Spatial Multiplexing Technique for Improving Dynamic Range of Speckle Correlation based Optical Lever

Vijayakumar Anand,Shanti Bhattacharya,Joseph Rosen

doi:10.1038/s41598-019-52394-0

Abstract

Speckle correlation based optical levers (SC-OptLev) possess attractive characteristics suitable for sensing small changes in the angular orientations of surfaces. In this study, we propose and demonstrate a spatial multiplexing technique for improving the dynamic range of SC-OptLev. When the surface is in its initial position, a synthetic speckle intensity pattern, larger than the area of the image sensor is created by transversely shifting the image sensor and recording different sections of a larger speckle pattern. Then, the acquired images are stitched together by a computer program into one relatively large synthetic speckle pattern. Following the calibration stage, the synthetic speckle intensity pattern is used to sense changes in the surface’s angular orientation. The surface is monitored in real-time by recording part of the speckle pattern which lies within the sensor area. Next, the recorded speckle pattern is cross-correlated with the synthetic speckle pattern in the computer. The resulting shift of the correlation peak indicates the angular orientations of the reflective surface under test. This spatial-multiplexing technique enables sensing changes in the angular orientation of the surface beyond the limit imposed by the physical size of the image sensor.

Highlights

In 1826, Poggendorf invented the Optical Lever (OptLev) for improving the sensitivity of theodolites to an accuracy of 5 seconds of an arc and later, it was used by Gauss, Weber, Ising, Mol, and Burger for improving the accuracy of the measurements in their respective experiments[1]
We propose a spatial multiplexing technique to improve the dynamic range beyond the range of ref.[37], without significantly affecting the sensitivity of the SC-OptLev
The speckle intensity pattern Iβ(x0, y0,t)Rect[(x0, y0)/D] recorded in real-time by the image sensor is zero-padded to match the size of the synthetic speckle pattern and is denoted by Iβ’(x0,y0,t)

Summary

Methodology

If D is the size of the image sensor along the x and y directions, the maximum angular variation of the surface that can be detected using C-OptLev is β1-max = ± 0.5tan−1(D/2 L). Under the assumption that the scattered light of the diffuser plate covers at least the entire image sensor, or more, in the initial state of no surface tilt, the maximum detectable angular variation in the case of SC-OptLev is β2-max = ±0.5tan−1(D/L)[37]. Iβ is cross-correlated with the larger synthetic intensity pattern stitched computationally according to Eq (1) from the p recorded speckle patterns. The speckle intensity pattern Iβ(x0, y0,t)Rect[(x0, y0)/D] recorded in real-time by the image sensor is zero-padded to match the size of the synthetic speckle pattern and is denoted by Iβ’(x0,y0,t). In [46,47], entropy was used to find the values of (o,b) that would reconstruct an object with the minimum background noise

Experiments

Conclusion