Cylinders and compound lenses.  Optical cross.  Flat transposition. 

PAGE References to Optical Formulas Tutorial:  (first reference is to edition 1 / second reference is to edition 2).

Toric surfaces and lenses

Looking at a lens from the front, when we were dealing with lenses that were just spheres it would not have mattered how we made a cut for a cross-section on the lens: the curves in every direction would have been circular and would have come from a circle that had the same radius as every other curve. (All of our cuts or cross-sections will be through the 'optical center' or the point where the lens is either the thickest or the thinnest.)

On the lenses that we are dealing with now, when we make these cuts or cross-sections, the curves will be different, depending on how you cut the lens.

The lenses that we make virtually all have spherical front surfaces. When we make toric or sphero-cylindrical lenses, the back surface is of the type where there are a lot of different curvatures, depending on what direction we make the cross-section.

Lets look at a cylinder again. The can that we were dealing with had one flat direction, one circular direction, and every other direction was curved but was not a circle. A true cylindrical lens will have one direction that has no power, a direction 90 degrees away that has power (either plus power or minus power) and every direction in-between will have an approximate power that is in-between the other two powers but which is not based on a true circle and therefore will not give an actual, true power.

If we combine a lens that is a spherical lens, (which means it has the same power in all directions) with a cylindrical lens (which means it has no power in one direction and some power in the other direction) we end up with a sphero-cylindrical lens: a lens with two major powers 90 degrees apart. This lens is a combination of a spherical +2.00 lens with a cylinder that has no power in one direction and another +2.00 power in the other direction. The result is a lens with +2.00 power in one direction, and +4.00 power in the second direction.

Read pages (39-40 / 52-54) in the Optical Formulas Tutorial, if you have not already done so, but do not do any of the exercises in the book yet.

The horizontal meridian is the 0-180 line, when we look at a lens as a circle. So, in the lens diagrammed to the left, we have a power of +2.00 on the horizontal or 180 meridian. This +2.00 power is ACTUALLY the +2.00 from the spherical component plus 0.00 from the cylindrical component.

On the vertical meridian, or the 90th meridian, we had a power of +4.00. This is actually +2.00 from the sphere, plus +2.00 from the cylinder.

We write the strictly spherical prescription as +2.00 D or +2.00 DS or +2.00 sphere. So, if the lens was ONLY the first one in the diagram, where there is +2.00 everywhere on the lens, then the prescription could be written any of those ways.

We write a cylinder as pl +2.00 x180. This is saying that there is pl or plano or 0.00 or no power on the 180 meridian, and there is +2.00 90 degrees away from that meridian. (The x means 'axis'.) So if we had a lens that was ONLY the second one on the diagram, we would have the prescription pl +2.00 x180.

If we want the third diagram shown here, where there is +2.00 D on the 180 and +4.00 D on the 90, we say +2.00 +2.00 x180, which means: +2.00 on the 180 meridian, and another +2.00 ADDED TO THAT on the 90th meridian.


 

What does a prescription of -3.00 -1.00 x090 mean?

  1. It means that we have -3.00 D on the 90th meridian. This is the spherical portion, and we are considering the lens to be a sandwich of a spherical lens with a cylindrical lens. The cylinder has NO POWER on the 090 in this example.
  2. It means that we have -3.00 from the sphere PLUS -1.00 from the cylinder 90 degrees AWAY from the axis of 090. 90 + 90 = 180, and -3.00 + (-1.00) = -4.00, so the lens has -4.00 power on the 180 meridian.
The optical cross or lens cross or lens diagram that is discussed on pages (40-44 / 54-60) is simply a way of showing what power belongs on what meridian of the lens. Read through these pages and follow the examples, but do not do the exercises yet.  DO NOT READ the cross cylinder form Optical Formulas Tutorial unless your instructor tells you to do so. This notation is less common in the U.S., but in some areas you may see it.

Remember as you put the prescription on the optical cross or take it off the optical cross, all you are doing is showing the two major meridians where there is precise power. If you have been using the focimeter (lensometer) at work, you are showing the powers that you get on the power wheel, plus the axis that you get for one of them.


PUTTING THE PRESCRIPTION ON THE OPTICAL CROSS
  1. Draw the optical cross.
  2. Label one leg of the optical cross with the sphere reading and the axis of the prescription.
  3. Add together the sphere and the cylinder amount. Label the second leg of the optical cross with this power.
  4. If the axis is less than or equal to 90, add 90 to it. If the axis is greater than 90, subtract 90 from it. Label the second lag of the optical cross with this meridian.
TAKING THE PRESCRIPTION OFF THE OPTICAL CROSS
  1. Choose one power/axis combination. 
    • If you are doing minus cylinder form, choose the most plus or least minus -- the highest one on the scale on page (43 / 57).
    • If you are doing plus cylinder form, choose the least plus or most minus -- the lowest one on the scale on page (43 / 57).
  2. Write the power from this power/axis combination as the sphere power.
    3. Write the axis from this power/axis combination as the axis.
  3. Subtract:   [the power you did not use in step 1]  minus  [ the power you used in step 1].
  4. Write the result of step 3 as the cylinder amount.

Lets do a few more, and I will show you the answers. As before, you do them first, then click on the answers.

    Place on the optical cross:
  1. +5.00 +1.00 x135
  2. -1.25 -3.25 x045
  3. +3.50 -3.50 x090
  4. pl -1.25 x 110
  5. +0.50 -1.75 x115
Write the prescription in minus cylinder form:

  Write the prescription in plus cylinder form:

 
 

Answers are here.

Now go back to Optical Formulas Tutorial and do the exercises in the sections that we've covered.  DO NOT DO Crossed Cylinder notation, unless your instructor tells you to do so.
  


 
  Next is Toric Transposition.