Digital holographic interferometry for characterizing deformable mirrors in aero-optics

Measuring and understanding the transient behavior of a surface with high spatial and temporal resolution are required in many areas of science. This paper describes the development and application of a high-speed, high-dynamic range, digital holographic interferometer for high-speed surface contouring with fractional wavelength precision and high-spatial resolution. The specific application under investigation here is to characterize deformable mirrors (DM) employed in aero-optics. The developed instrument was shown capable of contouring a deformable mirror with extremely high-resolution at frequencies exceeding 40 kHz. We demonstrated two different procedures for characterizing the mechanical response of a surface to a wide variety of input forces, one that employs a high-speed digital camera and a second that employs a low-speed, low-cost digital camera. The latter is achieved by cycling the DM actuators with a step input, producing a transient that typically lasts up to a millisecond before reaching equilibrium. Recordings are made at increasing times after the DM initiation from zero to equilibrium to analyze the transient. Because the wave functions are stored and reconstructable, they can be compared with each other to produce contours including absolute, difference, and velocity. High-speed digital cameras recorded the wave functions during a single transient at rates exceeding 40 kHz. We concluded that either method is fully capable of characterizing a typical DM to the extent required by aero-optical engineers.