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Optical Testing
To order this item outside the United Kingdom, please contact us.
Optical Testing
  • Author: Joseph M. Geary
  • Publisher: Willmann-Bell
  • Hardback
  • Pages: 604 pages
  • Iillustrations: 660
  • Dimensions: 6 by 9 inches
  • First published: 2014
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Optical Testing
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Optical Testing no WLBOT £ 69.95 £ 8.00 24 hours
Outline
Optical Testing — A Practical Introduction for Scientists, Engineers, Optical Designers, Students and Optical Workshop Personnel is written for those working in optics with a practical introduction to optical testing methodologies, instrumentation, and procedures, and assist in the development of their professional careers.

No optical component or system should be built without a prior specification which defines base parameters, tolerances, and system performance. Optical testing is done to verify whether the specification and performance criteria have been met. Customers need to make sure that they get what they pay for. Providers are bound both by moral and contractual obligations to provide what the customer ordered at the price quoted. Thus, the need for optical testing is incumbent upon both sides of the transaction, and both should have sufficient testing capabilities to validate the resulting optical product.

The book begins with the measurement of camera lenses using classical optical bench testing techniques: Collimators and the T-Bar Nodal Slide. Lens measurements include the determination of lens effective focal length (EFL), axial color, and F-number. Aberration measurements in the image plane include spherical aberration, coma, field curvature, astigmatism and distortion.

Aberrations
Aberrations determine the amount of detail that can be observed in the image. High quality imagery is of little value unless sufficient power or energy reaches the sensor. This is where basic radiometric concepts are introduced, particularly as applied to lens behavior. Power-related measurements such as lens transmission, relative illumination falloff, and veiling glare are discussed. Image formation is accomplished via glass and/or mirrored surfaces that are curved (spherical for the most part). Consequently, it is important to be able to measure the basic parameters of refractive index and radius of curvature. Depending on the application, test objects observed with the imaging system could either be finite size resolution targets or point 'star' sources.

The aberrations measured on an optical bench are recorded as image plane coordinates, i.e., axial and lateral displacements relative to a reference location. But aberrations can also be described in the exit pupil in terms of wavefronts. Hence the book also explores aberrations as described in the pupil and how pupil aberrations are connected to the point spread function. Then the phenomenon of interference is introduced (with a practical application involving the measurement of optical windows).

The specific property carrying information about pupil aberration is the optical path difference (OPD) between a reference wavefront and the aberrated wavefront. Interferometry is the methodology used to measure OPD. Variations in OPD are presented to the metrologist as fringe patterns which must be reduced and analyzed to extract aberration content.

The reality of pupil aberrations is visualized next through the auspices of the point diffraction interferometer, with an industry workhorse, the Fizeau interferometer, described and its operating principle discussed in some detail.

Using the Fizeau as our principle metrology instrument we examine a broad range of test configurations for measuring a wide variety of optical components and systems — mirror flats, spheres, aspheres, and Cassegrain telescopes. The main asphere of interest is the parabolic mirror (both on- and off-axis). The latter also includes an in-depth discussion of the null lens. Test configurations for refractors such as singlets, and multi-element camera systems are considered. Testing non-rotationally symmetric optics such as rectangular aperture cylindrical lenses and mirrors is reviewed. Alternative interferometer types such as the Twyman-Green are also examined. Finally, an exploration is made of the Fizeau interferometer as an imaging system in the context of a null lens test.

Once fringe patterns have been acquired they need to be reduced to provide salient information such as peak-to-valley, rms wavefront, and aberration content. Both manual and automatic techniques are discussed. Interferogram analysis via phase shifting is introduced. Shop tests of optical surfaces via the use of localized fringe techniques (test plates) are reviewed. A reflection from a thin parallel glass plate broaches the topic of multiple ray interference. Next, numerous indirect aberration measurement techniques are explored. Included are the classical knife-edge test, lateral shear interferometry, the Hartmann and Shack-Hartmann test. The use of a radiometric technique known as the axial intensity (or Strehl) scan is also explored.

The effect aberrations have on image quality of finite scenes can best be described by use of the modulation transfer functions (MTF). The basic MTF concept is introduced and expanded with the help of Linear Optics and Fourier Optics analytic approaches. Various MTF measurement methods are examined, including slit and knife-edge scan techniques. Also discussed is a radiometric approach known as pupil auto-correlation. For telescopes such as the Cassegrain the MTF is also influenced by light scatter from mirror surfaces due to micro-roughness. Consequently, the measurements of surface roughness by both direct and indirect methods are discussed.

Up to this point the book has concentrated on making measurements on optical systems using light based instrumentation. It concludes with a discussion of direct measurements on light fields themselves. Included are discussions on wavefront sensors, polarization and coherence, and broadband and spectral radiometrics.

Table of Contents
Preface . . . . . . . . . .. . . . . . . . . . . . . . . . . . xv

Chapter 1 Optical Testing . . . . . . . . . . . . . . . . . . .1
  1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 1
  1.2 Working Definition . . . . . . . . . . . . . . . . . . . 1
  1.3 Hands-On . . . . . . . . . . . . . . . . . . . . . . . . 1
  1.4 Measurement Error . . . . . . . . . . . . . . . . . . . .2
    1.4.1 Accuracy and Repeatability. . . . . . . . . . . . . .2
    1.4.2 Calculating Error . . . . . . . . . . . . . . . . . .2
    1.4.3 Calibration . . . . . . . . . . . . . . . . . . . . .3
  1.5 The Lesson of HST . . . . . . . . . . . . . . . . . . . .3
  1.6 The Journey . . . . . . . . . . . . . . . . . . . . . . .4
  1.7 Instructor Note . . . . . . . . . . . . . . . . . . . . .8

Part I Optical Bench Testing . . . . . . . . . . . . . . . . . 9

Chapter 2 Geometric Optics Review. . . . . . . . . . . . . . . 11
  2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 11
  2.2 Paraxial Ray-Trace Equations (PRTE) . . . . . . . . . . .11
  2.3 Optical Power. . . . . . . . . . . . . . . . . . . . . . 13
  2.3.1 Power of Single Optical Surface . . . . . . . . . . . .13
  2.3.2 Power of Two-Component System . . . . . . . . . . . . .15
  2.4 Optical Power and Effective Focal Length . . . . . . . . 16
  2.5 Gaussian Lens Formula . . . . . . . . . . . . . . . . . .17
  2.6 Magnification. . . . . . . . . . . . . . . . . . . . . . 17
  2.7 Stops and Pupils. . . . . . . . . . . . . . . . . . . . .18
  2.8 F-number . . . . . . . . . . . . . . . . . . . . . . . . 19
  2.9 Marginal and Chief Rays . . . . . . . . . . . . . . . . .20
  2.10 Homework . . . . . . . . . . . . . . . . . . . . . . . .21

Chapter 3 Collimators . . . . . . . . . . . . . . . . . . . . .23
  3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 23
  3.2 Collimator Structures . . . . . . . . . . . . . . . . . .23
  3.3 Collimator Light Sources. . . . . . . . . . . . . . . . .26
  3.4 Setting up and Aligning a Collimator . . . . . . . . . . 30
    3.4.1 Alignment Process. . . . . . . . . . . . . . . . . . 30
    3.4.2 Establishing Collimation: Autocollimation Procedure .32
  3.5 Alternative Techniques . . . . . . . . . . . . . . . . . 34
    3.5.1 Beam Diameter Versus Distance. . . . . . . . . . . . 34
    3.5.2 Shear plate . . . . . . . . . . . . . . . . . . . . .35
  3.6 Aligning a Multi-element Lens to a Collimator. . . . . . 36
  3.7 Homework . . . . . . . . . . . . . . . . . . . . . . . . 38

Chapter 4 EFL Measurements . . . . . . . . . . . . . . . . . . 41
  4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 41
  4.2 Nodal Points. . . . . . . . . . . . . . . . . . . . . . .41
  4.3 T-Bar Nodal Slide (TBNS) Description . . . . . . . . . . 42
  4.4 Measuring EFL via Nodal Method . . . . . . . . . . . . . 43
  4.5 T-Bar Nodal Slide Calibration . . . . . . . . . . . . . .43
  4.6 Measuring EFL via Lateral Magnification . . . . . . . . .45
  4.7 Measuring EFL (λ) — Axial Color . . . . . . . . . . . . .46
  4.8 Measuring the Entrance Pupil and F-number . . . . . . . .47
  4.9 Measuring EFL Change with Temperature . . . . . . . . . .48
  4.10 Some Thoughts on Measurement. . . . . . . . . . . . . . 49

Chapter 5 Aberrations Part I. . . . . . . . . . . . . . . . . .51
  5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 51
  5.2 Positional Aberrations: Field Curvature and Distortion . 51
  5.3 Measuring Positional Aberrations on TBNS . . . . . . . . 51
    5.3.1 Measuring Field Curvature . . . . . . . . . . . . . .51
    5.3.2 Measuring Distortion. . . . . . . . . . . . . . . . .55
  5.4 Aberrations Affecting Quality of "Point Image" . . . . . 57
    5.4.1 Spherical Aberration . . . . . . . . . . . . . . . . 57
    5.4.2 Coma . . . . . . . . . . . . . . . . . . . . . . . . 58
    5.4.3 Astigmatism. . . . . . . . . . . . . . . . . . . . . 58
  5.5 Linear Hartmann Screen and Ray-Fan Plots . . . . . . . . 59
  5.6 Measuring the “Point” Degrading Aberrations on TBNS . . .62
    5.6.1 Measuring Spherical Aberration . . . . . . . . . . . 62
      5.6.1.1 Annular Zone Method . . . . . . . . . . . . . . .62
      5.6.1.2 Minimum Blur Method . . . . . . . . . . . . . . .63
      5.6.1.3 Linear Hartmann Screen . . . . . . . . . . . . . 63
      5.6.1.4 Axial Intensity Method . . . . . . . . . . . . . 65
    5.6.2 Coma . . . . . . . . . . . . . . . . . . . . . . . . 65
    5.6.3 Astigmatism. . . . . . . . . . . . . . . . . . . . . 66
  5.7 Homework . . . . . . . . . . . . . . . . . . . . . . . . 67

Chapter 6 Refractive Index . . . . . . . . . . . . . . . . . . 69
  6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 69
  6.2 Glass Properties . . . . . . . . . . . . . . . . . . . . 69
    6.2.1 Refractive Index . . . . . . . . . . . . . . . . . . 69
    6.2.2 Dispersion . . . . . . . . . . . . . . . . . . . . . 69
    6.2.3 Glass Chart . . . . . . . . . . . . . . . . . . . . .73
    6.2.4 Partial Dispersion . . . . . . . . . . . . . . . . . 74
  6.3 Measuring Refractive Index. . . . . . . . . . . . . . . .74
    6.3.1 Microscope Method. . . . . . . . . . . . . . . . . . 74
    6.3.2 Critical Angle . . . . . . . . . . . . . . . . . . . 78
    6.3.3 Brewster’s Angle . . . . . . . . . . . . . . . . . . 80
    6.3.4 Prism Refractometer . . . . . . . . . . . . . . . . .82
      6.3.4.1 Governing Equation. . . . . . . . . . . . . . . .82
      6.3.4.2 Procedure for Making n(λ) Measurements . . . . . 84
  6.4 Dispersion . . . . . . . . . . . . . . . . . . . . . . . 87
  6.5 Homework . . . . . . . . . . . . . . . . . . . . . . . . 88

Chapter 7 Radius of Curvature . . . . . . . . . . . . . . . . .89
  7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 89
  7.2 Surface Sagitta ("SAG") . . . . . . . . . . . . . . . . .89
    7.2.1 General Spheric Expansion . . . . . . . . . . . . . .89
    7.2.2 Surface Sag . . . . . . . . . . . . . . . . . . . . .90
  7.3 Measuring Radius of Curvature . . . . . . . . . . . . . .90
    7.3.1 Eyeball Estimate . . . . . . . . . . . . . . . . . . 90
    7.3.2 Via Microscope . . . . . . . . . . . . . . . . . . . 91
    7.3.3 Via Interferometer . . . . . . . . . . . . . . . . . 92
    7.3.4 Test Plates . . . . . . . . . . . . . . . . . . . . .94
    7.3.5 Sag and the Spherometer . . . . . . . . . . . . . . .94
  7.4 Derivation of Ball Radius Correction . . . . . . . . . . 96
  7.5 Measuring RoC of an Asphere. . . . . . . . . . . . . . . 99
  7.6 Homework . . . . . . . . . . . . . . . . . . . . . . . . 100

Chapter 8 Image Resolution . . . . . . . . . . . . . . . . . . 101
  8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 101
  8.2 Air Force Resolution Target . . . . . . . . . . . . . . .101
  8.3 Aerial Resolution Measured on TBNS . . . . . . . . . . . 103
    8.3.1 Aerial Resolution on Best Focal Surface. . . . . . . 104
    8.3.2 Aerial Resolution on Flat Observation Surface. . . . 104
  8.4 Recorded Resolution on Flat Formats . . . . . . . . . . .105
  8.5 Tangential and Radial Corrections. . . . . . . . . . . . 106
  8.6 Area Weighted Average Resolution (AWAR) . . . . . . . . .110
  8.7 Sensor Example: Photographic Film . . . . . . . . . . . .110
    8.7.1 Film Basics . . . . . . . . . . . . . . . . . . . . .112
    8.7.2 Lens Resolution Test on Film . . . . . . . . . . . . 114
  8.8 Homework . . . . . . . . . . . . . . . . . . . . . . . . 116

Chapter 9 Radiometry and Lenses . . . . . . . . . . . . . . . .117
  9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 117
  9.2 Radiometry Basics . . . . . . . . . . . . . . . . . . . .117
    9.2.1 Intensity . . . . . . . . . . . . . . . . . . . . . .117
    9.2.2 Radiance . . . . . . . . . . . . . . . . . . . . . . 118
    9.2.3 Lambertian Radiator . . . . . . . . . . . . . . . . .119
    9.2.4 Power through a Lens . . . . . . . . . . . . . . . . 120
    9.2.5 Image Irradiance . . . . . . . . . . . . . . . . . . 120
  9.3 Image Irradiance and Lens F-number . . . . . . . . . . . 121
  9.4 Diffusers. . . . . . . . . . . . . . . . . . . . . . . . 123
    9.4.1 Plate Diffusers . . . . . . . . . . . . . . . . . . .123
    9.4.2 Integrating Spheres . . . . . . . . . . . . . . . . .123
  9.5 Lens Transmission Measurements. . . . . . . . . . . . . .124
    9.5.1 How to Measure Transmission . . . . . . . . . . . . .124
    9.5.2 Spectral Transmission: Double-Pass Method . . . . . .126
  9.6 Relative Illumination Falloff (RIF) . . . . . . . . . . .129
    9.6.1 Power Through Tilted and Shifted Apertures . . . . . 129
    9.6.2 Lenses and RIF . . . . . . . . . . . . . . . . . . . 129
    9.6.3 Measuring RIF on TBNS. . . . . . . . . . . . . . . . 130
  9.7 Veiling Glare . . . . . . . . . . . . . . . . . . . . . .133
    9.7.1 Sources of Veiling Glare . . . . . . . . . . . . . . 133
    9.7.2 Measuring Veiling Glare . . . . . . . . . . . . . . .133
  9.8 Homework . . . . . . . . . . . . . . . . . . . . . . . . 134

Chapter 10 Star Tests . . . . . . . . . . . . . . . . . . . . .137
  10.1 Introduction . . . . . . . . . . . . . . . . . . . . . .137
  10.2 The PSF . . . . . . . . . . . . . . . . . . . . . . . . 137
  10.3 Physical Translation of Sampling Aperture. . . . . . . .139
    10.3.1 Profile Measurements . . . . . . . . . . . . . . . .139
    10.3.2 LSF Measurement . . . . . . . . . . . . . . . . . . 143
    10.3.3 Knife-Edge Distribution (KED) . . . . . . . . . . . 143
  10.4 Sampling Aperture Arrays (CCD) . . . . . . . . . . . . .145
  10.5 Scans and Convolution . . . . . . . . . . . . . . . . . 146
  10.6 Axial PSF Scans. . . . . . . . . . . . . . . . . . . . .151
  10.7 Radial Energy Distribution (RED). . . . . . . . . . . . 153
  10.8 Star Image Resolution . . . . . . . . . . . . . . . . . 153
  10.9 Homework . . . . . . . . . . . . . . . . . . . . . . . .155

Part II Pupil Aberrations and Interference. . . . . . . . . . .157

Chapter 11 Aberrations Part II . . . . . . . . . . . . . . . . 159
  11.1 Introduction . . . . . . . . . . . . . . . . . . . . . .159
  11.2 Description of a Wavefront . . . . . . . . . . . . . . .159
  11.3 Interaction of Wavefronts with Optical Systems . . . . .160
  11.4 Wavefront Description. . . . . . . . . . . . . . . . . .161
  11.5 Image Plane and Exit Pupil Aberrations Relationship. . .166
  11.6 Defocus . . . . . . . . . . . . . . . . . . . . . . . . 168
    11.6.1 Derivation via Sag Equation . . . . . . . . . . . . 168
    11.6.2 Difference between W020 and Wd. . . . . . . . . . . 169
    11.6.3 Defocus and Minimum Blur . . . . . . . . . . . . . .171
  11.7 Wavefronts and Diffraction . . . . . . . . . . . . . . .171
  11.8 Homework . . . . . . . . . . . . . . . . . . . . . . . .172

Chapter 12 Interference and Optical Windows . . . . . . . . . .175
  12.1 Introduction . . . . . . . . . . . . . . . . . . . . . .175
  12.2 General Interference Equation . . . . . . . . . . . . . 175
  12.3 Fringe Contrast. . . . . . . . . . . . . . . . . . . . .179
  12.4 Interference of Tilted Beams . . . . . . . . . . . . . .179
  12.5 Window Wedge . . . . . . . . . . . . . . . . . . . . . .181
  12.6 Effect of Window Wedge on Image . . . . . . . . . . . . 185
  12.7 Non-Linear Windows. . . . . . . . . . . . . . . . . . . 186
  12.8 Homework . . . . . . . . . . . . . . . . . . . . . . . .186

Chapter 13 Visualizing Pupil Aberrations . . . . . . . . . . . 189
  13.1 Introduction . . . . . . . . . . . . . . . . . . . . . .189
  13.2 Optical Windows and Entrance Pupil . . . . . . . . . . .189
    13.2.1 Fringe Contours due to Window Reflections . . . . . 189
    13.2.2 Window Single-Pass Wavefront . . . . . . . . . . . .190
    13.2.3 Window Wavefront and Imaging . . . . . . . . . . . .192
  13.3 Exit Pupil Aberrations and the Point Diffraction .. . . 194
    13.3.1 PDI Structure . . . . . . . . . . . . . . . . . . . 194
    13.3.2 Operational Principle. . . . . . . . . . . . .. . . 195
    13.3.3 PDI System . . . . . . . . . . . . . . . . . . . .  195
  13.4 PDI Reference and Test-Beam Relationship . . . . .. . . 197
    13.4.1 Pinhole Size . . . . . . . . . . . . . . . . . . . .197
    13.4.2 PDI Transmission and Metal Film Thickness . . . . . 198

Chapter 14 The Fizeau Interferometer. . . . . . . . . . . . . .203
  14.1 Introduction . . . . . . . . . . . . . . . . . . . . . .203
  14.2 The Fizeau Interferometer . . . . . . . . . . . . . . . 204
    14.2.1 Basic Layout . . . . . . . . . . . . . . . . . . . .204
    14.2.2 Align and View Modes . . . . . . . . . . . . . . . .204
    14.2.3 Test Optic Imaging . . . . . . . . . . . . . . . . .205
    14.2.4 The Transmission Flat . . . . . . . . . . . . . . . 206
    14.2.5 Wavefront versus Optical Surface. . . . . . . . . . 207
    14.2.6 Fringe Contrast . . . . . . . . . . . . . . . . . . 208
  14.3 Sensors in the Observation Plane. . . . . . . . . . . . 209
  14.4 Factory Fizeau . . . . . . . . . . . . . . . . . . . . .209
  14.5 Practical Concerns . . . . . . . . . . . . . . . . . . .211
    14.5.1 Mechanical and Acoustical Vibration . . . . . . . . 212
    14.5.2 Air Currents . . . . . . . . . . . . . . . . . . . .212
    14.5.3 Mounting . . . . . . . . . . . . . . . . . . . . . .212
    14.5.4 Transmission Flat Costs. . . . . . . . . . . . . . .213

Part III Interferometer Test Configurations . . . . . . . . . .215

Chapter 15 Test Configurations I . . . . . . . . . . . . . . . 217
  15.1 Introduction . . . . . . . . . . . . . . . . . . . . . .217
  15.2 The Null Fringe . . . . . . . . . . . . . . . . . . . . 217
  15.3 Testing Flats. . . . . . . . . . . . . . . . . . . . . .217
    15.3.1 Fringe Order and Piston. . . . . . . . . . . . . . .218
    15.3.2 Hill or Valley? . . . . . . . . . . . . . . . . . . 221
    15.3.3 Determining Radius of Curvature . . . . . . . . . . 223
  15.4 The Reference or Retro Flat. . . . . . . . . . . . . . .224
  15.5 Window Testing in Cavity Mode. . . . . . . . . . . . . .224
  15.6 Testing Spherical Surfaces. . . . . . . . . . . . . . . 226
    15.6.1 The Transmission Sphere . . . . . . . . . . . . . . 226
    15.6.2 Concave Spheres . . . . . . . . . . . . . . . . . . 226
    15.6.3 The Retro Sphere. . . . . . . . . . . . . . . . . . 228
    15.6.4 Convex Spheres . . . . . . . . . . . . . . . . . . .228
    15.6.5 Radius of Curvature Determination. . . . . . . . . .229
  15.7 The Test Point . . . . . . . . . . . . . . . . . . . . .229
  15.8 Homework . . . . . . . . . . . . . . . . . . . . . . . .229

Chapter 16 Test Configurations II . . . . . . . . . . . . . . .231
  16.1 Introduction . . . . . . . . . . . . . . . . . . . . . .231
  16.2 Refractors and Dispersion . . . . . . . . . . . . . . . 231
  16.3 Afocal Systems . . . . . . . . . . . . . . . . . . . . .232
  16.4 Testing Lenses . . . . . . . . . . . . . . . . . . . . .234
    16.4.1 Object at Infinity: Photographic Lenses . . . . . . 234
      16.4.1.1 Multi-Element . . . . . . . . . . . . . . . . . 234
      16.4.1.2 Testing Singlets and Achromats . . . . . . . . .235
    16.4.2 Testing Finite Conjugate Lenses . . . . . . . . . . 237
  16.5 Testing Lenses Off-Axis . . . . . . . . . . . . . . . . 238
  16.6 Telescopes . . . . . . . . . . . . . . . . . . . . . . .239
  16.7 Retrace Error (Ray Mapping Error). . . . . . . . . . . .240
  16.8 Homework . . . . . . . . . . . . . . . . . . . . . . . .243

Chapter 17 Test Configurations IIIA . . . . . . . . . . . . . .245
  17.1 Introduction . . . . . . . . . . . . . . . . . . . . . .245
  17.2 Basics of Aspheric Surfaces. . . . . . . . . . . . . . .246
  17.3 Departure from Sphere. . . . . . . . . . . . . . . . . .248
  17.4 Surface Normals. . . . . . . . . . . . . . . . . . . . .249
  17.5 W040 versus W040N . . . . . . . . . . . . . . . . . . . 251
    17.5.1 Spherical Aberration Generated by a Parabolic Mirror251
    17.5.2 Axial and Angular Distribution . . . . . . . . . . .252
  17.6 The Null Lens . . . . . . . . . . . . . . . . . . . . . 252
    17.6.1 The Offner Null Lens . . . . . . . . . . . . . . . .253
    17.6.2 Physical Embodiment of an Offner Null Lens . . . . .254
    17.6.3 Testing Parabolic Mirror at the Focal Point . . . . 255
  17.7 Homework . . . . . . . . . . . . . . . . . . . . . . . .257

Chapter 18 Test Configurations IIIB . . . . . . . . . . . . . .259
  18.1 Introduction . . . . . . . . . . . . . . . . . . . . . .259
  18.2 Null Lens Test of an OAP . . . . . . . . . . . . . . . .259
  18.3 Alignment . . . . . . . . . . . . . . . . . . . . . . . 260
  18.4 Test Pallet. . . . . . . . . . . . . . . . . . . . . . .260
  18.5 Coarse Alignment Steps. . . . . . . . . . . . . . . . . 261
    18.5.1 Coarse Interferometer Alignment . . . . . . . . . . 264
    18.5.2 Fine Alignment of OAP. . . . . . . . . . . . . . . .268
  18.6 Image Distortion . . . . . . . . . . . . . . . . . . . .270
  18.7 Homework . . . . . . . . . . . . . . . . . . . . . . . .270

Chapter 19 Test Configurations IV. . . . . . . . . . . . . . . 271
  19.1 Introduction . . . . . . . . . . . . . . . . . . . . . .271
  19.2 Cylindrical Optics . . . . . . . . . . . . . . . . . . .272
    19.2.1 Fiber Optic Reference (FOR) . . . . . . . . . . . . 272
    19.2.2 Cylindrical Lenses . . . . . . . . . . . . . . . . .272
    19.2.3 FOR Operating Principle. . . . . . . . . . . . . . .273
    19.2.4 Cylindrical Mirrors . . . . . . . . . . . . . . . . 275
  19.3 Convex Compound Mirrors . . . . . . . . . . . . . . . . 276
  19.4 Free Electron Laser Grazer . . . . . . . . . . . . . . .276
    19.4.1 X-Ray Mandrels . . . . . . . . . . . . . . . . . . .278
  19.5 Concave Compound Mirrors (Wolter Telescopes) . . . . . .282
  19.6 Homework . . . . . . . . . . . . . . . . . . . . . . . .283

Chapter 20 Other Interferometers for Optical Testing. . . . . .285
  20.1 Introduction . . . . . . . . . . . . . . . . . . . . . .285
  20.2 Twyman-Green Interferometer . . . . . . . . . . . . . . 285
    20.2.1 Internal Arrangement. . . . . . . . . . . . . . . . 285
    20.2.2 Quality of Internal Components . . . . . . . . . . .287
    20.2.3 LUPI Twyman-Green Interferometer . . . . . . . . . .288
    20.2.4 The Insides of a Commercial (Boxed) TGI. . . . . . .289
    20.2.5 TGI Test Configurations . . . . . . . . . . . . . . 289
      20.2.5.1 Testing Very Small Lenses with TGI . . . . . . .289
    20.2.6 The MIC-1 . . . . . . . . . . . . . . . . . . . . . 291
  20.3 Shack Cube Interferometer . . . . . . . . . . . . . . . 293
  20.4 Point Diffraction Interferometer (PDI) . . . . . . . . .296
  20.5 Koster’s Prism Interferometer (KPI) . . . . . . . . . . 296
  20.6 Homework . . . . . . . . . . . . . . . . . . . . . . . .299

Chapter 21 Interferometer as an Imaging System. . . . . . . . .301
  21.1 Introduction . . . . . . . . . . . . . . . . . . . . . .301
  21.2 Building the Fizeau Model. . . . . . . . . . . . . . . .302
  21.3 An Interferometer/Null Lens/Parabolic Mirror Model . . .303
  21.4 Imaging Model. . . . . . . . . . . . . . . . . . . . . .304
  21.5 Revised Double-Pass Model . . . . . . . . . . . . . . . 306
  21.6 Interferometer Imaging . . . . . . . . . . . . . . . . .307
    21.6.1 Retrace Error . . . . . . . . . . . . . . . . . . . 307
    21.6.2 Distortion . . . . . . . . . . . . . . . . . . . . .307
  21.7 Interferometer/Null Lens/OAP System . . . . . . . . . . 308
  21.8 An Empirical Test . . . . . . . . . . . . . . . . . . . 309

Part IV Collecting and Analyzing Fringe Data . . . . . . . . . 313

Chapter 22 Fringe Analysis . . . . . . . . . . . . . . . . . . 315
  22.1 Introduction . . . . . . . . . . . . . . . . . . . . . .315
  22.2 Peak-to-Valley, Average, Variance, and RMS . . . . . . .315
  22.3 OPD Profiles . . . . . . . . . . . . . . . . . . . . . .318
  22.4 Full Pupil Variance and RMS . . . . . . . . . . . . . . 321
    22.4.1 Average Volumes under a Mountain. . . . . . . . . . 321
    22.4.2 Average Volumes under an OPD Mountain . . . . . . . 322
    22.4.3 Calculation Example . . . . . . . . . . . . . . . . 322
  22.5 Strehl Ratio . . . . . . . . . . . . . . . . . . . . . .324
    22.5.1 Definition. . . . . . . . . . . . . . . . . . . . . 324
    22.5.2 Relationship to Variance . . . . . . . . . . . . . .325
    22.5.3 Numerical Example . . . . . . . . . . . . . . . . . 326
    22.5.4 Axial Location of δs . . . . . . . . . . . . . . . .326
    22.5.5 Shape of OPD Plot at δds. . . . . . . . . . . . . . 327
  22.6 Homework . . . . . . . . . . . . . . . . . . . . . . . .327

Chapter 23 Fringe Analysis II . . . . . . . . . . . . . . . . .329
  23.1 Introduction . . . . . . . . . . . . . . . . . . . . . .329
  23.2 Inputting Data . . . . . . . . . . . . . . . . . . . . .329
    23.2.1 Fringe Following . . . . . . . . . . . . . . . . . .329
    23.2.2 Phase Shift Interferometry (PSI) . . . . . . . . . .332
    23.2.3 Discontinuities. . . . . . . . . . . . . . . . . . .335
  23.3 Fitting Data using Polynomials . . . . . . . . . . . . .337
    23.3.1 Example using Fourier Series . . . . . . . . . . .  337
    23.3.2 Zernike Polynomials . . . . . . . . . . . . . . . . 337
  23.4 Fitting Interferometric Data using Zernikes . . . . . . 340
    23.4.1 Qualitative Explanation . . . . . . . . . . . . . . 340
    23.4.2 Quantitative Explanation . . . . . . . . . . . . .  341
  23.5 Sample Analysis. . . . . . . . . . . . . . . . . . . .  342
  23.6 Calculating Seidel Magnitudes from the Zernikes. . . .  344
  23.7 Obscured, and Non-Circular Apertures . . . . . . . . .  344
  23.8 Instantaneous PSI. . . . . . . . . . . . . . . . . . .  347

Chapter 24 Test Plates and Multiple Beam Interference . . . .  349
  24.1 Introduction . . . . . . . . . . . . . . . . . . . . . .349
  24.2 Optical Testing and Localized Fringes . . . . . . . . . 349
    24.2.1 Understanding Localized Fringes . . . . . . . . . . 349
    24.2.2 Local Irradiance and Fringe Spacing. . . . . . . . .350
    24.2.3 Optical Contact . . . . . . . . . . . . . . . . . . 353
    24.2.4 Test Plates . . . . . . . . . . . . . . . . . . . . 354
  24.3 Interference between Multiple Rays . . . . . . . . . . .355
    24.3.1 Optical Path and Phase Changes . . . . . . . . . . .355
    24.3.2 Reflection and Transmission Amplitudes at Interface 357
    24.3.3 Stokes Relations . . . . . . . . . . . . . . . . . .359
    24.3.4 Final Form for ER . . . . . . . . . . . . . . . . . 360
    24.3.5 Reflected Irradiance. . . . . . . . . . . . . . . . 361
  24.4 Homework . . . . . . . . . . . . . . . . . . . . . . . .362

Part V Indirect Test Methods . . . . . . . . . . . . . . . . . 363

Chapter 25 Foucault Knife-Edge Test I . . . . . . . . . . . . .365
  25.1 Introduction . . . . . . . . . . . . . . . . . . . . . .365
  25.2 Foucault Knife-Edge Test: Basic Description . . . . . . 365
  25.3 Relating the Parameters . . . . . . . . . . . . . . . . 366
    25.3.1 Example . . . . . . . . . . . . . . . . . . . . . . 367
  25.4 The Knife-Edge and Spherical Aberration . . . . . . . . 369
  25.5 Rotationally Symmetric Optic and Knife-Edge. . . . . . .372
  25.6 Asymmetric Aberrations . . . . . . . . . . . . . . . . .376
  25.7 Ronchi Test . . . . . . . . . . . . . . . . . . . . . . 377

Chapter 26 Foucault Knife-Edge Test II . . . . . . . . . . . . 379
  26.1 Introduction . . . . . . . . . . . . . . . . . . . . . .379
  26.2 Departure from Sphere . . . . . . . . . . . . . . . . . 379
  26.3 Departure from Parabola . . . . . . . . . . . . . . . . 380
  26.4 Participatory Example/Problem . . . . . . . . . . . . . 381
    26.4.1 Finding the Slope Profile. . . . . . . . . . . . . .381
    26.4.2 Finding the DFP Profile. . . . . . . . . . . . . . .381
      26.4.2.1 Stacking Local Tilts. . . . . . . . . . . . . . 382
      26.4.2.2 Stacking Local Sticks . . . . . . . . . . . . . 383
      26.4.2.3 Adding Up Areas. . . . . . . . . . . . . . . . .384
  26.5 Homework . . . . . . . . . . . . . . . . . . . . . . . .385

Chapter 27 Lateral Shear Techniques . . . . . . . . . . . . . .387
  27.1 Introduction . . . . . . . . . . . . . . . . . . . . . .387
  27.2 Principle of Pupil Shear . . . . . . . . . . . . . . . .388
  27.3 Defocus: 1-D Math Analysis . . . . . . . . . . . . . . .388
  27.4 Diffraction Gratings . . . . . . . . . . . . . . . . . .391
  27.5 Pupil Shear via Grating . . . . . . . . . . . . . . . . 393
  27.6 Ronchi Test as Lateral Shear . . . . . . . . . . . . . .394
    27.6.1 Moiré . . . . . . . . . . . . . . . . . . . . . . . 395
    27.6.2 Orders Generated for a Focused Beam on a Ronchi . . 397
    27.6.3 Discussion . . . . . . . . . . . . . . . . . . . . .399
  27.7 Homework . . . . . . . . . . . . . . . . . . . . . . . .400

Chapter 28 Hartmann Tests . . . . . . . . . . . . . . . . . . .401
  28.1 Introduction . . . . . . . . . . . . . . . . . . . . . .401
  28.2 Determining Mirror Surface Profile. . . . . . . . . . . 401
    28.2.1 Single Hole . . . . . . . . . . . . . . . . . . . . 401
    28.2.2 Linear Hartmann Plate. . . . . . . . . . . . . . . .403
    28.2.3 Rectilinear Hole Array. . . . . . . . . . . . . . . 407
  28.3 Measuring TRA using a Hartmann Plate . . . . . . . . . .408
  28.4 The Shack-Hartmann Approach . . . . . . . . . . . . . . 411
  28.5 Scanning Hartmann Sensor (SHAPE) . . . . . . . . . . . .414
  28.6 Homework . . . . . . . . . . . . . . . . . . . . . . . .416

Chapter 29 Axial Intensity . . . . . . . . . . . . . . . . . . 419
  29.1 Introduction . . . . . . . . . . . . . . . . . . . . . .419
  29.2 AIP for Unaberrated System . . . . . . . . . . . . . . .419
  29.3 Diffractive Depth of Focus . . . . . . . . . . . . . . .424
  29.4 AIP of a Slightly Spherically Aberrated System . . . . .425
  29.5 AIP for Significant Spherical Aberration . . . . . . . .425
  29.6 Using AIP to Measure Spherical Aberration . . . . . . . 426
  29.7 Things That Can Affect AIP Symmetry . . . . . . . . . . 426
    29.7.1 Sampling Aperture. . . . . . . . . . . . . . . . . .426
    29.7.2 F-number . . . . . . . . . . . . . . . . . . . . . .427
    29.7.3 Gaussian Beams. . . . . . . . . . . . . . . . . . . 429
  29.8 Homework . . . . . . . . . . . . . . . . . . . . . . . .430

Chapter 30 Modulation Transfer Function I . . . . . . . . . . .431
  30.1 Introduction . . . . . . . . . . . . . . . . . . . . . .431
  30.2 What is Modulation? . . . . . . . . . . . . . . . . . . 431
  30.3 Imaging and Convolution . . . . . . . . . . . . . . . . 433
  30.4 Convolution and Fourier Transform . . . . . . . . . . . 434
    30.4.1 The Delta Function . . . . . . . . . . . . . . . . .434
  30.5 The Optical Transfer Function. . . . . . . . . . . . . .436
  30.6 Homework . . . . . . . . . . . . . . . . . . . . . . . .439

Chapter 31 MTF Measurement I . . . . . . . . . . . . . . . . . 441
  31.1 Introduction . . . . . . . . . . . . . . . . . . . . . .441
  31.2 Slit Scanning of Finite-Area Sinusoidal Images . . . . .441
  31.3 Slit and Knife-Edge Images . . . . . . . . . . . . . . .444
    31.3.1 Image of a Slit . . . . . . . . . . . . . . . . . . 444
    31.3.2 Image of Knife-Edge . . . . . . . . . . . . . . . . 446
  31.4 MTF via LSF . . . . . . . . . . . . . . . . . . . . . . 448
  31.5 Acquiring LSF Data. . . . . . . . . . . . . . . . . . . 449
  31.6 Square Bar MTF (MTFS) . . . . . . . . . . . . . . . . . 449
    31.6.1 Alternate Scan Implementation . . . . . . . . . . . 453
  31.7 Homework . . . . . . . . . . . . . . . . . . . . . . . .454

Chapter 32 MTF Measurement II. . . . . . . . . . . . . . . . . 455
  32.1 Introduction . . . . . . . . . . . . . . . . . . . . . .455
  32.2 Variable Lateral Shear Interferometry . . . . . . . . . 455
  32.3 Total Power within Pupil Overlap . . . . . . . . . . . .456
  32.4 Auto-Correlation . . . . . . . . . . . . . . . . . . . .457
    32.4.1 Basic Auto-Correlation . . . . . . . . . . . . . . .457
    32.4.2 Auto-Correlation of Circular Pupil . . . . . . . . .458
  32.5 Pupil Auto-Correlation (PAC) . . . . . . . . . . . . . .459
  32.6 Connecting Pupil Auto-Correlation with Total Power Φ . .460
  32.7 Pupil Auto-Correlation Interferometer (PACI) . . . . . .462
    32.7.1 Kelsall Interferometer . . . . . . . . . . . . . . .462
  32.8 Pupil Auto-Correlation and the Optical Transfer Function463
    32.8.1 Short Derivation . . . . . . . . . . . . . . . . . .463
    32.8.2 Example Optical Transfer Function on Circular Pupil 465
    32.8.3 Reinterpretation of Pupil Auto-Correlation. . . . . 466
    32.8.4 The Modulation Transfer Function Connection . . . . 467
  32.9 Homework . . . . . . . . . . . . . . . . . . . . . . . .467

Chapter 33 Surface Roughness . . . . . . . . . . . . . . . . . 469
  33.1 Introduction . . . . . . . . . . . . . . . . . . . . . .469
  33.2 Direct Measurement of Surface Roughness. . . . . . . . .469
    33.2.1 Mechanical Profilometer . . . . . . . . . . . . . . 469
    33.2.2 Optical Profilometry . . . . . . . . . . . . . . . .470
  33.3 Analysis of Profilometer Data . . . . . . . . . . . . . 472
    33.3.1 Peak-to-Valley and Average . . . . . . . . . . . . .472
    33.3.2 RMS Roughness . . . . . . . . . . . . . . . . . . . 474
    33.3.3 Histogram and Gaussian Fits. . . . . . . . . . . . .474
  33.4 Surface Periodicity. . . . . . . . . . . . . . . . . . .477
  33.5 Mechanical versus Optical Profilometry . . . . . . . . .481
  33.6 Measuring Scattered Light. . . . . . . . . . . . . . . .482
    33.6.1 Total Integrated Scatter . . . . . . . . . . . . . .482
    33.6.2 Angle Resolved Scatter (ARS) . . . . . . . . . . . .484
  33.7 Homework . . . . . . . . . . . . . . . . . . . . . . . .487

Part VI Measurement of Light Fields . . . . . . . . . . . . . .489

Chapter 34 Measuring Light Fields I . . . . . . . . . . . . . .491
  34.1 Introduction . . . . . . . . . . . . . . . . . . . . . .491
  34.2 Wavefront Sensors . . . . . . . . . . . . . . . . . . . 491
    34.2.1 Direct WFS . . . . . . . . . . . . . . . . . . . . .491
    34.2.2 Indirect Wavefront Sensors . . . . . . . . . . . . .492
    34.2.2.1 Lateral Shear Interferometer WFS . . . . . . . . .492
    34.2.2.2 Hartmann-Based WFS. . . . . . . . . . . . . . . . 494
    34.2.3 Indirect WFS (Radiometric) . . . . . . . . . . . . .494
      34.2.3.1 Axial Intensity . . . . . . . . . . . . . . . . 496
      34.2.3.2 Curvature Sensing . . . . . . . . . . . . . . . 497
      34.2.3.3 Phase Retrieval . . . . . . . . . . . . . . . . 501
      34.2.3.4 Light Level . . . . . . . . . . . . . . . . . . 503
  34.3 Wavefront Calibration . . . . . . . . . . . . . . . . . 505

Chapter 35 Measuring Light Fields II: Polarization . . . . . . 507
  35.1 Introduction . . . . . . . . . . . . . . . . . . . . . .507
  35.2 Measuring Pure Polarization States . . . . . . . . . . .508
  35.3 The Polarization Ellipse. . . . . . . . . . . . . . . . 512
  35.4 Ellipsometers Proper . . . . . . . . . . . . . . . . . .513
  35.5 The Quarter-Wave Plate . . . . . . . . . . . . . . . . .515
  35.6 Polarization and Wavefront Sensors . . . . . . . . . . .516
  35.7 Coherence Measurements . . . . . . . . . . . . . . . . .521
    35.7.1 Spatial Coherence . . . . . . . . . . . . . . . . . 521
    35.7.2 Temporal Coherence . . . . . . . . . . . . . . . . .522
  35.8 Homework . . . . . . . . . . . . . . . . . . . . . . . .525

Chapter 36 Measuring Light Fields III: Radiometrics . . . . . .527
  36.1 Introduction . . . . . . . . . . . . . . . . . . . . . .527
  36.2 The Standard Lamp . . . . . . . . . . . . . . . . . . . 527
  36.3 Radiometer. . . . . . . . . . . . . . . . . . . . . . . 528
    36.3.1 Broadband Radiometry . . . . . . . . . . . . . . . .529
    36.3.2 Sensor Head Calibration . . . . . . . . . . . . . . 530
    36.3.3 Photometry. . . . . . . . . . . . . . . . . . . . . 531
  36.4 Gratings and Monochrometers. . . . . . . . . . . . . . .533
    36.4.1 Reflection Gratings . . . . . . . . . . . . . . . . 533
    36.4.2 Blazed Grating. . . . . . . . . . . . . . . . . . . 534
    36.4.3 Monochrometers . . . . . . . . . . . . . . . . . . .537
  36.5 Spectroradiometers . . . . . . . . . . . . . . . . . . .538
    36.5.1 Basic System . . . . . . . . . . . . . . . . . . . .538
    36.5.2 Order Overlap . . . . . . . . . . . . . . . . . . . 539
    36.5.3 Spectroradiometers Proper . . . . . . . . . . . . . 540
    36.5.4 Spectroradiometer Calibration. . . . . . . . . . . .541
  36.6 Energy Measurements . . . . . . . . . . . . . . . . . . 543
  36.7 Radiance Measurements . . . . . . . . . . . . . . . . . 543

Chapter 37 Spectrometry . . . . . . . . . . . . . . . . . . . .547
  37.1 Introduction . . . . . . . . . . . . . . . . . . . . . .547
  37.2 Spectrometer . . . . . . . . . . . . . . . . . . . . . .547
  37.3 Fabry-Perot Interferometer . . . . . . . . . . . . . . .548
    37.3.1 Multiple Ray Interference Transmission . . . . . . .549
    37.3.2 Fringe Sharpness . . . . . . . . . . . . . . . . . .550
    37.3.3 Spectral Resolution . . . . . . . . . . . . . . . . 554
    37.3.4 Interference (Spike) Filter . . . . . . . . . . . . 556
  37.4 Spectrophotometry. . . . . . . . . . . . . . . . . . . .557
    37.4.1 Visible Spectrophotometer . . . . . . . . . . . . . 558
    37.4.2 Fourier Transform Infrared Spectrophotometer (FTIR) 560

Chapter 38 Energy and Photographic Film in the Digital Age . . 567
  38.1 Introduction . . . . . . . . . . . . . . . . . . . . . .567
  38.2 Generating the Characteristic Curve . . . . . . . . . . 568
    38.2.1 Sensitometer . . . . . . . . . . . . . . . . . . . .568
    38.2.2 Densitometer . . . . . . . . . . . . . . . . . . . .569
    38.2.3 The Plot . . . . . . . . . . . . . . . . . . . . . .570
  38.3 The Nutting Model. . . . . . . . . . . . . . . . . . . .570
  38.4 The Microdensitometer . . . . . . . . . . . . . . . . . 572
  38.5 Film Speed and RMS Granularity . . . . . . . . . . . . .574
  38.6 Film MTF. . . . . . . . . . . . . . . . . . . . . . . . 574
  38.7 Film Spectral Response . . . . . . . . . . . . . . . . .575
  38.8 IR Presensitization Photography . . . . . . . . . . . . 576
  38.9 Format Sizes. . . . . . . . . . . . . . . . . . . . . . 578

Appendix A Answers To Selected Homework Problems . . . . . . . 579
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 583
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585

    


Notice
We are constantly checking the accuracy of the technical data. We are prepared to provide more detailed information on request. Technical data is subject to change without notice.

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Opticstar News
New DS-616C XL+ Model
posted: 24th August 2017
Opticstar DS-616C XL+.
Star product, improved.

The new Opticstar DS-616C XL+ deep-sky CCD is the successor to the popular DS-616C XL that earned the annual star product award back in 2013. It maintains all the features of the original model as well as other improvements.


DS-616C XL is Astronomy Magazine's Star Product
posted: 12th September 2013
Opticstar DS-616C XL is Astronomy magazine's product of the year.
Star product.

The Opticstar DS-616C XL deep-sky CCD camera has earned the annual star product award from Astronomy, the world's best-selling astronomy magazine. Read about it in the September 2013 issue.

Online Shopping
Credit & Debit Cards
updated: 22nd August 2017
Online shopping.
We accept all the credit and debit cards shown above. Online payments are cleared by Barclays. Online payment integration by Worldpay. Please read our
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Willmann Bell
Books for Astronomy
updated: 28th October 2018
Willman Bell books.
Acclaimed books from Willmann Bell...
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Opticstar News
Imaging Brochure
updated: 10th February 2014
Opticstar brochure.
Download the Opticstar imaging catalogue here.
more
Articles
CCD Temperature And Dark Current Correction
Dark current.
An important step in CCD image calibration is the...
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A&M 152mm f/8 Review
"Fantastic Performance" "Beauty of a Ferrari"
updated: 25th March 2009
A&M 152mm f/8 TMB.
Read the latest review about the A&M 152mm f/8 A&M/TMB on Cloudy Nights. According to the review this telescope combines the "beauty of a Ferrari" with "fantastic performance". The review also states that "the manufacturer's claims are valid".
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