Problems with OptiCampus Vertical Imbalance Formulae.
HELP! I am coming up with different results with computing vertical imbalance for distance the old fashioned way. Here is my sample:
OD -9.00 +3.25 x150
OS -7.25 +3.50 x180
Add 2.75 OU
Vertical Displacement = 10mm
When I compute this, I compute the power of the OD lens @ 90deg to be a cyl of 2.44 (60deg shift in axis is 75% of power of cyl) which makes the power -6.56. In the OS I compute the power to be -3.75. This makes the imbalance 2.81 base down OD.
However, when I feed these numbers into Opticampus it tells me the vertical imbalance is 3.09 base down OD.
What am I doing wrong? The only thing I can think is that the Opticampus formula is computing a different cyl power 60 deg away on the right eye axis.
I believe that it is figuring the axis to be 66% @ 90
Power@90-OD= -9.00 + 3.25*sin(60)^2 = -6.56
Prism OD = 6.56
Prism OS = 3.75
Prism Imbalance = 6.56 - 3.75 = 2.81
I'm getting the same thing your getting and I am pretty confident in my result, it may be a bug in the software.
You are using the "power" through the vertical meridian of the lens to estimate the vertical prism produced by the lens. While this will get you in the ballpark, more complicated mathematics are required to compute the exact amount of vertical prism induced by a sphero-cylindrical lens whenever you are considering an oblique meridian (that is, not a principal meridian).
In fact, a small amount of horizontal prism is also induced when looking through the vertical meridian of a lens with cylinder power at an oblique axis, although the "sine-squared" approximation would not reveal this horizontal prism.
OptiCampus.com uses the exact mathematics for all calculations of prism. Moreover, OptiCampus.com calculates the vertical prism produced at a horizontal inset associated with the average near PD of the wearer, since the eyes converge whlie reading, which will also differ slightly from the result obtained by considering only the vertical reading level. These calculations can be found in most textbooks on ophthalmic optics.
That said, for calculations of vertical imbalance or slab-off prism compensation, the "sine-squared" approximation will typically suffice, since the exact amount of vertical prism imbalance is seldom necessary and the exact calculations are more tedious to do by hand. However, it is just as easy for the website to calculate the exact value, once the necessary calculations have been programmed.
Thank you for the clarification.
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