The Down Under Lens
Frequently Asked (and Unasked) Questions
| Q. Does light really go from right to left south of the equator? A. No, but the concept makes for an interesting Lens Design Problem. |
| Q. Do lens designers south of the equator really use a coordinate system going from right to left? A. No, but the concept makes for an interesting Lens Design Problem. |
| Q. If an “up here” lens prescription is given to a “down under” person to make, is the prescription read from bottom to top? A. I doubt it! |
| Q. Did you actually check with any “down under” people before creating this problem? A. No, and we hope that this Lens Design Problem does not offend any of our “down under” colleagues! |
| Q. All this “up here” and “down under” confuses me. Is there a simpler way to state the lens design problem? A. Sure! In one sentence: Design a reversible lens where you do not reverse the signs of the radii. This means you design a lens with a given entrance pupil diameter, field of view, focal length, and RMS wavefront error. When you reverse the surface order (flip the lens) from front-to-back but do not change the signs of the radii, the lens must still have the same entrance pupil diameter, field of view, focal length, and RMS wavefront error. The goal of the problem is simply to maximize the product of the common entrance pupil diameter and semi-field of view of such a reversible lens. |
| Q. Are intermediate images allowed? A. Yes. That is why the magnitude of the focal length is specified to be 100 mm, since a lens with an intermediate image has a negative focal length. Intermediate images are allowed in either the “up here” version of the lens or the “down under” version of the lens, or both. |
| Q. Why do the entrance pupil diameter, field of view, and focal length need to be the same in the “up here” lens and the “down under” lens? A. Obviously, so the two versions of the lens would be interchangeable in their use! Plus, it makes the problem more challenging. You should have to work to win the Shafer Cup! |
| Q. Do we need to allow for extra 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 aperture stop location may be different for the two versions of the lens. During the design phase, you may be using a virtual aperture stop (negative thickness from the stop to the first optical surface). This is a useful trick if you are not sure exactly where in the lens is the best location for the stop. However, since this is not optically possible, the final lens must have a real stop somewhere in the lens. |
| 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 heights. 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 are not blocked, 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 the stop surface – it, and only it, can stop rays (at least for this Lens Design Problem). Note that the aperture stop must be fully filled for both versions of the lens. |
| 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 (where the chief ray crosses the optical axis). 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 0.070 wave 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 in X and Y from the chief ray image 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 distortion. Since distortion is not specified, 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 RMS 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. How is the RMS wavefront error calculated? A. For any field point, it is computed as the RMS of the OPD values at the exit pupil location for that field point. The exit pupil location is defined as where the chief ray (real ray through the center of the aperture stop) crosses the optical axis in image space. A rectangular grid of 50 x 50 rays is traced to the entrance pupil for each field point where the RMS wavefront error is computed. The entrance pupil location for a given field point is defined as where the real chief ray crosses the optical axis in object space. Any rays in this grid which are blocked by the circular aperture on the stop surface are not included. The OPD value at the exit pupil for each unblocked ray is included in the RMS wavefront error calculation. The RMS wavefront error will be computed at 25 evenly-spaced field points from on-axis to the specified semi-field of view. The RMS wavefront error must be ≤ 0.070 wave at each of these field points. Prior to computing the RMS of the wavefront error, piston and tilt are removed from the wavefront but focus is not removed, as described in the answer to the last question. |
| 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 are evaluated equally. If the RMS wavefront error calculated by CODE V is greater than 0.070 wave at any point in the field of view, the evaluator will reduce either the field of view or the entrance pupil diameter until the wavefront requirement is satisfied. This will be done so as to try to minimize the overall impact on the merit function – but this is not guaranteed! Note that any entrance pupil diameter or field of view adjustments made by the evaluator are final and no appeal is allowed. (Of course, you will not know that your values have been changed until the results are announced at the IODC and the Shafer Cup is presented, and by that time it is too late to complain!) |
| Q. What if my values for the entrance pupil diameter and field of view differ from the evaluator’s values for my lens? A. The evaluator’s values win, of course. After all, the evaluator is 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 Lens Design Problem 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 chair the problem again 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. |
Your answer on intermediate images muddled things for me – is a -100mm EFL acceptable (1 intermediate image) or must the focal length be positive (even number of intermediate images)?