how to extract the conic constant and RoC from a measured profile of an aspheric lens.

I've used a confocal microscope to measure the height profile of an aspheric MLA and need to extract the conic constant and RoC from the data. I have used the "Solver" add-on for Excel to do this but would like to be able to verify my results. I do not have many if any of the toolboxes.

standard asphere equation is z(r)= c*r^2/(1+sqrt(1-(1+k)c^2r^2) where c=1/RoC, z is lens sag, r is the distance from the center of the lens and k is the conic constant.

[Quentin Chaboche]

Hi,

I would say the best way to go is to fit the profile.

If you do not have any toolbox you will have to code your own algorithm, I personnaly use Newton-Gauss algoritm, which is quite simple.

You can also use fminsearch. It minimizes a function. You can define this function as the summed absolute difference of your data with the model (or RMS deviation or wathever). I feel like this way does not always converges well.

If you want a simpler but quite rough approximation for the RoC, you can fit a sphere around the vertex. It will not be exact, your RoC will be under-estimated.

Then you will need the half-diameter of your lens (call it a=diam/2), as well as the height of your lens (call it h). You can invert the formula to get the conic.

.

For the RoC, you can also use the focal distance of your lens.