Optics

Case 10.1

A 50-year-old school crossing guard complains of difficulty in seeing cars at a distance; her current eye glass prescription is −4.50 diopter (D) oculus uterque (OU), and she is 20/50 OU. The new manifest refraction contains a cylinder correction, oculus uterque (OU) −7.00 + 1.50 × 90, and corrects to 20/25 OU. One week later, the patient returns complaining that although her vision has improved with her new eyeglasses, she feels that her eyes are being pulled from her head. She tells you that in the past, other doctors have tried to cure her astigmatism with glasses, but each time, she cannot tolerate those glasses. She is asking you to remove the astigmatism prescription from her glasses.

FIGURE 10.1

10.1 Crossing Guard

PRESENTATION

Bottom Line Up Front: I would not prescribe this patient astigmatic correction; instead, I would prescribe the spherical equivalent of her manifest refraction, which is -6.25 OU. I would explain to the patient that her vision would be better than her old glasses, but not as clear as the prescription with the astigmatic correction. I would reassure her that overall, she would be happy, and that I shall continue to make more adjustments until she is satisfied.

Device: Glasses with myopic and astigmatic correction

Optical Principle: Astigmatism: In eyes with astigmatism, the image does not focus on a single point. Variations in the curvature of the cornea or lens at different meridians prevent the image from focusing to a single point. In fact, in astigmatic eyes, there is no single focal point, but instead a set of 2 points.

Explanation: The correction of astigmatism with correcting lenses follows the same optic principles as correction for myopia or hyperopia. However, the required power (cylinder) must be determined separately. If the refraction is appropriate, the image would fall into one point in the retina. Cylinders in spectacle eyeglasses produce optical distortions, called meridional aniseikonia, that cause unequal magnification of retinal images from various meridians. Patients vary in their ability to tolerate distortion, and young patients are able to adapt much easier than adults.

In the case above, the patient has a long-standing history of inability to tolerate astigmatic correction. Elimination of the cylinder and axis in her prescription could benefit her. In order to eliminate the cylinder, we need to calculate the spherical equivalent, which takes the average spherical power of all the meridians of the spherocylindrical lens and provides a somewhat blurred retinal image.

Step 1: Review the existing manifest prescription in diopters:

-7.00-sphere +1.50 cylinder × 090 degrees axis

Step 2: Calculate the spherical equivalent of the prescription by eliminating the cylinder by using the spherical equivalent optics formula:

Spherical equivalent formula = sphere + (1/2) cylinder

Sphere = -7.00, cylinder = +1.50

Spherical equivalent = -7.00 + (1/2)(1.50)

Spherical equivalent = -7.00 + 0.75

Spherical equivalent = -6.25

Step 3: Give the patient a new spherical equivalent prescription of -6.25 to both eyes to alleviate the symptoms she is having from the cylinder prescription.

Case 10.2

A medical student rotating through your clinic finds the circle of least confusion rather confusing. The circle of least confusion is the location where all rays meet to focus if the lens had a spherical power equal to the average spherical power of all the meridians of the spherocylindrical lens. This averaging method is called the spherical equivalent of the lens. He wants to know how in the world you calculate the circle of least confusion for your patients.

FIGURE 10.2

10.2 Circle of Confusion

PRESENTATION

Bottom Line Up Front: The circle of least confusion is the same as the spherical equivalent, which is easily derived from the patient’s manifest refraction by using the formula:

Spherical equivalent formula = sphere + (1/2) cylinder

Device: Conoid of Sturm

Optical Principle: The conoid of Sturm has two focal ellipses with each one parallel to one of the principal meridians of the spherocylindrical lens. At the dioptric mean of the two ellipses, there is a circular area that is called the circle of least confusion, which is calculated by determining the spherical equivalent.

Explanation: As an example, I would provide the medical student a manifest refraction, so that he can calculate the circle of least confusion aka spherical equivalent.

Step 1: Give the medical student a simple example of a manifest prescription to review such as +2.00 sphere + 1.00 cylinder × 045 degrees.

Note: When using the spherical equivalent formula, you ignore the axis in the manifest prescription as it is not pertinent in the spherical equivalent calculation.

Step 2: Calculate the spherical equivalent of the prescription by eliminating the cylinder.

Spherical equivalent formula =sphere + (1/2) cylinder

Sphere = +2.00, Cylinder = 1.00

Spherical equivalent = +2.00 + (1/2)(1.00)

Spherical equivalent = +2.00 + 0.50

Spherical equivalent = +2.50

Step 3: The medical student could give the hypothetical patient a manifest prescription of +2.00 sphere + 1.00 cylinder × 045 degrees, or a spherical equivalent prescription of +2.50 + 2.50 is the spherical equivalent, which correlates with the circle of least confusion within the conoid of Sturm.

Case 10.3

A recent college graduate patient picks up her new eyeglasses from the optical shop. The optical shop attached a paper with lens prescription, which did not match the prescription she received from you.

The patient complains to the technician that her lenses were made with an incorrect prescription.

Paper attached with her glasses +5.00 sphere – 3.00 cylinder × 120

Prescription written by her ophthalmologist +2.00 sphere + 3.00 cylinder × 030