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Preface to the First Edition xvii

Preface to the Second Edition xxiii

1 Basic Imaging 1

1.2 Image Formation 2

1.2.1 Pinhole Imaging 2

1.2.2 Lens Cameras 4

1.2.3 Telescopes 6

1.3 Detectors 9

1.3.1 The Human Retina 9

1.3.2 Photographic Emulsions 11

1.3.3 Electronic Detectors 14

1.3.4 Linearity, Saturation, and Blooming 21

1.4 Sensor Geometry 21

1.4.1 Aspect Ratio 23

1.4.2 Pixel Count 24

1.5 Image Capture 25

1.5.1 Angular Field of View of a Detector 26

1.5.2 Sampling the Image 27

1.5.3 Angular Size of a Single Pixel 29

1.5.4 Matching Pixels to the Point-Spread Function 29

2 Counting Photons 33

2.1 What Is a Signal? 33

2.2 What Is Noise? 33

2.3 Signals and Noise 35

2.3.1 The Poisson and Gaussian Distributions 38

2.3.2 Collecting More Photons by Image Summing 39

2.3.3 Measuring Noise 40

2.3.4 Signals Become More Complicated 41

2.3.5 Unwanted Signals and More Sources of Noise 42

2.4 Signals and Noise in Images 43

2.4.1 Signal and Noise in a Raw Image 44

2.4.2 Signal and Noise in a Dark Frame 47

2.4.3 Signal and Noise in a Dark-Subtracted Image 47

2.4.4 The Effect of the Sky Background on Signal and Noise 49

2.4.5 Signal and Noise in Multiple Averaged Images 51

2.5 Signal and Noise Effects from Flat-Fielding 53

2.6 A Little Sermon on Signals and Noise 55

3 Digital Image Formats 57

3.1 File Format Basics 57

3.2 FITS: The Standard Format in Astronomy 59

3.3 Overview of FITS 59

3.4 The FITS Header 61

3.4.1 Mandatory Keywords 62

3.4.2 Array Value Keywords 63

3.4.3 Observation Keywords 64

3.4.4 Comment Keywords 65

3.4.5 Header Value Formats 65

3.5 The FITS Binary Data Array 66

3.6 The FITS Tailer 68

3.7 Nonconforming FITS Files 68

3.7.1 Nonconforming Headers 68

3.7.2 Nonconforming Data Arrays 68

3.7.3 Uncoordinated FITS Headers and Data Arrays 69

3.7.4 Reading Variant FITS Files 69

3.8 TIFF: The Standard in the Graphic Arts 70

3.9 BMP: Images for Windows 72

3.10 AVI: Interleaved Audio/Video from Webcams 73

3.11 JPEG: File Compression for the Internet 73

3.12 RAW, NEF, and CRW: Proprietary Raw Images 75

4 Imaging Tools 77

4.1 Sensors and Optics 77

4.1.1 Sensor Size and Field of View 77

4.1.2 Pixel Size and Resolution 81

4.1.3 Spectral Sensitivity 83

4.2 Optics for Imaging 84

4.3 Auxiliary Optics 89

4.3.1 Reducing Focal Length 89

4.3.2 Increasing Focal Length 90

4.3.3 Correcting Field Curvature 90

4.3.4 Correcting Coma 91

4.4 Finding Celestial Objects 91

4.4.1 Flip Mirrors, Finder Scopes, and Go-To Mounts 92

4.5 Telescope Mountings 93

4.5.1 Tracking Sensitivity 93

4.5.2 Rate Errors and Periodic Errors 94

4.5.3 Testing and Tuning a Clock Drive 95

4.5.4 Periodic Error Correction (PEC) Drives 97

4.6 Filters 97

4.6.1 Filter Types 98

4.6.2 Filters for H-Alpha and Other Emission Lines 100

4.6.3 Light Pollution Rejection (LPR) Filters 100

4.6.4 Blue-Block and Violet-Block Filters 102

4.7 Recognizing and Correcting Equipment Problems 102

4.7.1 Hot Spots 103

4.7.2 Field Flooding 104

4.7.3 Vignetting 106

4.7.4 Dust Donuts 107

4.8 Reaping the Benefits Ill

5 Imaging Techniques 113

5.1 Accurate Polar Alignment 113

5.2 Good Guiding 116

5.2.1 Off-Axis Guiding 116

5.2.2 Auxiliary Telescope Guiding 117

5.2.3 Software Virtual Guiding 117

5.3 Critical Focus 118

5.3.1 TheFocuser 119

5.3.2 Focus Techniques 119

5.3.3 Automated Focusing 121

5.4 Correct Exposure 121

5.5 Shooting Calibration Frames 123

5.5.1 Basic, Standard, and Advanced Calibration 123

5.5.2 Making Bias Frames 124

5.5.3 Making Dark Frames 124

5.5.4 Making Flat-Field Frames 125

5.5.5 Defect Mapping 128

5.6 Imaging with Digital SLR Cameras 128

5.7 Deep-Sky Imaging 130

5.7.1 Strategies for Deep-Sky Imaging 130

5.7.1.1 Digital Snapshots 130

5.7.1.2 Guided One-Shot Imaging 132

5.7.1.3 Guided and Unguided Track-and-Stack Imaging 132

5.7.2 Making Good Deep-Sky Images 134

5.7.3 Imaging Deep-Sky Targets 135

5.8 Lunar, Planetary, and Solar Imaging Techniques 141

5.8.1 Obtaining Excellent Images 142

5.8.2 Focal-Ratio Matching Optics 143

5.8.2.1 Field of View 145

5.8.3 Recording High-Resolution Images 146

5.8.4 Making High-Resolution Images 147

5.8.5 Solar System Targets 151

5.9 The Role of "Technique" 155

6 Image Calibration 157

6.1 What's in a CCD Image? 159

6.1.1 Photon Flux 159

6.1.2 Nonuniformity 161

6.1.3 Dark Current 162

6.1.4 Zero-Point Bias 163

6.1.5 Quantization 164

6.1.6 Calibration is Peeling the Image Onion 164

6.2 Calibration Frames 165

6.2.1 Bias Frames 165

6.2.1.1 Using a Single Bias Value 167

6.2.1.2 Bias with Drift-Subtraction 168

6.2.1.3 When to Make a Master Bias Frame 169

6.2.2 Dark Frames 170

6.2.2.1 "Image-Times-Five" Rule for Dark Frames 171

6.2.2.2 Thermal Frames 173

6.2.2.3 Standard and Scalable Dark Frames 174

6.2.2.4 Dark Frame Matching 176

6.2.2.5 Changing CCD Temperature 177

6.2.2.6 When to Use a Single Dark Value 178

6.2.2.7 Cosmic Ray Events 178

6.2.2.8 Electroluminescence 178

6.2.2.9 How to Make Master Dark Frames 179

6.2.3 Flat Frames 180

6.2.3.1 Four Types of Flat-Field Frames 184

6.2.3.2 How to Shoot Light-Box and Dome Flats 184

6.2.3.3 How to Shoot Twilight Flats 186

6.2.3.4 How to Shoot Sky Flats 186

6.3 Methods of Calibration 187

6.3.1 Basic Image Calibration 187

6.3.2 Standard Image Calibration 189

6.3.3 Advanced Image Calibration 191

6.4 The Calibrated Image 193

6.4.1 Photons, Dark Current, and Readout Noise 193

6.4.2 Noise from Calibration 196

6.4.3 Image Stacking 199

6.4.4 How to Spot Calibration Errors 199

6.4.4.1 Bias Drift 199

6.4.4.2 Changing CCD Temperature 201

6.4.4.3 Changing Optical Configuration 202

6.5 Defect Mapping and Correction 203

7 Image Analysis 205

7.1 Pixel Measurements 205

7.1.1 Pixel Coordinates 206

7.1.2 Pixel Value 207

7.2 Whole-Image Analysis 208

7.2.1 Image Statistics 208

7.2.1.1 Minimum Pixel Value 208

7.2.1.2 Maximum Pixel Value 208

7.2.1.3 Mean Pixel Value 209

7.2.1.4 Median Pixel Value 209

7.2.1.5 Standard Deviation 209

7.2.1.6 Low-Point and High-Point Pixel Values 210

7.3 The Image Histogram 210

7.4 Image Feature Analysis 212

7.4.1 Pixel Statistics 212

7.4.1.1 Defining a Region of Interest 212

7.4.1.2 Minimum Pixel Value 213

7.4.1.3 Maximum Pixel Value 214

7.4.1.4 Mean Pixel Value 214

7.4.1.5 Variance 214

7.4.1.6 Standard Deviation 214

7.4.1.7 Signal-to-Noise Ratio 215

7.4.1.8 Median Pixel Value 216

7.4.1.9 Mean of Median Half 216

7.5 Determining a Centroid 216

7.6 Distance on a CCD Image 219

7.7 Image Profiles 220

7.8 Astrometry 221

7.9 Photometry 221

7.9.1 Defining the Star Image 221

7.9.2 Photometric Image Profile 223

7.10 Spectroscopy 225

8 Measuring CCD Performance 227

8.1 Goals in CCD Testing 227

8.2 Basic CCD Testing 229

8.2.1 How to Make Basic CCD Test Images 229

8.2.2 Basic Test Analysis 229

8.2.2.1 Step 1: Mean and Standard Deviation in the Bias 230

8.2.2.2 Step 2: Mean and Standard Deviation of the Flats 230

8.2.2.3 Step 3: Measure the Dark Current 231

8.2.2.4 Step 4: Compute the Conversion Factor 231

8.2.2.5 Step 5: Compute the Readout Noise 232

8.2.2.6 Step 6: Compute the Dark Current 232

8.2.3 What Results to Expect 232

8.3 Advanced CCD Testing 234

8.3.1 Constructing a Low-Light Level Source 234

8.3.2 Setting the Low-Level Light Source for Use 238

8.3.3 How to Make Advanced CCD Test Images 238

8.3.3.1 Make the Bias Frame Set 239

8.3.3.2 Make the Skim Frame Set 239

8.3.3.3 Make the Flat Frame Set 239

8.3.3.4 Make the Dark Frame Set 240

8.3.4 Analyzing the Advanced Test Image Set 240

8.3.4.1 Check the Bias Frames for Noise and Interference 241

8.3.4.2 Charge Skimming Check 243

8.3.4.3 Plotting the Transfer Curve 244

8.3.4.4 Checking the Linearity of the CCD 247

8.3.4.5 Determining the Dark Current 247

8.3.4.6 Check the Uniformity of the CCD 248

9 Astrometry 249

9.1 Astrometric Catalogs and Coordinates 249

9.1.1 The Astrometric Dilemma 250

9.1.2 Astrometric Catalogs and Reference Frames 251

9.2 Astrometric Theory 252

9.2.1 Standard Coordinates 253

9.2.2 Plate Coordinates 254

9.2.3 Improved Plate Constants 257

9.2.4 Solving for Position 257

9.3 Practical Astrometry 258

9.3.1 CCD Images for Astrometry 258

9.3.2 Scanned Photographs for Astrometry 260

9.3.3 Making Astrometric Measurements 263

9.4 Applied Astrometry 264

9.4.1 Astrometry of Newly-Discovered Objects 264

9.4.2 Astrometry of Asteroids and Comets 265

9.4.3 Using Astrometry to Identify Objects 266

9.4.4 Image Scale and Orientation 266

9.4.5 Astrometry in Education 267

10 Photometry 271

10.1 Magnitudes: How Bright Is This Star? 271

10.1.1 Magnitudes Are Comparisons 272

10.1.2 Aperture Photometry 272

10.1.2.1 Summing the Star's Light 273

10.1.2.2 Subtracting Sky Background 274

10.1.2.3 Raw Instrumental Magnitude 275

10.1.2.4 Statistical Uncertainty 276

10.2 Putting Photometry to Work 278

10.3 Photometric Systems 279

10.3.1 From CCD Images to the Standard System 286

10.3.2 Atmospheric Extinction 286

10.3.3 Transformation to the UBV(RI) System 291

10.4 Photometrie Observing 292

10.4.1 Preparing to Observe 292

10.4.2 Differential Photometry 293

10.4.3 All-Sky Photometry 296

10.4.4 "Do-What-You-Can" Photometry 298

10.5 Desiderata for Photometry 300

10.6 Don't Be Afraid to Try! 301

11 Spectroscopy 303

11.1 What is Spectroscopy? 303

11.2 Spectra and Spectrographs 304

11.2.1 Prisms and Gratings 304

11.2.2 Practical Spectrographs 305

11.2.3 The Objective Prism Spectrograph 305

11.2.4 The Grating-Prism Spectrograph 307

11.2.5 The Slit Spectrograph 309

11.2.6 The Fiber-Fed Spectrograph 310

11.3 Properties of Spectrum Images 311

11.4 Extracting a Spectrum from an Image 313

11.4.1 Spectra from Objective Prism Images 314

11.4.2 Spectra from Slit Spectrographs 316

11.4.3 Spectra from Fiber-Fed Spectrographs 318

11.5 Spectrum Calibration and Analysis 319

12 Geometric Transforms 321

12.1 Translation 321

12.2 Rotation 325

12.3 Scaling 328

12.4 Practical Translation, Rotation, and Scaling 329

12.5 Flipping and Flopping 331

12.6 Cropping and Floating 332

12.7 Resampling 334

13 Point Operations 337

13.1 Point Operations: An Overview 337

13.2 Remapping Pixel Values 339

13.2.1 Isolating the Range 340

13.2.2 Transfer Functions 343

13.2.2.1 Linear Transfer Function 347

13.2.2.2 Gamma Transfer Function 349

13.2.2.3 The Logarithmic Transfer Function 350

13.2.2.4 The Gammalog Transfer Function 351

13.2.2.5 The Negative Transfer Function 352

13.2.2.6 The Sawtooth and Quantize Transfer Functions 353

13.3 Direct Specification of the Transfer Function 353

13.4 Direct Endpoint Specification 355

13.4.1 Stretch Scaling 356

13.4.2 Nonlinear Stretch Scaling 357

13.5 Histogram Endpoint Specification 357

13.6 Histogram Specification 358

13.6.1 Histogram Equalization 362

13.6.2 Gaussian Histogram Shaping 362

13.6.3 Exponential Histogram Shaping 363

14 Linear Operators 365

14.1 Convolution in One Dimension 365

14.1.1 One-Dimensional Examples 369

14.1.2 Multiple Convolutions with One-Dimensional Kernels 371

14.2 Convolution in Two Dimensions 372

14.2.1 Convolution using Kernels 373

14.2.2 Properties of the Convolution Kernel 375

14.2.3 Kernels as Spatial Filters 377

14.2.3.1 Smoothing Kernels (Low-Pass Filters) 378

14.2.3.2 Sharpening Kernels (High-Pass Filters) 381

14.2.4 Edge-Detection and Gradient Kernels 385

14.2.4.1 Bas-Relief Operators 385

14.2.4.2 Sobel, Kirsch, and Prewitt Operators 386

14.2.4.3 Line-Detection Operators 387

14.2.4.4 The Laplacian Operator 388

14.3 Convolution by Unsharp Mask 388

14.4 Generated Kernels for Unsharp Masking 390

14.4.1 The Boxcar Unsharp Mask 390

14.4.2 The Triangular Unsharp Mask 391

14.4.3 The Gaussian Unsharp Mask 392

14.4.4 The Power-Law Unsharp Mask 393

14.4.5 Other Unsharp Masks 394

15 Non-Linear Operators 397

15.1 Rank Operators 398

15.1.1 Minimum and Maximum 398

15.1.2 The Median Operator 399

15.1.3 The Rank-Order Operator 401

15.1.4 The Multiplicative Rank Processes 403

15.2 Non-Linear Enhancement Operators 405

15.2.1 The Extreme Value Operator 406

15.2.2 Local Adaptive Sharpening 408

15.3 Noise Filters 410

15.4 Morphological Operators 412

15.4.1 Isophote Lines 413

15.4.2 Frei and Chen Operators 415

15.4.3 The Skeleton Operator 418

15.4.4 Dilation, Erosion, Opening, and Closing Operators 419

15.5 The Topographic Operator 419

15.6 Digital Development 422

16 Image Operations 425

16.1 Image Math 425

16.1.1 Addition 425

16.1.2 Subtraction 426

16.1.3 Multiplication 428

16.1.4 Division 429

16.1.5 Absolute Difference 429

16.1.6 Merge 430

16.1.7 Average 432

16.2 Image Ranking 433

16.2.1 Median Ranking 433

16.2.2 Minimum Ranking 435

16.2.3 Maximum Ranking 435

16.3 Calibrating Images 436

16.3.1 Dark Subtraction 436

16.3.2 Flat-Fielding 438

16.3.3 Basic Calibration 440

16.3.4 Standard Calibration 441

16.3.5 Advanced Calibration 441

16.4 Image Registration 442

16.4.1 Registration with Translation Only 443

16.4.2 Registration with Translation, Rotation, and Scaling 444

16.5 Blinking Images 447

16.6 Track-and-Stack Image Summing and Averaging 447

17 Images in Frequency Space 453

17.1 Exploring Frequency Space 453

17.1.1 Spatial Frequency 453

17.1.2 The Frequency Spectrum 454

17.1.3 Sinusoid Basics 455

17.2 Fourier Theory 456

17.2.1 Periodic Functions: The Fourier Series 456

17.2.2 Nonperiodic Functions: The Fourier Integral 458

17.2.3 Properties of the Fourier Transform 462

17.2.4 Convolution via Fourier Transform 464

17.2.5 Parseval's Theorem 466

17.2.6 The Discrete Fourier Series 466

17.2.7 The Fast Fourier Transform 469

17.3 Image Processing using the Fourier Transform 470

17.3.1 Butterworth Spatial Frequency Filters 472

17.3.2 Feature Masking in Frequency Space 474

17.3.3 Feature Enhancement in Frequency Space 475

18 Wavelets 477

18.1 The Wavelet Transform 477

18.1.1 The Wavelet Function 479

18.1.2 Properties of the A Trous Wavelet Transform 479

18.1.3 Spatial Filtering with the Wavelet Transform 483

18.1.4 Spatial Filtering with Star Images 485

18.2 Wavelet Noise Filters 485

18.2.1 When Is an Image Feature Significant? 486

18.2.2 Transforming Poisson Noise to a Gaussian Deviate 488

18.2.3 Measuring Noise in Images 489

18.2.4 Rejecting Noise and Retaining Significant Features 491

18.2.5 The Solution: An Iterative Wavelet Noise Filter 492

18.3 Wavelet K-Sigma Filtering 494

18.4 Using Wavelets 497

19 Deconvolution 499

19.1 The Inverse Convolution Problem 500

19.2 Image Estimation by Iteration 501

19.3 Van Cittert Image Estimation 506

19.4 Richardson-Lucy Image Estimation 507

19.5 Using Deconvolution with Astronomical Images 509

20 Building Color Images 513

20.1 Human Color Vision 514

20.1.1 The Trichromatic Basis of Color Vision 514

20.1.2 Luminance and Chrominance 514

20.1.3 Reproducing Color 516

20.2 Celestial Light 516

20.2.1 Starlight and Continuous Spectra 519

20.2.2 Nebulae and Emission Spectra 521

20.2.3 The Challenge of Celestial Color Imaging 522

20.3 Red/Green/Blue Tri-Color Imaging 523

20.3.1 Step 1: Capture Filtered Images 525

20.3.2 Step 2: Correct the Filtered Images 528

20.3.2.1 Subtract the Skylight Background 528

20.3.2.2 Color Balance with G2V Stars 531

20.3.3 Create the Color Image 534

20.3.4 Summary: White-Balance Using G2V Stars 535

20.4 Using Field Stars for White Balance 536

20.4.1 Summary: White-Balance Using Field Stars 537

20.5 Color Images from Filter-Matrix Cameras 537

20.6 Color Space: Geometric Interpretations of Color 539

20.6.1 RGB Color Space 539

20.6.2 HSL Color Space 541

20.6.3 Lab Color Space 544

20.7 Luminance/RGB (LRGB) Color Imaging 545

20.7.1 Creating an Artificial Luminance Image 547

20.7.2 Enhancing the Luminance Image 547

20.7.3 Creating LRGB Images 547

20.8 Practical RGB and LRGB Color Imaging 549

20.8.1 Selecting Filters 549

20.8.2 Shooting RGB and LRGB Images 550

20.8.3 Trade-offs: RGB versus LRGB 552

20.9 LLRGB (Multi-Luminance) Imaging 552

20.10 Extended-Range and Narrowband Color 553

20.11 Color Imaging with CMY Filters 554

20.11.1 Selecting CMY Filters 555

20.11.2 CMY versus RGB Imaging 555

20.12 The Subjective Side of Color Images 555

21 Processing Color Images 557

21.1 Properties of Color Images 557

21.1 Calibrate to Remove Dark Current and Vignetting 564

21.1.1 Calibrating Bayer-Array Color Images 564

21.1.2 Calibration for Digital Cameras 565

21.1 Stacking to Enhance Signal-To-Noise Ratio 567

21.2 Making Great Images with a Digital Camera 570

21.3 Color Images in Color Spaces 572

21.3.1 RGB Color Space 573

21.0.1 HSL Color Space 574

21.0.1 Lab Color Space 576

21.1 Color in Color Images 576

21.1.1 White Balance 576

21.1 Luminance Enhancement of Color Images 578

Appendix A Glossary 581

Appendix B Resources 597

B.l CCD Imaging 597

B.l.l CCD Imaging Books 597

B.2 Astronomical Optics 598

B.2.1 Telescope Design 598

B.2.2 Telescopes and Vision 599

B.3 Astrometry 599

B.3.1 Astrometry Books and Articles 599

B.3.2 Astrometry Software 600

B.3.3 Astrometry Reference Catalogs 601

B.4 Photometry 601

B.4.1 Photometry Books and Articles 601

B.4.2 Photometric Data: Extinction Stars and Standard Stars 602

B.4.3 Photometry Organizations 602

B.4.4 Photometric Filters 603

B.4.5 Photometry Software 603

B.5 Spectroscopy 603

B.5.1 Spectroscopy Books and Articles 603

B.5.2 Spectroscopic Catalogs 604

B.6 Image Processing 604

B.6.1 Image Processing Books: General 604

B.6.2 Image Processing: Science Applications 605

B.6.3 Image Processing: Image Restoration 606

B.6.4 Image Processing and the Fourier Transform 607

B.6.5 Image Processing and Wavelets 607

B.6.6 Image Processing Algorithms 607

B.6.7 Image Processing Software 608

B.7 Color Imaging 610

B.7.1 Color Imaging Books 610

Appendix C Tutorials 613

C.l Basic Skills 616

C.2 Calibration 621

C.3 Image Evaluation 627

C.4 Astrometry 631

C.5 Photometry 635

C.5.1 Single-Star Photometry 636

C.5.2 Single-Image Photometry 638

C.5.3 Multiple-Image Photometry 639

C.6 Spectroscopy 642

C.7 Image Enhancement 644

C.7.1 Brightness Scaling 644

C.7.2 Histogram Shaping 647

C.7.3 Convolution Filtering 649

C.7.4 Unsharp Masking 650

C.7.5 Deconvolution 650

C.7.6 Wavelet Spatial Filtering 653

C.7.7 Morphological Processing 654

C.8 Fast Fourier Transform 655

C.9 Multiple Image Processing 659

C.9.1 Track and Stack 659

C.9.2 Multi-Image Processing 663

C.9.3 Multi-Image Alignment 663

C. 10 Image Registration and Blinking 663

C. 11 Deep-Sky Images 665

C. 12 Planetary Images 670

C.l3 Color Images 672

C.l4 Conclusion 674

Index 675

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Digital Camera and Digital Photography

Digital Camera and Digital Photography

Compared to film cameras, digital cameras are easy to use, fun and extremely versatile. Every day there’s more features being designed. Whether you have the cheapest model or a high end model, digital cameras can do an endless number of things. Let’s look at how to get the most out of your digital camera.

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