Absolute angle measurement using dual-wavelength laser speckle: theory and method

This paper presents a method utilising the speckle pattern formed by dual-wavelength illumination for the measurement of the two out-of-plane surface angles with respect to the sensor frame. Theoretical expressions are derived relating the observed speckle shift between patterns formed by two wavelengths for tilted surfaces with both on-axis and off-axis detector positions. These expressions are verified experimentally, showing RMS errors of between 0.5–1.0 . Finally, an on-axis implementation of the concept is presented using dual-wavelength illumination generated from two modes of a standard FP diode laser. Simplified expressions for the calculation of surface angles from measured speckle shift using this arrangement are presented, given in terms of three sensor constants; the responsivity or sensitivity of the sensor, C, and the zero surface tilt speckle shifts, Ax0 and Ay0. Experimental results using this sensor for a range of surface tilts between 0.0° and 7.5° showed an RMS error of 0.10° in θx and 0.19° in θy.