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Kinoform surface

The kinoform surface is a geometrical ray approximation to a diffractive surface whose sag is an axially symmetric spheric or aspheric profile and whose diffractive microstructure is also axially symmetric. Such a surface exhibits both refraction and diffraction that deflects light radially. The figure below shows schematically the effect of a planar kinoform on a ray of light travelling parallel to the optical axis and incident on the kinoform:

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The sag equation is that of an aspheric surface. In addition to the sag equation, the kinoform has a phase function that describes the diffractive microstructure. In the figure above this is indicated by the radial color gradient. The phase function is an even polynomial in the radius:

\varphi=b_2 r^2 + b_4 r^4 + \ldots ; r^2=x^2+y^2

The polynomial is defined by its series of coefficients (b2, b4, etc.). The radius is divided by the normalization radius rnorm so that the coefficients are dimensionless. The phase and coefficients are expressed in radians.

The polynomial coefficients are entered in the parameters section of the surface data editor.

A ray diffracted into the first order by the kinoform has its momentum incremented parallel to the surface, by an amount equal to

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Upon passing through the surface, the optical path length (OPL) of the ray is incremented by

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The effect of refraction is included, if the refractive index after the surface differs from the refractive index before the surface.

The diffraction order is specified by a surface parameter. The deflection momentum is proportional to the order. Usually the diffractive microstructure is defined so that most energy is diffracted into the first order.

Parameters

m
Diffraction order (initial value is one)
a2, a4,..., a16
Aspheric coefficients for surface sag
nterm
Number of terms of the phase polynomial that will be included in the sum. The order of the polynomial is twice this number.
rnorm
Normalization radius rnorm
b2, b4,..., b396
Coefficients of the phase polynomial

For compatibility with the ZEMAX BINARY_2 surface, the maximum exponent in the phase polynomial is 396 for a total of 198 terms.

See also