Extended Asphere
The extended asphere surface is similar to the Even Asphere surface; see "Even Asphere". However, the extended asphere can support aspheric coefficients up to order 480, whereas the even asphere is limited to 16. Also, a slightly different method is used for computing the coefficients of the polynomial terms. The sag of the surface is given by the following expression:
where the first expression is identical to the Standard surface, and the second term is a power series sum over a normalized radial coordinate. The normalized radial coordinate ρ is used because then the coefficients αi all have units of lens units. The parameter terms are defined in the following table.
PARAMETER DEFINITIONS FOR EXTENDED ASPHERE SURFACES
| Parameter # | Definition |
| 13 | Maximum term number. The maximum is 240. |
| 14 | Normalization radius. All ray-intercept points are divided by this number to determine the x and y coordinates for polynomial evaluation. |
| 15 | Coefficient in lens units on ρ^2 |
| 16 | Coefficient in lens units on ρ^4 |
| 17-254 | 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 ρ14 , which is term number 7, then specify "7" in the maximum term number column. Note that the term number is 7, because it is the 7th 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. For modeling surfaces that are not well described by polynomials, see "Grid Sag" or "User Defined".
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