How to Use the Find Best Asphere Tool
http://www.zemax.com/kb/articles/228/1/How-to-Use-the-Find-Best-Asphere-Tool/Page1.html
By Mark Nicholson
Published on 2 May 2008
This article describes a fast method to identify which surfaces in a design will best benefit from aspherization.
Introduction
Making one or more surfaces in an optical 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 costs in both manufacture of the element and in tolerancing to assess the sensitivity of the system to perturbation of the aspheric surface. Therefore, more is not always better: the designer must carefully assess which surfaces to make aspheric, and generally will want to use the least degree of asphericity needed to give the desired performance.
ZEMAX's Find Best Asphere tool is a useful way to identify which surface will benefit most from aspherization. In a manner similar to Test Plate fitting, the tool replaces spherical surfaces with aspherical surfaces of user-specified degree. The user can run the tool multiple times, varying the degree of asphericity each time, and can decide whether to keep the suggested asphere or discard it.
Further, adding an aspheric surface can increase costs in both manufacture of the element and in tolerancing to assess the sensitivity of the system to perturbation of the aspheric surface. Therefore, more is not always better: the designer must carefully assess which surfaces to make aspheric, and generally will want to use the least degree of asphericity needed to give the desired performance.
ZEMAX's Find Best Asphere tool is a useful way to identify which surface will benefit most from aspherization. In a manner similar to Test Plate fitting, the tool replaces spherical surfaces with aspherical surfaces of user-specified degree. The user can run the tool multiple times, varying the degree of asphericity each time, and can decide whether to keep the suggested asphere or discard it.
An example
The example file (which can be downloaded from the zip file at the end of the last page of this article) shows a derivative of the Cooke triplet, optimized for best RMS wavefront error. All radii and thicknesses are variable, except the last radius of curvature which is controlled by an f/# solve and maintains the lens as f/5 during optimization.
The merit function for this design was build using the default merit function tool, and consists of RMS wavefront error and lens center/edge thickness boundary constraints. Five rings were used by the Gaussian Quadrature pupil sampling algorithm. Since n rings allows aberrations of order r2n - 1 to be controlled exactly, this gives control of 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 maximum order of the selected polynomial. 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 the lowest merit function yet found, 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:
Changing the desired order of asphere and pressing Run Again yields these results:
The merit function for this design was build using the default merit function tool, and consists of RMS wavefront error and lens center/edge thickness boundary constraints. Five rings were used by the Gaussian Quadrature pupil sampling algorithm. Since n rings allows aberrations of order r2n - 1 to be controlled exactly, this gives control of 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 maximum order of the selected polynomial. 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 the lowest merit function yet found, 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:
Changing the desired order of asphere and pressing Run Again yields these results:
Initial Design: 0.102
Conic asphere: 0.086
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
Note the currently defined merit function is used, and all parameters that are variable 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. In addition, 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 useful for bounding aspheres: see this Knowledge Base article and the User's Guide Optimization chapter for more details.
Note also that like all local optimization results, there is no way to know if the solution found is the optimum "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.
No attempt is made to determine whether the resulting asphere is practical to fabricate, or is more or less costly to manufacture as compared to making other surfaces aspheric.
Note also that like all local optimization results, there is no way to know if the solution found is the optimum "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.
No attempt is made to determine whether the resulting asphere is practical to fabricate, or is more or less costly to manufacture as compared to making other surfaces aspheric.