The aberration correction of aspheric lenses makes them critical components in many optical systems, as they can reduce the number of optical components required while maintaining or improving performance. Knowing how to properly specify aspheric lenses is essential for maximizing performance without unnecessarily increasing cost. Specifications have a direct impact on the cost of the finished part and may not be supported by available manufacturing capabilities.
The following rules of thumb specifically refer to computer numerical controlled (CNC) ground and polished glass aspheres. Different considerations become important when specifying aspheres manufactured through different processes, such as plastic molding.
Many parameters beyond index of refraction and Abbe number factor into selecting the best glass material for a custom aspheric lens. Harsh environmental conditions may increase the importance of chemical properties such as water, acid, and abrasive resistance, which can be found on glass datasheets. These factors also impact manufacturing yields, which in turn affect cost. In applications involving extreme temperatures and sudden temperature changes, the coefficient of thermal expansion becomes a key factor for designing optomechanical assemblies. High-energy applications, such as laser materials processing or medical lasers, often benefit from low-absorption materials such as IR or KrF Grade Fused Silica.
However, over-specifying these parameters or letting optical design software optimize your design by varying the glass type may unnecessarily limit you to rare materials with high costs and lead times. Letting your optical designer and supplier know the exact use conditions of your final system will help make sure that your custom aspheres deliver the required level of performance without costly over-specification.
Specifying the Aspheric Surface
While the entire surface of a spherical lens can be specified using just the radius of curvature, the surface of an aspheric lens is more complicated to characterize, as the local radius of curvature varies across surface. Rotationally symmetric aspheres are typically defined with a surface sagitta, or sag, given by the even aspheric polynomial:
Z: sag of surface parallel to the optical axis
s: radial distance from the optical axis
C: vertex curvature, inverse of vertex radius
k: conic constant
A4, A6, A8...: 4th, 6th, 8th… order aspheric coefficients
When specifying a custom asphere, it is important to make sure that you and your optical supplier are using the same form of the aspheric polynomial to prevent miscommunication. Even if an asphere design is optimized using a different function, such as a Q-type polynomial, it can also usually be described using the even aspheric polynomial.
Providing a full sag table with the surface height at various radial distances also helps ensure that both parties fully understand the desired aspheric profile. Sag can be directly measured through in-process metrology as the aspheric surface is manufactured.
Convex aspheres are typically easier to manufacture than concave because there are more tooling options, so opting for a convex aspheric surface is often more cost-effective.
Inflection Points and Steep Angles
Because the local radius of curvature of an asphere varies across its surface, there may be locations known as inflection points where it changes sign between positive and negative. Inflection points can make an asphere more difficult to manufacture because they can create a local curvature too small to be manufactured or measured. Some metrology techniques, such as stitching interferometry, cannot measure surfaces with an inflection.
When using OpticStudio from Zemax, the Surface-Curvature Cross-Section plot can identify inflection points as locations where the radius of curvature crosses a value of zero curvature (Figure 1).
Aspheres can also often feature steep surface angles, which do not lend themselves to broadband anti-reflective (AR) thin film coatings because of their angle dependence. Surface angle is often limited in broadband applications requiring this type of coating, but select optical suppliers are able to apply broadband coatings to steeply angled surfaces.
Tolerancing Aspheric Surfaces
Surface irregularity, or asphere figure error, describes how much the sag of an aspheric surface deviates from that of its ideal shape. This restricts low frequency, or larger, surface errors across the asphere and is typically more important to specify than waviness and surface roughness, which describe higher spatial frequency errors. Irregularity can be improved by post-polishing processes, but over-specifying irregularity may unnecessarily increase cost. Relaxing irregularity specifications to 1-1.5μm P-V minimizes the sensitivity of specifying the clear aperture of the lens, simplifying the manufacturing process. Clear aperture is described in more detail later. High performance can be achieved in many applications with an irregularity in this range, but highly-sensitive applications may require an irregularity as low as <0.06μm.
The spatial frequency of irregularity directly impacts the real-world performance of the lens, which is described by the Strehl ratio of the lens. The Strehl ratio of an asphere is defined as the ratio of peak focal spot irradiance of the real lens to its ideal, diffraction-limited peak irradiance. Higher spatial frequency irregularity with more periods over the aperture of the lens correspond with a lower Strehl ratio, or a larger focused spot.
The required irregularity specification can be relaxed by forgoing a specification of power, or a constant deviation of the radius of curvature from that of an ideal surface. Power can be defined as a number of fringes which appear when measuring the surface using interferometry. It is common to have a power tolerance of 5-10 fringes.
Tolerancing Higher Spatial Frequency Errors
As stated earlier, waviness and surface roughness describe higher spatial frequency errors and are not always necessary to specify. However, they may be important for certain applications such as high-precision and high-power laser systems.
Waviness, or mid-spatial frequency error, characterizes ripple-like surface errors occuring in a frequency of 5-100 instances across the surface. Waviness is typically introduced by small, sub-aperture tools used for polishing aspheric surfaces and is commonly defined as a slope error over a specific distance, known as the measurement window. The exact measurement window must be specified. Including a maximum slope specification for an asphere creates a threshold that reduces the impact of mid-spatial frequency errors (Figure 2).
A typical slope error tolerance is 0.5-1μm over a measurement window of 1mm, but high-precision applications may have a tolerance as low as 0.15μm over a 1mm measurement window. Talk to your optical component manufacturer if a waviness tolerance is required, as this may increase costs due to the added testing.
Surface roughness, or high spatial frequency error, describes the asphere’s smoothness, or the quality of the polish on its surface. It is not always required to specify surface roughness, but it can affect scatter and the ability to withstand high laser power on the surface. When defining surface roughness, it is necessary to clarify both the amplitude and the spatial frequency range of interest, as the selection of test equipment may filter out certain high frequencies. Typical roughness values for computer numerically controlled (CNC) polished aspheres are 10-20Å, but the most demanding applications may have surface roughness specifications as low as 1Å.
Clear Aperture and Edge Thickness
The clear aperture (CA) of an asphere is the unobscured portion of the lens through which light can pass. It typically covers around 90% of a lens, while the remaining 10% towards the edges of the lens is not required to meet all specifications of the lens. Some applications call for a CA as high as 95%, but there are benefits to not increasing the CA. For both spherical and aspheric lenses, this area is used for mounting. Also, a smaller CA provides more of the surface for the subaperture polishing tools used to manufacture aspheres to move beyond the lens’ CA, reducing errors at the edges of the lens.
The edge thickness (ET) of the lens must also be considered. Too small of an ET will lead to edge chipping. Similarly to allowing for flexibility in the CA, allowing for a larger ET provides more material to prevent issues during sub-aperture polishing. A recommended minimum edge thickness is 1mm, but this can be pushed as low as 0.7mm when necessary. When a lens is manufactured it is oversized in diameter so that it can be edged down during centering, and this recommended minimum edge thickness applies to the oversized lens before it is centered, not the final lens. Having too large of an ET relative to the lens diameter may add unneeded cost and weight to the lens.
Connecting these Specifications to Your Application
From reducing the number of components required in an imaging assembly to minimizing the final focused spot size in a laser materials system, aspheric lenses greatly improve the performance and efficiency of a wide range of optical applications. Keeping the key considerations above in mind when specifying custom aspheric lenses will ensure that your aspheres achieve the performance required for your final application to be successful without unnecessarily increasing cost. Discuss these parameters with your optical component supplier to ensure that you are both in agreement regarding what specifications and tolerances are needed.
This article was written by Cory Boone, Lead Technical Marketing Engineer, Edmund Optics (Barrington, NJ). For more information, contact Mr. Boone at