Approximate matrix expression for the thickness of any lens generalized to allow for prism

Harris, W. F.; Abelman, Herven

doi:10.1111/j.1475-1313.1991.tb00210.x

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…but both the prism due to lens power and Ihe ground prism becomes now loeal magnitudes. Mathematically, the ground prism p^, can be obtained from ihc generalized nialrix form of ihe Prentice equation (Harris and Abelman, 1991).…”

Section: Resultsmentioning

confidence: 99%

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Local dioptric power matrix in a progressive addition lens

Alonso

Gómez‐Pedrero

Bernabéu

1997

Ophthalmic and Physiological Optics

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In this paper we use the formalism of the Dioptric Power Matrix to visualise and characterise the properties of a Progressive Addition Lens. For progressive addition lenses, the dioptric power matrix is point-dependent, and we have measured its elements over the lens surface by means of an automatic focimeter. We show the obtained contour plots corresponding to the matrix elements, and we compare them with the traditional sphere and cylinder graphs. Although the two representations give the same information, the advantages and disadvantages between them are analysed. The dioptric power matrix method turns out to be specially useful for the computation of prismatic effects along the lens surface.

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Section: Resultsmentioning

confidence: 99%

“…. 1991Harris and Abelman. 1991), with which computation about optical and geometrical properties of the lens can be done in a significantly faster and elegant way.…”

Section: 2a)mentioning

confidence: 99%

Local dioptric power matrix in a progressive addition lens

Alonso

Gómez‐Pedrero

Bernabéu

1997

Ophthalmic and Physiological Optics

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“…For that reason, we can think of it as a local ground prism. In fact, Equation ( 18) is a generalization of the implicit expression for the prismatic power presented by a thin lens with allowance for prism given by Harris and Abelman (1991).…”

Section: Generalized Expression For the Prentice's Lawmentioning

confidence: 99%

A generalization of Prentice's law for lenses with arbitrary refracting surfaces

Gómez‐Pedrero¹,

Alonso²,

Canabal³

et al. 1998

Ophthalmic Physiologic Optic

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A generalization of the Prentice's law is presented in this paper. The idea consists of removing some (but not all) of the approximations that comprise the paraxial approach. In that way, we obtain a new formulation that permits us to compute the prismatic power of a lens made up of arbitrary refracting surfaces, and to improve the precision obtained by Prentice's law when applied to monofocal lenses. The resulting formalism is simple and manageable and its derivation leads us to a precise definition of the local dioptric power matrix, introduced in a previous paper, as well as a better understanding of the same.

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Thickness extrema at the edge of astigmatic lenses including those with straight, circular and elliptical edges

Harris¹

1996

Ophthalmic and Physiological Optics

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The problem of locating the points of maximum and minimum thickness at the edge of a lens, and of calculating the thickness at those points, is examined for lens powers and for edge shapes in general. The edge extremal problem, as the problem is called, is solved explicitly for general powers along straight cut edges. The extremal problem is also analysed for lenses with circular and elliptical edges but explicit solutions are obtained only for centrally cut lenses, that is, lenses with coincident optical and geometrical centres. For edges that are neither straight nor centrally cut ellipses (including circles), it appears that explicit solutions cannot be obtained for the edge extrema: one has to resort to numerical solution of implicit equations or to the calculation of thickness at sufficiently many points around the edge. For the centrally cut ellipse the edge extremal problem turns out to be the eigenvalue problem of linear algebra. In general the thickness extrema at the edge do not lie on the principal meridians of the lens, nor do they lie on meridians that are mutually perpendicular. With minor modification the results apply equally well to the edge extrema for sagitta of a surface.

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Approximate matrix expression for the thickness of any lens generalized to allow for prism

Abstract: A single approximate matrix expression is derived that gives the thickness at any point on any lens. The lens may have dioptric power or prism power or both. The expression gives, amongst other things, the equation for lines of constant thickness.

Cited by 4 publications

References 7 publications

Local dioptric power matrix in a progressive addition lens

Local dioptric power matrix in a progressive addition lens

A generalization of Prentice's law for lenses with arbitrary refracting surfaces

Thickness extrema at the edge of astigmatic lenses including those with straight, circular and elliptical edges

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