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
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,
Figure 1. Definition of the aspheric surface variables: r = radial distance
from the vertex; z = sag height. Courtesy of REO Inc.