Mechanical stress is developed in optical systems from various internal and external influences, including inertial, pressure, dynamic, temperature, and mechanical loads. Excessive stress can lead to permanent deformations of optical mounts and support structures by exceeding the yield strength of the material resulting in misalignments of optical elements and loss in optical performance.
Stress must also be minimized to avoid loss in structural integrity and ultimate failure of parts and components including flexures, adhesive/epoxy bonds, and optical elements. Detailed stress analyses and the selection of an application dependent glass design strength are often necessary to avoid brittle fracture of glass optics. Determination of the design strength involves accounting for the fracture mechanics failure mechanism, the detailed stress distribution, the specific glass type, the presence of surface flaws, and subcritical crack growth due to environmentally enhanced fracture. Time-to-failure curves may be constructed to determine a design strength to meet lifetime service requirements.
In addition, the presence of mechanical stress in optical glass affects optical system performance by creating anisotropic variations in the index of refraction due to the photoelastic effect. The presence of stress birefringence creates both wavefront and polarization errors in the optical system.
8.1 Stress Analysis Using FEA
Finite element methods are routinely employed to predict mechanical stress in optical substrates and support structures. FEA stress analysis is typically more labor-intensive and time-consuming as compared to displacement and dynamic models. Extra attention to detail and higher-fidelity models are required to capture peak stresses in locations of fillets and holes. In addition, more elements are required because stress is numerically computed as a derivative of the displacement (i.e., strain) and is one order lower in accuracy than the prediction of displacements. Mesh convergence studies are typically performed to ensure that the element fidelity meets the desired level of accuracy, which requires varying the mesh density over several model iterations.
Performing a FEA stress analysis for a point or contact load will result in a stress singularity at the point of the applied load. In this instance, the use of Hertzian contact stress equations is recommended to predict the local stresses based on FEA predicted loads. Analytical solutions are always recommended to validate FEA stress analyses and to provide first-order estimates during preliminary design stages.