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Using a phoropter to determine a prescription for eyeglasses. An eyeglass prescription is an order written by an eyewear prescriber, such as an optometrist, that specifies the value of all parameters the prescriber has deemed necessary to construct and/or dispense corrective lenses appropriate for a patient.
A secant plane is a plane containing a nontrivial section of a sphere or an ellipsoid, or such a plane that a sphere is projected onto. Secant planes are similar to tangent planes, which contact the sphere's surface at a point, while secant planes contact the surface along curves.
While in principle aspheric surfaces can take a wide variety of forms, aspheric lenses are often designed with surfaces of the form = (+ (+)) + + +, [3]where the optic axis is presumed to lie in the z direction, and () is the sag—the z-component of the displacement of the surface from the vertex, at distance from the axis.
To measure the radius of a sphere—e.g. the curvature of a lens—the spherometer is leveled and read, then placed on the sphere, adjusted until the four points exert equal pressure, and read again. The difference gives the thickness of that portion of the sphere cut off by a plane passing through the three feet.
On top is a depiction of a perfect lens without spherical aberration: all incoming rays are focused in the focal point. The bottom example depicts a real lens with spherical surfaces, which produces spherical aberration: The different rays do not meet after the lens in one focal point.
The sphere has the smallest total mean curvature among all convex solids with a given surface area. The mean curvature is the average of the two principal curvatures, which is constant because the two principal curvatures are constant at all points of the sphere. The sphere has constant mean curvature.
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For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...