Hi everyone,
Could someone please explain how I can reconstruct the cornea shape using elevation data from a topography system? The data is in rectilinear coordinates and depicts the difference in elevation with respect to a reference sphere.
At first, I believed that simply adding the height of the reference sphere to the data at each location (x,y) would suffice. However, the attached article made me ponder by citing complicated methods like Zernike polynomials.
Is there anything I'm overlooking?
Let me know your thoughts.
Thank you,
Payman.
Despite the fact that this is not my field of work, you are right; it is enough to replicate a surface with X,Y and Z data and a good spread of data in a particular topological coordinate system model; In the case of a cornea it seems to be logical to use a system with manifold capabilities, this is the principle of several methods nowadays, but based on the formulation and the goals of the paper, what they are trying to simulate are some optical features, that is why they are testing the behavior of polynomial equations to simulate generic corneas characteristics and deformations. So, in this case, they are right in their approach. By the way, such an exciting paper and applicability.
I think how the cornea may change shape relative to the changing shape of the eye ball, i.e. does it maintain a spherical shape or can it also become an ellipsoid in which case then how do you transition between the two models. Google the paper below, it suggests the change in model you might consider.
Change in corneal shape and corneal wave-front aberrations with accommodation
Thank you, Henry and Julian, for your helpful suggestions and for taking the time to review my question. For my scenario, I'll give a try to Zernike polynomials.
My issue is that the elevation data is the difference between the best fit sphere and the actual elevation. The real data from spherical coordinates has been mapped into the rectilinear grid, and I now want to return it back to spherical coordinates, which distorts the grid spacing. It seems that in earth science they deal with the same issue by some scaling techniques. Is this taken into account by Zernike polynomials?
A distortion will exist or be expected because of dealing with different projections of the same space. A best fit sphere minimizes the error, therefore what I would do is knowing the orientation of the rectilinear coordinate system, determine the center of the sphere and its xyz offsets and orientation, aligning them in that system. Then at a regular angular intervals of choice to cover the required surface area, determine the spherical coordinates.
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