Optical Shop Testing

Chapter 18 - Mathematical Representation of an Optical Surface and Its Characteristics

18.1.  DEFINITION OF AN OPTICAL SURFACE

Aspherical surfaces are extremely important in optical systems and have been
studied and described by many authors, for example, by Schulz (1988) and Shannon
(1980). Of special interest are surfaces with rotational symmetry, which may be
defined by means of the following relation, taking the z axis as the axis of revolution:

where S2 = x2 + y2 and c = 1/r = 1/radius of curvature. Also, A1, A2, A3, and A4 are
the aspheric deformation constants, and K is a function of the eccentricity of a conic
surface (K = -e2), called the conic constant. If the Ai are all zero, the surface is a
conic surface of revolution, according to the following Table 18.1:

In an ellipsoid with rotational symmetry about the z axis, the excentricity is
defined as

 

where a is the major semi-axis, along the z axis and b is the minor semi-axis, along
the y axis. For the case of the oblate spheroid, the same definition (18.2) holds but
then a is the minor semiaxis, along the z axis and b is the major semi-axis, along the y
axis. Thus, the excentricity is an imaginary number and K > 0, since a < b.

 

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