Vertical Imbalance Compensation Formula

[OpticalS978]

OD Sph = -7.00
OD Cyl = -3.00
OD Axis = 30
OS Sph = -4.00
OS Cyl = 0
OS Axis = 0
Reading Level Distance(mm) = 10.0

On OptiCampus calculator http://opticampus.opti.vision/tools/vertical.php above input gives the answer:
Prism Compensation (Δ): 5.51, Base Up in RIGHT Eye

But when I manually calculate with below formula:

(ReadingLevelinCM * (odSph + (odCyl * sq (sin (odAxis-90))))) - (ReadingLevelinCM * (osSph + (osCyl * sq (sin (osAxis-90)))))

I get 5.25 Diopter prism.
What is the mistake in my formula?

[Robert Martellaro]

The sin^2 formula is an approximation, Darryl used a more complex formula for determining the power at 90 when there is cylinder component. The approximation is accurate enough to determine the cancelling prism used in a slab-off. Typically, I'll round down to the nearest half diopter.

Hope this helps,

Robert Martellaro

[OpticalS978]

Any chance I can get that formula?

The sin^2 formula is an approximation, Darryl used a more complex formula for determining the power at 90 when there is cylinder component. The approximation is accurate enough to determine the cancelling prism used in a slab-off. Typically, I'll round down to the nearest half diopter.

Hope this helps,

Robert Martellaro

[Robert Martellaro]

Any chance I can get that formula?

It can get very technical, right out of the gate. Books that come to mind are from Keating and Jalie.

https://www.elsevier.com/books/geometric-physical-and-visual-optics/keating/978-0-7506-7262-7

http://abdocollege.org.uk/product/pr...ses-5th-ebook/

I don't have either book, but they are probably on the shelves of the lens and medical equipment designers. You'll probably find the formulas you're looking for in these books.

Hope this helps,

Robert Martellaro