For normalised Zernike coefficients, recommended in ANSI Z80.28, the sphere power is:

Ssph = 4 sqrt(3) C2,0 /  RP2.

where RP is the pupil radius in mm, and C2,0 is the (rms) amplitude of the Z20 Zernike mode in micrometers.

http://webstore.ansi.org/RecordDetail.aspx?sku=ANSI+Z80.28-2010

http://www.cheapcodes.org/3998-ANSI-Z80-28-2010.html

Thank you. Could you please tell me the formula for cylinder (Astigmatism 00 and 450) power in terms of the diopters.

Power for the cylinder terms varies with azimuth

S(0)  = +2 sqrt(6) C2,2 / RP2.      at 0 degrees

S(90) = -2 sqrt(6) C2,2 / RP2.     at 90 degrees

Peak-peak variation in power Scyl = 4 sqrt(6) C2,2/ RP2.  This is what is normally referred to as the cylinder power.

Similarly for the Z2-2 coefficient at 45 and 135 degrees.

The Zernike distortions are orthogonal, so the net cylinder power is given by the root-sum-of-squares of the Z2-2  and Z2+2 coefficients.

In typical ophthalmic practice, the reported cylinder term is asymmetric, corresponding to a lens with zero power in the reference axis.  This is achieved by adding a sphere term with half the peak-peak power.  The reported sphere distortion is adjusted by subtracting an equivalent value from the reported sphere power.

Thanks for your time.

Can you please, share this document with me ?

Dear Reddikumar

Refer to our work jmo 59 1034, 2012