 Basic Remarks 491
13.2 Systematic Errors 492
13.3 Drift 493
13.4 Statistical Errors 494
13.4.1 The Standard Deviation 495
13.4.2 The Standard Deviation of the Average 496
13.4.3 The Average Error of the Function Value 496
13.5 Statistical Errors of Equivalent Widths 498
13.5.1 The Equivalent Width of Spectral Lines 498
13.5.2 The Error of the Equivalent Width 500
Suggested Readings 502
14 Massive Stars: Example Targets for Spectroscopy 503
A Short Story 503
14.1 Some Example Targets 503
14.2 Dots in the Sky 504
14.3 The Heavy Weights: Massive Stars 506
14.4 Winds That Sail on Starlight 511
14.5 The Velocity Law 512
14.6 Aspheric Geometries: Be Star Disks as Prototypes 513
14.7 O Stars: Extreme Radiators, Thin Winds and Rotating Shocks 524
14.7.1 Discrete Absorption Components and Co-rotating Interaction Regions 525
14.7.2 Turbulent Wind Clumps 528
14.8 Wolf–Rayet Stars: Massive, Small Hot Stars Below Thick Winds 531
14.9 Clumps as Wind Tracers 539
14.10 A Short Remark on Evolution 543
14.11 Dance of the Giants 544
14.12 So What…? 551
Suggested Readings 553
15 The Next Step: Polarization 555
A Short Story 555
15.1 Beyond Spectroscopy 555
15.2 Polarized Light in Astronomy 556
15.3 Description of Polarization with the Stokes Parameters 557
15.4 Properties of Stoke Parameters 559
15.5 The Mueller Calculus 560
15.6 The Retarder Matrix 561
15.7 The Polarizer Matrix 562
15.8 Spectropolarimetry 563
15.9 The William–Wehlau Spectropolarimeter 564
15.10 Polarimetric Investigations of Massive Stars 569
15.10.1 Interstellar Polarization 569
15.10.2 Intrinsic Linear Polarization 570
(A) Wavelength Dependence 570
(B) Time-Dependence 574
15.10.3 Intrinsic Circular Polarization 574
Suggested Readings 578
16 Epilogue: Small Telescopes Everywhere 579
A Short Story 579
16.1 Small versus Big 579
17 Acknowledgements 584
A Short Story 584
A The MIDAS Data Reduction 586
A Short Story 586
A.1 The MIDAS Environment 586
A.1.1 Nomenclatura 587
A.1.2 Start, Help and End 588
A.1.3 Image Import 588
A.1.4 The Display 591
A.1.5 Image Size Estimation 592
A.1.6 Image Statistics 592
A.1.7 Copies of the Original Image 593
A.1.8 Image Rotation 593
A.1.9 The MIDAS Descriptor 593
A.1.10 Look-Up Tables (LUT) 594
A.1.11 Positioning the Graphic Window 594
A.2 Spectrum Extraction 595
A.2.1 AVERAGE/ROW 595
A.2.2 EXTRACT/AVERAGE 597
A.2.3 EXTRACT/LONG 599
A.3 Wavelength Calibration 600
A.3.1 Calibration with Two Absorption Lines 600
A.3.2 Many Spectral Absorption Lines 602
A.3.3 Prism Spectra 605
A.3.4 The Use of a Comparison Spectrum 606
A.3.5 Spectral Resolving Power 607
A.4 Rectification 608
A.5 Spectral Analysis 609
A.5.1 The Equivalent Width 609
A.5.2 Measuring the Signal-to-Noise Ratio 610
A.5.3 Spectral Co-adding 611
A.5.4 Window Texts 613
A.5.5 Exporting Reduced Spectra: Fits/ASCII/Postscript 614
A.5.6 Postscript 614
A.5.7 Printing 615
B Important Functions and Equations 616
B.1 The Bessel Function 616
B.2 The Poisson Distribution 617
B.3 The Fresnel Equations 619
B.4 The Spline Function 621
B.5 The Continuous Fourier Transform 625
B.5.1 Rules for the One-Dimensional Fourier Transform 625
B.5.2 Correspondences of the One Dimensional Fourier Transform 625
C Diffraction Indices of Various Glasses 626
D Transmissivity of Various Glasses 634
E Line Catalogues for Calibration Lamps 642
E.1 Line Catalogue Sources 642
E.2 Line Catalogue for the Glow Starter RELCO SC480 643
F Manufacturers and Distributors 658
F.1 Spectrographs 658
F.2 Fiber Optics 659
F.3 Optical Elements: Laboratory Material 659
Suggested Reading 660
A Short Story 660
Bibliography 662
Index 669