Frequently Asked (and Unasked) Questions

**Q. Why are there no specifications for focal length, entrance pupil diameter, field of view, or other traditional optical parameters typically needed to define a lens?**

A. Because those parameters are not relevant to the problem goal of maximizing the used diameters of the ball lenses. Not specifying them allows a much greater variety of possible solutions.

**Q. How do you expect me to design a lens with no specifications?**

A. But it does have specifications! (1) You must use the 100 lens, (2) you must maximize the diameters of the two ball lenses used by your lens system, and (3) you must maintain diffraction-limited performance over the field of view. There are just no traditional specifications such as focal length, field of view, etc.

**Q. What is the lens configuration?**

A. The lens configuration is not specified. Other than being all refractive and requiring the 100 lens be somewhere in the overall lens, the lens configuration is totally wide open. Think outside the box and give it your best shot!

**Q. So this is the optical equivalent of “bring me a rock?”**

A. Almost. You do have to include the 100 lens somewhere. Other than that, yes. It is sort of like “bring me a rock with some quartz in it.”

**Q. Why is there an RMS wavefront requirement if all you care about is the used diameters of the ball lenses?**

A. To make the problem more challenging, of course! Otherwise a first-order solution might be sufficient and the problem would probably be a lot easier. You should have to work to win the Shafer Cup!

**Q. Can you clarify how the merit function is computed?**

A. The real on-axis marginal ray (the on-axis ray hitting the edge of the aperture stop) has four intersections with the two ball lenses: one at the front and one at the back of the first ball lens, and one at the front and one at the back of the second ball lens. Of these four intersections, let Y_{M} be the height of the intersection with the largest magnitude (i.e., ignoring the sign). Similarly, the full-field real chief ray (full field ray going through the center of the aperture stop) has four intersections with the two ball lenses. Of these four intersections, let Y_{C} be the height of the intersection with the largest magnitude. The merit function is Y_{M} X Y_{C}.

This merit function does not represent anything physically or optically, especially since the maximum heights may be on different surfaces. It is simply the way we chose to evaluate the used diameters of the ball lens surfaces while precluding simple on-axis only solutions.

**Q. This merit function does not necessarily maximize the diameters of both ball lenses does it?**

A. Technically no. The merit function is the product of the largest marginal ray height Y_{M} and the largest chief ray height Y_{C} on any of the four ball lens surfaces. If these two quantities happen to occur on the same ball lens, then that ball lens’s diameter is probably maximized, but the other ball lens’s diameter may not necessarily be maximized. If the quantities Y_{M} and Y_{C} occur on different ball lenses, it is likely that the diameters of both of the two ball lenses will be close to being maximized.

**Q. Why did you pick this particular merit function?**

A. The merit function was picked as one way to measure the used diameters of the ball lenses and reward larger fields of view, so simple on-axis only designs would be penalized. The reason for the goal of maximizing the diameters of the ball lenses is so that if the lens were made, the ball lenses would look very much like the “zeroes” in the number 100.

**Q. Can we use TIR within the ball lenses or any other optical element?**

A. The problem description prohibits any TIR action. All rays must refract at every surface.

**Q. Do we need to allow for extra lens diameter beyond the clear apertures for mounting?**

A. No. Lenses are allowed to go to zero edge thickness at the maximum clear aperture, which would not leave any extra diameter for mounting. Lens thicknesses are also allowed to go to zero thickness, and lens spacings are allowed to go to zero at the axis and at the clear apertures.

Of course, this is not realistic from a manufacturing or mounting standpoint, but the Lens Design Problem has never been practical or realistic!

**Q. What do you mean by no restrictions on the aperture stop location?**

A. The aperture stop can be anywhere between the object and the image. If the aperture stop is not on a lens’s front or rear surface, then a plano dummy surface must be used to define the stop surface. The stop surface cannot be virtual (negative thickness from the stop to the first optical surface, which, although it ray traces correctly, is not physically possible).

**Q. Is vignetting allowed?**

A. Vignetting is not specified. What is specified is that the aperture stop be fully filled at all points in the field of view. This means the upper and lower marginal ray intersections at the stop surface for all field angles must have the same ±Y height. If you have pupil aberration in your system, you may require vignetting factors to fully fill the aperture stop.

The aperture stop is a physical aperture somewhere in the lens system. The radius of this aperture is the height of the on-axis real marginal ray at the stop surface. For any point in the field of view, all the rays that hit the stop surface within this aperture must not be blocked (i.e., must make it to the image plane), and all the rays that hit the stop surface outside this aperture are blocked. No other surface is allowed to block rays. That is why it is called a stop surface – it, and only it, can stop rays!

**Q. Why are piston and tilt removed prior to the RMS wavefront error calculation, but focus is not removed?**

A. The wavefront error is computed by comparing the actual wavefront to a reference sphere centered at the chief ray intersection at the image surface. The radius of the reference sphere is the distance from the chief ray intersection on the image surface to the axial location of the exit pupil. If the radius of the reference sphere is not an exact multiple of the wavelength, then there will be a constant term in the wavefront which can be quite large. This is piston, and can be much larger than the maximum allowed wavefront error due to aberrations. This piston term is removed so only the residual wavefront error due to aberrations is included in the calculation.

Removing tilt from the wavefront is accomplished by shifting the center of the reference sphere laterally from the chief ray location so as to get a better fit to the wavefront. It effectively tilts the reference sphere relative to the wavefront to get a better fit. This lateral image shift is equivalent to a distortion. Since distortion is not specified for this problem, the tilt component of the wavefront is also removed.

Removing residual focus error from a wavefront is accomplished by shifting the center of the reference sphere axially. This is the same as adding a focus shift to the image, and the amount of the focus shift may vary across the field of view due to curvature of field or other causes. We want to evaluate the wavefront error across the field of view at a fixed image location, namely, the image location specified in the lens prescription. So any focus error in the wavefront is not removed.

**Q. What happens if you calculate that my lens has an RMS wavefront error at some point in the field of view greater than 0.070 wave, even if I think it meets the requirement?**

A. This may happen because different lens design programs may use different numbers of rays or use different algorithms to compute the RMS wavefront error. To eliminate these differences, all the entries will be converted to CODE V format and evaluated using CODE V. This ensures that all the entries will be evaluated equally.

If the RMS wavefront error calculated by CODE V is greater than 0.070 wave at some point in the field of view, I will reduce the field of view and/or the entrance pupil diameter until the wavefront requirement is satisfied. I will try to do this so as to minimize the overall impact on the merit function – but this is not guaranteed! Note that any entrance pupil diameter and/or field of view adjustments made by me are final and no appeal is allowed. (Of course, you will not know that I changed your parameters until I announce the results at the IODC and present the Shafer Cup, and by that time it is too late to complain!)

**Q. What if my values for the maximum on-axis marginal ray height and/or maximum chief ray height on the ball lenses differ from your values for my lens?**

A. My values win. After all, I am the judge of which values are the right ones!

**Q. Who thought up this crazy lens design problem?**

A. Dave Shafer, of course. That is why we call the contest the Shafer Cup Competition!

**Q. Is that Juergens idiot going to run the problem again? He gives the worst presentations!**

A. Unfortunately, yes, he is going to both chair the problem and give the presentation at the IODC. We feel your pain! However, do not despair – after all, he is getting old and is bound to retire someday (assuming he remembers to retire…).