Dynamic deformation measurements of a rotating disc by twin-pulsed 3D digital holography and interpolation of phase maps

摘要

This paper describes the application of twin-pulsed 3D digital holography to the measurement of the dynamic deformation of a disc while it rotates. Object rotation produces interferometric fringes that are related to deformations for instance, stress due to the centrifugal forces, out-to plane vibrations, and the object angular displacement. Furthermore an unbalanced disc that rotates may present a characteristic vibration amplitude pattern at a specific frequency. An optical arrangement that illuminates, with a twin pulsed laser, from three different positions the object was used to recover the x, y and z displacement components in a rotating object. The technique is able to distinguish the disc rotation from the displacement along the x-y plane and the out-of-plane z displacement. Two laser pulses are fired in order to take two digital holograms with a time separation of 20 μs. This is done for each of the three object illumination positions. Triads of twin-pulsed digital holograms taken at different times during object rotation are processed independently, and their optical phase maps retrieved by the conventional Fourier transform method together with the combination of data from the three illumination positions. The phase term related to the deformation is found experimentally where the intrinsic sensitivity vector is related to the rotation via the vector cross product, forming parallel fringes. To recover the rotation and deformation data the unwrapped phase maps were used as 'tilt' phase planes and all three sensitivity vectors in order to recover the in-plane, and out-to plane displacements. An interpolation algorithm was developed to correlate the time depending phase maps, leading to obtain object vibration frequency data. Experimental results are presented, showing in particular that the rotating object has an unbalancing due to the detected vibration frequency.