HIGH-PRECISION ROTATION SPEED MEASUREMENT METHOD BASED ON FEMTOSECOND OPTICAL FREQUENCY COMB

Abstract

A rotation speed measurement method based on a femtosecond optical frequency comb is provided. In the method, a rotation axis of a rotating object to be measured and an optical path main axis are coplanar, and perpendicular to each other, and a first converging lens focuses an emitting beam obtained by expanding the laser on a surface of the rotating object. A repetition frequency and a carrier-envelope offset frequency of the femtosecond optical frequency comb are locked during the measurement. A repetition frequency difference is read from a frequency counter. A rotation speed of the rotating object is calculated as follows:

[00001]$M=\frac{c\Delta f_r}{4\pi f_r\sin \alpha R}=\kappa \frac{\Delta f_r}{R}.$

Claims

1. A rotation speed measurement method, a measurement system used in the rotation speed measurement method comprising a femtosecond optical frequency comb, a laser beam expander, a polarization beam splitter, a quarter-wave plate, a first converging lens, a second converging lens, a first photodetector, a second photodetector, an electrical mixer, and a frequency counter; and the rotation speed measurement method comprising: (S1) outputting, by the femtosecond optical frequency comb, a first laser; expanding, by the laser beam expander, the first laser into an emitting beam; allowing the emitting beam to pass through the polarization beam splitter, the quarter-wave plate, and the first converging lens sequentially, wherein an angle between a fast axis of the quarter-wave plate and a horizontal polarization direction of the polarization beam splitter is 45°; focusing, by the first converging lens, the emitting beam on a surface of a rotating object to be measured, and collecting scattered light from the surface of the rotating object to be measured; allowing the scattered light to pass through the quarter-wave plate, and to be reflected by the polarization beam splitter to the second converging lens; and focusing, by the second converging lens, the scattered light on the first photodetector; (S2) outputting, by the femtosecond optical frequency comb, a second laser; receiving directly, by the second photodetector, the second laser; measuring, by the second photodetector, a repetition frequency f.sub.r of the femtosecond optical frequency comb; measuring, by the first photodetector, a repetition frequency f.sub.r′ of the femtosecond optical frequency comb after scattered by the rotating object to be measured; and inputting the repetition frequency f.sub.r and the repetition frequency f.sub.r′ to the electrical mixer, and measuring, by the frequency counter, a repetition frequency difference Δf.sub.r; and (S3) calculating a rotation speed M of the rotating object to be measured according to the repetition frequency difference Δf.sub.r; wherein the repetition frequency difference Δf.sub.r is directly proportional to the rotation speed M of the rotating object to be measured; the femtosecond optical frequency comb comprises a plurality of longitudinal modes evenly spaced apart, and an electromagnetic field of the femtosecond optical frequency comb is expressed as formula (1): $\begin{array}{cc}E\left(t\right)=\underset{n=-\infty }{\overset{+\infty }{.Math.}}{A}_n{e}^{-i2\pi \left(n{f}_r+f_0\right)t};& \left(1\right)\end{array}$ wherein f.sub.r is the repetition frequency of the femtosecond optical frequency comb; f.sub.0 is a carrier-envelope offset frequency of the femtosecond optical frequency comb; the femtosecond optical frequency comb is superposition of a series of lasers with a frequency component of nf.sub.r+f.sub.0; A.sub.n is a complex amplitude of a corresponding frequency component; when the femtosecond optical frequency comb is focused on the surface of the rotating object, individual frequency components of the femtosecond optical frequency comb will produce a doppler shift according to Doppler effect; and for a laser with a frequency off a doppler shift Δf is expressed as formula (2): $\begin{array}{cc}\Delta f=\frac{2\mathrm{fv}\sin \alpha }{c};& \left(2\right)\end{array}$ wherein v is a linear velocity at the surface of the rotating object to be measured; c is light speed; α is equal to half of a focused beam angle; and for a laser with a certain frequency, the doppler shift Δf is directly proportional to the linear velocity at the surface of the rotating object to be measured; by substituting the formula (2) into the formula (1), an expression of the femtosecond optical frequency comb after being scattered by the rotating object to be measured is expressed as formula (3): $\begin{array}{cc}{E}^{\prime }\left(t\right)=\underset{n=-\infty }{\overset{+\infty }{.Math.}}{B}_n{e}^{-i2\pi \left[n{f}_r\left(1+\frac{2v\sin \alpha }{c}\right)+f_0\left(1+\frac{2v\sin \alpha }{c}\right)\right]t};& \left(3\right)\end{array}$ B.sub.n is a complex amplitude of a corresponding frequency component of the scattered light; as indicated by the formula (3), after being scattered by the rotating object to be measured, the repetition frequency of the femtosecond optical frequency comb changes, and the repetition frequency f.sub.r′ is expressed as formula (4): $\begin{array}{cc}{f}_r^{\prime }=f_r\left(1+\frac{2v\sin \alpha }{c}\right);& \left(4\right)\end{array}$ Doppler effect causes shift of the repetition frequency of the femtosecond optical frequency comb, and the repetition frequency difference Δf.sub.r is expressed as formula (5): $\begin{array}{cc}\Delta f_r=f_r^{\prime }-f_r=\frac{2v{f}_r\sin \alpha }{c};& \left(5\right)\end{array}$ a relationship between the linear velocity and the rotation speed M is expressed as formula (6), wherein R is a radius of the rotating object to be measured, and the rotation speed M is in revolutions per second:
v=2πRM  (6); the formula (6) is substituted into the formula (5) to obtain formula (7): $\begin{array}{cc}\Delta f_r=\frac{4\pi RM{f}_r\sin \alpha }{c};& \left(7\right)\end{array}$ wherein the repetition frequency difference Δf.sub.r is directly proportional to the rotation speed M of the rotating object to be measured; and the formula (7) is converted into formula (8) to calculate the rotation speed M from the repetition frequency difference Δf.sub.r: $\begin{array}{cc}M=\frac{c\Delta f_r}{4\pi f_r\sin \alpha R}=\kappa \frac{\Delta f_r}{R};& \left(8\right)\end{array}$ wherein k is a scale factor, and expressed as follows: $\begin{array}{cc}\kappa =\frac{c}{4\pi f_r\sin \alpha };& \left(9\right)\end{array}$ wherein the scale factor κ is calculated according to formula (9), or based on a slope of a curve of a rotation speed of a standard rotating object whose rotation speed is known versus the repetition frequency difference Δf.sub.r.

2. The rotation speed measurement method of claim 1, wherein a rotation axis of the rotating object to be measured is coplanar with an optical path main axis, and is perpendicular to the optical path main axis; and the repetition frequency f.sub.r and the carrier-envelope offset frequency f.sub.0 of the femtosecond optical frequency comb are locked.

3. The rotation speed measurement method of claim 2, wherein the repetition frequency f.sub.r and the carrier-envelope offset frequency f.sub.0 of the femtosecond optical frequency comb are phase locked to a microwave atomic clock or an optical frequency standard.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0029] FIG. 1 schematically shows a structure of a high-precision rotation speed measurement system based on a femtosecond optical frequency comb according to one embodiment of the present disclosure; and

[0030] FIG. 2 shows a relationship between a repetition frequency difference and a rotation speed of a rotating object to be measured according to one embodiment of the present disclosure.

[0031] In the figures: 1-femtosecond optical frequency comb; 2-laser beam expander; 3-polarization beam splitter; 4-quarter-wave plate; 5-first converging lens; 6-second converging lens; 7-first photodetector; 8-second photodetector; 9-electrical mixer; 10-frequency counter; and 11-rotating object to be measured.

DETAILED DESCRIPTION OF EMBODIMENTS

[0032] The disclosure will be further described in detail in conjunction with the accompanying drawings and embodiments.

[0033] Provided herein is a high-precision rotation speed measurement method based on a femtosecond optical frequency comb. As shown in FIG. 1, a measurement system used in the method includes a femtosecond optical frequency comb 1, a laser beam expander 2, a polarization beam splitter 3, a quarter-wave plate 4, a first converging lens 5, a second converging lens 6, a first photodetector 7, a second photodetector 8, an electrical mixer 9, and a frequency counter 10.

[0034] Specifically, the femtosecond optical frequency comb 1 output a first laser, and the first laser is expanded by the laser beam expander 2 into an emitting beam with large diameter, and then the emitting beam passes through the polarization beam splitter 3, the quarter-wave plate 4, and the first converging lens 5 sequentially. Specifically, an angle between a fast axis of the quarter-wave plate 4 and a horizontal polarization direction of the polarization beam splitter 3 is 45°. The first converging lens 5 focuses the emitting beam on a surface of a rotating object to be measured 11 and collects scattered light from the surface of the rotating object to be measured 11. After the scattered light passes through the quarter-wave plate 4, the scattered light will be reflected by the polarization beam splitter 3, and then focused on the first photodetector 7 by the second converging lens 6. The femtosecond optical frequency comb 1 further outputs a second laser, and the second laser is directly received by the second photodetector 8. The second photodetector 8 detects a repetition frequency f.sub.r of the femtosecond optical frequency comb 1, the first photodetector 7 detects a repetition frequency f.sub.r′ after scattered by the rotating object to be measured 11, the repetition frequency f.sub.r and the repetition frequency f.sub.r′ are input to the electrical mixer 9, and a repetition frequency difference Δf.sub.r is measured by the frequency counter 10.

[0035] The femtosecond optical frequency comb 1 in this embodiment is an erbium-doped fiber femtosecond optical frequency comb with a repetition frequency of 100 MHz. The locked reference standard is the rubidium atomic clock. The stability of the locked repetition frequency with a sampling time of 1 s is 6.5×10.sup.−12. The magnification of the laser beam expander 2 is 50 times, the diameter of the emitting beam after expansion is about 3 cm, and the polarization beam splitter 3, the quarter-wave plate 4, the first converging lens 5 and the second converging lens 6 are all greater than 3 cm.

[0036] In order to obtain the scale factor κ in formula (8), the measurement method and the measurement device of the disclosure are used to measure a rotating flywheel with a constant speed, and by fitting the curve of the rotation speed and the repetition frequency difference, the scale factor κ=1.373854 (unit: revolution.Math.m) in formula (8) is obtained.

[0037] The relationship between the repetition frequency difference and the rotation speed in this embodiment is shown in FIG. 2.

[0038] In this embodiment, the rotating object to be measured is a flywheel with a diameter of 10.5 cm and driven by a high-speed and high-precision motor. The measurement steps are described as follows.

[0039] (1) The rotation axis of the flywheel is coplanar with the optical path main axis, and perpendicular to the optical path main axis. The emitting beams are focused by the first converging lens 5 on the surface of the flywheel. (2) The repetition frequency f.sub.r and the carrier-envelope offset frequency f.sub.0 of the femtosecond optical frequency comb 1 are locked. (3) The repetition frequency difference Δf.sub.r is read from the frequency counter 10. (4) The rotation speed M of the flywheel is calculated via the formula (8).

[0040] The objects, technical solutions and beneficial effects of the disclosure have been described in detail above in conjunction with the embodiments. Described above are merely preferred embodiments of the disclosure, which are not intended to limit the disclosure. It should be understood that any modifications and replacements made by those skilled in the art without departing from the spirit of the disclosure should fall within the scope of the disclosure defined by the appended claims.