Empirical Case Study

altIn the 1960’s Sloan and Hopkins studied the addition of aspheres to the Double Gauss2. They assumed that an aspheric plate could be placed at the aperture stop. We have repeated this exercise but expanded the number of cases to include cases found in the patent literature mentioned above. We followed the original paper’s convention, reporting optical performance in terms of MTF at 15 line pairs/mm. (Higher contrast is better since it means a sharp resolution). This was conducted by using an automated lens design program that iterated to maximize the optical performance. These solutions were not solved in a closed form fashion.

The above table captures the results of this study. There are eleven optical surfaces (including a plate at the iris) in the Double Gauss and these are represented by columns. Each row in the table represents a different configuration in terms of placement of the asphere. The numbers under the surfaces show the aspheric departure in microns.

The last three columns capture the optical performance or relative error function (RMS Wavefront Error — the lower the better) and MTF at the center and edge of the field of view.


The results show that aspheres can offer a great increase in optical performance. Some of these solutions, however, defy theoretical wisdom of asphere placement. The most promising solution for aspherizing a Double Gauss, for instance, utilizes a double asphere on the last element. In this solution one aspheric surface has an inflection point (convex at the center, concave at the edge). An inflection asphere is more difficult to manufacture but it offers an excellent performance increase. The asphere with the inflection has the axial beam covering only the convex portion while the off-axis beams wander to the edge of the asphere. The inflection point attempts to correct astigmatism at the edge of the asphere, while controlling field curvature and spherical aberration at the center.

When designing an optical system with aspheres, then, it is important that the lens designer keep an open mind about the placement of the aspheric surfaces. They should also carefully monitor for dueling aspheres to reduce stress on aspheric fabrication. If used correctly, however, aspheres can reduce size and weight of an optical system by minimizing the number of elements required to achieve good image quality.

This article was written by Scott Sparrold, Senior Optical Engineer, Edmund Optics, Inc. (Barrington, NJ). For more information, contact Mr. Sparrold at This email address is being protected from spambots. You need JavaScript enabled to view it., or visit http://info.hotims.com/28052-200.


  1. “Aberrations of the Symmetrical Optical System” W.T. Welford, Academic Press pg 134
  2. “Design of Double Gauss Systems Using Aspherics”, T.R. Sloan and R.E. Hopkins, Applied Optics 1911, Vol 6. No. 11, November 1967
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