Let us start off by discussing what is an asphere? An asphere is a spherical lens with a constantly changing local radius. In our illustration below an asphere has the best fit sphere (BFS), which is a radius that touches the edge and center of the lens.
Departure is the distance from the BFS to the aspheric form. Form error can be explained by how much the manufactured asphere contrasts with the theoretical aspheric form. Slope error is the derivative of form error and quantifies how quickly the form error changes. The aspheric surface is typically defined using an even aspheric equation. Other forms of defining aspheric surfaces exist although most optical fabrication machines utilize the even aspheric equation.
Look, Mom, I Designed My First Asphere!
Over the years we have seen some very interesting asphere designs. We preface the following comments by stating clearly, we are not optical designers; so please use your best judgment when designing. With that said, here are 10 considerations to keep in mind when you are designing your next asphere from a manufacturing perspective. Some of these tips are specific to ground and polished aspheres.
Include a sag table with your asphere so the manufacturer can confirm the prescription. Also, please increment the sag table by a reasonable step such as 0.5 or 1mm. We are looking to match our sag table with yours and this helps make sure we are looking at the same part.
Define which aspheric equation you are using. Most manufacturers prefer the even aspheric equation. Other forms would include Q-Forbes and Q-Con among others.
Avoid using odd term coefficients.
Attempt to avoid using an A2 term as this changes the vertex radius and causes the vertex radius tolerance to become slightly insignificant.
Consider equivalent materials. This can potentially save money as well as speed up material availability leading to quicker lead times.
Get your manufacturer involved early on in the design phase so you can include manufacturability in your design considerations.
Do not tolerance the deformation terms or conic constant.
Watch the minimum local radius on concave aspheres, minimum 15mm.
The edge thickness at processing diameter, which is typically 2-4mm outside the final diameter should be 1mm or more. This allows us to hold onto the outer diameter as well as providing more options to manufacture the asphere.
There are several different methods of manufacturing aspheres. Each method has strengths and weaknesses, which depends on material, specifications, size, and quantity just to name a few. Below is a table highlighting each method.
Aspheres geometry can come in several different flavors. Each type presents specific challenges and considerations for manufacturers. These challenges will also be different for each type of manufacturing process. For example, a gull-wing asphere with mounting flanges may not be very difficult for precision molding, but the same lens would be impossible to manufacture using a grinding/polishing method. Below is a table that highlights different potential geometries along with benefits and considerations for each.
Materials are typically chosen based on the end user application. There are several considerations that need to be accounted for such as the wavelength of the application, thermal and mechanical stability, cost, manufacturing method, and any other possible considerations. Each material presents manufacturing challenges that must be considered. Below is a chart that provides which materials can be made with each process.
Tolerancing an asphere is perhaps the single largest point of confusion and one could easily write an entire article on each tolerance. Over the course of the next few blogs that is exactly what we will do. In the meantime, here is a chart that describes several asphere specific tolerances along with a button below to download our tolerancing chart on precision optics for spherical and aspherical tolerances.
How do you know that your asphere meets design specifications? What if your design needs to be specifically tweaked to each lens to squeeze that last bit of performance from your system? This is where inspection data can be extremely beneficial. We have an entire guide on inspection data that explains all aspects of qualifying optics. The industry standard has been a profilometer trace for aspheric-specific inspection data. This involves using a precision stylus that has been atomically balanced, which traces the surface of the lens. The resulting trace is compared with the theoretical design of the aspheric surface and the form error, vertex radius error and slope error can also be identified. Feel free to check out our interferometry blog if interested in learning more about the various forms of interferometry and optical measurements.
Two potential problems with profilometry can occur. First is you can potentially miss out on asymmetric error induced on your part; and second, it is possible you can scratch the surface of the part with the stylus. 3D non-contact metrology is an exceptional alternative for this potential risk. LaCroix specifically uses an Optipro Ultrasurf to provide 3D measurements of aspheric surfaces. This instrument is capable of seeing the entire surface of the asphere rather than a single trace. With the complete data set we can correct the asymmetric error and provide a higher quality 3D aspheric surface. The data below is of a 6 inch asphere that our profilometer showed a peak to valley form error measurement of roughly 0.4 um of form error; however, the profilometer did not capture the asymmetric error of the part. Our 3D measurement revealed the asymmetry and form error was actually 1.3407 um. After a quick 3D correction, the 3D form error was reduced to .294um and .133 um in 2D with less than 0.1 um/mm of slope error using a 1 mm integration window.
Our hope with this series is to shed light on aspheric manufacturing; specifically, to help enable optical designers and engineers to gain a better understanding of how aspheres are manufactured as well as how to properly tolerance aspheres in order to meet their performance goals and obtain manufacturable lenses. Optics is an exciting field and we are passionate about helping you with your next project. Please contact one of our engineers today if you have a project you would like some feedback or a quote on.