Abbe’s theory

Abbe’s theory-The theory of image formation

In 1866, Ernst Abbe and Carl Zeiss cooperated together to improve the optical performance of microscopes. Only until then microscopes and microscope objectives were being produced by trial and error; some having exceptional optical performance but others having undesirable features. Abbe and Zeiss knew that they could only get an optimum and consistent performance on a complete theoretical basis. (Gundlach, 2005)

Abbe discovered after many calculations and experiments that the diffraction image in the back focal plane of the objective is essential for image formation. (Gundlach, 2005)

“No microscope permits components (or the features of an existing structure) to be seen separately if these are so close to each other that even the first light bundle created by diffraction can no longer enter the objective simultaneously with the non-diffracted light cone.” Ernst Abbe, 1873. (Gundlach, 2005)

Abbe’s theory is based on the necessity for the light rays diffracted by the specimen to be collected by the objective and allowed to contribute to the image; if these diffracted rays are not included, the fine details which give rise to them cannot be resolved. (University, 2005)

The image of a light absorbing specimen is formed due to diffraction. The specimen is seen by the light as a complex superposition of gratings with varying grating constants and holes. Some of the light will pass through the specimen undeviated and will only give rise to a uniformly bright image. The deviated (diffracted) light carries the information about the structures in the specimen. (Logg, 2006)

Figure 2 is a plot showing the image of a grating when blocking different diffraction orders (as shown to the left). I_grating shows what the intensity image of the grating should look like. (Logg, 2006)

References:

Gundlach, H., 2005. Innovation 15. [Online] Available at: http://www.zeiss.co.uk/C125716F004E0776/0/D1B2BF1284180E37C125717C003EDF5A/$File/Innovation_15_18.pdf Logg, K., 2006. O1 - Optical Microscopy. [Online] Available at: http://www.fy.chalmers.se/microscopy/students/imagecourse/O1.pdf University, M. W. D. a. T. F. S., 2005. Molecular Expressions. [Online] Available at: http://micro.magnet.fsu.edu/optics/timeline/people/abbe.html