Yves Le Grand on matrices in optics with application to vision: Translation and critical analysis

Abstract

An appendix to Le Grand’s 1945 book, Optique Physiologique: Tome Premier: La Dioptrique de l’Œil et Sa Correction, briefly dealt with
the application of matrices in optics.  However the appendix was omitted from the well-known English translation, Physiological Optics, which appeared in 1980.  Consequently the material is all but forgotten.  This is unfortunate in view of the importance of the dioptric power matrix and the ray transference which entered the optometric

literature many years later.  Motivated by the perception that there has not been enough care in optometry to attribute concepts appropriately this paper attempts a careful analysis of Le Grand’s thinking as reflected in his appendix.  A translation into English is provided in the appendix to this paper.  The paper opens with a summary of the basics of Gaussian and linear optics sufficient for
the interpretation of Le Grand’s appendix which follows.  The paper looks more particularly at what Le Grand says in relation to the transference and the dioptric power matrix though many other issues are also touched on including the conditions under which distant objects will map to clear images on the retina and, more particularly, to clear images that are undistorted.  Detailed annotations of Le Grand’s translated appendix are provided. (S Afr Optom 2013 72(4) 145-166)