Eyepiece design simplification through the use of aspherics

Harvey M. Spencer* DRS Sensors and Targeting Systems, Torrance, California

ABSTRACT

The eyepiece design is one of the most challenging of all for the optical designer, since the result will be judged by the human eye, which is a very sensitive and subjective instrument. The combined effects of field curvature and astigmatism, geometric distortion, and the chromatic aberrations yield an optical system that is truly unique. No two eyepiece designs present an image that looks quite the same, and even different samples of the same design can produce different looking images due to the effects of manufacturing tolerances. In some cases the design must accommodate a large exit pupil to allow for head movement, and these dynamics introduce even more visual effects; image "swimming", changes in distortion leading to "corner pulling", and color fringing to name a few. When the design must be compact and weigh very little, the number of lens elements permitted is few and the design process becomes all the more difficult. The use of aspherics in the eyepiece design can compensate for the necessary limit on the number of lens elements. A case history in the design of a successful eyepiece is presented, showing the tradeoffs made in the selections of materials, aspheric complexity, fabrication concerns and packaging limitations. The performance capabilities of these designs will be discussed. The tools used to analyze optical image quality and the criteria upon which success was judged is also presented. The example used is a large exit pupil eyepiece designed to view either a miniature color CCD or LED display. Keywords: optical design, eyepiece, asphere

1. DESCRIPTION OF THE DESIGN PROBLEM

It is important at the outset before any optical design can begin, to receive a comprehensive set of requirements for the optical system. This includes in addition to the usual first-order optical properties, any packaging constraints defined by the maximum volumes and weights and other "special" requirements particular to the specific system to be designed. Along with these requirements must be the tolerance range associated with each, as nothing can be fabricated with exact precision. In the optical system discussed here, an eyepiece for viewing a color display mounted on a handheld weapon, the relationship between the user's eye and the eyepiece is critical. Because of recoil considerations, adequate distance must be provided to allow a safe viewing distance while at the same time precluding vignetting. Additionally, weight is

a very important consideration because the soldier must carry the weapon with the sight for long periods of time and over great distances. Although the optics is a relatively small part of the total weight, in a miniaturized optical sight such as this the elimination of a few 10's of grams can spell success or failure in meeting the weight specification. Eyepiece distortion must be kept independently low since the eyepiece will be used to the view the imagery on the display produced by many different sights each having their own characteristic distortion. The optical requirements for this eyepiece are given in Table 1.

* h_spencer@drs-sts.com; phone 1 310 750-3209; fax 1 310 750 3203; www.drs.com

Table 1: Optical design requirements effective focal length, mm. 18.8 eye relief, mm 27 exit pupil diameter, mm 10 field-of-view, degrees 20.6 x 27.2 wavelength band, µm 0.47 - 0.64 diopter adjustment +6 to -2 display format, mm 7.2 x 9.6 pixel size, µm 15 x 15 magnification 12X geometric distortion, % < 2 lens element weight, gms < 30 (goal)

Optical Design and Engineering, edited by Laurent Mazuray,Philip J. Rogers, Rolf Wartmann, Proceedings of SPIE Vol. 5249

(SPIE, Bellingham, WA, 2004) · 0277-786X/04/$15 · doi: 10.1117/12.509866

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2. CANDIDATE EYEPIECE DESIGNS Eyepiece design over the years has identified design forms with optical capabilities that are well analyzed and understood. A survey of design forms in the well known (but perhaps dated) MIL-HDBK-141 reveals many different design forms and their capabilities. Many of the design forms are named for their first inventor. The relatively high magnification, wide spectral band, long eye relief and the large pupil diameter required here clearly limit the choices. A simple singlet magnifier lens is not color corrected nor provides any control over field curvature and is quickly eliminated from consideration. The Huygenian eyepiece has only a short eye relief and the internal field stop is only suited to an aerial image such as presented by a microscope objective. The Ramsden eyepiece is a step up in performance, but lateral color is not well corrected and the eye relief is still short. The Kellner eyepiece is an even better choice but still suffers from a short eye relief. The Orthoscopic eyepiece is much better corrected for lateral color and field curvature than any of the previous design forms and is often used as a replacement for the Kellner in high performance systems. Its four optical elements is probably the practical maximum for this application due to weight considerations. All of the eyepieces in the MIL-HDBK-141 are of conventional optical glass with all-spherical surfaces. Modern optical design software has progressed significantly since the time that this publication was written (1962). It didn’t even exist in the times of many eyepiece invertors. Even more importantly, machining and fabrication methods have advanced to the point where aspheric optical surfaces are practical and common. Both machined and molded optical elements can now be fabricated in both glass-like and plastic materials to bring a higher level of correction to the eyepiece designs of the past. The approach to this problem was to use conventional starting point design forms and determine where aspheric surfaces could help the design to achieve the required performance in the smallest and lightest weight package.

3. ANALYSIS OF THE DESIGN FORMS

3.1 Kellner design type Starting with the Kellner design form, an optical optimization was performed using preferred optical glass types and spherical surfaces. The requirement for a long eye relief distance and low distortion made the design difficult. Figure 1 shows the ultimate performance obtained. This 4-panel presentation will be used through this paper. The upper left panel shows a raytrace of the lens over a 10mm pupil. The upper right panel tabulates the rim ray curves at four field points; on axis, full elevation, full azimuth, and at the corner. Again, the curves are over the full 10mm pupil. The scale factor is +/- 8 pixels. The lower left panel is a through focus MTF, which is useful in determining the maximum MTF for each field point and target bar orientation and how much eye accommodation will be required to bring that field point into focus. The solid curves are for horizontally-oriented bars and the dashed curves are for vertically-oriented bars. The separations between the peaks represent field curvature and astigmatism. Since the lens is traced from the eye to the focal plane, the defocus at the focal plane should be converted to diopters at the virtual image to be viewed by the observer by the formula

defocuseflD

2

1= (1)

where the efl and defocus are in meters. Full scale in this panel represents approximately +/- 3 diopters full scale. Although the design is optimized over a 10mm exit pupil and the rim ray curves are plotted as such, the MTF was calculated over a centered 5mm pupil to simulate the human eye in a nearly fully dilated condition. The 10mm total pupil allows for eye misalignment without vignetting. The final panel is a plot of field curvature and geometric distortion. The displacement of the tangential and sagittal field curves from each other is a measure of the system astigmatism. Again, the diopter values implied by the defocusing should be taken into consideration and are approximately +/- 6 diopters full scale.

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The all-spherical Kellner design suffers from significant spherical aberration as well as field curvature and astigmatism. For this focal length eyepiece, 0.3mm corresponds to 1 diopter of defocus at the eye. It can be seen that this design has approximately 5 diopters of astigmatism at the edge of the field of view. Additionally, the spherical aberration and large uncontrolled tails of the rim ray curves indicate that noticeable image "swimming" will be evident when the eye moves within the 10mm exit pupil. This design has a calculated weight of about 27 grams, nearly the design goal of 30 grams. Clearly, this will not be a suitable design for our eyepiece. The logical refinement of this design to increase performance yet preserve the number of lens elements was to incorporate an aspheric surface. Either glass or plastic could have been chosen for the substrate, but since the goal was weight reduction, plastic is the logical choice and will be used throughout the designs described here. The performance of this design can be seen in Figure 2. This design is significantly better than the previous one. The aspheric surface, which is located at the surface closest to the focal plane, exerts considerable control and correction on the chief rays, allowing the simultaneous reduction of field curvature and astigmatism while at the same time achieving low geometric distortion. The lens element located in front of the focal plane is acrylic plastic, allowing for fabrication of the aspheric surface using diamond turning or injection molding. The advantage of plastic over glass for this application is that a prototype can be fabricated inexpensively by diamond-turning and used to investigate the eyepiece through actual use. When the design shifts into production, it can then become economical to invest in the tooling required for injection molding.

Fig. 1: Kellner design form with spherical surfaces.

6 diopters

16 pixels

3 diopters

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The weight of the lens elements has decreased from the previous 30 grams for the all-spherical glass design down to 20 grams due to the 3-5X reduction in thedensity of plastic over various types of optical glass. 3.2 Orthoscopic design type The significant increase in optical performance combined with a simultaneous decrease in weight seen in the previous Kellner design example encourages a more aggressive attempt. Adding another optical element seems permissible, since the 20-gram design is well below the 30 gram goal. The eyepiece design forms having more than 3 lens elements generally have at least two cemented interfaces. It is not desirable to cement glass to plastic, owing to the large difference in coefficient of linear expansion between the two materials. Either the Symmetrical eyepiece design form or the Orthoscopic eyepiece could have been chosen for this next attempt. The Symmetrical design features two cemented achromatic doublets and although has the capability to cover a substantial field with long eye relief, it’s distortion correction is not nearly as good as that of the Orthoscopic eyepiece. Since distortion must be kept low in the design, the decision was made to proceed forward with the Orthoscopic design. The performance of this design is illustrated in Figure 3.

Fig. 2: Kellner design form with an aspheric surface.

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It was found that this design is capable of much better optical performance than the Kellner type eyepiece. Specifically, spherical aberration is much lower and control of astigmatism at the edge of the field is much better. Distortion is about the same. The cemented interfaces are necessary with fields of view this large and to preclude total internal reflection within the eyepiece. A side benefit is the elimination of four coated surfaces. Weight has now become a problem, as it has grown to 49 grams, much above the goal of 30 grams. To increase performance further in this design it will be necessary to add aspheric surfaces. The first re-design attempt converts the design to all plastic optics to bring the weight under control and puts an aspheric surface on the surface closest to the focal plane. The optical performance of this design in given in Figure 4. Virtually all of the aberrations have been reduced by this improvement. Very importantly, the weight has dropped to 11 grams. The field has become very flat and spherical aberration is much reduced. About the only nagging problem is the magnitude of the geometric distortion at the 7/10ths zone, corresponding to approximately full elevation in the display. All things considered, this design would probably be well accepted by the user.

Fig. 3: Orthoscopic design form with spherical surfaces.

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To investigate the improvement that would result from adding one final aspheric to the design, it was decided to allow the surface nearest to the eye to depart from a sphere. These results are shown in Figure 5. The improvement here is marginal. Geometric distortion has been lowered and spherical aberration has been reduced slightly. The field aberrations and MTF values are virtually the same. Since distortion has been an issue in this system, it could be considered worthwhile to incorporate two aspheres to eliminate that concern.

Fig. 4: Orthoscopic design form with one aspheric surface.

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4. CONCLUSION This paper has discussed the systematic design process that has been followed to develop an eyepiece design form, configured ultimately of all plastic lens elements with some strategically chosen aspheric surfaces. The optical literature and patent database contain surprisingly little reference to such design forms. It was found that adding an aspheric surface to a design form generally allowed achieving similar performance to an eyepiece design of the next level of complexity, as measured by the number of lens elements. When the lens elements were made of plastic, tremendous weight reduction was realized.

REFERENCES

1. B. H. Walker, “ Optical Design for Visual Systems”, p.47-67, SPIE Press, 2000 2. Military Standardization Handbook (MIL-HDBK-141), U.S. Defense Supply Agency, 1962

Fig. 5: Orthoscopic design form with two aspheric surfaces.

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