The 2023 IODC Shafer Cup Competition

The Yin Yang Lens


Yin and yang is an ancient Chinese philosophical concept that describes how obviously opposite or contrary forces may actually be complementary, interconnected, and interdependent in the natural world, and how they may give rise to each other as they interrelate to one another. Yin and yang can be thought of as complementary, rather than opposing, forces that interact to form a dynamic system in which the whole is greater than the assembled parts. According to this philosophy, everything has both yin and yang aspects (for example, shadow cannot exist without light).

This design problem applies the concept of yin and yang to color correction in a lens. The idea is that you cannot have positive yang, or good color correction, at some wavelengths without negative yin, or bad color correction, at other wavelengths. With all achromats this is true, but the wavelength separation between the yin and the yang wavelengths is usually designed to be as large as possible. The question to be answered in this problem is for a very narrow wavelength separation with identical paraxial image distances, how much difference in image quality (yin vs. yang) is possible between the yin and yang wavelengths.

Problem Statement

The Yin Yang Lens design problem is to design a maximum-etendue lens with diffraction-limited image quality over the field of view at 550 nm and yet have bad on-axis image quality at 540 nm when evaluated at the same image location.


Focal length:100 ± 0.1 mm at 550 nm.
Entrance pupil diameter:Maximize.
Semi-field of view:Maximize.
Number of lenses:Not specified.
Overall length:≤  500.0 mm from first optical surface vertex to the image.
Maximum diameter:Not specified.
Distortion:Not specified.
Stop location:No restrictions.
Lens type:All refractive; no reflectors or TIR.
Lens configuration:Rotationally symmetric. All lenses must have non-negative edge thicknesses at the clear apertures and non-negative spacings at the axis and at the clear apertures.
Cemented surfaces:Not allowed.
Intermediate images:Not allowed.
Surface shape:Spherical or plano only (no aspheres or diffractives).
Wavelengths:540 and 550 nm.
Glasses:Schott N-BK7 and Schott N-SF6.
Object:Flat, at infinity.
Image:Flat image plane in air.
Image distance:Non-negative. Paraxial image distance must be the same for 540 nm and 550 nm (within 0.0001 mm). The same image distance is used for 540 nm and 550 nm.
Vignetting:Only the stop surface clear aperture can block rays.
Image quality:RMS wavefront error at 550 nm ≤ 0.070 wave over the field of view (piston and tilt removed, focus not removed). On-axis RMS wavefront error at 540 nm shall be as high as possible (focus not removed).

Merit Function

The merit function is the etendue of the lens (entrance pupil diameter in mm times the semi-field of view in degrees) times the on-axis RMS wavefront error in waves at 540 nm.


The coveted Shafer Cup will be awarded to the entry with the highest merit function and a separate Shafer Cup will be awarded to the entry with the highest merit function from a student (undergraduate or graduate).

Send your entry to Entrants may submit more than one entry, but only the one with the highest merit function will be considered. Please include the following information with your submission:

  • Name,
  • Affiliation (if an educational institution, indicate if you are a student),
  • Country,
  • Approximate number of years of lens design experience you have,
  • Lens design program(s) used,
  • Lens file (text format) or lens prescription,
  • Lens layout (to help the evaluator verify the prescription is correct),
  • Your values for entrance pupil diameter, semi-field of view, and the on-axis RMS wavefront error at 540 nm (although they will also be verified by the evaluator),
  • Approximate number of hours you spent on the problem (not counting the time any global optimizers were grinding away on their own), and
  • Indicate whether you used a global optimizer on the problem or not.
  • (Optional) Describe your design methodology (warning – may be used in the talk and/or in the written paper if it is unique enough or interesting enough).

Lens files for CODE V and Zemax can be read directly by the evaluator. For all other programs, include a lens prescription with a sufficient number of significant digits in a readily understandable text format. All entries will be converted to CODE V format for common verification of compliance to the specifications and evaluation of the merit function.

All entries must be received by midnight, Pacific Daylight Time, April 1, 2023. If you have any questions about the problem, refer to the frequently asked questions (FAQ) page on the IODC web site, or contact Richard Juergens at

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