A heterodyne interferometer, with a retro-reflector measurement mirror, is used to measure the displacement of a linear translation stage, shown below. The laser source used (a Zeeman laser) has a wavelength stability of 1 part in 108 (rectangular distribution) at a nominal wavelength of 632.99 nm. Mounted on the stage is a biological sample in a petri dish, to be moved up to a distance of 500 mm away from the interferometer into a microscope. The petri dish is located 40 mm, measured with 0.1mm resolution, above the base of the stage where the interferometer measures. The stage itself can rotate (around the axis normal to the page) up to 0.0001 rad ±1% upon moving due to poor design. Assume also that the motion axis and the measurement axis are aligned to be co-linear to within 1 µrad. Calculate the uncertainty (k = 2) in a displacement measurement due to wavelength instability, index of refraction of air uncertainty (nair=1.00029 with uncertainty of 1 part in 109 ), Abbe Error, and planar Cosine error. The phase displacement relation for a heterodyne interferometer is given by φ = 2πNnz/ λ where the interferometer fold factor, N, is four for this design. For the system shown in question and your uncertainty analysis results, what would you change in the system to decrease the uncertainty in the measurement?
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