2010 IODC Lens Design Problem – The Green Lens
Frequently Asked Questions
Q. What do you mean by all radii have the same value?A. All surfaces that are not flat must have the same magnitude (absolute value) of their radii of curvature. The surfaces can be positive or negative (centers of curvature on the object side or the image side of the surface), and can be convex or concave, but the absolute values of the radii must all have the same value.
Q. What is the lens form?
A. The lens form must be all refractive (no reflectors or diffractives). The lens can have as many lens elements as you want or need, can be any length, and any diameter. There is no restriction on lens form other than all surfaces must be plano or spherical (no aspheres).
Q. What do you mean by positive axial and edge thickness and spacings?
A. All lens elements must be physically realizable and must not overlap other lens elements. To be physically realizable, a lens element cannot have a negative center thickness and cannot have a negative edge thickness at its maximum clear aperture. To not overlap other lens elements, elements cannot have a negative spacing to the next element, either along the axis or at either element's clear aperture.
Q. What do you mean by no restrictions on the aperture stop location?
A. The aperture stop can be anywhere in the lens, from being in front of the lens (in object space), to being somewhere inside the lens, to being behind the lens (in image space). If the aperture stop is not on an optical element's surface, then a dummy surface must be used to designate the stop. The dummy surface may be in air or inside an element.
Q. What is the curvature of the aperture stop surface?
A. If the aperture stop is on a dummy surface or on a plano surface, the stop surface is plano. If it is on an element's curved surface, the stop is curved, and the aperture for it is on the curved surface.
Q. The problem states that no vignetting is allowed. What does this mean specifically?
A. This means that the aperture stop surface is fully filled by all points in the field of view. The f/number (and consequently, the entrance pupil diameter) is defined by a circular aperture on the stop surface. This aperture is the value of the on-axis marginal real ray on the stop surface. All rays that fill this aperture must make it to the image plane for all points in the field of view, and all rays outside this aperture will be blocked. No other surface is allowed to block the rays. This is accomplished by setting a limiting aperture only on the aperture stop surface; all other surfaces will have floating apertures, meaning they will not block rays.
Note that this does not necessarily mean that the vignetting factors are zero. It means that in a lens layout, the upper and lower marginal rays for all field points cross exactly at the edge of the aperture on the stop surface. If there is pupil aberration in the lens, this may mean that vignetting factors are non-zero.
Q. How is the field of view determined?
A. You must submit a value for your field angle with your lens submission (it will probably be part of your lens prescription also). The field of view is determined by two conditions, where the magnitude of the distortion exceeds 5% or where the RMS wavefront error exceeds 0.070 wave at 532 nm, whichever comes first.
Q. How is distortion calculated?
A. Classically, distortion is calculated at the paraxial image plane location. However, for this problem it is calculated at the specified image surface location. Let y be the paraxial image location at the specified image surface of the chief ray for a given field point, and Y be the real chief ray location for that field point. Then the distortion is calculated as
Q. How is the entrance pupil diameter determined?
A. You must submit a value for your entrance pupil diameter (EPD) with your lens submission (it will probably be part of your lens prescription also). Using this diameter, if the RMS wavefront error anywhere over the field you specify is greater than 0.070 wave at the specified wavelength (0.532 micron), then the EPD will be reduced by the evaluator until the maximum RMS wavefront error anywhere in the field is 0.070 wave.
Q. So does the EPD determine the field or does the field determine the EPD?
A. Essentially both. This is the main tradeoff you as the designer must make in solving the problem. You may be able to increase the field by using a smaller EPD, or you may be able to use a larger EPD with a smaller field. You make the tradeoff so as to maximize your product of EPD and field angle.
Q. If the RMS wavefront error is greater than 0.070 wave, will the evaluator reduce the field, the EPD, or both?
A. The evaluator will reduce whichever one will maximize the merit function of the entry.
Q. How is RMS wavefront error computed?
A. For any field point, it is computed as the RMS of the OPD values at the real exit pupil location for that field point. This exit pupil location is defined as the position where the chief ray (ray through the center of the aperture stop) crosses the optical axis in image space.
A rectangular grid of 512 x 512 rays across the real entrance pupil is traced to the real exit pupil. The grid spacing is uniformly spaced across the entrance pupil (this is not necessarily optically correct, but is a compromise to accommodate lens design programs that may not properly account for pupil aberration in the computation of RMS wavefront error). Any rays which are vignetted by the circular aperture on the stop surface are not included. The OPD value for each unvignetted ray at the exit pupil is included in the RMS calculation.
Tilt and focus are NOT removed prior to computing the RMS wavefront error. Removing tilt would in effect be the same as allowing additional distortion, and removing focus is the same as using a different image surface location from that specified in the prescription. Thus, the reference is the chief ray and not the centroid.
Note that due to possible differences in computing RMS wavefront error between different lens design programs, the value of the RMS wavefront error as computed by the evaluator will be rounded to the third digit.
Q. What if my value for entrance pupil diameter and/or field disagrees with the evaluator's value for my lens?
A. The evaluator's decision is final with no appeal allowed.
Q. Can teams enter?
A. A team of people brings together different experiences and capabilities and the synergy is greater than any one person can bring to bear on a problem, plus a team can devote more time to the problem than an individual possibly can. Thus it would be unfair to allow teams to compete against single contestants. However, a team may come up with a much better solution, and part of the goal of the problem is to find the best solutions to the problem. So teams are allowed to enter the contest and their results will be tabulated and reported, but only individual entries will be considered when determining the winner of the contest. An individual contestant cannot also be on a team (to avoid individuals using "lessons learned" from the team). If several teams enter, we may opt to have an individual winner and a team winner, but this will be decided at a later time, after the entries have been received.
