Extended Polynomial
The extended polynomial surface is similar to the polynomial surface, except more terms are allowed. The surface also supports a base conic asphere surface upon which the polynomial aspheric terms are added. The surface sag is of the form:
where N is the number of polynomial coefficients in the series, and Ai is the coefficient on the ith extended polynomial term. The polynomials are a power series in x and y. The first term is x, then y, then x*x, x*y, y*y, etc. There are 2 terms of order 1, 3 terms of order 2, 4 terms of order 3, etc. The maximum order is 20, which makes a maximum of 230 polynomial aspheric coefficients. The position values x and y are divided by a normalization radius so the polynomial coefficients are dimensionless.
For example, the 12th term in the polynomial expansion, which is extra data term number 14, is the coefficient on the term in x2y2 . The coefficients Ai all have units which are the same as the lens units, such as millimeters or inches.
PARAMETER DEFINITIONS FOR EXTENDED POLYNOMIAL SURFACES
| Parameter # | Definition |
| 13 | Maximum term number (up to 230) |
| 14 | Normalization radius. All ray-intercept points are divided by this number to determine the x and y coordinates for polynomial evaluation. |
| 15-244 | Polynomial terms. |
The "Maximum term number" is used to specify the maximum polynomial term to be used in calculating the surface sag. This number is provided to speed the ray tracing calculation, as terms beyond this number are ignored. For example, if the last term in the series you wish to use is xy3 , which is term number 13, then specify "13" in the maximum term number column. Note that the term number is 13, because it is the 13th term in the polynomial expansion. The normalization radius scales the X and Y intercept coordinates of the ray so that the polynomial terms are all dimensionless and the coefficients are all in lens units.
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