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Chapter 3:
Abbe Theory of Image Formation and Diffraction of Light in Transmitted Light Microscopes
The late 1800s saw a great effort on the part of microscope manufacturers to understand the basis of image quality, resolution, and contrast in their products. There was also a perceived commercial advantage in having a product that could be marketed as “scientifically designed.” Both of these aims were achieved through the work of Ernst Abbe, a physicist who worked at the microscope factory of Carl Zeiss. This chapter explains the seminal contributions of Abbe to the construction of microscope objectives and his diffraction theory and its role in image formation in the light microscope. The diffraction theory of Abbe and his experimental sets of gratings, apertures, and lenses used to observe the diffraction pattern in the back focal plane of the microscope objective provided evidence that there is an upper limit to the ability of a lens to resolve very fine spatial details. An optical imaging system uses surfaces that refract (lenses) and/or reflect (mirrors) the light from an object to form its image. This chapter also explains how a lens forms the image of an object; describes the role of diffraction in the process of image formation; and shows how the collection angle of the objective, the refractive index of the medium between the specimen and the objective, and the wavelength of the light affect the limiting optical resolution. Finally, it discusses how optical aberrations confound this limit, derived on the basis of diffraction theory in the absence of aberrations. 3.1 The Contributions of Abbe In the beginning of the 19th century, there were attempts to provide a scientific basis to imaging in the optical microscope. Both Fraunhofer and Airy attempted to use the theory of diffraction and interference to understand image formation. Nevertheless, it was in Jena, Germany, where Ernst Abbe made his important contribution to this problem. Abbe studied physics and mathematics, first two years at University of Jena, and then three additional years at University of Göttingen, where he concentrated on the theory and practice of precision measurements. Abbe took courses that included individual practice on the construction of precision measuring instruments.
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Image acquisition


Image processing


Optical imaging

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