No abstract

No abstract

No abstract

We have developed a system for measuring three dimensional position. Unlike most coiwentional position measuring techniques, which measure z, y and t directions separately, our system produces a single data set from which all three positions can be derived analytically. The zero position of the,system does not need to be reset before a measurement can be made, and the position does not require tracking between measurements.The interferometric system uses two curved mirrors to produce two spherical wavefronts. At the interferometer output the wavefronts appear to be radiating from two close point sources. At 'a large distance T from the apparent points of origin, the interference between the two wavefronts is measured. Displacing one of the mirrors produces a significant change in the interference pattern. By applying four step phase stepping to the interference pattern we can deduce the phase difference between the two wavefronts and then the relative positions of the centers of the wavefronts. An axially symmetric paraboloid described by, t ( z , y) = a + bz + cy + d(z2 + y') is fitted to the phase map using B least squares technique. The parameters that describe the paraboloid are related to the difference in z,y and t poshion of the origins of the two wavefronts by the three following equations.2T 2 6 where: Az, Ay and 4 z are the displacements in the z,y and t directions respectively. Froni these equations and the known value v, we can determine Az , Ay and Az from the coefficients of the paraboloid. This enables us to measure position in three dimensions.A simulation was run on the system and the systematic errors were found to be 8pm pTp error in Az and Ay and a 1Opm p-p error in A t when measuring inside a l m m range in all directions. The simulation assumed that the phase was measured at a distance r=7cm over a 6mm by 4mm rectangle.A diagram of the interferometer used is shown below. The spherical mirrors, SDI1 and S M 2 , in the arms of the interferometer reflect spherical wavefronts back towards the beam splitter, BS, where they are combined and sent through an imaging system to the CCD camera. The pinhole was necessary to spatially filter unwanted reflections from the beam splitter and other optical components.SbI2 was mounted on piezos to apply the necessary phase shifts of X/4 required for the four-step phase stepping algorithm and the position of SM1 was varied to test the system. The position of SM1 was also monitored using an LVDT (Linear Voltage Differential Transducer) to provide a reference displacement. Moving mirror SMI LVDT T ' .~ .__. Beam Figure 1: Experimental SetupWe found the interferometer was able to measure Ax and Ay with an accuracy of 1OMm p-p and At t o an accuracy of 15pm p-p over a lnim range in all directions. The range of measurement,s could be reduced or increased arid the error would also reduce or increase respectively. Most of these errors arise from the modelling of the difference of two spheres with a parabola. Variation of Az during the phase stepping routine also cont...

Heterodyne interferometry is a well known technique commonly used to measure phase difference in two beam interferometers operating with narrow-band light [l]. Unfortunately, it is much more difficult to use heterodyne methods with white light because of the need to shift the frequency of each wavelength component of the beam in one arm by the same amount. However, interferometers operating in white light are useful because of their ability to distinguish zero path difference. We present a heterodyne interferometer operating in white light where the desired frequency shift is produced using polarisation effects after the interferometer. The configuration used allows a reference beam to be created outside the interferometer which is independent of the interferometer phase and allows displacement measurements to be made.The white light phase that is measured is the phase of the temporal-coherence function of the light source modified by the system spectral response and dispersion in the interferometer. White light phase is not necessarily linear with path difference [2] and we use the interferometer to measure the variation of the white light phase with path difference where the path difference is found using the same system operating with laser light. The interferometer could easily be modified to make surface profile measurements and when combined with measurements of the fringe envelope can be used to measure the complex temporal-coherence function.As shown in Figure 1 white light from a dispersive, polarising Michelson-type interferometer is passed through a U4Fresnel rhomb then through a rotating polariser and is detected using a photodiode. Light from a laser source propagates the same path as the white light beam and is measured at detector at separate detector. Light from a second polarised laser passes directly through the rotating polariser and is used as a reference signal with a phase independent of the interferometer path difference. The intensity of all three beams vary sinusoidally at twice the angular speed of the rotating polariser and their phase relative to the reference depends on the interferometer path difference. Note that the phase of the laser beam is used as a measure of path difference as there is a linear relationship between them. laser white reference ro,a(ing light . light laser beam polariser 1s.w nhnce (rad) Figure 1 Diagram of system for measuring white light phase variation.h h is approximately equal to the mean wavelength. This is limited by the electronic noise in the phase meter used and could potentially he improved. Independent phase measurements could be made at a rate of about 200s , The laser phase and white light phase was measured over a range of path differences (about 7.5pm) and the deviation of the white light phase from a straight line can be seen in Figure 2.