Spatially integrated speckle intensity: maximum resistance to decorrelation caused by in-plane target displacement.

Laser speckle produced from a diffuse object can be used in determining the angular position of a rotating object. When the object rotates the backscattered speckle pattern, which changes continuously but repeats exactly with every revolution, is sampled by a suitably positioned photodetector. The photodetector output signal is periodic, and one period is stored in the memory as a reference. Shaft position can then be determined by the comparison of this stored reference signal with the current photodetector output signal. When the shaft is axially displaced, for example, by vibration, the backscattered speckle pattern changes on the photodetector and the similarity between the reference signal and the current signal is reduced. We examine the cross correlation of the real-time photodetector output signal and the stored reference signal as a function of axial shaft position. Use of a rotating shaft when collecting data is shown to be an efficient means by which to make effectively several thousand independent estimates of the maximum axial displacement tolerable before decorrelation of the photodetector output. Theoretical results and experiments conducted show that the decorrelation displacement varies, according to optical configuration, to a maximum value of 0.7 of the beam diameter. This has important implications for a proposed laser torquemeter as well as additional applications in which changes to the sampled speckle pattern, including decorrelation, are either desirable or undesirable.