Innovative holographic particle velocimeter: a multibeam technique

July 1, 1993 / Vol. 18, No. 13 / OPTICS LETTERS

1101

Innovative holographic particle velocimeter: a multibeam technique Valery Zimin, Hui Meng, and Fazle Hussain Department of Mechanical Engineering, University of Houston, Houston, Texas 77204-4792 Received January 26, 1993 An innovative multibeam holographic particle velocimetry technique is described for three-dimensional flowvelocity measurement. Characterized by suppressed speckle noise, decreased image depth of field, and efficient

use of laser energy, the multibeam holographic particle velocimeter overcomesdrawbacks of techniques that are based on conventional in-line and off-axis holography.

Fluid turbulence phenomena are pervasive in nature and engineering applications, but, unfortunately, we lack adequate understanding of them and hence a means of control.1 Despite recent advances in direct numerical simulation, experimental technology has not kept pace to permit validation of computational results. There is a pressing need for an experimental technique that can measure well-resolved flow-velocity (and thus vorticity) vector fields in three-dimensional (3D) space and time. Holographic particle velocimetry (HPV), which measures 3D flow velocity by displacements of tracer particles in the flow, is being developed for this purpose. 1 - 3

In this

Letter we propose an innovative HPV technique. In the initial versions of HPV,1 ,2 the classic Gabor or in-line scheme has been used. The high-intensity forward scattering and low spatial frequency recording permit the use of low laser pulse energy and low film resolution (thus high sensitivity). These advantages permit high-speed holocinematography by the use of lasers with high pulse repetition rates such as copper-vapor lasers. Also, the simplicity and insensitivity to vibration of the in-line scheme makes its use convenient. However, particle images reconstructed from an in-line hologram are often severely contaminated with speckle noise. The characteristic speckle size s, defined as a statistical average of the distance between adjacent regions of maximum and minimum brightness, is comparable with the particle size d. Generally, s depends on the angle of aperture fl that the radiation (which gives rise to speckle) subtends,4 s A/fQ, where A is the laser wavelength. If the aperture of the imaging optics is sufficiently large, then fl is defined by the scattering angle of particles. In the presence of an in-line reference wave, the principal interference effects will take place with respect to this central strong ray, so that the maximum angle between interfering rays is halved,

intensifies with increasing particle concentration and particle seeding depth,3 the spatial resolution of this measurement technique is restricted. In addition, the small forward-scattering angle leads to a large depth of field 8z (which gives rise to uncertainty in the axial location of the particle). This practically restricts velocity measurement to the two transverse components. Off-axis holography overcomes these drawbacks. Since speckle is mainly a result of the interference among the scattered waves from the virtual-image field combined with the transmitted illuminating wave,3 it can be spatially avoided in off-axis holography. By use of side particle scattering, which has a more uniform angular distribution than forward scattering does, an off-axis hologram records a scattering aperture much larger than that of an inline hologram. Therefore the reconstructed particle image has a smaller az and thus preserves depth information more precisely. Nevertheless, this is obtained at the price of higher (3 orders of magnitude) laser pulse energy owing to the dramatic decrease of scattering intensity away from the small diffraction range in the forward direction. The use of side scattering poses a practical limit to holocinematography, since lasers with both high pulse energy (-10-1 J) and high pulse repetition frequency (of the order of 10 kilohertz) as well as high beam coherence are not generally available. Furthermore, the use of a separate reference beam makes the off-axis scheme sensitive to facility vibration and requires the laser to have a good longitudinal coherence. 16 d

H

.

D

4

0

and hence s is doubled : s

2A/fl.

In in-line holography, f-

(1)

20 [Fig. 1(a)], where 0 =

A/d is the Airy diffraction angle and hence s - d. Therefore speckle, being of the order of d, hinders the recognition of the particle images. Since the speckle 0146-9592/93/131101-03$6.00/0

(a)

(b)

Fig. 1. Scattering aperture angle for (a) single-beam illumination and (b) multibeam illumination. © 1993 Optical Society of America

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OPTICS LETTERS / Vol. 18, No. 13 / July 1, 1993 high-speed moviecamera

Fig. 2. Multibeam holographic particle velocimeter (recording part) for 3D, three-component measurement of the velocity field of a selected region of flow (version 1).

To avoid the drawbacks of both in-line and offaxis holography while preserving their advantages, we propose an innovative multibeam HPV technique. The main idea is to create several bundles of highintensity forward-scattered light to form a large aperture angle, which drastically decreases the size of the speckles so that they do not interfere with particle images. If each of the beams intersects the axis at an angle co (which can be much larger than C),then fl = 2((o + 0) [Fig. 1(b)],thus suppressing s [relation (1)]. In addition, a large fl also decreases 6z, as in the off-axis scheme, but by use of forward scattering (in each beam); hence the laser energy is efficiently utilized. The reference beam can pass through the flow domain, minimizing its path difference with the object wave as well as its sensitivity to vibration. Figure 2 shows a multibeam HPV recording scheme for measurement of a selected region of a flow (version 1). We produce multiple beams by splitting a collimated laser beam, using a faceted reflector. These beams are then reflected by mirrors evenly distributed azimuthally such that they intersect in the flow subdomain of interest. The illuminated par-

tides in this subdomain produce strong forward scattering. A lens collects the forward scattering as well as the unscattered part of illuminating beams and forms an image of the particle field in front of the holographic film. In the focal plane, a high-pass filter (consisting of a thin opaque ring) blocks the direct beams so that only the scattered light arrives at the film. The reference beam necessary for hologram recording is generated on axis from the initial collimated beam through the hollow center of the faceted reflector. In order to minimize its path difference with the object wave, the reference beam is sent through the flow chamber and a pinhole lowpass filter. In hologram reconstruction, the same imaging lens can be used backward to compensate for any distortion it caused during recording. In the reconstruction, the speckle size s is equal to A/(ow+ 0) in the presence of the transmitted reference wave, which can be cut out, if needed, by a high-pass filter3 to further reduce s by half. The achievable image quality by use of the multibeam configuration in Fig. 2 for a water suspension of 21-,um-diameter polystyrene particles was investigated experimentally. A crystal with eight identical reflecting surfaces (3 mm X 4 mm in size) was used as the beam splitter, and eight mirrors were arranged evenly around a circle (10-cm diameter) to steer the beams into the intersection region 40 cm away. Thus the angle 2&wbetween beams on opposite sides of the axis was 14°. A Nikon standard objective (f = 50 mm, f # 1.4) was placed at a distance 2f from the center of the interrogation domain. The high-pass filter consisted of 12.5-mm-diameter metal ring of width 1 mm. Clear recognition of particles could be maintained for particle concentration as high as 80 mm-3. This and various other parameters were compared with results from an in-line and offaxis holography, as is shown in Table 1. The scheme in Fig. 2 is suitable for a small flow subdomain and can be used to obtain flow details or to study fine-scale turbulence (providing vorticity and helicity). For applications requiring large flow volume (approximately

10 cm x 10 cm x 10 cm),

such as near-field combusting jet flows and vortex ring collision, we propose another version (version 2) of the multibeam HPV, shown in Fig. 3. A large collimated beam, partitioned by a lens array and recollimated by a common lens (LI), provides multiple illumination beams. Their large intersection region defines the interrogation volume. An objective lens (L2 ) after the flow chamber focuses the undisturbed

Table 1. Comparison of In-Line, Off-Axis, and Multibeamn Imaging Qualitiesa

Method In-line Off-axis Multibeam

Scattering Efficiency -10-4 -10-7 -10-4

Image Depth Uncertainty &z (/m)

Maximum Seeding Density Permitting Recognition (particles/mm 3 )

400 55 80

8

15 mm X 15 mm X 50 mm

100 80

15 mm X 15 mm X 50 mm 4 mm X 4 mm x 4 mmb

Interrogation Volume (mm3)

aExperimental conditions were as follows: d = 21 Am, suspension depth 50 mm, recording distance 50 mm, A = 514.5 nm, and illumination beam diameter 15 mm. bDetermined by the reflector facet area and thus can be increased if a larger reflector is used.

July 1, 1993 / Vol. 18, No. 13 / OPTICS LETTERS holographicfilm

L3

high-pass filter

L2

flow region >L

low-pass M filter

reference beam

\/ \

illuminating beam

Fig. 3. Multibeam holographic particle velocimeter (recording part) for 3D, three-component measurement of the velocity field of a large interrogation volume of flow (version 2).

plane waves, which are then blocked by an array of dots acting as high-pass filters. L2, combined with another lens (L3), images the particle field in front of the film by using the scattered light, which serves as the object wave. The reference beam is separated from the illumination beam before the lens array, is sent through the flow region, is filtered by a pinhole, and is then projected to the holographic film at an angle. This scheme is thus essentially off axis, and

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the reconstruction process is similar to that for ordinary off-axis holography. Despite the larger interrogation volume, speckle noise is expected to be lower than in version 1 because of spatial separation of the virtual image. In summary, we have described an innovative multibeam HPV technique characterized by suppressed speckle noise, decreased image depth of field, and efficient use of laser energy. Version 2 (Fig. 3) accommodates a larger interrogation region, but version 1 (Fig. 2) is easier to implement because of simpler components and is more convenient to use owing to the linear design. This technique marks a major advance toward the ambitious objective of measurement of 3D velocity and vorticity distributions in turbulent flows. This research is supported by Office of Naval Research grant N00014-93-1-0532. We thank T. Scott Simmons and David Liu for helpful discussions.

References 1. H. Meng and F. Hussain, Fluid Dyn. Res. 8, 33 (1991). 2. L. W. Weinstein,

G. B. Beeler,

and A. M. Linder-

man, in Digest of AIAA Shear Flow Control Conference (American Institute of Aeronautics and Astronautics, Washington,

D.C., 1985), paper no. ALAA-85-0526.

3. H. Meng, W. L. Anderson, F. Hussain, and D. Liu, "Intrinsic speckle noise in in-line particle holography," J. Opt. Soc. Am. A (to be published). 4. A. E. Ennos, in Laser Speckle and Related Phenomena, J. C. Dainty,

ed., Vol. 9 of Springer

Series on Top-

ics in Applied Physics (Springer-Verlag, Berlin, 1975), pp. 207, 210.