Importance of Polarization Analysis
A proper optical design of a valuable optical system should include a polarization analysis to reduce the probability of systems missing performance, cost, and schedule targets. Many disasters could have been avoided with proper polarization modeling.
For example, many coatings have a limited range of high performance, and may have very different behavior at the limits of wavelength or angle. This can cause excessive loss of light or a large change of polarization and loss of resolution. Commercial polarizing beam splitters (PBS) from different vendors use many different designs to achieve their high performance in a sweet spot of wavelength and angle. Systems which meet specification with one PBS have had yield problems and even failed when a different PBS was substituted.
One very expensive polarization-related failure occurred in a gimballed mirror for a satellite-to-submarine communication system. The system transmits circular polarization to the submarine, so the sub’s receiver works equally well at all orientations. The mirror was required to maintain polarization such that no state would couple into an orthogonal state by more than 2%. The vendor only verified that s-polarized light reflected into s-light and that p reflected into p-light within the 2% error target. No other orientations were checked, based on the false assumption that arbitrary light can just be analyzed as a combination of x and y components. This vendor test ignores the effect that retardance and diattenuation between the s and p-light have on the output state for 45° and circularly polarized light. At the federal customer-level, the polarization coupling with circular polarization was measured as 4%. A Polaris-M polarization analysis with Mueller matrices and the specified coatings would have quickly revealed the large diattenuation and retardance in the coating choice and led to a coating change during the design. Instead the program lost 18 months and costs increased by over two million dollars.
A set of binoculars were designed using Schmidt-Pecham prisms for the 180° image rotation. These prisms split the pupil through different prism paths. The binocular’s image performance was disappointing and an interferogram revealed different phases in the left and right sides of the exit pupil of each optic. Further measurements indicated very different polarization states in the left and right sides of the exit pupil. Since the Schmidt-Pecham prism has a different (mirror-image) set of internal reflections for the two prism sides, the polarization change is different for half the rays entering each eye. A special phase compensating coating had to be designed for one of the internal reflections to match the polarizations and phases. Again, a Polaris-M polarization analysis of the PSF would have immediately revealed a non-diffraction limited image for the original design.
A DOE project required a number of beams split from a single laser to enter a spherical region from many directions with the resulting light polarized in an overall dipole pattern. As light undergoes multiple reflections, the polarization orientation changes, even if the mirrors are non-polarizing with equal s and p-reflection. A Jones matrix calculation of the reflection sequences didn’t account for this overall polarization rotation, called the geometrical transformation. After the system was built, the misalignment from the dipole polarization pattern was discovered. Uncovering the source of the problem, redesigning the relay mirrors and housings, and reassembling the system took over one year. This mistake could have been avoided using Polaris-M’s three dimensional polarization ray tracing matrix method.
Another disastrous polarization failure happened on a promising liquid crystal TV project. A terrific prototype projection system with complex polarization optics had been approved by a large optics company after enthusiastic feedback from a consumer electronics chain. The LC TV was rapidly being ramped up into production. To arrange vendors for the beamsplitters and polarization elements, specifications and tolerances were required for all the elements and assemblies. These tolerances had not been explored during the prototyping phase and the tolerances weren’t understood. Rather than performing a complex polarization tolerance analysis, the optics company’s team defaulted to putting rather tight tolerances on all the retardances, coatings, and beamsplitters, figuring this was a safe choice; the system must perform well if the tolerances are small enough.
A few months later vendors were reporting that deliveries would be delayed because they didn’t have processes and test equipment to meet the customers tight polarization specifications. The optics company didn’t know what tolerances really needed to be, and everything slowed down. The vendors were waiting for guidance from the optics company’s design team, but the exchange of technical information was difficult since the design team didn’t have optical models with enough detail. The vendors didn’t want to deliver significant quantities of parts out of specification. The clock ran out when the electronics chain didn’t begin receiving pre-Christmas deliveries on-time for in-store display. They chain not only cancelled their order but also filed a lawsuit against the large optics company for breach of contract. To avoid such problems, Polaris-M will prepare sensitivity tables for retardances, extinction ratios, and element orientations and perform Monte Carlo yield calculations to determine the system polarization tolerances.
To avoid such problems, Polaris-M will prepare sensitivity tables for retardances, extinction ratios, and element orientations and perform Monte Carlo yield calculations to determine the system polarization tolerances.