Some recent research arising from our project investigating the application of speckle velocimetry (SV) project for Mars rovers and other autonomous vehicles (EPSRC grant - EP/H019839/1) has been accepted for publication.
During the course of the SV work it became apparent that the observed speckle shift was very dependent upon the surface shape beneath the vehicle (a factor over which we have no control!) and that an extended theory of the speckle displacement was necessary to understand how best to minimise any errors introduced to the velocity measurements. What followed can only be described as maths – lots of maths – as we attempted to understand the original theory and how to modify it to include the influence of surface shape. Finally after many reams of scrap paper (mostly the lunchtime crosswords), and several iterations of an experiment designed to measure the speckle translation scaling factors with sufficient accuracy - we had a working theory – but only for when the detector is perpendicular to the surface. After a bit of head scratching we released what was wrong – the original theory [ref] also broke down for off-axis detector positions, so by removing some approximations we finally arrived at a working theory validated for both on-axis and off-axis detector positions.
This paper also presents an interesting practical example of how new 3D printing technology can help in research. For the experimental validation of the new speckle shift theory we needed some very accurate test surfaces, a series of ramps with different gradients and an octagonal cross-section. This allowed not only the magnitude of the gradient to be varied but also the direction by rotating the ramp in in 45o increments to vary both components of the surface gradient in a controlled manner. Having our technician make up these parts would have been time consuming and costly, so we had the parts 3D printed. This was done by external company using a Selective Laser Sintering process to create Nylon parts with a precision of ±0.1mm. The finished ramps have a surface texture like an extra-strong mint that is ideal for laser speckle generation and cost the princely sum of £6.20 per ramp!
Update: The full paper is available now from Optics Express (http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-21-25466):
Objective speckle displacement: an extended theory for the small deformation of shaped objects
T O H Charrett and R P Tatam
Optics Express, Vol. 22, Issue 21, pp. 25466-25480 (2014)
Or via CERES https://dspace.lib.cranfield.ac.uk/ (Cranfield University institutional repository).