chapter 2, Basic Considerations

In I Review and Summary from: Advanced Optics Using Aspherical Elements

Editor(s): Bernhard Braunecker, Rüdiger Hentschel, Hans J. Tiziani

Published: 08 January 2008

Chapter DOI: 10.1117/3.741689.ch2

Chapter Page Count: 15 pages

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Front Matter

1. Introduction

I Review and Summary
2. Basic Considerations

3. Applications

4. Materials of Aspheres

5. Processing Technologies

6. Metrology

7. Coating Technologies

8. Assembly Technologies

9. Future Trends

10. Mathematical Formulation

II Experts' Contributions
11. Applications

12. Materials

13. Processing Technologies

14. Metrology

15. Coating Technologies

16. Assembly

17. Editor and Author Biographies

Back Matter

Preview

Chapter Contents

2.1 Preliminary Remarks
2.1.1 Optical element and wavefront propagation
2.1.2 Optical design and tolerancing
2.1.3 Production and metrology errors
2.1.4 System performance criteria
2.2 Definition of Aspherical Optical Elements
2.2.1 Basic characteristics of aspherical elements compared with spherical elements
2.2.2 Mathematical representation of aspherical surfaces
2.2.3 Specifying tolerances for aspherical optical elements
2.2.4 Surface texture
2.3 Drawing Indications
2.4 Information Exchange over Aspherical Elements
2.5 Study about Surface Errors
2.5.1 Aspherical laser collimator
2.5.2 Comparison of different surface-finishing technologies
2.5.3 Coherent beam propagation
2.5.4 Application case: Line marking on sport fields
2.6 References

Excerpt

2.1 Preliminary Remarks

We will start with a single lens to illustrate the physics of imaging and will find the equivalence of material and geometry parameters for the image quality.

2.1.1 Optical element and wavefront propagation

Optical imaging is generally performed by lenses, that is, by pieces of glass of thickness d and two properly shaped glass-air surfaces. Such a component can be considered as a “black box,” hopefully transparent, which transfers an optical input wave of amplitude A_In(r) and phase Φ_In(r),

into an outgoing wave,

where i is the imaginary unit, and r is the radial coordinate normal to the light propagation direction z. We describe here the most simple case of a monochromatic wave originating from a far distant point source.

Such a lens alters the amplitude and the phase. We observe the phase change in Fig. 2.1, where a plane wave is transformed into a spherical wave. The spherical wave converges to an intensity spot at a distance f, called the focal length of the lens. Although an amplitude change results in a light intensity loss, this is ignorable here, and the phase term is much more important. It determines the optical quality, that is, the sharpness and contrast of an image. We see in Fig. 2.1 that a wavefront error of the perfect spherical output wave would result in an undesirable spot broadening.

DOI: 10.1117/3.741689.ch2

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