A laser-based multilateration system for measurement of metre-scale low-slope freeform non-specular surfaces.

The manufacture of metre–scale mirror segments for telescopes requires measurement with low uncertainty to enable accurate form correction. The uncertainty of this measurement has a direct effect upon the time to manufacture these segments; it is therefore critical, to the viability of large optic manufacture, that a method for low uncertainty measurement of these surfaces is developed and evaluated. The state-of-the-art system for measurement of metre–scale surfaces has a length measurement uncertainty of 1.2 µm over 1 m. Multilateration is a method for determining Cartesian coordinates of measured positions utilising range displacement measuring stations. A four laser tracker multilateration system has been proposed and tested with the aim to determine whether a system can measure the specified surfaces with measurement uncertainties below 1 µm. Influence factors that affect the multilateration input parameters have been identified and utilised in Monte Carlo simulation of the multilateration system to estimate the uncertainty associated with the coordinate measurement. A small flat optic (0.2 m 0.2 m) was measured with the multilateration measurement setup to have z-coordinates with a standard deviation, σz = 0.25 µm, and a large flat optic (0.4 m 0.4 m) was measured with the multilateration measurement setup to have z-coordinates with a standard deviation, σ∆ z = 0.73 µm. The 10 x 10 point multilateration measurement of the large optic was repeated 10 times; the 100 points on the surface have a square root mean variance, σz = 0.46 µm. Monte Carlo simulations indicate the independence of measurement area and measurement noise for the experimental setup tested. It is concluded that a laser–based multilateration system can measure a metre–scale optic with z-coordinate measurement uncertainty below 1 µm. A 15.5 h measurement of the larger flat was carried out to determine the effect of time dependent parameters on measurement uncertainty. The measurement solution had a standard deviation of 1.88 µm: a factor of approximately 2.4 times the equivalent short–term multilateration measurement solution. Simulations have shown how this measurement drift is strongly related to temperature change in the local environment of the measurement setup. This has been confirmed by long–term measurements of laser tracker stationary SMR.