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We derive the quantum noise limit for the optical beam displacement of aTEM00 mode. Using a multimodal analysis, we show that the conventional splitdetection scheme for measuring beam displacement is non-optimal with 80%efficiency. We propose a new displacement measurement scheme that is optimalfor small beam displacement. This scheme utilises a homodyne detection setupthat has a TEM10 mode local oscillator. We show that although the quantum noiselimit to displacement measurement can be surpassed using squeezed light inappropriate spatial modes for both schemes, the TEM10 homodyning schemeout-performs split detection for all values of squeezing.Comment: 13 pages, 7 figure

Optimal optical measurement of small displacements