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Ernst Abbe's Theory of Image Formation in the Microscope
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Book Description

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This book is an English translation of Die Lehre von der Bildentstehung im Mikroskop von Ernst Abbe, the only published detailed account of Abbe’s theory of image formation in the microscope. The original German edition, written and published by Otto Lummer and Fritz Reiche in 1910, was an expanded version of the lectures given by Abbe in 1887. The book presents an introduction to geometrical optics, discusses image formation theory based on optical diffraction, and deals with optical images of several kinds of objects being illuminated on and off axis. It also introduces coherent imaging as two back-to-back diffraction processes and discusses the resolution limit of an imaging system. The book concludes with a discussion of the effect of artificial blocking of certain diffraction orders on the final image.

This translation, which includes annotations and other added material, can serve as a self-study book for readers who wish to learn optics and optical image formation. It is also a tribute to the original authors’ scientific achievements and devotion to the teaching and dissemination of precious knowledge.


Book Details

Date Published: 19 October 2023
Pages: 246
ISBN: 9781510655232
Volume: PM352

Table of Contents
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Translators’ foreword
Special foreword

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

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


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

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