eGuide

High-Yield OptimizationStreamlining the path to more easily manufacturable designs

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Introduction

Optical designers need to build solutions that meet performance specifications and can be manufactured with as little wastage as possible. Traditionally optical design via computer optimization uses a numerical merit function to represent the optical performance of the simulated system. The conventional design approach is to maximize the nominal performance of the design, and then as a separate step, add fabrication tolerances to the nominal parameters so that upon manufacturing the resulting system still performs to specification. This usually results in designs that are very sensitive to manufacturing and alignment errors, which means the optical product is difficult to repeatedly manufacture successfully.

A new method, called High-Yield Optimization, improves on this traditional method. High-Yield Optimization desensitizes optical systems to manufacturing degradations during the design process rather than as a post-design step. The High-Yield Optimization method produces designs that meet tight performance specifications, provide a higher manufacturing yield, and lower manufacturing costs through less waste.

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Optimizing for as-built performance, rather than nominal performanceMost performance specifications apply at just the image surface. Computer optimization thus tends to yield designs which have relatively small sums for the aberrations at the image surface, but larger aberrations at any one intermediate surface. For example, consider the f/2, 200mm EFL aspheric singlet with zero field of view as shown in Figure 1. The image quality is perfect at the image surface, with a zero RMS spot radius. But there is significant spherical aberration introduced at the first surface—roughly 8.5 waves. At the second surface, a compensating amount of spherical aberration is introduced—the same magnitude but opposite sign. The net aberration is zero, but this is achieved by a delicate balance of large amounts of aberration. This is how tolerance sensitivity gets introduced—any defect in the surface will alter the angles of the rays, disturbing the aberration balance.

Figure 2 shows a singlet with the same aperture and focal length, also with nearly zero net aberration. This design has much lower ray angles at the first surface.

The impact can be seen by a tolerance analysis of these nominal designs. Using identical tolerances on the two base radii, element decenters, and element tilts, the predicted as-built RMS spot radius is 115 microns for the first design and just 19.3 microns for the second design. Note “as-built” refers to the simulated results considered manufacturing defects, while “nominal” refers to idealized performance without any defects considered.

To optimize for best as-built performance, rather than best nominal performance, the tolerance defects must be accounted for in the design process. Including this consideration in the design is very valuable, particularly for global optimization where radically different design forms may be considered that have similar nominal but drastically different as-built performance.

Figure 2 – Singlet with lower ray angles on the first surface

Figure 1 – Singlet with higher ray angles on the first surface

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How High-Yield Optimization worksDuring the optimization process, High-Yield Optimization penalizes rays that have a large angle of incidence at every surface. As rays are traced to evaluate the optical performance, such as RMS spot radius, the individual ray angles of incidence (or the exit angles, whichever is larger) are stored and added to the merit function. When the merit function is evaluated, rays with large angles of incidence are penalized, even if those rays provide a good optical image quality. The idea is to coax the optimization search into finding optical design solutions that have both good image quality and rays with low angles of incidence, which in turn reduces the tolerance sensitivity of the resulting design when fabricated.

High-Yield Optimization is fast and applies to all types of aberration-inducing surfaces. It is general to all optical systems and is not dependent upon any symmetry or first order properties of the system.

The innovation of High-Yield OptimizationComputing the actual sensitivity to optical tolerances is costly and time consuming, but this overhead can be avoided. Using the angles of incidence as a proxy for the actual tolerances vastly speeds up the numerical optimization. Furthermore, by optimizing simultaneously on these ray angles and the image quality, the optimization process produces designs that will have good performance when actually built in the “real world”—rather than just have good performance in a computer simulation. High-Yield optimizes the “as-built” performance, not just the “nominal” performance.

Improved optical designHigh-Yield Optimization dramatically improves optical designs. As the following example shows, the designs created using High-Yield Optimization yield higher performances than those built without accounting for common manufacturing defects.

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Nine Element Objective The example shows the design of a lens with the following specifications: 9 all spherical air spaced elements, stop after the 5th element, f/3.0, EFL 100.0 mm, full field of view 28.0 degrees, and visible wavelengths. Boundary conditions are 2.0 mm minimum air and edge thickness and 100.0 mm maximum center thickness for both glass and air, no more than 1.0% distortion, and no vignetting. The optical performance goal was to minimize the RMS spot radius.

Starting with parallel plates, the design was optimized using the OpticStudio Global Search algorithm for about 4 hours on a modest 4 core computer. All radii and spacings were made variable, and all glasses were automatically selected. After about 30 minutes of run time no significant decreases in the RMS were observed. The resulting design is shown in Figure 3.

A tolerance analysis was performed on this candidate design using the default tolerances in OpticStudio. All default tolerances and settings were used. The default tolerance analysis considered 181 possible defects, including potential specification, irregularity, and alignment errors. To simplify this discussion, only two computed values were considered—the nominal RMS spot radius for the perfect design and the as-built RMS spot radius estimated from the Root-Sum-Squared analysis of all 181 of the individual sensitivities. The nominal RMS is 1.89 microns and the as-built RMS is 106.3 microns. The substantial loss of performance is due to sensitive surface tolerances caused by rays with high angles of incidences.

Starting from the same design and specifications as the previous example, the new High-Yield Optimization method was applied to optimize for as-built performance, and the identical design procedure repeated. The new design is shown in Figure 4.

The same tolerance procedure as the previous design was repeated. The new design has a nominal RMS of 5.34 microns, and an as-built RMS of 29.7 microns. With High-Yield Optimization, the as-built performance is substantially improved, while only sacrificing a few microns in nominal performance. This is the key message of the High-Yield Optimization method—the optimization sacrifices idealized performance in exchange for improved as-built performance.

Figure 3 – Best design found without High-Yield

Figure 4 – Best design found with High-Yield

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Figure 5 – Without High-Yield Optimization Figure 6 – With High-Yield Optimization

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Comparing aberrations As the following results show, designs created with High-Yield Optimization greatly reduce the amount of aberrations in the optical system. The Seidel diagrams below show the change in aberrations for the nine element objective discussed on the prior page. Figure 5 shows the aberrations found in Figure 3. Figure 6 shows the reduced number of aberrations found in Figure 4.

Figure 7 - Comparing RMS spot radius before and after High-Yield Optimization

RSS analysis Tolerance analysis was performed on both designs. Using the default tolerance defects and values, 181 individual defects were considered. The design without High-Yield Optimization resulted in Nominal/As-Built performance of 1.89/106.3 microns. Whereas the design with High-Yield Optimization resulted in Nominal/As-Built performance of 5.34/29.7 microns. The design optimized for high yield sacrifices nominal performance for reduced tolerance sensitivity, resulting in superior as-built performance.

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Yield analysis Monte Carlo tolerancing, rather than approximating RSS, shows that High-Yield Optimization increases the yield of the optical system. Monte Carlo chooses random values for every tolerance parameter, which supports multiple distribution models. All defects considered at once.

Conventional optimization: Mean RMS 48.5 microns• 10% of systems had RMS <28.7 microns

• 90% of systems had RMS <70.4 microns

High-Yield Optimization: Mean RMS 19.3 microns• 10% of systems had RMS <11.8 microns

• 90% of systems had RMS <28.9 microns

SummaryBecause all optical systems will have these defects when built, the High-Yield method delivers better net performance than the traditional design approach. This technique is a complete revolution and dramatic improvement for the optical design industry, particularly useful for consumer electronics companies who need to design for a high manufacturing yield and the medical and defense industries who need to meet tight design specifications.

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OpticStudio: The leading optical design software The top companies in aerospace, astronomy, automotive, biomedical research, consumer electronics, and machine vision, use OpticStudio to design optical system designs. No other software on the market today offers state-of-the-art optimization tools for improving performance like OpticStudio.

Optimize with precision for improved design performance

Manually adjust your system with optimization tools like the sliders in the Visual Optimizer or let the advanced optimization algorithms find the best design for you. These algorithms automatically maximize your system performance by changing parameters in your design, such as lens radii, thicknesses, and materials. Algorithms include the fast Local Optimizer and the exhaustive Global Search Optimizer. You can also rapidly optimize for MTF using Contrast Optimization, and optimize for “as-built” performance using High-Yield Optimization.

Ensure manufacturability with comprehensive tolerancing features

Tolerance to get it right the first time. Run a tolerance sensitivity analysis to calculate how each tolerance will affect your system performance or let OpticStudio calculate the allowable tolerances for you by running an inverse sensitivity analysis. Then, simulate the aggregate effect of all tolerances with a Monte Carlo tolerance analysis. This analysis generates manufacturing yield statistics, so you know what percentage of manufactured systems meet specifications.

Import, optimize, and export CAD parts with OpticStudio

For parts that are in the optical path, dynamically open native SOLIDWORKS, PTC Creo Parametric, and Autodesk Inventor parts and optimize them in OpticStudio. Or, use the built-in CAD program, Part Designer, to create custom shapes for any application.

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About ZemaxZemax’s industry-leading optical product design software, OpticStudio and LensMechanix, helps optical and mechanical engineering teams turn their ideas into reality. Standardizing on Zemax software reduces design iterations and repeated prototypes, speeding time to market and reducing development costs.

We touch nearly every optical system manufactured today, including virtual reality systems, cell phone cameras, autonomous-vehicle sensor systems, and intraocular lenses—even imaging systems for the Mars Rover. By listening to our customers, we deliver unmatched value and have the largest, most passionate user base in the industry.