The use of aspheric surfaces has become widespread as demand increases for ever smaller and more highly performing optics. This blog post describes a fast method to identify which design surfaces will best benefit from aspherization using OpticStudio's Find Best Asphere Tool.

Making one or more surfaces in a design aspheric is a common way to improve optical performance without increasing the number of surfaces. However, it is not always apparent which surfaces will most benefit from aspherization. Further, adding an aspheric surface can increase manufacturing costs. Thus, it is usually best to use the lowest degree of asphericity needed to give the desired performance.

OpticStudio's Find Best Asphere tool is a valuable way to identify which surface will benefit most from aspherization. The tool replaces spherical surfaces with aspherical ones of a user-specified degree and may be run multiple times to find the best performance.

An example

This example shows a Cooke triplet derivative optimized for best RMS wavefront error. All radii and thicknesses are variable, except the last radius of curvature controlled by an F/# solve and maintains the lens as f/5 during optimization. There are 6 spherical surfaces that could potentially be converted to aspheres.

This design has a merit function built using the Optimization Wizard that consists of RMS wavefront error and lens center/edge thickness boundary constraints. The Gaussian Quadrature pupil sampling algorithm used five rings. Since n rings allow aberrations of order r2n - 1 to be controlled precisely, this controls wavefront aberrations up to r9. The highest order aberration in the design currently is r6, higher-order spherical aberration.

The current value of the merit function is 0.102. We then run Tools...Optimization...Find Best Asphere:

The tool allows us to choose Start and Stop surfaces and the selected polynomial's maximum order. Each surface within the range is evaluated to see if it is a candidate asphere. To be considered, the surface must be of type Standard, have no conic value, define a boundary between air and glass (cemented surfaces usually make poor aspheres), and have a curvature that is either variable or controlled by a marginal ray angle or F/# solve. Surfaces that do not meet this test are ignored.

When a candidate surface is identified, the surface is converted into an asphere of the user-selected type. The aspheric terms are set as variables for optimization. The local damped-least squares optimizer is then called to optimize the modified system. If the resulting system has a lower merit function, the system is retained. The procedure repeats until all surfaces have been tested. Finally, the tool reports which surface, when converted to an asphere, provided the lowest merit function. 

For example:

Pressing Keep and Exit will change surface 1 to an Even Asphere type with optimized parameter up to the 6th order aspheric coefficient. Alternatively, changing the desired order of asphere and pressing Start again yields these results:

Initial Design: 0.102
Conic asphere: 0.087
4th order: 0.088
6th order: 0.084
8th order: 0.084
10th order: 0.083
12th order 0.082

The user can then choose what degree of asphere provides the most effective improvement in performance.

Considerations for use

The current merit function is used as the initial value for comparison in the tool, and all variable parameters are re-optimized during this process. The current merit function should be appropriate for an aspheric design, which may require higher sampling than a non-aspheric design for good optimization. Also, thickness controls other than just center and edge thickness may be required. The "full thickness" boundary constraint operands FTGT (Full Thickness Greater Than) and FTLT (Full Thickness Less Than) are helpful in bounding aspheres: see this Knowledgebase article and the Optimization chapter of the Help Files for more details.

Also note that, like all local optimization results, there is no way to know if the solution found in the "global minimum" for that combination of merit function, variables, and design parameters. For this reason, once the best candidate asphere is determined, it is usually a good idea to run the Hammer Optimizer on the resulting design to see if any further gains are possible.

Finally, keep in mind that OpticStudio does not attempt to determine whether the resulting asphere is practical to fabricate or is costly to manufacture than making other surfaces aspheric.

Often, a design can be improved without adding additional lenses through the use of an aspheric surface. Since adding an asphere can increase costs in both manufacture of the element and tolerancing, it is good practice to keep the amount and degree of aspheric surfaces to a minimum. To help with this, OpticStudio provides the Find Best Asphere tool that allows users to replace and test any surface with an asphere of varying degrees to find the optimum system performance. This article provided an example of a system that was optimized using the Find Best Asphere tool.

To learn more about OpticsStudio, the industry standard optical design software, try it for free! 

Blog Author:
Kerry Herbert
Field Marketing Manager
Zemax, LLC

Knowledge Base Article Author:
Andrew Locke