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Physiological optics 9 th lecture. Dr. Mohammad Shehadeh. Optical Prescriptions, Spectacle Lenses. Prescription of Lenses When prescribing a spectacle lens, the properties of the lens required are specified in the following way.

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physiological optics 9 th lecture

Physiological optics9th lecture

Dr. Mohammad Shehadeh

optical prescriptions spectacle lenses
Optical Prescriptions, Spectacle Lenses

Prescription of Lenses

  • When prescribing a spectacle lens, the properties of the lens required are specified in the following way.
  • A spherical lens alone is written as, for example, +2.00 DS (dioptre sphere) or –3.25 DS.
  • In the case of a cylindrical lens alone, both the dioptric power and the orientation of the axis must be specified.
  • The axis of the cylinder is marked on each trial lens by a line, and trial frames are marked according to a standard international convention

Thus, a cylinder of –2.0 dioptre power, placed with its axis (of no power) vertical is written as –2.0 DC axis 90° (DC = dioptre cylinder).

  • Often the correction of a refractive error entails the prescription of both a spherical and a cylindrical
  • component, i.e. a toric astigmatic correction. In such a case, at the end of refraction the trial frame
  • contains a spherical lens (e.g. +2.0 DS) and a cylindrical lens (e.g. +1.0 DC axis 90°).

The cylindrical lens is usually placed in front of the spherical lens to allow the axis line to be seen.

  • The prescription is written as +2.00 DS/ +1.00 DC axis 90°,
  • and this may be abbreviated to +2.00/ +1.0090°
transposition of lenses
Transposition of Lenses
  • When a lens prescription is changed from one lens form to another optically equivalent form, the process is called transposition of the lens.
simple transposition of spheres
Simple Transposition of Spheres
  • This applies to the alteration of the lens form of spherical lenses.
  • The lens power is given by the algebraic sum of the surface powers
simple transposition of cylinders
Simple Transposition of Cylinders
  • Simple transposition of the cylinder is often necessary when the examiner wishes to compare the present refraction with a previous prescription.

The lens depicted in Fig can be described in two ways.

(1) Let the cylindrical element be at axis 90°: the lens is now +2.0 DS/+1.0 DC axis 90°.

(2) Let the cylindrical element be of opposite power and at axis 180°: the lens is now +3.0 DS/–1.0 DC axis 180°.


This change in the description of the lens may be easily accomplished for any lens by performing the following steps.

  • (a) Sum. Algebraic addition of sphere and cylinder gives new power of sphere.
  • (b) Sign. Change sign of cylinder, retaining numerical power.
  • (c) Axis. Rotate axis of cylinder through 90°. (Add 90° if the original axis is at or less than 90°. Subtract 90° from any axis figure greater than 90°.)
toric transposition
Toric Transposition
  • Torictransposition carries the process one step further and enables a toric astigmatic lens to be exactly defined in terms of its surface powers.
  • A toric astigmatic lens is made with one spherical surface and one toric surface (the latter contributing the cylindrical power).
  • The principal meridian of weaker power of the toric surface is known as the base curve of the lens.
  • The base curve must be specified if toric transposition of a lens prescription is required

The toric formula is written in two lines, as a fraction.

  • The top line (numerator) specifies the surface power of the spherical surface.
  • The bottom line (denominator) defines the surface power and axis of the base curve, followed by the surface power and axis of the other principal meridian of the toric surface.

The steps of toric transposition are now defined taking the following case as an example.

  • to a toric formula to the base curve –6 D
  • (1) Transpose the prescription so that the cylinder and the base curve are of the same sign, for example:
  • becomes

(2) Calculate the required power of the spherical surface (the numerator of the final formula). This is obtained by subtracting the base curve power from the spherical power given in (b) in step 1

  • Put another way, to obtain an overall power of +4.0 D where one surface of the lens has the power –6 D, the other surface must have the power +10 D ( simple transposition of spheres).

(3) Specify the axis of the base curve. As this is the weaker principal meridian of the toric surface, its axis is at 90° to the axis of the required cylinder found in (b) in step 1. That is:


Some further examples for calculation are given below:

  • to the base curve +6 D
  • to the base curve –6D