Willmann-Bell Optical Testing

A practical introduction for optical designers, students and workshop personnel.

  • Author: Joseph M. Geary
  • Publisher: Willmann-Bell
  • Hardback
  • Pages: 604
  • Illustrations: 660
  • Dimensions: 6 by 9 inches
  • First published: 2014
  • UK warranty
Willmann-Bell Optical Testing
  • Product code: OT
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Description

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.


U.K. WARRANTY

INTERMEDIATE

OPTICS

ASTRONOMY
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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 Mirror. 251
        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


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Universal Product Code (UPC) n/a
Experience Level Intermediate
Format Hardback
Pages 604
Illustrations 660
Dimensions 6 by 9 inches
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