Photonics Spectra - November 2011

Aspheric Optics:

Ask for What You Want BY TREY TURNER AND MARK DAMERY, REO

Advances in production make aspheres more readily available and usable at shorter wavelengths, but the methodology is distinctly different from that of spherical optics. It is vital to understand the cost impact of various specifications – and to communicate top priorities. An experienced asphere manufacturer can propose minor changes to reduce cost significantly while still delivering target performance or better.

Aspheres give the designer a powerful tool that can help re- duce the total number of components in a system by de- creasing the optical aberrations contributed by each lens surface. For this reason, they are often found in applications that demand that the physical weight and size of the system be minimized, but that still require a high level of optical performance.

However, although aspheres can make the designer’s task easier, they are generally more difficult to fabricate than spherical surfaces and, hence, more costly. Understanding how single-point diamond-turned aspheric lenses for infrared and visible uses are fabricated and tested can help the purchaser properly specify aspheres and avoid creating requirements that drive up cost unnecessarily.

Specifying, fabricating aspheres

The shape of a spherical surface can be specified with a single number: the radius of curvature. In contrast, rotationally symmetric aspheric surfaces are most typically specified using a limited form of the general aspheric equation (Equation 1).

This equation may appear in slightly different forms, depending upon the exact sign convention used, so the designer should perform a reality check with the lens manufacturer to ensure that there are no misunderstandings. It is better to have the customer specifically state whether the curve is convex or concave, rather than simply rely on the sign of the curvature term in the equation to indicate shape. The designer should also provide a table of sag heights as a function of radial distance for the curve. This is useful because sag height is the quantity that is most easily measured directly during component fabrication.

Manufacturing tolerances for spherical surfaces are usually stated as power and irregularity values. Power is the amount that the average base radius of curvature deviates from the desired value, and irregularity is how much the part departs from its ideal shape (for example, a perfect sphere). Similarly, aspheres are specified with a tolerance on the base radius (analogous to power), plus a tolerance for sag deviation (equivalent to iregular-ity). The radius tolerance usually is given as a percentage, with ±0.1 percent being a typical value. A given percentage tolerance

z ;

1 ;√1 ;(1 ; K)c2r2 cr2 ;Ar4 ; Br6 ; Cr8 ; Dr10

Equation 1. z = sag height; r = radial distance from the vertex; c = base curvature (1/base radius); K = conic constant (0 = sphere, −1 = parabola, ≤1 = hyperbola); A, B, C & D = aspheric coefficients.

on radius becomes progressively more difficult to achieve as the absolute value of the radius gets smaller. As with irregularity, sag deviation is usually stated in (peak to valley) fringes, with a value of 0.5 fringes being typical.

High-precision aspheric lenses for infrared and, in some cases, even visible applications are often fabricated using single-point diamond-turning technology. However, to minimize time, the process often starts with production of a spherical surface that most closely matches the desired asphere. This is accomplished using the same type of generating equipment used for traditional spherical optics fabrication.

To produce the aspheric profile, single-point diamond turning is performed on a lathe configured very much like that used for machining metal parts, albeit built to achieve much higher precision. The cutting tools themselves are gem-quality diamonds. The addition of multiaxis tool motion synchronized with spindle rotation also enables the production of nonrotationally symmetric surfaces such as toroids and off-axis parabolas.

The initial setup for diamond turning involves centering the part on the spindle and setting several process variables, such as tool angle, tool location, depth of cut, feed rate, position of the coolant, and even the ambient temperature and humidity in the room. This process is time-consuming and thus costly. However,