The 2021 IODC Shafer Cup Competition

The Down Under Lens

Background

All lens designers “up here” (north of the equator) know that light travels from left to right. However, what is not well known is that “down under” (south of the equator), light travels from right to left. This causes problems if a design prescription done “up here” is sent “down under” to be made. One might think that all would be fine as long as the design is a “reversible lens.” But even that will not work. For those “up here,” for a ray traveling from left to right that sees a concave surface curved towards the left, towards the ray, the surface has a negative radius. But “down under,” a ray traveling from right to left that sees that same concave surface would see the surface curving away from it, and hence the surface would have a positive radius. Thus, when a “down under” person reads “up here” lens prescription values, the resulting lens may not work because of the difference in interpreting the signs of the radii.

For example, consider the “up here” lens shown below. The light, and the optical axis (+Z axis), goes from left to right. Object space is on the left side of the lens, and image space is on the right side of the lens. Positive surfaces have their centers of curvature on the +Z side of the surface and negative surfaces have their centers of curvature on the -Z side of the surface. Thus, from left to right, the signs of the surfaces are positive-plano-negative-positive-plano-negative.

If you give this order of surface signs from left to right to a “down under” person, the signs will be interpreted from the viewpoint of the optical axis (+Z axis) going from right to left. The sign convention is the same, namely, positive surfaces have their centers of curvature on the +Z side of the surface and negative surfaces have their centers of curvature on the -Z side of the surface. But since the +Z axis is going from right to left, the result is the “down under” version of the lens shown below. Object space is on the right side of the lens, and image space is on the left side of the lens.

The surfaces are in the same positions in both the “up here” lens and the “down under” lens, but from the “up here” perspective, the radii have changed signs because the “down under” optical axis is in the opposite direction. In general, positive lenses become negative lenses, and negative lenses become positive lenses. Clearly, this is a different overall lens, and probably will not image well.

Problem Description

The contest problem is to design a lens that images well whether it is made “up here” or “down under.”

Since conventional optical design software assumes that light goes from left to right, the “down under” version of the lens needs to be modeled from the “up here” perspective (optical axis going from left to right). Thus, instead of unchanged surface positions and changed radii (as described above), from the “up here” perspective, the “down under” version has a reversed order of surfaces from the “up here” version, and unchanged signs on all the radii.

For example, consider the lens below, which shows an “up here” design on the left and the corresponding “down under” version on the right, but oriented in the “up here” optical axis direction. In the “down under” version on the right, as seen in the “up here” optical axis direction, the “up here” lens surface order is reversed (for example, surface 1 in the “up here” lens becomes surface 8 in the “down under” lens); however, the radii do not change signs (for example, surface 1 in the “up here” lens is positive, and surface 8 in the “down under” lens is also positive).

Note that in this example, the stop location is the same in both versions, but for the contest problem the locations do not have to be the same.

Specifications

Focal length:	Magnitude = 100.00 ± 0.1 mm for both the “up here” lens and the “down under” lens.
Entrance pupil diameter:	Maximize. Must be the same for the “up here” lens and the “down under” lens.
Field of view:	Maximize. Must be the same for the “up here” lens and the “down under” lens. The field of view is circular and rotationally symmetric.
Wavelength:	587.56 nm (monochromatic).
Glass:	Schott N-BK7 (n = 1.5168).
Number of lenses:	No requirement.
Overall length:	No requirement. Note that the overall axial length from the first air-glass interface to the last glass-air interface is the same for the “up here” lens and the “down under” lens.
Maximum diameter:	No requirement.
Object:	Plano, at infinity for both the “up here” lens and the “down under” lens. Must be the first surface for both the “up here” and “down under” lens.
Image:	Flat image plane in air for both the “up here” lens and the “down under” lens; must be real (not virtual) in air for both lenses. The image is the last surface in both the “up here” and “down under” lens. The image distance may be different for the “up here” lens and the “down under” lens.
Lens form:	All refractive. All lens elements in both the “up here” lens and the “down under” lens must have positive axial and edge thicknesses, and all air spaces in both the “up here” lens and the “down under’ lens must have positive axial and edge spaces. Note that the lens diameters may be different in the “up here” lens and the “down under” lens. Intermediate images are allowed in either or both of the “up here” lens and the “down under” lens.
Surface form:	Spherical or plano only (no aspheres, diffractives, or segmented lenses). The overall lens is rotationally symmetric.
Image Quality:	RMS wavefront error ≤ 0.070 wave at 587.56 nm over the whole field of view for both the “up here” lens and the “down under” lens (piston and tilt removed, focus not removed).
Distortion:	No requirement. May be different in the “up here” lens and the “down under” lens.
Vignetting:	Aperture stop is fully filled at all points in the fields of view for both the “up here” lens and the “down under” lens.
Stop location:	No restrictions. May be different in the “up here” lens and the “down under” lens.

Merit Function

The goal of the problem is to maximize the product of the common entrance pupil diameter and field of view of the two lenses while satisfying the RMS wavefront error requirement for both the “up here” lens and the “down under” lens. The merit function is the product of the entrance pupil diameter in mm and the semi-field of view in degrees.

Merit Function = (entrance pupil diameter)×(semi-field of view).

Submissions

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

• Name,
• Affiliation (if an academic institution, indicate whether or not 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 prescriptions,
• Lens layouts (to help verify the prescriptions are correct),
• Your values for entrance pupil diameter, semi-field of view, and merit function (note that these will 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 or not you used a global optimizer on the problem.
• (Optional) Describe your design methodology and/or any special “tricks” that you used.

Lens files for CODE V, OSLO, and Zemax can be read directly by the evaluator. For other programs, include a lens prescription with a sufficient number of significant digits in a readily understandable text format (no binary files). All entries will be converted to CODE V format for common verification of compliance to the specifications and evaluation of the merit function.

The prestigious Shafer Cup will be awarded to the entrant with the highest merit function. A separate Shafer Cup will be awarded to the student entry with the highest merit function.

All entries must be submitted by April 1, 2021. 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 rcjuergens@msn.com.