TEM10 homodyne detection as an optimal small-displacement and tilt-measurement scheme

We present a detailed description of small displacement and tilt measurements of a Gaussian beam using split detectors and TEM10 homodyne detectors. Theoretical analysis and an experimental demonstration of measurements of these two conjugate variables are given. A comparison between the experimental efficiency of each scheme proves that the standard split detection is only 64% efficient relative to the TEM10 homodyne detection, which is optimal for beam displacement and tilt. We also demonstrate experimentally that squeezed light in the appropriate spatial modes allows measurements beyond the quantum noise limit for both types of detectors. Finally, we explain how to choose the detection scheme best adapted to a given application