10-pm-order mechanical displacement measurements using heterodyne interferometry.

In this paper, we present 10-pm-order mechanical displacement measurements using heterodyne interferometry. The measuring system includes a single-path heterodyne interferometer and a phase meter based on a phase-locked loop (PLL). It is not easy to measure a mechanical displacement of 10 pm or less owing to electronics and environmental noises in the interferometer. To solve this problem, the improvement of the noise floor is required for the phase meter. A PLL algorithm, which is programmed on a field-programmable gate array module, is used for efficient noise reduction of the phase meter. The interferometer combined with a stiff piezoelectric flexure stage is placed in a vacuum chamber. The measurement comparisons and the noise floor evaluations are performed between air and vacuum to evaluate effects from their environments. The interferometer has two spatially separated beams with different frequencies and two balanced optical arms. The measurement results demonstrate that the system combined with the above components is capable of measuring mechanical displacements of 11 pm in air and vacuum. A noise floor of 0.2 pm/Hz between 50 Hz and 100 Hz can be obtained in vacuum. In this paper, the setup of the interferometer, the signal processing of the PLL, experiments, and results are discussed.

Securing noise-adaptive selection of interference signal by nonlinear detection.

In an interferometer, the interference fringe signal is typically linearly detected and modulated to a specific frequency region. A nonlinear detector yields the interference fringes of the fundamental and high-harmonic waves in different frequency regions. We analyze the formation of nonlinearly detected interference fringes. We demonstrate, for the first time, that the interference fringes of high-harmonic waves can also be used to determine the position of zero optical path length difference between reference and object mirrors. This noise-adaptive selectability of the interference fringe signal is guaranteed by the fact that the positions of the peak envelopes of the interference fringes for the fundamental and high-harmonic waves are matched at zero optical path length. The proposed method is verified using experimental data. This technique can be applied not only to surface profiling but also to length measurements.

Comparison of length measurements provided by a femtosecond optical frequency comb.

This paper presents a comparison of length measurements between the wavelength and the adjacent pulse repetition interval length (APRIL) provided by a femtosecond optical frequency comb. A theoretical estimation of the frequency stability for stabilizing the wavelength and APRIL, the frequency parameters that affect the stability of the APRIL in air, and the ambiguity in the length measurement by the APRIL are investigated. We find that the APRIL can be used as a low-cost measurement for the absolute length over a range of hundreds of meters in laboratory conditions.

Active suppression of air refractive index fluctuation using a Fabry-Perot cavity and a piezoelectric volume actuator.

Air refractive index fluctuation (Δn(air)) is one of the largest uncertainty sources in precision interferometry systems that require a resolution of nanometer order or less. We introduce a method for the active suppression of Δn(air) inside a normal air-environment chamber using a Fabry-Perot cavity and a piezoelectric volume actuator. The temporal air refractive index (n(air)) at a local point is maintained constant with an expanded uncertainty of ~4.2 × 10(-9) (k = 2), a sufficiently low uncertainty for precise measurements unaffected by Δn(air) to be made inside a chamber.