Methodology of designing compact schlieren systems using off-axis parabolic mirrors

Abstract

Schlieren imaging is widely adopted in applications where fluid dynamics features are of interest. However, traditional Z-type schlieren systems utilizing on-axis mirrors generally require large system footprints due to the need to use high f-number mirrors. In this context, off-axis parabolic (OAP) mirrors provide an attractive alternative for permitting the use of smaller f-number optics, but well-documented methodologies for designing schlieren systems with OAP mirrors are lacking. The present work outlines a ray-tracing-based workflow applied to the design of a modified Z-type schlieren system utilizing OAP mirrors. The ray-tracing analysis evaluates the defocus and distortion introduced by schlieren optics. The results are used along with system size and illumination efficiency considerations to inform the selection of optimal optical components capable of producing high-quality schlieren images while minimizing the system footprint. As a step-by-step demonstration of the design methodology, an example schlieren system design is presented. The example schlieren design achieved an image resolution of 1.1 lp/mm at 50% contrast, with a 60% reduction in system length compared to traditional Z-type systems with f/8 mirrors; distortion characterizations of the designed schlieren system showed good agreement with ray-tracing predictions, and the distortion can be corrected through image post-processing. The current work provides a systematic approach for the design of compact schlieren systems with OAP mirrors and demonstrates the utility of this underutilized option.