Phoropter debate - refractive distance

**SpecialT** · 01-15-2006, 12:38 PM

As a side note, we should probably just let this thread die!

**Graduate** · 01-15-2006, 01:59 PM

Originally Posted by Darryl Meister

Flat transposition is transposition involving just the prescription, without regard to lens surfaces or physical cylinder form (which would be toric transposition). It doesn't matter, for instance, whether you fill a -2.00 +1.00 x 090 Rx using a front (plus) or back (minus) cylinder; the prescription is still the same. The dioptric power matrix is a method of decomposing a prescription into a 2x2 matrix, which offers several advantages in vision science and visual optics.

Can you put it this way- Flat transposition = optical prescription transposition.
Toric transposition = surface transposition

I am not yet an optician, just learner so please bear mistakes.

**Darryl Meister** · 01-15-2006, 03:29 PM

I think your 2x2 matrix is similar to what I was taught as a "sphero-cylinder cross" diagram, but I'm not sure. Do you have any links to that concept?

If you do a search on Google for "dioptric power matrix," it will actually turn up quite a few links (unfortunately, many of the articles that use this terminology appear in vision science journals, which typical require a subscription).

The elements of the 2x2 dioptic power matrix can be computed from an ordinary prescription using these formulas:

Px = S + C sin^2 A
Py = S + C cos^2 A
Pt = -C sin A cos A
Pt = -C sin A cos A

Px represents the curvital power through the horizontal meridian, and Py represents the curvital power through the vertical meridian. This is essentially the "sine-squared" power through these meridians. Pt represents the torsional component of power, and is essentially a measure of how the power changes between these two meridians. (Note that the two Pt terms in the matrix are equivalent.)

One of the advantages of using this representation of power, for instance, is that the matrices are additive, which means that you combine two prescriptions by just summing the elements of the matrices, without using additional formulas for combining obliquely crossed cylinders.