Relative beam misalignment errors in high accuracy displacement interferometers: calculation and detection

We consider the effects of misalignment in a two-beam interferometer resulting from lateral displacement as well as angular misalignment of the beams. Furthermore, a technique to determine such misalignments is discussed and examples of measurement strategies and expected performance are given. It is found that, when the waist of the beam used to illuminate the interferometer is larger than 0.7 mm (∼1000λ), such an approach allows alignment to be made resulting in a relative interferometric error smaller than 1×10⁻¹⁰ provided that the diffraction effect is fully accounted for.