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Spie Press Book

Interferometry for Precision Measurement
Author(s): Peter Langenbeck
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Book Description

Interferometry can be seen as the stethoscope of the precision optical engineer. This book presents various interferometric developments used in physical, optical, and mechanical engineering during the past half century. It is an expanded translation of one chapter of the German Wirtschaftliche Mikrobearbeitung, also by Langenbeck, published by Carl Hanser Verlag, Munich-Vienna, in 2009. The book is illustrated with many practical examples and photographs that are a direct consequence of the author’s vast experience in the subject. The author provides some little-known testing techniques that could lead to future innovation in interferometric testing, along with occasional "Notes for the practitioner," which give the reader tips for successful implementation of the author’s repertoire of techniques. The text will be of value to anyone interested in learning about interferometric evaluation of small mechanical and optical components.

Book Details

Date Published: 29 May 2014
Pages: 258
ISBN: 9780819491404
Volume: TT94

Table of Contents
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Table of Contents


1 Known Methods: An Assessment of the State of the Art—Newton and Fizeau
1.1 Introduction
1.2 Limited Use of Newton's Method
1.3 Other Methods of Interferometry
      1.3.1 Tolansky: one experimenter's indispensable knowledge
1.4 Desirable Features for Safe, Applicable, and Economic Interferometry
      1.4.1 Commercial coherent white light
      1.4.2 Light sources for increased distance from reference to sample
1.5 The Often-Neglected Angle of Light Incident to Work
      1.5.1 Selecting only one angle of incidence
      1.5.2 Instrumental consequences
      1.5.3 The multifunctionality of a prism's hypotenuse: beamsplitter, reference, and obliqueness provider
1.6 Knowing the Angle of Incidence with Respect to the Fringe Equivalent
      1.6.1 When the angle of total internal reflection is zero
      1.6.2 Calbration masters
      1.6.3 Are 5-μm fringes meaningful?
      1.6.4 Two-beam and multiple-beam walkoff
      1.6.5 Stray light need not be deviled
      1.6.6 The scatter flat test

2 From Extended Light Source to Collimated Illumination
2.1 Introduction
2.2 Technical Relevance of Oblique Incidence
2.3 Fast Adjustment of Tilt and Height
      2.3.1 Autoleveling with mechanical truing
      2.3.2 Autoleveling with optical position sensing
2.4 Variable-Angle u on Samples with Strong Slopes
2.5 Interference Contrast
      2.5.1 Autoleveling with mechanical truing
2.6 Notes on Recording Fringes

3 Interferences Visualized by Vector Diagrams
3.1 Vectorial Representation of Dual- and Multiple-Beam Interferometry
3.2 The Airy Case: Zero Wedge Angle
3.3 The Fizeau Case
3.4 The Function of the Zero-Order Beam (E0)
3.5 Advantages and Disadvantages Using Multiple-Beam Interferometry
3.6 An Application: Evaluating the Task of Nulling
      3.6.1 Experimental
3.7 Other Forms of Pointing Interferometer with Respect to Nulling
3.8 Fizeau Interferometers with Large Cavities
3.9 Stringent Requirements for Collimation
3.10 Acceptable Uniformity of Illumination

4 Optical Laboratory Equipment
4.1 Experimenting with Collimation: Autocollimation
      4.1.1 Autocollimation: The key to any interferometer
      4.1.2 The autocollimator
4.2 Fizeau Interference and Autocollimation
      4.2.1 Common applications of autocollimation
      4.2.2 Orthogonality of two spindle axes
      4.2.3 Price-worthy Fizeau instrumentation
4.3 Testing the Collimation of an Expanded Laser Beam
      4.3.1 Murty's parallel shearing plate
      4.3.2 Variable shear: two parallel plates
      4.3.3 Variable shear and tilt to suit
      4.3.4 Double wedge plate shearing interferometer
      4.3.5 Variable shear and tilt: enhanced sensitivity
      4.3.6 A useful, robust interferometer

5 Straight Lines and Right Angles
5.1 Measuring 90-deg Roof Angles on Mirrors and Prisms
      5.1.1 Reversion of wavefronts
      5.1.2 Measuring small angles with straight fringes
      5.1.3 Enhanced sensitivity for 90-deg roof angle quality assurance
      5.1.4 Plus or minus angular error? High or low on surfaces?
      5.1.5 Polarization
5.2 Function of the Trihedral Prism: the Corner Cube Prism (CCR)
      5.2.1 Retroreflectors in practice
      5.2.2 Quality assurance of the CCR
      5.2.3 Improving collimation
      5.2.4 An alternative to the CCR: the ball reflector or "cat's eye"
      5.2.5 Autocollimation test for equality of radii of curvature
      5.2.6 Separating angular errors from flatness errors on cubes and 90-deg prisms
      5.2.7 Measuring the parallelism of transparent laser rods
      5.2.8 90-deg angular calibration cubes

6 Polygons
6.1 Polygon Mirror Wheels
      6.1.1 Preparing and verifying axial surfaces of polygons
      6.1.2 Verifying facet flatness and angles
      6.1.3 Polygon rotation in 0.1-arcsec steps
      6.1.4 Polygon's relative pyramidal error (static)
6.2 Angular Standards Calibrated by Interferometry
      6.2.1 0.1-arcsec resolution within ±15 deg
      6.2.2 Arcsecond rotation

7 Optical Shop Daily Tasks
7.1 Centration in the Optical Shop
7.2 Optical Work
7.3 Centering a Spherical Generator
      7.3.1 Finding the turning center experimentally
7.4 Attributes of Centering: State of the Art
7.5 Can the Centering Procedure Be Made Less Laborious?
      7.5.1 An alternative solution?
      7.5.2 Rotating the optical beam of the sample
      7.5.3 Centering interferometry
      7.5.4 Enhanced sensitivity
      7.5.5 Fine control by the naked eye
      7.5.6 Further increasing centration sensitivity
      7.5.7 Conventional hardware for centration (air-bearing spindles)
      7.5.8 Centration without rotating the lens
7.6 Homogeneity
      7.6.1 Methods for error separation
      7.6.2 Fast qualitative assessment of homogeneity

8 Mass-Produced Specular Surfaces
8.1 Specular Surfaces that are Grossly Unflat
      8.1.1 Strioscopy: Is it quantitative?
      8.1.2 Further review of strioscopy
      8.1.3 Interferences in strioscopy: origin of coherent underground (reference)
      8.1.4 Mechanical focal-plane interaction
      8.1.5 Optical interaction: color coding
8.2 The One-Arm Interferometer
      8.2.1 Comments on the one-arm interferometer
      8.2.2 Removing the spatial carrier frequency
      8.2.3 Other interactions in the defocal plane

9 Nonspecular, Near-Flat, Mass-Produced Surfaces
9.1 Degenerate One Arm: The Lloyd Interferometer
      9.1.1 Higher-order Lloyd interferometer
      9.1.2 Alignment and interpretation
      9.1.3 Experimental
      9.1.4 Lloyd interferometer for dynamic testing
      9.1.5 Measuring the flatness of lapped granite plates/machine beds
      9.1.6 High or low?
      9.1.7 Summary of Lloyd interferometry
9.2 Instrumentation for Grazing Incidence Interferometry
      9.2.1 The prism interferometer
      9.2.2 The image in a prism interferometer
      9.2.3 Parameters influencing ΔP/P reading accuracy

10 Enhancing Regular Interferometric Sensitivity
10.1 Multiple Reflections
10.2 Advantages and Disadvantages of Multipass Interferometers
10.3 Relevance of Multiple Reflection and Off-Axis Illumination
10.4 Multipass Applications
      10.4.1 Multipass in comparator interferometry
      10.4.2 Angular metrology



With new material added to the English translation of Chapter 7 of the German Wirtschaftliche Mikrobearbeitung (Carl Hanser Verlag, 2009), the author presents developments in physical, optical, and mechanical engineering over the past 60 years. The enduring impetus for this work is owed to the late, great gentleman engineer, Gordon J. Watt, with his assertion that optical wavefronts used in interferometers and the surfaces used to build air bearings are complementary. A foremost example of this statement is the fact that a plano-convex lens is confined by surfaces that are equivalent to those defining the Watt air-bearing spindle. The spindle rotor consists of a truncated hemisphere, rigidly connected to a flat disk.

Soon after the author founded Intop Entwicklungen (Baden-Württemberg, Germany) in 1972, G. J. Watt and the author experienced an explosion of spindle-enabling applications and new machines whose performance relied completely on low-axial-error motion (less than 5 nm) and an angular error motion of less than 0.1 arcsec. The bearing's disk took on multiple integral functions: as a polygon wheel, as a polishing scaife for diamond tools, and as a chuck for thin substrates (memory substrates with memory scaling of 14.5). Interferometers for in-process quality control and final acceptance needed to be developed.

Increased interferometric sensitivity by multiple passes was adopted as a technique for measuring small departures from 90 deg, both for the metrology of corner cubes and for extremely sensitive tilt measurement (one of the three CCR mirrors being the front mirror on a problem spindle's nose). Interferometric techniques that facilitated the assembly of ultraprecision machining and metrology machines (3D orthogonal) were developed.

Likewise, decreasing interferometric sensitivity made possible the inspection of nonspecular surfaces. The cost for quality control of mass-produced components (for example, water faucet ceramic seals) was substantially reduced. The inspection technique being used became the standard for expedient handling of samples with interferometric precision.

This relatively recent development focused on measuring tilt error motions of air-bearing spindles, as is amply covered in this book. Tasks that occur every day in an optical shop—such as centering and homogeneity measurement—are treated extensively.

The author gladly shares his recollections and experience with students, scholars, and peers but also wants to give a warning: dealing with optics every day may turn a profession into an obsession!

The author appreciates SPIE for making this publication possible. He also expresses his warm thanks to Prof. Hans Tiziani for frequent, critical discussions.

Peter Langenbeck
May 2014

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