Properly Tolerancing Aspheric Lenses to Balance Cost and Performance

When developing an optic, the striving for optimal performance can often be met with the challenge of managing costs. Aspheric lenses, with their complex surface profiles, require some additional expertise to maintain this balance between precision and manufacturing expenses. Understanding how to effectively tolerance aspheres is an incredibly useful communication tool to get the most out of your lens. In this article, we will provide some context behind asphere tolerances, exploring the factors that influence cost and performance.

Importance of Tolerancing Optical Components

Tolerances play a crucial role in optical design, as they constrain the amount of optical path difference induced during fabrication and influence manufacturing cost. Balancing as-built performance with cost is essential, and tolerancing is a way of communicating this with your optical manufacturer.

Knowing how much deviation can afford in order to keep that performance that you need is a balancing act. Tolerancing charts provide a valuable starting point (see Figure 1).

While it is not advisable to simply work down a column in a tolerancing chart, categories like those shown in Figure 1 give an idea of the attributes you need to tolerance. As you move from left to right across these charts you will understand what values can make your system more expensive. While it might be obvious that tighter tolerances will be more difficult to manufacture and thus more expensive, it is useful to be aware of the relationships between certain specifications.

Mechanical Dimensions

Whether discussing spherical or aspheric lenses, certain parameters remain consistent in tolerance considerations: diameter, center thickness (CT), overall height, and sag. Achieving very tight thickness tolerances becomes more challenging when combined with stringent cosmetic requirements, fractional wavelength irregularity, or soft optical materials. Fabricators typically aim to hit the upper limit of thickness tolerances, as once you remove too much material you cannot add more CT. Tight thickness tolerances will reduce yield, subsequently driving up prices.

Thin edges should generally be avoided whenever possible due to their susceptibility to chipping, which can result in surface defects or even catastrophic failure. Moreover, they can pose difficulties during processing and measurement, making them less desirable for optical components.

It is crucial to avoid compounding conflicting dimensions in tolerance specifications. For instance, overall height depends on center thickness and sag, so tolerancing all three simultaneously may lead to unnecessary complications. Instead, prioritize tolerancing what is essential, particularly if certain dimensions are controlled for mounting features.

Aspect ratio, the relationship between diameter and center thickness, holds significant importance in mechanical dimension considerations. A high aspect ratio can result in glass flexing during fabrication, making it challenging to handle. The ideal aspect ratio for precision optics is typically around 6:1, to help avoid the production of thin, wafer-like optics that are difficult to manage during fabrication.

For optimal tolerancing, involve an optomechanical designer early in the process. Their expertise can help identify mounting surfaces and establish lens spacing, ensuring that all lens tolerances align with the requirements of your optomechanical assembly.

Do not forget that you and your fabricator will need some room to work - this is where clear aperture comes into play. Beyond the clear aperture, additional room is allocated for coating margins, polishing edge effects, and bevels. This is particularly important for aspheric lenses, which are typically processed oversized to accommodate tool runoff. Additionally, strong high-order terms can pose problems outside of the clear aperture. Even after manufacturing, the area outside of the clear aperture may be used for mounting purposes – do not pay for more of the surface than you need!

One final note: make sure to tolerance your clear aperture with linear units. In most tolerance charts clear aperture will be described as a percentage of the surface, but this is just to scale with size. These tolerance charts are recommendations for a wide audience, but on your official drawing be sure to use linear units.

Radius and Power

For spherical optics, the power tolerance serves as a means to control the radius by governing increments of sag change. This radius is derived from the difference in sag measured from a test plate. Additionally, a linear radius tolerance is employed, which dictates radius in linear units relative to the nominal radius. This measurement is commonly conducted using a distance measuring interferometer.

While a spherical radius can be toleranced using fringes of power or linear radius tolerance, aspheric lenses should only be toleranced with a linear radius tolerance. Fringes of power assume your lens to have a constant radius of curvature.

This is a measurement of surface deviation from the nominal surface. Data is supplied either interferometrically or via profilometry as a 3D surface map or 2D line scan. Do not tolerance the conic constant or aspheric terms in the asphere equation. Use radius and irregularity tolerance to control permissible form error.

MSF errors are periodic ripples that degrade surface quality. These errors often arise due to residual imperfections left by sub-aperture tooling during the fabrication process. Aspheric lenses, with their complex surface profiles, are particularly susceptible to these mid-spatial frequency errors. Post-processing techniques may be necessary to mitigate these surface irregularities and ensure optimal optical performance.

One effective approach for tolerancing mid-spatial frequency errors is through slope error. Slope error focuses on measuring the angles of perturbation over short integration lengths, thereby limiting and controlling the magnitude of these mid-spatial frequency errors.

Wedge

Wedge directly influences the image formation and propagation through optical systems. Ideally, the optical and mechanical axes should align perfectly. The centration process for spheres allows for post-processing to correct (with some limitation) centration. In contrast, aspheric lenses require precise control during fabrication to ensure proper centering. In many cases, aspheric lenses are approximated as spherical for wedge measurements (e.g. via beam deviation). However, this approach overlooks lateral displacement (or decenter) as it does not account for the unique geometry of the aspheric surface. To accurately characterize wedge in aspheric lenses, it is essential to consider both the aspheric tilt and the lateral displacement of the aspheric surface.

Cosmetics (Scratch-Dig)

Surface quality is often the primary cost driver for optical components, whether they are spherical or aspheric. Often confused with surface roughness, surface quality describes the localized, nonperiodic defects across an optical surface rather than the overall texture. Interestingly, cosmetic defects may have minimal impact on system performance and a surface quality of 60-40 is acceptable for most applications. However, exceptions arise in shorter wavelength systems or high-power/intensity optical systems, where tighter surface quality specifications are necessary. Our recommendation for tolerancing surface quality is to utilize the ANSI/OEOSC/ISO 10110-7:2017 standard for specifying scratch-dig. It includes both dimensional and comparison inspection specifications. In this, dimensional specifications measure digs by a defined area and scratches by a defined width. The comparison method is the more traditional visual inspection method (similar to MIL-13830B) that evaluates scratches via brightness and digs via 10X grade in micrometers. It is important to note that in the comparison method, designers need to specify the comparison standard to ensure consistency and accuracy in evaluating surface quality.

How Can I Tolerance a Most Cost-Effective Asphere?

Aspheres inherently incur higher costs compared to spherical lenses. They require small tools for polishing (and often grinding, too) and can only be processed one lens at a time. Beyond that, there are several factors that can drive the cost of aspheres: surface form error, local slope, cosmetics, material selection, tilt and decenter, and overall geometry. These specifications and tolerances determine the manufacturing process, with tighter tolerances requiring different equipment, further impacting costs.

While it is challenging to pinpoint the most influential factors on cost, a lot of what we discussed here is which of these tolerances will cause the fabricator to have longer process time and lower yields, which will greatly influence cost. Therefore, early collaboration between designers and manufacturers is crucial to determine specifications and tolerances that minimize costs while maximizing performance for your specific project.

While most aspheres can be toleranced similarly to spherical components, there are differences to consider. Key considerations include vertex radius, conic constant, aspheric coefficients, sag table, form error (including vertex radius and irregularity), mid-spatial frequency errors (tolerance slope plus integration length), and centration errors (requiring both tilt and decenter parameters). Striking the right balance in tolerancing is essential; under-tolerancing may lead to performance issues, while over-tolerancing can introduce unnecessary complexity and costs. Talk to your optical manufacturer early to find the best balance of minimal cost and maximum performance in the asphere tolerancing process.

This article was written by Jessica DeGroote Nelson, Senior Director of Optical Product Development, and Ian Schwartz, Product Line Manager, Edmund Optics (Barrington, NJ). For more information, visit here  .

---