Could someone please let me know what exactly is a power map. My understanding of Power Map is a pictorial represenation of the distribution of the power in a lens radially in case of intra-occular lenses and also for lenses in general. Do we have an ISO NORM or some kind of reference that can explain in detail or give a proper idea about how a power map should look like and the relation of it with Shack Hartmann wavefront sensor?
If an incoming ray is parallel to the optical axis and hits the lens at the coordinate (r1,Phi1) it will cross the optical axis in a distance f1 behind the lens. The local power is defined as the inverse distance 1/f1. Do this calculation with multiple rays hitting different points on the surface of the lens and you get the local power 1/f(r,Phi) as a function of the coordinates {r,Phi} on the lens surface. This is what typically is referred to as a "power map".
The wavefront is a surface that is perpendicular to all rays. Consequently, it contains the same information also included in the function f(r,Phi) and the power-map can be calculated based on the wave-front measurements.
How can we calculate the power map using the wavefront? Can you specify an algorithm or a better method for it?
You can treat the wavefront as a surface. The normals to the surface point in the direction of the light propagation at any point on the surface. Then you can trace the rays to find the intersection with the optical axis f(r,Phi) and deduce the power-map.
The most simple example is a spherical wavefront of radius R. The normal to a sphere always points to the center of the sphere. Thus the spherical wavefront corresponds to a uniform power-map with the power 1/R. In a spherical lens, the positive spherical aberrations results in a shorter radius of curvature at the edge compared to the center of the lens. The shorter the radius of curvature, the shorter the focal lenght and the larger the optical power.
Simon Schröder : I understood your method. There is no ISO Norm that defines what a power is and hence I was doubtful about this. Have you come across any kind of Norm or shall I take what you have written as information based on your knowledge and not on concrete papers? I am confused. for me, power map is something that shows the distribution of power over the Lens surface but this is something I know based on what I think.
Do we have a reliable source where this has been published properly?
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