By Dr. Scott Lerner, Principal Engineer, Imaging Optics; and Dr. Joy Ding, Senior Applications Engineer
Plastic (and glass) aspheric molded lenses with precision tolerances continue to enable ever more ambitious (mobile camera) compact aspheric design. So let’s discuss a few tips for compact aspheric lens design.
Spherical surfaces are often used in classical lens designs because they are easy to manufacture. Spherical surfaces have limitations, however, and one of those limitations is spherical aberration, which is an optical effect that causes incident light rays to focus at different points when forming an image. This effect can result in a less-than-perfect blurred image in optical systems. Aspheric surfaces, on the other hand, focus light to a small point, creating comparatively no blur and improving image quality.
While surfaces with spherical shapes are easier to make, many more spherical surfaces are generally needed to reduce image blurring compared to aspheric surfaces. This means that an aspheric lens can be used to replace multiple spherical lenses, thereby creating a device that is smaller, lighter, and potentially less expensive to produce.
As lens systems become more compact and complex, and image resolution becomes ever more critical, aspheric surfaces in optical systems are increasingly important. Unfortunately, traditional methods of aspheric design present inherent complications when it comes to manufacturing and testing these components. To step up your aspheric lens designs and work more efficiently, try these CODE V design and analysis tips.
Many optical systems need to operate over a wide temperature range. For example, the same cell phone camera module needs to produce superior imagery both in the harsh winters of Chicago and in the searing summers of the Death Valley, which can have a temperature difference of about 90 degrees Fahrenheit. Optical systems for military and aerospace applications are expected to perform well in an even wider range of temperature environments. Temperature change affects many parameters of an optical system, including element radii, element thickness, refractive index, and airspace thickness. Designing optical systems for a large temperature swing is a complex task. One trick for designing such optical systems is to combine glass and plastic elements.
Glass and plastic elements have diverse thermal properties that allow designs to maintain focus over a temperature range. Use the CODE V macro function @MTF_PEAKFOC to evaluate the change in lens focus with temperature (thermal focal shift).
Specifications for the sample lens are as follows:
= [(+1.1um) – (-1.4um)]/[70C-20C]
Compact aspheric designs often have more than a hundred variables, and the performance may have complex pupil and field dependence. Analyzing the designs requires fine sampling of the field and pupil. CODE V Macro-PLUS provides a powerful tool for data visualization to study the behavior of these designs.
Due to the complexity of compact aspheric designs, making sense of the analysis results can be a daunting task. For example, a through-focus MTF plot produced by CODE V includes a total of 30 curves, as shown below in the figure on the left. It is difficult to observe the relationship between the peak focus and the field from the large number of curves presented. In this case, we can use a macro to plot the Peak MTF focus versus field based on the through-focus MTF data, as shown in the figure on the right. Using Macro-PLUS to produce a distilled representation provides much clearer data visualization.
Another great application for Macro-PLUS is summarizing tolerancing analysis results. The tolerancing analysis produces a cumulative probability plot. When many fields are required, such as for a compact aspheric design, it is difficult to correlate performance with fields. For example, the results for a Monte Carlo Sagittal and Tangential tolerance analysis (TOLMONTE) that includes 11 fields are shown below.
To improve the interpretability of the data, you can use Macro-PLUS to plot a selected cumulative probability versus fields. The following figure distills results from TOLMONTE to a simple relationship between the 70% cumulative probability and relative field.
For classical lens design forms, the best foci typically lay on a curved image surface defined by Petzval Curvature. In contrast, for compact aspheric designs, the best foci may lay on a highly aspheric surface. Including the function @MTF_PEAKFOC in your optimization file to constrain the peak focus to a plane will improve the design depth of focus. In general, designing for a larger depth of focus improves as-built performance and may improve thermal performance as well.
Monte Carlo Analysis allows you to keep tabs on the as-built performance during optimization. However, ray tracing compact aspheric systems takes significantly longer than classical systems, and Monte Carlo tolerancing takes significantly longer as well. In this situation, you can perform a rapid Monte Carlo analysis, where fewer Monte Carlo runs take place, and then use a Macro-PLUS script to calculate the statistics of the Monte Carlo results. This way, you can maximize the information obtained using a minimum number of trials. Even as few as five trials can provide useful information, as shown in the two figures below (Example: Rapid Statistical Monte Carlo Study).
For a compact aspheric design, the best focus may vary significantly with fields due to the complex field-dependence of such systems. The thermal focal shift may also vary significantly over the field of view. The nominal design may have good MTF across the thermal range, as shown in the figures on the left, but with a significant thermal focal shift at large field angle, as shown in the figure on the right. The thermal focal shift will degrade the as-built design performance over the temperature range. Evaluating thermal focal shift over the full field can reduce this discrepancy.
CODE V provides design and analysis capabilities that enable optical engineers to take advantage of the unique image quality and cost benefits offered by designing with aspheres. Contact our Optical Engineering Services team for help with your most challenging design projects at firstname.lastname@example.org.