Binary 3
The Binary Optic 3 surface is very similar to the Binary Optic 2 surface. The key difference is that the Binary Optic 3 supports two concentric radial zones, with independent radius, conic, and polynomial aspheric deformation and diffractive phase data for each zone. The surface is divided into two zones by two radial coordinates, A1 , and A2 . The inner radial zone extends from the center of the surface to the radial coordinate A1 . The outer radial zone extends from A1 outward. The radial coordinate A2 is used for normalizing the phase coefficients in the outer zone, even though the surface may extend past the coordinate A2 . The outer zone is offset from the inner zone to make the surface sag continuous across the zone boundary, unless the optional "break" parameter is set to 1. OpticStudio requires that 0 < A1 < A2.
The sag of the surface in the inner zone is given by the following expression:
where N is the number of aspheric terms which may be set by the user as described below. The value for the inner zone curvature, c1, is the reciprocal of the radius of curvature specified in the Lens Data Editor. The inner zone conic constant is also set in the Lens Data Editor, in the usual conic column. A similar expression with different coefficients and an offset value is used to define the sag of the surface in the outer zone:
where the term zo is chosen to make the surface continuous across the boundary between the inner and outer zones at the radial coordinate A1 , or zo = z1 (A1) – z2 (A1 ) (the value of zo is temporarily set to zero while evaluating z2 for this calculation). The outer zone radius of curvature (from which the value c2 is computed) and the outer zone conic are set in the parameter data as described below. For a flat outer zone radius, use zero.
Both the inner and outer zones have a diffractive phase profile, with independent coefficients. The phase of the inner zone is given by:
where N is the number of polynomial coefficients in the series, β1i is the coefficient on the 2i th power of ρ1 , which is the normalized radial aperture coordinate, and M1 is the diffraction order. A similar expression describes the phase for the outer zone:
The phase offset serves a similar purpose to the sag offset, and is defined by
(the value of ẟo is temporarily set to zero while evaluating Ω2 for this calculation).
Note that the normalization radius A2 is used only for defining the radial aperture to normalize the phase coefficients for the outer zone. The outer zone of the surface, and the associated phase profile, may extend beyond this value.
The dual zone nature of this surface creates a complication when computing the phase of the surface as the zone boundary is crossed. The phase offset value ẟo makes certain the phase is continuous across the zone boundary. This is desirable for design and analysis purposes, because phase jumps of hundreds of waves make interpretation and analysis difficult. However, the phase offset is artificial, and this must be accounted for in the actual design. For optimum imaging properties, the outer zone should be in phase with the inner zone. This condition is met when the inner and outer zones differ in phase by an integral number of wavelengths at the boundary, or more to the point, if ẟo = J2π , where J is some arbitrary integer. This condition can usually be met by a small change in A1 , as long as there is some difference in the slope of the phase on either side of the boundary. To make this boundary condition simple to meet, OpticStudio computes sin ẟo and places this value in parameter 7. The merit function boundary operand PMVA can then be used to target this value to be zero. Note this value is computed from the phase data, and should not be user defined or made variable.
The difference in sag between the inner and outer zones can be accounted for two ways. If the "Break?" parameter is set to 0, then the outer one is shifted along the local z axis so that the surface is continuous at the zone boundary. If "Break?" is set to 1, then the outer sag is defined by the sag equation with no offset, and in general a discontinuity in the sag will result. This discontinuity will cause a large discontinuity in the OPD computations that OpticStudio cannot subtract out.
PARAMETER DEFINITIONS FOR BINARY OPTIC 3 SURFACES
| Parameter # | Definition |
| 1 | R2 |
| 2 | k2 |
| 3 | A1 |
| 4 | A2 |
| 5 | M1 |
| 6 | M2 |
| 7 | sin ẟo |
| 8 | Break? |
| 13 | Maximum term number, N (up to 60) |
| 14,15,16,17 | The coefficients α11, β11, α21, and β21 if N >= 1. |
| 18,19,20,21 | The coefficients α12, β12, α22, and β22 if N >= 1. |
| 22,23,24,25,etc. | The pattern continues in groups of 4 coefficients for N groups. |
Binary Optic Coefficients Sign Conventions
See "Binary Optic 1" for a discussion of sign conventions
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