Open AccessThe aberrations of a symmetrical optical instrument
Publication year - 1909
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1909.0082
Subject(s) - function (biology) , limit (mathematics) , expression (computer science) , coma (optics) , value (mathematics) , object (grammar) , computer science , spherical aberration , optics , mathematics , physics , mathematical analysis , artificial intelligence , lens (geology) , evolutionary biology , biology , programming language , machine learning
1. Attention has been called by Rayleigh in a paper cited below to the ease with which the general nature of the aberrations of optical instruments can be discussed by means of a modified characteristic function. The object of the present paper is to work this method in more detail in order to get a complete account of the aberrations and to connect it with the known method of calculating the aberrations of a particular system. We write down the doubly modified function in 2, and in 3 deduce from it the singly modified function used in the rest of the paper. The meanings of the coefficients are given in 4. Attention having been called in 5 to some features that limit the usefulness of the method, a new expansion of more practical value is found in 6. The meanings of the coefficients of this expression are given in detail in 7, and some relations between them (i. e. between the spherical aberration, coma, etc.) in 8. The numerical calculation is discussed in 9. In 10 another method of calculating the characteristic function is sketched out.