Physiological optics 9th lecture

Physiological optics
9th lecture
Dr. Mohammad Shehadeh
Optical Prescriptions, Spectacle
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
• 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
Conventional orientation
for cylindrical lenses.
• 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
• component, i.e. a toric astigmatic correction. In
such a case, at the end of refraction the trial
• 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
• 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
• When a lens prescription is changed from one
lens form to another optically equivalent
form, the process is called transposition of the
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 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
Toric Transposition
• Toric transposition 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
• The base curve must be specified if toric
transposition of a lens prescription is required
• with base curve –6 D.
• The toric formula is written in two lines, as a
• 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
• 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
(4) Add the required cylinder to the base curve
power with its axis as in (b) in step 1
• The complete toric formula is thus
• Some further examples for calculation are
given below:
• to the base curve +6 D
• to the base curve –6D

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