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A fiber heterodyne self-mixing interferometer with orthogonally polarized light compensation is achieved. This system can adapt to various complex scenes while still keeping ultra-high sensitivity and anti-disturbance capability. Ultra-high sensitivity microchip laser is used as the laser source and polarization maintaining(PM) fiber makes the light path easy to accommodate to complex spaces, such as remote or narrow and small space. Besides, orthogonally polarized light inside PM fiber can eliminate the measurement error on account of environment disturbance. At present, the displacement resolution could be less than 10nm, which shows a great potential in nano-metrology.
© 2016 Optical Society of America
1. Introduction
Self-mixing effect has advantages such as compactness, self-alignment, and high sensitivity compared with conventional Michelson interference [1–3]. External cavity frequency shift technique is used in self-mixing interference systems and converts them into heterodyne ones [4–6]. Microchip lasers pumped by laser diode have attracted various scientific and technological attentions due to its ultra-high sensitivity to feedback light which is enhanced by a fluorescence-to-photon lifetime ratio of 105-107 [7]. Versatile applications of frequency-shifted self-mixing microchip laser systems include laser feedback vibrometry(LFV) [8], laser feedback interferometer(LFI) [9], laser Doppler velocimetry(LDV) [10–12], and laser confocal feedback tomography(LCFT) [13,14]. However, the self-mixing interference measurement is sensitive to environmental disturbance because the entire light path contributes to interference. So almost all self-mixing applications are focused on velocimetry and vibrometry in which measurement results are not affected by low-frequency optical path disturbance.
Quasi-common-path self-mixing interferometer realizes high resolution and accurate displacement measurement by partly reducing the light path perturbation on account of optical devices such as acousto-optic modulators and laser cavity itself [15]. With the use of polarization and frequency multiplexing techniques, common-path heterodyne self-mixing interferometry can eliminate nearly all the dead-path influence inside interference path [16]. However, both the quasi-common-path and the common-path self-mixing interferometers are free space optical systems whose applications are limited in complex space and remote measurement because spatial beams cannot be intercepted during transmission.
In order to expand the applications of self-mixing interference in metrology field, we propose a fiber self-mixing interferometer with orthogonally polarized light compensation technique. Two linearly polarized beams are emitted from two well-spaced positions in one single Nd:YVO4 microchip laser. These two beams are then coupled into the slow and fast axes of polarization maintaining (PM) fiber, respectively. In the subsequent optical path, the orthogonally polarized lights experience identical light path. So this system can adapt to various complex scenes while still keeping ultra-high sensitivity and anti-disturbance.
2. Experimental setup
The schematic diagram of fiber self-mixing interferometer is illustrated in Fig. 1. A 3 × 3mm2, 0.75mm thick a-cut Nd:YVO4 crystal is pumped by two identical series-wound laser diodes at two well-spaced positions with an interval of 1.5mm. This crystal works as an all-inner-cavity microchip laser cavity with coated input face (99.9% reflection at lasing wavelength 1064nm, high transmission at the pump wavelength 808nm) and output face (99% reflection at 1064nm and about 95% reflection at 808nm). The threshold pump powers are about 30mW, and their slope efficiencies are about 24%. Two parallel linearly polarized beams are obtained, and they work in the single-longitudinal-mode regime. A rhombic prism is used to shift one of the beams parallel with a certain distance to win enough room for the coupling objective lens. Then two spatial beams are coupled into two polarization maintaining (PM) fibers (Fig. 2(a) shows the cross section of PM fiber) with two identical grin-lens, respectively. The polarization directions of spatial beams are in coincidence with the slow-axis of PM fibers. A fiber polarization beam combiner is used to convert the two linearly polarized beam into orthogonally polarized light in one single PM fiber, one component coincides with the slow axis and the other coincides with the fast axis. The orthogonally polarized light inside the PM fiber is then split by a polarization maintaining beam splitter into two parts, one(about 95%) for measurement and the other(5%) for detection(The operation mode of BS in Fig. 1 is illustrated in Fig. 2(b)). Another PM beam splitter and two photo diodes(PD1 and PD2) are set in the detection light path to separate the orthogonally polarized light in order to detect them separately. A fiber PM acousto-optic modulator(AOM) module is configured to shift the orthogonally polarized light with a predetermined frequency, which depends on the driving frequency of AOM module. The synthetic frequency shift of the AOMs module used in our system is Ω = 500kHz(the difference between two AOMS' driving frequencies) and the diffraction efficiency is about 50%. A 20m long PM fiber is set after AOM module for transmitting orthogonal light. Then a polarization beam splitter is utilized to split the orthogonal light into two linearly polarized beams. Two grin-lens are used to collimate beams exit from PM fiber and project them onto measuring and reference targets, which both have non-cooperative surfaces.
Fig. 1 Schematic diagram of fiber heterodyne self-mixing interferometer with orthogonally polarized light compensation technique. ML: Nd:YVO4 microchip laser; RP: Rhombic prism; GRIN1, GRIN2, GRIN3, and GRIN4: grin lens; PBS1: polarization beam combiner; PBS2, PBS3: polarization beam splitter; PD1, PD2:photo diode; BS: polarization maintaining beam splitter; AOMs: acousto-optic modulators module; T1,T2: measuring target and reference target, respectively.
In Fig. 3, both the exit end of PM fiber and measuring target are set inside narrow and small space where spatial light interferometer cannot be configured. What is more, spatial beam exiting from the PM fiber is projected onto the target surface without any auxiliary mirrors such as reflectors or retro-reflectors.
3. Experimental analysis
As shown in Fig. 4(a), heterodyne interference power spectrum obtained with oscilloscope has a beat-note(FB) with approximately 75MHz frequency. Here, FR is the relaxation oscillation peak. Similar frequencies mean that the operative modes of two microchip lasers can be regarded as the same, so the measurement error caused by the difference between two lasers can be ignored. Figure 4(b) is the magnified view of the heterodyne beat-note(with a frequency resolution of 3kHz) whose half-width depends on the line-widths of the beams taking part in heterodyne interference. The beat-note half-width(HW) is about 10kHz, as a result, the spectral line-width of each laser is determined to be Δν = 5kHz corresponding to 60km coherent length. The effective measurement distance is half of the coherent length because light goes through a round trip between laser and target before reentering into the cavity. Nevertheless, L = 60km/2 = 30km is long enough for vast majority applications.
Fig. 4 (a) heterodyne power spectrum obtained by oscilloscope and (b) magnified view beat-note with frequency resolution 3kHz.
The power spectra of orthogonally polarized light are shown in Figs. 5(a) and 5(b), respectively. Where FR indicates the relaxation oscillation peak and FS1 and FS2 are the frequency-shifted modulation signals with 2Ω frequency, while Ω is the synthetic frequency shift amount of the AOM module. When the targets move, the frequency of corresponding peaks in Figs. 5(a) and 5(b) will change based on the Doppler effect. Filters with central frequency at 1MHz are used to pick out Fs1 and Fs2, which contain the external cavity optical phase of measurement and reference targets, respectively. Then the displacement information will be obtained by magnifying and demodulating the electrical signals from filters. The signal-noise ratio is about 30dB, which is strong enough for the following signal processing module.
The power spectral behaviors of frequency-shifted self-mixing interference occurring in microchip laser can be interpreted by rate-equations with frequency shift feedback light [4,17].
Here, N(t) is the population inversion, E(t) is the electric field inside laser cavity, Efb(t) is the electric field of light feedback into laser cavity, γ is the decay rate of the population inversion while γc is the photon decay rate inside micro-cavity, γNo is the pump rate, B is the Einstein coefficient, ω and ωc are the optical running frequency and laser cavity frequency at the atomic frequency respectively, κ is reflectivity of target and τ is the round-trip time between laser and the target. The analytical expression of relative power modulation could be written asWhere G(2Ω) is a gain term which refers to frequency shift, Φ is the variation of external cavity optical path and is a fixed initial phase.
The target displacement ΔL is related to the feedback light phase variation ΔФby
According to above mentioned theoretical analysis, the external cavity phase information could be obtained by filtering the electrical signals from PD1 and PD2 with band-pass filters whose central frequency is exactly 2Ω. Then the filtered signals are demodulated by two-channel digital phase meter with driving signals of AOM module as reference signals in order to get displacement information of measuring and reference targets.
4. Experimental results and discussion
In experiments, the reference target stays still, so that the displacement information measured by the reference light path only reflects the fiber disturbance and thermal creep caused by optical devices inside the interference light path. The measuring target is fixed on a PI platform(PI P-621.1CD) which has 0.4nm resolution and 1nm repeatability. The result measured by measuring light path includes both the target displacement information and the disturbance inside interference path. Therefore, the environmental disturbance in the final result could be removed by subtracting the reference result from the measuring result.
To test the displacement resolution of this fiber self-mixing system, the PI precision stage is driven to move step by step. Figures 6(a)-6(c) present the measurement results of T1, T2, and the final displacement information D = R1-R2, respectively. R1 shows the external fiber cavity optical phase variation depend on both the displacement of T1 and the effect of environmental disturbance on PM fiber. R2 only presents the effect of environmental disturbance on the measurement result of external cavity optical phase. As shown in Fig. 6(a), the 10nm step displacement information is difficult to be distinguished from the noise. Nevertheless, Fig. 6(c) indicates that the final result of this system can identify 10nm step clearly.
Fig. 6 (a), (b) Displacement information of orthogonal beams (R1 and R2) and (c) the final result D.
Figure 7(a) shows the comparison results diagrams between our system and PI precision stage in 100μm. The RMS error σ of the displacement results is shown in Fig. 7(b), which is determined by subtracting a least-square fit from the data measured by this fiber self-mixing interferometer. The standard deviation is about 50nm in 100μm displacement range. The errors could be caused by the non-common part of the orthogonally polarized light or by the vibration disturbance of environment on measuring and reference targets.
Fig. 7 displacement measurement results. (a)Displacement measurement results in 100um range by fiber self-mixing interferometer. (b) The rms error in the measurement results and fitting ones.
5. Conclusion
In summary, a fiber heterodyne self-mixing interferometer with orthogonally polarized light compensation is demonstrated and has the potential to be employed in remote measurement or complex space measurement with high resolution and accuracy. Flexible light path and ultra-high sensitivity enable this interferometer to be used in narrow and complex space in which mirrors and retro-reflectors are unable to install even though they are crucial in traditional Michelson interferometer. Common-path compensation achieved by orthogonally polarized light along with the fast and slow axes of PM fiber is effective for remote precision displacement measurement, even in a severe disturbance environment. At present, the measurement resolution is not very high compared with the free-space self-mixing interferometer, because there is still little part non-common-path inside the whole interference path and fiber is more sensitivity to vibration disturbance than air light path. However, there is great opportunity to improve its performance, and improvements have already been underway.
Funding
National Natural Science Foundation of China (Grant No. 61475082); Beijing Municipal Science and Technology Commission (No. Z151100002415027).
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