John R. Rogers

Techniques and tools for obtaining symmetrical performance from tilted-component systems

Tilted-component systems are known to be characterized by aberrations with unusual field dependences, such as decentered coma and binodal astigmatism. In this paper, the origin of binodal astigmatism in a multielement system from the contributions of individual surfaces is explained in an intuitive manner, as a logical extension of the ordinary aberrations known to all optical designers. The insight provided by this graphical model allows an understanding of why the astigmatism of any given system behaves the way it does, and what needs to be done to convert it to ordinary quadratic behavior, so that what remains can be corrected by a final, rotationally symmetric subsystem. Conditions under which ordinary behavior may be obtained from a system of tilted ele- ments are explored. It is shown that a certain type of symmetry of the primary aberrations may be obtained (regardless of the tilt angles) if the initial, untilted system is monocentric. Graphical displays of the aberra- tion types are used to explore the behavior of the system across the field, and direct optimization of the Zernike coefficients is used to guide the performance of the system.

Secondary color correction and tolerance sensitivity: What can you get away with?

As many authors have documented, it is possible to correct secondary color without using special glasses, if there are substantial separations between lenses or groups that are chromatically uncorrected. The trick is to use the separations to “induce” secondary color by allowing the rays of different colors to separate from each other before being refracted by the group that follows. This approach works, but the use of separated and uncorrected groups that correct each other raises the question of tolerance sensitivity, because misalignments between the groups causes imperfect correction of the aberrations. It is generally good practice to correct aberrations within groups, rather than allow the groups to “crosscorrect” each other. On the other hand, the use of special glass types to control secondary color directly is often either discouraged for cost reasons, or simply not allowed because of thermal shock sensitivity. Moreover, some optical systems (particularly projector applications) require extremely good secondary color correction – often to a small fraction of a pixel. The important question is how much secondary color can be induced before the increased tolerance sensitivity negates the advantage of the color correction. In this paper, we examine the as-designed and as-built performance of several sample systems that rely on separated groups for the correction of secondary color, and compare the performance to that of systems designed without regard to secondary color correction.

Decentering zoom lens in stereomicroscope

We can move an entrance pupil of a zoom lens from on-axis to off-axis by decentering lens groups of a zoom lens. This decentering zoom lens makes an objective lens of a stereomicroscope small. As a result, we can develop a stereomicroscope with high magnification and high resolution.

Desensitization in aspheric and freeform optical design

The design of tilted, decentered, and non-rotationally symmetric or freeform optical systems has become an important part of optical design. We explore desensitization of traditional and freeform optical designs and compare their effectiveness.

Fast Infrared Exoplanet Spectroscopy Survey Explorer (FINESSE) prism spectrometer

The FINESSE spectrometer design (0.45 to 5 μm at a resolution of greater than 80 at f/12) is placed in context by reviewing history of unit magnification relays and spectrometers. Related imaging spectrometers are also described.

Contrast optimization: a faster and better technique for optimizing on MTF

Our new Contrast Optimization technique allows for robust and efficient optimization on the system MTF at a given spatial frequency. The method minimizes the wavefront differences between pairs of rays separated by a pupil shift corresponding to the targeted spatial frequency, which maximizes the MTF. Further computational efficiency is achieved by using Gaussian Quadrature to determine the pattern of rays sampled. Examples are given to demonstrate the advantages of the technique.

IODC 2017 illumination design problem: the centennial illuminator

For the 4th time, the International Optical Design Conference (IODC) included an Illumination Design contest. This year, the contest involved designing the illuminator to produce a “100” logo to celebrate the OSA’s 100th anniversary. The goal of the problem was to produce the highest logo luminance with greater than 30% uniformity. There were 7 entries from 2 different countries. Two different commercial optical/illumination design packages were used. The winning solution, was provided by Steve Mulder.

Compensator selection considerations for a zoom lens

The selection of compensators for a cam-driven zoom lens is more complex than for a prime lens, because tolerances cause the back focal distance to shift by different amounts in different zoom positions, i.e, the system loses parfocality. Adjustment of the back focal distance can bring one, but not all, of the zoom positions back into focus. Furthermore, compensator selection is more complex because it is usually desirable to avoid adjustments within the moving groups. In this paper, we examine the effects of tolerances and compensators on a photographicformat zoom lens. We begin by assigning reasonable tolerances to all surfaces, materials, and groups, and then examine in detail how these tolerances affect the image quality. We determine the relative amount of degradation caused by transverse tolerances (decenters and tilts) compared to rotationally symmetric tolerances (power, index, thicknesses and spacings). For the rotationally symmetric tolerances, we examine the efficacy of shifting the detector, shifting the fixed groups, and respacing elements within the fixed groups. Similarly, for the transverse tolerances, we examine the efficacy of implementing decenter compensators within the fixed groups.

Slope sensitivities for optical surfaces

Setting a tolerance for the slope errors of an optical surface (e.g., surface form errors of the “mid-spatial-frequencies”) requires some knowledge of how those surface errors affect the final image of the system. While excellent tools exist for simulating those effects on a surface-by-surface basis, considerable insight may be gained by examining, for each surface, a simple sensitivity parameter that relates the slope error on the surface to the ray displacement at the final image plane. Snell’s law gives a relationship between the slope errors of a surface and the angular deviations of the rays emerging from the surface. For a singlet or thin doublet acting by itself, these angular deviations are related to ray deviations at the image plane by the focal length of the lens. However, for optical surfaces inside an optical system having a substantial axial extent, the focal length of the system is not the correct multiplier, as the sensitivity is influenced by the optical surfaces that follow. In this paper, a simple expression is derived that relates the slope errors at an arbitrary optical surface to the ray deviation at the image plane. This expression is experimentally verified by comparison to a real-ray perturbation analysis. The sensitivity parameter relates the RMS slope errors to the RMS spot radius, and also relates the peak slope error to the 100% spot radius, and may be used to create an RSS error budget for slope error. Application to various types of system are shown and discussed.

Global optimization and desensitization

Sensitivity to tolerances is a well-known problem in optical design. In many cases, multiple designs having different tolerance sensitivities will solve the optical design problem. Often, the solution with the best “as-designed” performance is not the solution with the best “as-built” performance. In the end, it is not the as-designed quality of the optics that matters; it is only the as-built quality that matters. As we demonstrate in this paper, typical merit functions used in optimization (e.g., RMS spot diameter or RMS wavefront variance of the pre-tolerance system) are often poorly correlated to actual, as-built image quality; in many cases the correlation is extremely poor. One known strategy to avoid this is to add something to the merit function that penalizes design forms that are particularly sensitive. The ultimate success of a merit function is determined by the extent to which it correlates with as-built performance. Such a strategy is of particular importance during a global optimization design phase, in which the optimizer will generate many different design forms, some of which may differ significantly from the starting design, both in appearance and in tolerance sensitivity. In this paper we examine the addition of a “sensitivity” parameter to the merit function. We discuss the selection of the weighting factor for the sensitivity parameter, as well as the correlation of the merit function (both with and without the sensitivity parameter) to as-built performance.