# Technical Note: Custom Ellipsoidal Replicated Mirrors

### Key Features

Custom replicated ellipsoid mirrors provide solutions to many challenges encountered by instrument designers. These mirrors can be fabricated in an infinite number of mounting configurations which can both simplify the alignment process, and position the mirror in the most economical location in the instrument.

### Optical Surface

Ellipsoids can be specified in many ways including the eccentricity (e = cos a/cos b< l ), the conic constant K (K = -e2) and the vertex radius, or both the major and minor radii (x2/a2 + y2/b2 =1, where a and b are the radii). For either method, the other characteristics can be calculated such as the spacing between f1 and f2 (d = 2 (a2 -b2)1/2), or the distance from the vertex to f1 (v = a-(a2 -b2)1/2). Hyperboloids are specified similarly.The tolerances of the shape of the ellipsoid or hyperboloid are very important. The most direct approach is to tolerance the distance between the vertex and f1, and the spacing between f1 and f2.

For an off-axis section of an ellipsoid, the center of the section must be specified as well. This can be done by specifying the angle between the axis of the ellipsoid and a ray from f1 to the ellipsoid section center. It also can be done by specifying the x-y coordinates of the center of the section relative to the ellipsoid. For either method, a tolerance must be given. By doing so, the equivalent of power will also be specified. Variation from a true ellipsoid may be given by specifying irregularity or by specifying the amount of energy in a blur circle diameter at the focal point.

### Alignment

Specifying the alignment of the mounting surface to the optical surface can be somewhat simple or very complex. The first decision to be made is whether the part will be pre-aligned or aligned in assembly. If aligned in assembly, the required number of degrees of freedom must be specified. Linear displacements and rotational interactions must be considered when aligning aspherics. Aspherics such as ellipsoids, are further complicated by having an object point and an image point. To reflect the light from the object onto the image plane using a fixed mount for these aspherics is impractical unless the resolution requirements are somewhat loose. Still, it is practical to provide alignment of the mounting surface for some degrees of freedom and provide adjustment for others. A linear adjustment on an ellipsoid may cause some acceptable level of deterioration in resolution while still locating the image plane in the correct position.

The specifications provided here represent the most common values for each parameter. If no alternate value is supplied, we will manufacture to these specifications.

### Specifications

The specifications provided here represent the most common values for each parameter. If no alternate value is supplied, we will manufacture to these specifications.

 Surface/Coating Quality 80/50; F/F per MIL-F-48616 (typical) Surface Roughness 25Å rms (typical) Power λ/4 pv @ 633nm (typical) Irregularity λ/4 pv @ 633nm (typical) Coating Aluminum overcoated with SiO (typical) Reflectance ≥85% (avg) 400 - 800nm (typical) Radius tolerance ±1.0% (typical)

### Ordering Information

We make custom ellipsoidal replicated mirrors according to customer defined specifications. These optics can be manufactured in both on-axis and off-axis configurations. Contact our applications experts to define the product that will provide the best performance for your application.