Contents

Translators’ foreword

Special foreword

Preface

Introduction

1 Imaging laws of geometrical optics

1 Construction of a ray refracted by a spherical surface

2 Imaging of an arbitrary luminous axial point

3 Imaging of luminous objects

4 Imaging by a centered system of refracting spherical surfaces

5 Imaging equations according to Abbe

6 Imaging by wide-angle ray bundles (sine condition)

2 Imaging of self-luminous objects

7 Diffraction problems solved on the basis of Maxwell’s theory

8 The Kirchhoff principle

9 Discussion of expression for the intensity at the observation point

10 Comparison of the Kirchhoff principle with the Fresnel–Huygens principle

11 Fraunhofer diffraction

12 Auxiliary consideration

13 Diffraction phenomena occurring in pairs of conjugate planes of optical systems

14 Determination of factors ⍺, σ(μ), and ψ(μ′) based on energy considerations

15 Expression of light disturbance at the observation point

16 Determination of light disturbance at the observation point using the Kirchhoff principle

17 Calculation of diffraction on an aperture of specific form for points in the plane conjugate to the object plane in the presence of a luminous surface element

3 Imaging of illuminated objects

18 Presence of several luminous points

19 Presence of several luminous surface elements

20 Single luminous slit

21 Two parallel and neighboring slits

22 An illuminated slit of finite width

23 Finite slit whose two halves possess a constant difference in phase

24 Slit of finite width with oblique incidence of light

25 Switching of the order of integration in the calculation of the resulting light disturbance

26 Pointwise and similar imaging of the object

27 Dissimilar imaging of the object

4 Imaging of a grating with artificial clipping of diffraction orders

28 General intensity equation

29 Case I: Only the central image (the 0th order) goes through

30 Case II: Besides the central image, the left and right first maxima go through

31 Case III: Only the ith maxima on both sides contribute to imaging; the central image is blocked

Appendix

Bibliography on the theory of imaging of illuminated objects

Translators’ notes

A brief introduction to geometrical optics

On the 0.5 λ/NA resolution limit in the imaging of periodic patterns

Abbe’s 15 December 1876 Letter to J. W. Stephenson

Index

Translators’ foreword

This work was originally published in 1910, five years after Ernst Abbe’s death. The original book, published by Friedrich Vieweg und Sohn, was compiled by Otto Lummer, professor of physics at the University of Breslau, and his then-assistant Fritz Reiche. The book is an expanded version of notes taken by Lummer, who attended Abbe’s lectures on the subject in Jena in 1887. It is the only detailed publication of Abbe’s theory on image formation in the microscope. The entire book is based on classical optics; therefore, the arguments made in it are still valid today. In particular, the concept of a coherently illuminated image as two back-to-back diffraction processes of the object was beautifully described in it for the first time. In the section “Imaging of illuminated objects” in his 1933 classic textbook Optik, Max Born stated clearly that “this theory was developed by Abbe and was demonstrated by beautiful experiments. See E. Abbe, Theory of Image Formation in the Microscope.”

…

It is our hope that this translation can serve as a self-study book for a wider circle and younger generations of readers who wish to learn optics and optical image formation. It is also a tribute to the original authors for their scientific achievements and devotion to the teaching and dissemination of precious knowledge. For practicing lithographers who try to extend the resolution limit one nanometer at a time, may a read through this book stimulate more innovative ideas down the road.

Anthony Yen and Martin Burkhardt
California and New York
2022