Nanometric Precision Distance Metrology via Hybrid Spectrally Resolved and Homodyne Interferometry in a Single Soliton Frequency Microcomb

Laser interferometry serves a fundamental role in science and technology, assisting precision metrology and dimensional length measurement. During the past decade, laser frequency combs—a coherent optical-microwave frequency ruler over a broad spectral range with traceability to time-frequency standards—have contributed pivotal roles in laser dimensional metrology with ever-growing demands in measurement precision. Here we report spectrally resolved laser dimensional metrology via a free-running soliton frequency microcomb, with nanometric-scale precision. Spectral interferometry provides information on the optical time-of-flight signature, and the large free-spectral range and high coherence of the microcomb enable tooth-resolved and high-visibility interferograms that can be directly read out with optical spectrum instrumentation. We employ a hybrid timing signal from comb-line homodyne, microcomb, and background amplified spontaneous emission spectrally resolved interferometry—all from the same spectral interferogram. Our combined soliton and homodyne architecture demonstrates a 3-nm repeatability over a 23-mm nonambiguity range achieved via homodyne interferometry and over 1000-s stability in the long-term precision metrology at the white noise limits.

Figure 1

Architectural approach of the spectrally resolved ranging via soliton microcomb. Reference and measurement pulses of the soliton frequency comb, separated by ${\tau }_{\mathrm{TOF}}$. The measurement pulse has a relative phase shift $\phi (v)$ [$=2\pi v\times {\tau }_{\mathrm{TOF}}$] to the reference pulse, and it makes an interference in every frequency mode of the soliton frequency comb. The information of ${\tau }_{\mathrm{TOF}}$ is thus engraved on the interference pattern in the frequency domain, monitored via the spectrometer. The wide free-spectral range of frequency microcombs enables its comb-tooth-resolved spectral interferogram to be directly read out by readily available optical spectrum analyzers.

Figure 2

Soliton microcomb-based precision dimensional metrology. (a) Soliton microcomb-based precision dimensional metrology via spectrally resolved interferometry. BS, nonpolarizing beam splitter; $M_{\mathrm{REF}}$, reference mirror; $M_{\mathrm{MEA}}$, measurement mirror; EDFA, erbium-doped fiber amplifier; CL, free-space collimator lens. Left inset describes schematic for the dual-pumped soliton microcomb generation. (b) Example optical spectrum of the soliton microcomb from the high-$Q$ ${\mathrm{Si}}_3{\mathrm{N}}_4$ microresonator, with the hyperbolic secant-square spectrum. Left inset: enlargement of the comb-tooth-resolved spectrum. Right inset: frequency stability of free-running repetition rate ($f_r$). (c) Example measured high-coherence spectral interferogram (blue) from the reference and measurement pulses, along with the superimposed spectra of the C-band amplified soliton microcomb (gray). Red line shows the ASE noise induced by the EDFA from the same spectral interferogram of the blue line. Inset: enlargement of the low-coherence ASE spectral interferogram with the low-visibility interference.

Figure 3

Measurement linearity and distance measurement beyond the nonambiguity range. (a) Nonambiguity range extension by the combined platform of ASE-noise-based spectral interferometry, soliton microcomb spectral interferometry, and homodyne interferometry. To determine integer $M$ of the homodyne interferometry, the coarse distance measurement from the microcomb (with $\lambda /2$, where $\lambda =c_o/v$.) is used. At the same time, to determine integer $m$ of the microcomb, the ASE SRI is used. (b) Time-domain signal reconstruction from the frequency-domain interference. A typical signal-to-noise ratio of the time-domain signal is larger than 100. (c) Measurement linearity is evaluated by measuring the target distance with $25-\mu \mathrm{m}$ incremental translation of a motorized stage. (c1) Modeled results of positioning error for different spectral shapes. (c2) Residual error comparing SRI, homodyne interferometry, and the encoder. (c3) Inset: measured distance beyond the nonambiguity range. The wrapped distance (light blue) is unwrapped with calculated nonambiguity in dark blue color. For comparison, a distance measurement from fiber-comb-based spectrally resolved interferometry is also plotted in orange color.

Figure 4

Nanometer-scale precision distance measurement: reliability and repeatability evaluation. (a) Long-term distance metrology sampled over 1000 s. (b) Left: histogram distribution of microcomb spectral interferometry and ASE spectral interferometry, with $1\sigma$ standard deviation of 81.6 (blue) and 285 nm (red) at 1000-s measurement. Right: histogram distribution of homodyne interferometry, with $1\sigma$ standard deviation of 10.4 nm at 1000-s measurement (green color). The 3.6-nm standard deviation is an example obtained from 900 to 1000 s (yellow color). (c) Measurement repeatability verification through Allan deviation of the long-term ranging data. 3-nm measurement repeatability is achieved from drift-compensated homodyne interferometry. The white noise limit is denoted by the dashed gray line, while flicker noise is not observed within our 100-s averaging time. Measurements from a few-hertz-stabilized fiber mode-locked laser frequency comb laser metrology are illustrated for comparison. Black dashed lines denote simulation results about intensity fluctuation induced measurement repeatability. Orange dashed line denotes the free-running soliton microcomb frequency instability-induced measurement repeatability at 8 mm.