Odd Cosine
The odd cosine surface is an extension of the Odd Asphere surface, with 16 radial terms plus up to 6 additional cosine terms. The sag is given by:
The first term is the sag for a Standard surface (plane, sphere, or conic). The second term is similar to the Odd Asphere surface, but the number of coefficients is fixed at 16. The third term supports m cosine terms, where the integer m must be between 0 and 6, inclusive. The coordinate s is the normalized radial coordinate given by s = r / R, where R is the user defined normalization radius. If R is zero or negative, the cosine terms are ignored. The surface may not be continuous in the first derivative if any B values is not an integer. The βi coefficients have units which depend upon the index i, and the Ai coefficients have units of length in lens units. The angle θ is measured in radians and is related to the x and y coordinates on the surface by: tan θ = y/x.
The coefficient B is dimensionless and C is in units of radians. The coefficients are entered in the corresponding extra data columns, as shown in the following table.
PARAMETER DEFINITIONS FOR ODD COSINE SURFACES
| Parameter # | Definition |
| 13 - 28 | The odd aspheric coefficients βi . |
| 29 | The number of cosine terms m, must be between 0 and 6 |
| 30 | The normalization radius R for the coordinate s in the cosine portion of the sag formula. |
| 31 - 54 | The A, P, B, and C terms in the cosine portion of the sag formula. |
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