Binary 4

The Binary Optic 4 surface is similar to the Binary Optic 2 and 3 surfaces. The key difference is that the Binary Optic 4 supports a variable number of concentric radial zones, with independent radial size, radius, conic, diffraction order, polynomial aspheric deformation, and diffractive phase data for each zone. The number of zones, even asphere coefficients, and phase coefficients, are all user definable, up to the maximum allowed number of values in an extra data file (see the Import section of the Surface Properties). Each zone requires 4 values (aperture, radius, conic, and diffraction order) plus a variable number of even aspheric and binary phase coefficients. The total number of terms is Nz*(4 + Na + Np) where Nz is the number of zones, Na the number of asphere terms, and Np is the number of phase terms. The total may not exceed 242 terms. Nz must be between 1 and 60; Na and Np must be between zero and 20.

The surface is divided into zones. The first zone extends from the vertex to the radial coordinate, A1, the second zone from A1 to A2, and this continues through the last zone. The radial coordinates are also used for normalizing the aspheric and phase coefficients within their respective zones. Each zone is offset from the prior zone to make the surface sag continuous across the zone boundary. OpticStudio requires that the first zone have a radial aperture larger than zero, and each subsequent zone must be larger than the previous one.

The sag of the surface in zone j is given by the following expression:

Note c, k, and the α terms are all unique to each zone. The term zo is chosen to make the surface continuous across the boundary between the current and prior zone at the radial coordinate Aj – 1 , or

(the value of zo is temporarily set to zero while evaluating zj for this calculation). The normalized coordinate p is given by r / Aj.

All zones also may have a diffractive phase profile, with independent coefficients. The phase in zone j is given by:

where Np is the number of polynomial coefficients in the series, β1i is the coefficient on the 2i th power of ρj ,  which is the normalized radial aperture coordinate, and Mj is the diffraction order.

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 Φj for this calculation).

Note that the normalization radius for the outermost zone is used only for defining the radial aperture to normalize the coefficients for the outer zone. The outer zone of the surface, and the associated phase profile, may extend beyond this value.

The multiple 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 = Q2π, where Q is some arbitrary integer. This condition can usually be met by a small change in Aj , 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 for each of the zone boundaries and places the sum of the squares (SS) of this value in parameter 4. 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.

PARAMETER DEFINITIONS FOR BINARY OPTIC 4 SURFACES

Parameter # Definition
1 Nz
2 Na
3 Np
4 SS sin ẟo
13 The radial aperture of zone 1.
14 The radius of curvature of zone 1.
15 The conic constant of zone 1.
16 The diffraction order of zone 1.
Next Na The aspheric sag coefficients for zone 1.
Next Np The phase coefficients for zone 1.
Remainingterms The pattern continues in groups of 4+Na+Np coefficients for Nz groups.

Binary optic coefficients sign conventions

See "Binary Optic 1" for a discussion of sign conventions.

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