Conjugate
The conjugate surface is defined by two user-specified points. OpticStudio always uses the surface vertex as the reference point; the two points required to define the conjugate surface are specified relative to this vertex. The conjugate surface will always perfectly image one point to the other point, assuming the surface is a mirror. Although the conjugate surface can have any material type, it is useful to think of it as being defined by its reflective properties.
If the z-coordinates of the two points are either both positive or both negative, then the image formed from one of the points to the other is real. In this case, the distance from one of the points to an arbitrary point on the surface, plus the distance from the arbitrary point on the surface to the second point, is constant for all points on the surface. One additional constraint is needed to make the surface unique: the surface must pass through the vertex of the local coordinate system. If the surface is reflective, then one point is the conjugate of the other, hence the name.
The surface generated by these two points satisfies the following expression if both z1 and z2 have the same sign:
Note that the surface must intersect the point (0,0,0). Several types of surfaces can be formed with this model. For example, a sphere can be formed by setting the x and y values to zero, and the two z values each to the radius of the sphere. An elliptical surface of arbitrary orientation can be formed by specifying non-zero values for either the x or y values.
If z1 and z2 have opposite signs, then the image formed from one of the points to the other is virtual. In this case, the distance from one of the points to an arbitrary point on the surface, minus the distance from the arbitrary point on the surface to the second point, is constant for all points on the surface. Like the real imaging case, the surface must pass through the vertex of the local coordinate system.
The surface generated by these two points satisfies the following expression if z1 and z2 have opposite signs:
Note that the surface must intersect the point (0,0,0). Several types of surfaces can be formed with this model. For example, a hyperbola can be formed by setting the x and y values to zero, and the two z values to opposite values. If the z values are equal but opposite, then a plane will be generated.
The coordinates of the two construction points are specified in the parameter columns, as shown in the following table. Neither the z1 nor the z2 value can be zero.
PARAMETER DEFINITIONS FOR CONJUGATE SURFACES
| Parameter # | Definition |
| 1 | x1 |
| 2 | y1 |
| 3 | z1 |
| 4 | x2 |
| 5 | y2 |
| 6 | z2 |
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