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Interconverting the matrix and principal‐meridional representations of dioptric power and reduced vergence
Author(s) -
Harris W. F.
Publication year - 2000
Publication title -
ophthalmic and physiological optics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.147
H-Index - 66
eISSN - 1475-1313
pISSN - 0275-5408
DOI - 10.1111/j.1475-1313.2000.tb01128.x
Subject(s) - vergence (optics) , zonal and meridional , matrix (chemical analysis) , representation (politics) , vertex (graph theory) , mathematics , physics , combinatorics , optics , law , chemistry , graph , atmospheric sciences , chromatography , politics , political science
Summary Converting the traditional representation of power as sphere, cylinder and axis to the dioptric power matrix F is usually performed by means of Long's equations and the reverse process by means of Keating's equations. It is sometimes useful to be able to convert directly between the matrix and power expressed in terms of principal powers F| and F 2 along corresponding principal meridians at angles a and a 2 . The equations for interconverting F and the principal‐meridional representation expressed as F^{a }F 2 are presented here. Equivalent equations allow direct interconversion of the reduced vergence matrix L and the principal‐meridional representation of vergence L{a)L 2 . Vergence becomes infinite at line and point focuses. Similarly effective power and back‐ and front‐vertex power are infinite for some systems. Nevertheless it is possible unambiguously to represent infinite vergence and vertex power in principal‐meridional form. However, information is usually lost in these infinite cases when the principal‐meridional representation is converted to the matrix representation, and the former is not recoverable from the latter. As a consequence the matrix representation is usually unsatisfactory for vergences and vertex powers that are infinite. On the other hand, the principal‐meridional representation of vergence and power is always satisfactory. If one adopts the position that effective powers and vertex powers are really vergences rather than powers then one concludes that the matrix provides a satisfactory representation for powers of thin systems in general but not for vergences. Implied by a vergence at a point is an interval of Sturm. The equations for characterizing the interval from the reduced vergence are presented.