A good optical design does not end once nominal parameters are achieved under ideal conditions. It ends only once it is known that the system will still work correctly with the deviations that the manufacturing process will actually introduce.
Why a mathematically correct design can fail on the assembly line
A design optimized for ideal, nominal parameter values can be very good in theory and, at the same time, extremely sensitive to the smallest deviation from those values. If a system requires nearly perfect manufacturing of every element to reach its intended performance, in real production — where no element is ever made with zero error — that design will generate a high reject rate, or fail to reach the required quality at all.
Types of tolerances in an optical system
The tolerances most commonly analysed are surface radius of curvature (deviation from the nominal value), element thickness and the spacing between successive elements in the system, decentration — the offset of an element's axis relative to the optical axis of the whole system, tilt of a surface or an entire element relative to its intended orientation, and deviations in material properties, such as the real refractive index of a glass compared with its catalogue value, or its homogeneity within the element.
Sensitivity analysis: which parameters degrade the system the most
Before moving to a full statistical analysis, it is worth checking how strongly each individual parameter affects the system's functional outcome — for example, image quality expressed through MTF, aberrations, or transmission. Sensitivity analysis lets you distinguish critical parameters, which require tight tolerances and precise — and therefore more expensive — manufacturing, from those that can be toleranced much more loosely without a noticeable loss of system quality. This distinction has a direct impact on production cost: not every element needs the same precision.
Monte Carlo simulation of production spread
Sensitivity analysis checks the effect of changing one parameter at a time, but in real production all parameters deviate simultaneously, randomly and independently of one another. Statistical Monte Carlo simulation randomizes the values of all toleranced parameters at once, within their assumed tolerances, and repeats this procedure for a large number of system variants, producing a probability distribution of the outcome — for example, what percentage of manufactured units will meet the required image-quality criterion given the specified tolerances.
Tolerancing tools in OSLO
OSLO from Lambda Research includes dedicated tolerance-analysis tools that combine sensitivity analysis of individual parameters with statistical Monte Carlo simulation of production spread. This lets you not only check whether the nominal design meets requirements, but also estimate what percentage of a manufactured batch will fall within acceptable limits under the given manufacturing tolerances — and adjust the design or the production requirements accordingly before the system goes into production.
From tolerances to a manufacturing specification
The result of tolerance analysis is a concrete, numerical range of allowable deviation for each system parameter — information that can be carried directly onto the technical drawing and the specification handed to the optical-component manufacturer. A well-executed tolerance analysis also lets you decide deliberately which parameters are worth tightening at the cost of higher manufacturing price, and which can be loosened without risk to the system's functionality, instead of ordering production with arbitrarily chosen, uniformly tight tolerances across every element.
Summary
Tolerance analysis closes the design process with the question "will it work once it is actually manufactured?" — a question just as important as "does the system work in theory?". OSLO lets you answer it systematically: sensitivity analysis shows which parameters are critical, and Monte Carlo simulation shows a realistic distribution of outcomes across an entire production run. The result is a tolerance specification that balances system quality against manufacturing cost, instead of guessing how much precision is really needed.