Optical Design Using Excel

Preface i

Outline of contents ii

Chapter 1 - Geometrical optics 1

1.1 Characteristics of lasers 2

1.2 The three fundamental characteristics of light which form the basis of geometrical optics 3

1.3 Fermat's principle 4

1.4 Principle of reversibility 7

1.5 Paraxial theory using thin lenses 7

1.6 The five Seidel aberrations 15

1.7 The sine condition 21

1.8 Aplanatic lenses 23

1.9 Reflection and transmission 24

Chapter 2 - Examples of simple optical design using paraxial theory 27

2.1 Types of lenses 28

2.2 Applied calculations for simple optical systems 35

2.3 Considerations relating to the design of laser optical systems 42

Chapter 3 - Ray tracing applications of paraxial theory 47

3.1 Deriving the equations for ray tracing using paraxial theory 48

3.2 Problems of ray tracing calculations using paraxial theory 50

Chapter 4 - Two-dimensional ray tracing 53

4.1 Ray tracing for a spherical surface 54

4.2 Ray tracing for a plane surface 56

4.3 Ray tracing for an aspheric surface (using VBA programming) 57

4.4 Ray tracing for an aberration-free lens 60

4.5 Optical path length calculation for an aberration-free lens 62

4.6 Ray tracing for an optical system which is set at a tilt 65

4.7 How to use the ray trace calculation table 68

4.8 A method for generating a ray trace calculation table using a VBA program 73

4.9 Sample ray tracing problems 76

Chapter 5 - Three-dimensional ray tracing 101

5.1 Three-dimensional ray tracing for a spherical surface 102

5.2 Three-dimensional ray tracing for a cylindrical surface 105

5.3 Simulation for two cylindrical lenses which are fixed longitudinally (or laterally) but allowed to rotate slightly around the optical axis 106

5.4 Three-dimensional ray tracing for a plane surface which is perpendicular to the optical axis 108

5.5 Three-dimensional ray tracing for an aberration-free lens 109

5.6 Three-dimensional ray tracing for a lens which is set at a tilt 115

5.7 How to use the three-dimensional ray trace calculation table 121

5.8 Operating instructions for using the ray trace calculation table, while running  the VBA program 125

5.9 Three dimensional ray tracing problems 128

Chapter 6 - Mathematical formulae for describing wave motion  137

6.1 Mathematical formulae for describing wave motion 138

6.2 Describing waves with complex exponential functions 142

6.3 Problems relating to wave motion 146

Chapter 7 - Calculations for focusing Gaussian beams 149

7.1 What is a Gaussian beam? 150

7.2 Equations for focusing a Gaussian beam  154

7.3 The M² (M squared) factor 156

7.4 Sample Gaussian beam focusing problems 159

Chapter 8 - Diffraction: theory and calculations 167

8.1 The concept of diffraction 168

8.2 Diffraction at a slit aperture 170

8.3 Diffraction calculations using numerical integration 171

8.4 Diffraction at a rectangular aperture 173

8.5 Diffraction at a circular aperture 174

8.6 Diffraction wave generated after the incident wave exits a focusing lens 177

8.7 Diffraction calculation problems 178

Chapter 9 - Calculations for Gaussian beam diffraction 183

9.1 The power and the central irradiance of a Gaussian beam 184

9.2 General equations for waves diffracted by an aperture 189

9.3 Diffraction wave equations for a focused beam 191

9.4 Diffraction wave equations for a collimated beam  194

9.5 Diffraction calculation program 197

9.6 Operating instructions for diffraction calculation programs 198

9.7 Gaussian beam diffraction calculation problems  206

Appendix 219

Appendix A Paraxial theory: A detailed account 220

Appendix B A table of refractive indices for BK7 225

Appendix C Equations for plane waves, spherical waves and Gaussian beams 226

Appendix D Numerical integration methods 239

Appendix E Fresnel diffraction and Fraunhofer diffraction 241

Appendix F Wave-front conversion by a lens 245

Appendix G List of Excel calculation files on the companion Website 247

References 249

Index 250