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A scanning laser Doppler velocimeter (LDV) without any moving mechanism in its sensor probe is proposed. In the proposed scanning LDV, the measurement position is axially scanned by change in the wavelength of the light input to the sensor probe, instead of using a moving mechanism in the sensor probe. For this purpose, a tunable laser and diffraction gratings are used, and the sensor probe including the gratings is separated from the main body including the tunable laser. To demonstrate the scanning function based on the proposed concept, an experiment was conducted using optical fibers, a commercial tunable laser and a setup of the sensor probe consisting of bulk optical components. As the experimental result, it is found that the measurement positions estimated from the measured beat frequencies are in good agreement with the theoretical values. The scan ranges over a wavelength range of 30 nm are estimated to be 29.3 mm when the beam angle to the measurement position at the wavelength of 1540 nm is 10° and 20.8 mm when the beam angle is 15°. The result indicates that the scanning function by means of changing the wavelength input to the sensor probe is successfully demonstrated for the first time. The proposed method has the potential for realizing a scanning LDV with a simple, compact and reliable sensor probe.
©2011 Optical Society of America
1. Introduction
The differential laser Doppler velocimeter (LDV) is a standard instrument for measuring the velocity of a fluid, gas flow or rigid object in various research fields and industries because of its noninvasive nature, small measurement volume giving excellent spatial resolution, and a linear response. In the velocity measurement, measuring the velocity distribution of fluid flow or moving objects is required in many applications. Several methods for scanning the measurement position using mechanical movement have been proposed [1–7]. In these scanning LDVs, a moving mechanism is used in transmitting optics just before a measurement position, for example, a movable lens [1] and rotating mirrors [2] for axial scanning (i.e., the scan direction is parallel to the optical axis), and an oscillating mirror [3,4], a rotating diffraction grating [5], a rotating transparent plate [6] and rotating wedge prisms [7] for scanning in transverse scanning (i.e., the scan direction is perpendicular to the optical axis).
A typical conventional scanning LDV has large optical system. In some applications such as the industrial and biomedical use [8–11], the LDV with an easily-handled sensor probe, generally separated from the main body, has been highly desirable. Many types of non-scanning LDVs using compact sensor probes have been developed [9,10,12,13]. When one intends to apply the conventional scanning methods to a LDV with a sensor probe, it is essential to include a moving mechanism in the probe, or otherwise the probe itself needs to be scanned. However, the sensor probe including a moving mechanism has disadvantages because it can be easily misaligned or damaged due to mechanical shock and is subject to abrasion, and therefore it requires special care for handling and maintaining. It has also the disadvantage in terms of miniaturizing the sensor probe. Hence, developing the scanning method that can solve these problems is highly attractive to realize a scanning LDV with a compact and reliable sensor prove. The authors have proposed a non-mechanical integrated scanning LDV using arrayed waveguide gratings (AWGs) and phase shifters [14]. However, it has been just the theoretical one.
In this paper, a differential-type axial scanning LDV without a moving mechanism in its sensor probe is proposed. In the proposed scanning LDV, the measurement position is scanned by change in the wavelength as a characteristic of the light input to the probe. Through the experiment, the scanning function by this method is demonstrated for the first time.
2. Principle
Figure 1 illustrates the concept of the proposed scanning LDV. We introduce a new approach to obtaining a scanning function: the measurement position is scanned by change in the wavelength of the light input to the sensor probe, instead of using a moving mechanism in the probe. For this purpose, a tunable laser and diffraction gratings are used. The proposed scanning LDV consists of the main body including the tunable laser and the sensor probe including two gratings separated from the main body. The beam from the tunable laser propagates through a polarizer and a polarization maintaining fiber (PMF), and is input to the sensor probe. In the probe, the beam from the fiber is collimated and split into two beams, and each of the beams is incident on each of two gratings. The diffracted beams from the gratings cross at the measurement position. The scattered beams pass through a receiving lens and are monitored by a photodetector (PD) as a beat signal. The signal is transferred to the signal analyzer in the main body. When the wavelength of the beams incident on the gratings is changed, the diffraction angle of the beams is also changed, and then the measurement position can be scanned in the axial direction. Diffraction gratings have been conventionally used in Doppler velocimetry for splitting a beam [5,15–20], dividing beams with different wavelengths [18,19], shifting the frequency of a beam [21,22], or getting an achromatic function [15,23,24]. In contrast, in the proposed scanning LDV, diffraction gratings are used for scanning a beam as the wavelength changes. The receiving lens in the sensor probe will only be exact for one wavelength, but this does not affect the reception so much over the limited range of wavelengths.
Even if the tunable laser requires a moving mechanism, the sensor probe doesn’t require any moving mechanism in the proposed scanning LDV, because the tunable laser can be separated from the probe. Hence, the proposed concept brings the potential for realizing a scanning LDV with a simple, compact and reliable sensor probe. The proposed concept can also be adopted to miniaturize the whole scanning LDV system by using an integrated non-mechanical tunable laser such as the combination of a semiconductor optical amplifier (SOA) and a tunable waveguide ring resonators [25,26].
The scan range can be derived from the simple geometrical model shown in Fig. 2 . Based on the grating equation, the diffraction angle of the mth-order diffracted beam, ϕmo(λ), is given by
where λ is the wavelength, d is the grating period and ϕ i is the incident angle on the grating. Let the angle between the direction normal to the grating surface and the optical axis (the z axis) be α. Using the relation θ = α + ϕmo(λ) where θ is the beam angle to the measurement position, the beat frequency F(v, λ) is expressed asand the measurement position along the optical axis, Lz(λ), is given bywhere v is the velocity component perpendicular to the optical axis at the measurement position and Lx is the position of the grating along the x axis. The fringe spacing in the measurement volume is given byWhen the change in ϕmo(λ) is small, the ratio of the position change to the wavelength change is derived by differentiating Eq. (3) with respect to λ as
Here, the angular dispersion of the mth-order diffracted beam, dϕmo/dλ, is given by
From Eq. (5), the scan range over a specific wavelength range increases as the angular dispersion dϕmo/dλ increases or the beam angle θ = α + ϕmo(λ) decreases. From Eq. (6), using smaller d is desirable to increase dϕmo/dλ. It is clear from Eq. (1) that only the diffracted beams with small diffraction orders exist when d is as small as the order of the wavelength or smaller.
3. Experiment
To demonstrate the scanning function in the axial direction based on the proposed concept, an experiment was conducted using optical fibers, a commercial tunable laser (ANDO AQ4321A) and a setup of the sensor probe consisting of bulk optical components. The experimental setup is illustrated in Fig. 3 . The beam from the tunable laser is input to a polarization beam splitter (PBS) via a single-mode fiber (SMF). One of the beam output from the PBS propagates through a PMF and the vertically polarized beam is launched into the optics of the sensor probe setup. The optics consists of lenses, a mirror, a splitter, reflection-type ruled diffraction gratings with a grating period d of 1.67 μm, and an InGaAs PD (Thorlabs PDA10CS). The beam passes through a collimation lens and lenses for focusing, and is split into two beams by the splitter. Each of the beams is diffracted by each grating and the 1st-order diffracted beam is incident on the target of a rotating disk with an 8-cm diameter. The beams are scattered at the surface of the rotating target, and monitored by a PD. Its beat signal is measured by a digital oscilloscope (Tektronix TDS1001B) and the beat frequency is calculated with the fast Fourier transform (FFT). The angular velocity of the target, ω, is monitored by an encoder and a frequency counter (Kenwood FC-758A). The wavelength from the tunable laser is changed over 30 nm of around 1540 nm. The maximum wavelength scanning rate of the tunable laser is nominally 100 nm/sec, but in this experiment each wavelength is set manually.
To investigate the scan in the axial direction simply and accurately, the rotating target movable in the vertical direction (the direction along the y axis) is used and the surface of the target is angled with an angle β. The vertical position of the target is adjusted so that a peak of the beat signal appears in its spectrum. In this condition the measurement position is placed at the surface of the target. When the measurement position in the axial direction, Lz(λ), is changed during the scan, the distance between the measurement position and the center of the rotation, r, is changed as the vertical position of the target is adjusted as shown in Fig. 3(b), and then, the detected velocity of the surface of the target, v = rω, is also changed according to the change in r. Because the beat frequency is proportional to v, the beat frequency changes in proportion to r according to the axial scan. Hence, the axial scan can be accurately measured just by measuring the change in the beat frequency, and the measurement position Lz(λ) can be detected by monitoring the ratio of the beat frequency to ω.
Let the axial position of the center of the rotation of the target be Lzc. Since r = [Lz(λ) – Lzc]/sinβ, and therefore v = [Lz(λ) – Lzc]ω/sinβ, the beat frequency expressed as Eq. (2) for m = 1 is reduced to
Equation (7) shows that the ratio F(ω, λ)/ω changes as a factor [Lz(λ) – Lzc]sin(α + ϕ 1 o(λ))/λ when the measurement position is scanned. If the changes in ϕ 1 o(λ) and λ are small, the change in F(ω, λ)/ω is dominated by the change in Lz(λ). Hence, the occurrence of the scan can be detected as the change in F(ω, λ)/ω.
To determine the incident angle on the gratings, its angular dispersion dϕmo/dλ is calculated. Figure 4 plots the calculated 1st-order angular dispersion dϕ 1 o/dλ of the grating with d = 1.67 μm at λ = 1540 nm derived from Eqs. (1) and (6). The angular dispersion increases as the incident angle ϕ i approaches zero. The increase of dϕ 1 o/dλ contributes to increasing the scan range. However, the scan line is easily deviated from the axial direction in case that the incident angles on two gratings have a slight difference because the angular dispersion is more sensitive to the deviation of ϕ i at smaller ϕ i. Hence, in the experiment, ϕ i is set to 55° where the angular dispersion is insensitive to the deviation of ϕ i. The gratings used in this experiment diffract only the 0th- and 1st-order beams when ϕ i = 55° and λ is around 1540 nm. The diffraction angle of the 1st-order beam is 6.0° for ϕ i = 55° at λ = 1540 nm.
Fig. 4 Calculated 1st-order angular dispersion dϕ 1 o/dλ for various ϕ i at λ = 1540 nm. d = 1.67 μm.
We investigated two setups with different beam angles to the measurement position: θ = 10° (“setup (1)”) and 15° (“setup (2)”) at λ = 1540 nm. We set β to 57° and Lzc to 273 mm. Here, we set Lz(λ = 1555 nm) = Lzc.
Figure 5 plots the calculated fringe spacing in the measurement volume Δxs as a function of λ for setup (1) and setup (2). The fringe spacing slightly changes dependent on the wavelength change, whereas the change is small over the wavelength range of about 30 nm. It indicates that the beat frequency depends on the wavelength under a constant velocity.
Fig. 5 Calculated fringe spacing in the measurement volume Δxs as a function of λ for setup (1) and setup (2).
4. Results and discussion
Figure 6 plots the examples of the measured spectra of the beat signals for setup (1) for a constant angular velocity (4π rad/s). The spectra were measured for three different wavelengths (1530, 1540 and 1550 nm). Each spectrum has a sharp peak corresponding to the velocity of the rotating target at the measurement position. The beat frequency is significantly shifted as the wavelength changes because the measurement position changes and the velocity of the target at the measurement position changes accordingly. The beat frequencies estimated from the peak of each spectrum are ranged over 16.5 – 81.3 kHz, that corresponds to the shift of the measurement position of 19.8 mm in the axial direction. During this measurement, the target was vertically moved over 13.1 mm, that corresponded to the shift of the measurement position of 20.1 mm in the axial direction. These values are in good agreement with each other. It indicates that the scan range can be estimated from the measured beat frequencies. The peak amplitude of the spectrum for λ = 1540 nm becomes the largest because the focusing of the receiving optics was adjusted at around λ = 1540 nm.
Fig. 6 Examples of measured spectra of beat signals for setup (1) for constant angular velocity (4π rad/s). The wavelengths λ are 1530 nm, 1540 nm and 1550 nm.
Figure 7 plots the measured relationship between the beat frequency F(ω, λ) and the angular velocity ω for setup (1) at λ = 1540 nm. The beat frequency is estimated from the peak of the spectrum. The theoretical values are also plotted. The measured values agree well with the theoretical values, and the beat frequency is proportional to the angular velocity.
Fig. 7 Measured relationship between F(ω, λ) and ω for setup (1) at λ = 1540 nm. Theoretical values are also plotted.
Figure 8 plots the measured values of F(ω, λ)/ω for various λ for setups (1) and (2). The theoretical values derived from Eq. (7) are also plotted. The angular velocity was set to around 2.9π – 4.5π rad/s. The beat frequency is significantly shifted as the wavelength changes. The shift is caused by the change in the measurement position. The measured values agree well with the theoretical ones.
Fig. 8 Measured values of F(ω, λ)/ω for various λ for setups (1) and (2). Theoretical values are also plotted.
Figure 9 plots the relative measurement positions Lz(λ) – Lzc estimated from the measured beat frequencies for various λ for setups (1) and (2). The theoretical values derived from Eq. (3) are also plotted. It is found that the measurement position is shifted nearly linearly as the wavelength changes. In both setups, the estimated measurement positions are in good agreement with the theoretical values. The scan ranges are estimated to be 29.3 mm for setup (1) and 20.8 mm for setup (2) over the wavelength range of 30 nm. These results indicate that the measurement position can be successfully scanned by changing the wavelength input to the sensor probe.
Fig. 9 Relative measurement positions Lz(λ) – Lzc estimated from measured beat frequencies for various λ for setups (1) and (2). Theoretical values are also plotted.
The average values of the difference in measurement position between the experiment and the theory are –0.20 mm for setup (1) and 0.28 mm for setup (2), and the standard deviations of the difference are 0.52 mm for setup (1) and 0.24 mm for setup (2). These values are very small compared with the scanning range. The angular misalignment of the grating is one of the causes of the error in measurement position. It should be noted that the position error is caused by the combination of some kinds of geometrical errors in the optical components in addition to the angular misalignment of the gratings. If one intends to estimate the misalignment of the gratings for example, it is essential to separate the effects of these errors.
In this experiment, the scan range is larger for setup (1) because the beam angle to the measurement position is smaller whereas the conditions of the wavelength range, the angular dispersion and the working distance are all the same between setups (1) and (2). The scan range would be further enhanced by reducing the beam angle, at the sacrifice of the sensitivity determined by the ratio of the beat frequency to the velocity. The scan range can also be enhanced by increasing the wavelength range or the angular range of the diffraction to be used. From Eq. (6), the usable angular range Δϕmo is proportional to the wavelength range Δλ and inversely proportional to the grating period d. The smaller grating period d can be chosen by selecting a tunable laser which can emit smaller wavelengths. Thus the scan range can be enhanced by appropriately choosing the combination of gratings and a tunable laser so that the ratio Δλ/d increases.
In the setup used in this experiment, spatial filtering is not used, and the sign of the measured velocity component cannot be measured. To apply the proposed method to actual fluid velocity measurements, the techniques to overcome these points should be introduced as future works.
This experiment demonstrates the scan along the direction parallel to the optical axis. The scan along the direction perpendicular to the optical axis will also be possible by modifying the proposed method, for example, by changing the arrangement of gratings, lenses and mirrors, or adding other optical components.
5. Conclusion
A scanning LDV without any moving mechanism in its sensor probe is proposed. In the proposed scanning LDV, the measurement position is scanned by changing the wavelength as a characteristic of the light input to the sensor probe, instead of using a moving mechanism in the sensor probe. For this purpose, a tunable laser and diffraction gratings are used, and the sensor probe including the gratings is separated from the main body including the tunable laser. The result of the experiment using optical fibers, a commercial tunable laser and a setup of the sensor probe consisting of bulk optical components clarifies that the scanning function is successfully obtained by changing the wavelength input to the sensor probe. The proposed method would be useful to realizing a scanning LDV with a simple, compact and reliable sensor probe which can be applied to many fields including industry and biomedicine.
Acknowledgment
This work in part was supported by a research-aid fund of the Suzuki Foundation and Grant-in-Aid for Scientific Research (B) 21360196 (KAKENHI 21360196). The author thanks Kiyoshi Nakagawa of Kagawa University for providing the tunable laser and other experimental equipment.
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