The subpixel resolution of optical-flow-based modal analysis

Abstract This research looks at the possibilities for full-field, non-contact, displacement measurements based on high-speed video analyses. A simplified gradient-based optical flow method, optimised for subpixel harmonic displacements, is used to predict the resolution potential. The simplification assumes an image-gradient linearity, producing a linear relation between the light intensity and the displacement in the direction of the intensity gradient. The simplicity of the method enables each pixel or small subset to be viewed as a sensor. The resolution potential and the effect of noise are explored theoretically and tested in a synthetic experiment, which is followed by a real experiment. The identified displacement can be smaller than a thousandth of a pixel and subpixel displacements are recognisable, even with a high image noise. The resolution and the signal-to-noise ratio are influenced by the dynamic range of the camera, the subset size and the sampling length. Real-world experiments were performed to validate and demonstrate the method using a monochrome high-speed camera. One-dimensional mode shapes of a steel beam are recognisable even at the maximum displacement amplitude of 0.0008 pixel (equal to 0.2 μm) and multiple out-of-plane mode shapes are recognisable from the high-speed video of a vibrating cymbal.