Monday, May 22, 2006



a. Surface type

  • Spherical - power and radius is the same in all meridians

  • Aspheric - radius changes from the center to the outside (becomes less curved usually)

  • Cylindrical- different powers in different meridians

b. Cylinder Optics: (Figure 30)

The power meridian is always 90 degrees away from the axis. Therefore, if the axis is 45 degrees, the power meridian is at 135 degrees.

Example: Plano + 5.00 x 45 = +5.00 @ 135° and Plano @ 45°

  • A cylinder is specified by its axis

  • The power of a cylinder in its axis meridian is zero.

  • Maximum power is 90 degrees away from the axis. This is known as the power meridian.

  • The image formed by the power meridian is a focal line parallel to the axis.

  • Example: Plano + 5.00 x 045° will have a focal line at 45 degrees.

  • There is no line focus image formed by the axis meridian, because the axis meridian has no power.

c. Astigmatism Types

With the rule astigmatism is corrected with a plus cylinder lens between 60 and 120 degrees.

Against the rule astigmatism is corrected with a plus cylinder between 150 and 30 degrees.

Therefore, oblique astigmatism is from 31 to 59 and 121 to 149 degrees.

Irregular astigmatism occurs when by retinoscopy or keratometry, the principal meridians of the cornea, as a whole, are not perpendicular to one another. Although all eyes have at least a small amount of irregular astigmatism, this term is clinically used only for grossly irregular corneas such as those occurring with keratoconus or corneal scars. Cylindrical spectacle lenses can do little to improve vision in these cases, and so for best optical correction, rigid contact lenses are needed.

d. Astigmatism of Oblique Incidence:

Tilting a spherical lens produces astigmatism. Tilting a plus lens induces plus cylinder with its axis in the axis of tilt. Tilting a minus lens induces minus cylinder with its axis in the axis of tilt. Therefore, if a lens is tilted along its horizontal axis, the increased plus or minus astigmatism will occur along axis 180. A small amount of additional sphere of the same sign is induced as well.

Click on image to enlarge.

e. The Interval or Conoid of Sturm: (Figure 31)

The interval is a conical image space bound by the two focal lines of a spherocylinder lens. At the center of the Conoid of Sturm is the Circle of Least Confusion. The Circle of Least Confusion is the dioptric midpoint of a cylindrical lens and is defined as the spherical equivalent of the cylindrical lens. This is where the horizontal and vertical dimensions of the blurred image are approximately equal. The goal of a spherical refractive correction is to choose a lens that places the Circle of Least Confusion on the retina. The smaller the Interval of Sturm, the smaller is the blur circle (Circle of Least Confusion).

Click on image to enlarge.

f. Spherical Equivalent:

Dioptric midpoint of a sphero-cylindrical lens. ½ cylinder power + sphere power. This is also known as the Circle of Least Confusion.

When one wishes to utilize only partial correction of the astigmatism, it is still desirable to keep the circle of least confusion on the retina. This is why we use the spherical equivalent formula to maintain the circle of least confusion on the retina.

g. Power Transposition: converting plus to minus cylinder and vice versa

To convert plus to minus cylinder and vice versa, add sphere power to cylinder power = new sphere power, change sign of cylinder power, change axis by 90 degrees.

Examples: +2.50 +3.50 x 95 = +6.00 – 3.50 x 005

–2.75 – 2.00 x 010 = -4.75 + 2.00 x 100

h. Base Curves of Lenses

  • The base curve is used to designate the lens form.

  • The base curve varies not only for different ranges of power but also for the same ranges of powers among different lens manufacturers.

  • The following definitions are standard for lenses (exceptions can be found):

  • For single vision spherical lenses it is the weaker of the two curves. The base curve will be the back or concave side of a plus lens and the front or convex side of a minus lens.

  • For astigmatic single vision lenses, it is the lesser (weaker/flatter) of the two curves on the side in which the cylinder is ground. For plus cylinder form lenses, the cylinder is ground on the front surface of the lens while for minus cylinder form lenses, the cylinder is ground on the back surface of the lens.

  • Because almost all lenses are designed in a minus cylinder form, manufacturers identify their lenses in terms of the front curve.

  • For multifocal lenses, the base curve is on the spherical side containing the reading segment.


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