# Multi-mode fibre laser Doppler anemometer (LDA) with high spatial resolution for the investigation of boundary layers

## Authors

- First Online:

- Received:
- Accepted:

DOI: 10.1007/s00348-003-0684-z

- Cite this article as:
- Büttner, L. & Czarske, J. Exp Fluids (2004) 36: 214. doi:10.1007/s00348-003-0684-z

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## Abstract

A novel LDA system using laser diode arrays and multi-mode fibers in the transmitting optics is presented. The use of high numerical aperture multi-mode step-index fibres results in measurement volumes with, for example, 80 µm length and minimal speckle effects. Because of the high spatial resolution and low relative fringe spacing variation of Δ*d*/*d*≈5×10^{−4} the multi-mode fibre LDA is predestined for investigating turbulent flows. Boundary layer measurements carried out show excellent agreement with theoretical velocity profiles.

## 1 Introduction

Usually, a short measurement volume ensuring high spatial resolution as well as a low variation of fringe spacing (known as "virtual turbulence") for a precise determination of turbulence data are required for measurements of laminar and turbulent boundary layers using the laser Doppler technique. Because of the wavefront curvature of the generally employed single-mode Gaussian beam, only one requirement can be fulfilled if no beam stops are used in the receiving optics. However, the multi-mode fibre laser Doppler anemometer presented in this contribution offers both features at the same time.

Normally, single-mode fibres have been employed in LDA systems for beam delivery from the laser to the measurement head as they preserve coherence properties from fundamental mode lasers. On the other hand, multi-mode fibres can transmit significantly higher power and need only low alignment effort for incoupling.

Because of these reasons experiments were carried out to employ multi-mode fibres even for beam delivery (Kaufmann and Fingerson 1985; Ruck and Durst 1983; Bopp et al. 1989), but because of the observed signal degeneration caused by speckles this technique could never become established. This work presents a multi-mode fibre LDA system, which minimises the speckle effect and allows the generation of short measurement volumes with low measurement errors. This is achieved by the use of light from multi-mode fibres with high numerical apertures. Because of its low degree of spatial coherence the length of the measurement volume is reduced drastically. The multi-mode radiation shows a behaviour similar to classical geometrical light with nearly plane wavefronts so that the fringe spacing variation is reduced to Δ*d*/*d*≈ 5×10^{−4}.

## 2 The principle

*l*

_{z}indicates the length of the intersection volume and

*a*

_{z}the length of the measurement volume. At the bottom of Fig. 1 a measurement of the interference contrast is shown, illustrating the spatial restriction of the measurement volume.

*a*

_{z}/

*l*

_{z}is determined by the degree of spatial coherence of the light source. It is inverse proportional to the beam quality factor

*M*

^{2}(Buettner and Czarske 2001), which is determined by the core diameter

*D*, the numerical aperture

*A*

_{N}of the fibre and the wavelength

*λ*, and is approximately given by:

*L*

_{D}means the path length difference between the lowest and the highest guided mode and

*L*the fibre length. If this is large compared to the low temporal coherence lengths of the laser (Buettner and Czarske 2001; Morgan et al. 1993), the visibility of the speckle pattern is reduced. Experimentally, by using a 30 m, 0.37 NA fibre, a reduction of the speckle visibility down to 6% was achieved (Buettner and Czarske 2001). It is important to note, that a decrease of the coherence length leads only to a reduction of the speckle visibility, but not to a reduction of the visibility of the fringe pattern. Even at low temporal coherence lengths, the fringe system will show complete modulation (Buettner and Czarske 2001).

## 3 The results

*λ*=810 nm wavelength and a step-index fibre with

*D*=100 µm core diameter and

*A*

_{N}=0.22 numerical aperture were used to set up the multi-mode fibre LDA. A measurement volume of 80 µm length, 300 µm lateral extension and 100 fringes resulted. Laser power of 100 mW was available in the measurement volume. The beam quality factor of

*M*

^{2}≈43 led to a ratio of only

*a*

_{z}/

*l*

_{z}=3.5% between the length of the interference volume and the length of the intersection volume. The relative variation of fringe spacing Δ

*d*/

*d*was measured to less than 5×10

^{−4}, see Fig. 2.

This demonstrates, that the multi-mode fibre LDA offers both a high spatial resolution and a low variation of fringe spacing ("virtual turbulence") at the same time, which, in the case of LDA's with single-mode radiation, are complementary features.

*Re*

_{x}=5.8×10

^{3}, 2.3×10

^{4}and 5.8×10

^{4}. Coordinates were normalised in order to compare the measured boundary layers with the theoretical Blasius profile. The Reynolds numbers are significantly smaller than 3.5×10

^{5}...1×10

^{6}, which is considered as the critical range for laminar to turbulent transition, so that laminar boundary layers can be assumed. All measurements are in excellent agreement with theory.

## 4 Conclusion

The features of the multi-mode fibre LDA can be summarised as follows. A high spatial resolution is achieved owing to the low degree of spatial coherence of the multi-mode light, which reduces the length of the measurement volume to a few tens of micrometers in length. A small variation of fringe spacing of less than 5×10^{−4} and 100 signal periods ensures a small uncertainty for the velocity measurement. Turbulence data can be determined precisely. The parasitic speckle effect can be suppressed sufficiently by choosing fibres with high intermodal dispersion. A reduction of the speckle visibility down to 6% was demonstrated experimentally. The use of multi-mode fibres in the LDA-sending optics allows the employment of high power and low cost laser diode arrays with poor beam quality usually used for laser material processing. Only low alignment effort is needed to couple the light into multi-mode fibres, so that a simple and robust set-up can be realised. The principle can be extended by means of a two-wavelength technique to achieve a directional discrimination by the quadrature-homodyne technique (Buettner and Czarske 2002; Büttner and Czarske 2003). The multi-mode fibre LDA was applied in wind tunnel experiments to measure flat-plate Blasius boundary layers. All measurements are in excellent agreement with the theory. Measurements of a turbulent boundary layer were presented.

## Acknowledgement

The support from the Deutsche Forschungsgemeinschaft (FKZ Cz55/4-4) is greatly acknowledged.