A method is presented of associating to each thin lens a matrix operator which transforms a finite number of regions of object space into regions of image space. By making use of the fact that the logical relation “or” has properties similar to the ordinary notion of addition, we can obtain by matrix multiplication a single matrix which represents the transformation properties of a combination of any number of thin lenses axially aligned. In such a way we can store in a single resultant matrix all the information as to possible locations of an image in any of a finite number of regions covering image space, when the object is located in any of the similarly divided regions of object space. The method is very simple in principle and practice, and it is hoped that the loss of information due to the treating of whole regions together will result in an increase in the speed and facility with which one might determine the general features of a system of lenses.
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