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Submitted on 1 Jan 1972
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THE POHLMAN CELL AND ITS USE IN HOLOGRAPHY
A. Lafferty, R. Stephens
To cite this version:
A. Lafferty, R. Stephens. THE POHLMAN CELL AND ITS USE IN HOLOGRAPHY. Journal de Physique Colloques, 1972, 33 (C6), pp.C6-48-C6-51. �10.1051/jphyscol:1972610�. �jpa-00215128�
JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 11-12, Tome 33, Nouembre-Ddcembre 1972, page 48
THE POHLMAN CELL AND ITS USE IN HOLOGRAPHY
A. J. LAFFERTY (*) and R. W. B. STEPHENS (* *) Imperial College, London, Grande-Bretagne
Rhumb. - Dans cet article est decrit le dispositif de visualisation acoustique appele cc cellule de Pohlman >) ainsi que son utilisation dans un syst6me d'holographie acoustique. Sont alors comparkes la visualisation holographique sans lentille et l'imagerie faite en utilisant une lentille acoustique liquide a focale variable.
La cellule de Pohlman utilise le couple exerce par un champ acoustique sur un petit disque sus- pendu librement dans un fluide (disque de Rayleigh) tel que le disque tende a prksenter sa face large au rayonnement incident. L'effet est quadratique en vitesse de dkplacement acoustique.
Abstract. - In this paper an account is given of a specific acoustical visualization device, called
a <c Pohlman cell >), and its use in an acoustical holographic system. A comparison is later made
between lens-less holographic visualization and imaging by means of a variable focus liquid acoustic lens.
The Pohlman cell depends for its action upon the couple exerted on a disc by an acoustic field (a Rayleigh disc) so that it tends to set << broadside-on )> to the incident radiation, the magnitude of the effect being proportional to the square of the acoustic particle velocity.
A number of techniques exist for the visualization of a two dimensional cross-section of an acoustic field. Most of methods available have now been extended to three-dimensional representation by the application of Gabor's [I] holographic imaging technique. Few of the acoustic visualization devices however match the overall performance of the optical photographic emulsion and holography with sound waves may be said to be in search of an (( acoustical emulsion >).
The Pohlman [2], [3] cell is an acoustical visuali- zation device previously used in non-destructive testing applications. The cell depends for its action upon the couple exerted by acoustical radiation impinging on a thin disc freely suspended in a fluid.
Such a disc is described as a Rayleigh disc and tends to set itself (< broadside-on )) to the incident radiation, the magnitude of the effect being proportional to the square of the acoustic particle velocity.
Lord Rayleigh [4] showed that the time-averaged couple
E
exerted on the disc in a sound field is givenby -
L = - + p o a 3
I
V l 2 s i n 2 n ,where p, is the density of the suspending fluid, a the radius of the disc,
I
VI
the particle velocity and n the angle a normal to the disc makes with the direc- tion of the incident sound. This formula was later corrected by King [5] taking into account the inertiaof the disc and the effect of the diffracted field, giving for the couple
(Z)
on the disc in a standing wavei
(m, - m,) (1+
2 / 5 ( k ~ ) ~ cos2 cc)x sin2 kh -
m , - mw(l f 1/5(ka)~)
where h is the acoustic path length from a reference plane to the disc, k is the acoustic wave number, m, is the mass of the disc and m, the mass of dis- placed fluid ; m, is the hydrodynamic mass of the disc and is equal to - 8 po a3, 11, I, and I, are the moments
3
of inertia equivalent to these masses. If the disc is small compared to the sound wavelength then ka -4 1 and terms in (ka)2, ( k ~ ) ~ , etc. may be neglected.
The couple on a disc a t a standing wave node becomes negligible and that on a disc a t an antinode (sin kh = I, cos kh = 0) simplifies to
Emtinode
= - Z p o a 3 sin 2 a 31
Vl 2 i
ml-m,+m, m1 -mwwhere the term containing the masses may be re- written as a function (F) of the relative densities of the fluid (p,) and the disc material (p,) leading finally to
(*) Imperial .College (Univ. of London) London .England. - = - ~ p , a 3 s i n 2 a l V 1 2 F
(**) Chelsea College. (Univ. of London) London England. 3
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972610
THE POHLMAN CELL AND ITS USE IN HOLOGRAPHY C6-49
When sound is incident on a suspension of such discs, the distribution of sound intensity will produce a similar distribution in values of the couple
(z).
If the discs are optically reflective, then light upon them in the opposite direction to that of the sound, will produce by reflection the same optical intensity distribution as the intensity of the acoustic field.
1. Design of the Pohlman cell. - The cell essen- tially consists of a suspension of fine aluminium particles in water to which has been added a dis- persing agent (a detergent). The diameter of the particles fall in the range of 20 y-40 y and are obtained by separation from a commercial sample of aluminium powder using a flotation method. The suspension forms a sandwich between an acoustic transparent Myler membrane and a glass window. Both the membrane and the optical window are mounted on brass frames which fit together by a fine screw thread, giving any desired thickness of suspension. The diameter of detecting aperture is 10 cm.
2. Recording the acoustical hologram. - The hologram is recorded in an anechoic water tank, the cell being illuminated by white light through an end window cut into the tank. The ultrasonic sources are two matched PZT ceramic transducers, originally one inch in diameter but stopped down to one cen- timetre by their brass mountings, giving a wider beam. The transducers are mounted so as to reduce side-lobes in their far field radiation pattern, continuous wave ultrasound is used throughout at a frequency of 0.963 MHz. Figure 1 shows the experimental
tank
11
lT7
osci~~ator0 scope
arrangement for recording the hologram, the angle between reference and object beams is called the design angle and dictates the spatial frequency of the recorded fringes. Figure 2 is a typical two-beam fringe pattern as ,it appears on the Pohlman cell, in the absence of a diffra~ti~ng object. Figure 3 is
a hologram of a letter (( E )) cut out of thin brass plate. The letter is 2 cm high with its narrower arms 2 mm wide and the acoustic wavelength in water is about 1.5 mm at this frequency. Figure 4a-h in sequence is a reconstruction of the hologram photo- graphed at various planes between the object and the source. An image of the reference source, reflected by the object back into the cell, is evident Fig. 4(g) alongside the object source. The hologram is recorded on Kodak TriX film and reconstructed with a low power Helium-Neon 6 328 laser. The reduction in linear dimensions of the hologram during the recording is by a factor of about 0.05. With this reduction the image is only a mm or so high. A lens of focal length 20 cm is used in the reconstruction to focus the laser through the hologram and the central diffracted order and unwanted twin image are removed by special filtering.
C6-50 A. J. LAFFERTY AND R. W. B. STEPHENS
small clamp. The lens has an aperture diameter of 10 cm and its brass frames were covered by sound absorbing material.
The liquid used is a silicone fluid of viscosity 50 centistokes, it is chemically inert and stable over the desired range of temperature and pressure. The velocity of sound in the fluid is 1.05 x lo3 metres per second giving a sound refractive index of about 1.4 with respect to water (*). The acoustic mis-match is therefore low, and distortion due to buoyancy
3. Imaging with a variable focus liquid lens. - It is also possible to image any desired plane on to the Pohlman cell with an acoustic lens. If a solid lens is used, a lens fabricated from perspex or poly- styrene, then it must be physically moved in order to image different planes. However, the radius of curvature of a liquid lens, the liquid being contained by elastic membranes, may be continously varied, and in small amounts, by adjusting the volume of liquid in the lens. Moreover the change of focus may be carried out without moving the lens and so any part of an acoustic field may be imaged in a manner analogous to the operation of a human eye.
(*) The low density is close
viscosity means low attenuation t o that of water.
and the fluid
THE POHLMAN CELL AND ITS USE IN HOLOGRAPHY C6-51 forces of the fluid bulk are not problematical. Addi-
tional properties of the fluid which confirm its choice are its insolubility and water resistance.
5. Imaging on the Pohlman cell. - By allowing the rubber bulb to slowly contract using the clamp, the focal length of the lens could be changed slowly.
The acoustic field of the same object (letter G E ))) as used in holographic imaging is scanned on the Pohlman cell and shown in figure 5a-e in sequence.
Object distances from 10 cm up to the maximum obtainable in the tank (60 cm) can be accommodated by the lens. It can be seen that image contrast is much reduced, as might be expected in the absence
of the powerful laser source used in holographic imaging.
6. Summary. - Both conventional and holo- graphic imaging of complete sound fields have been demonstrated using a Pohlman cell. It is expected that the image contrast, particularly in conventional imaging, may be considerably improved by the presence of an electric field in the suspension. Mean- while, the holographic process has been utilized for investigating the pattern of sound fields inac- cessible to conventional measurements 161 and the results show good agreement with theoretical pre- diction.
References
111 GABOR D., A new microscopic principle. Nature [4] Lord RAYLEIGH, The theory of sound, 2 (1897),
161 (1948) 777. 253b.
[2] POHLMAN R., 2. Angew Phys. 1 (1948) 181. [5] KING L. V., Inertia and diffraction corrections for [3] POHLMAN R., Schweizerische Bauzeitung 67 (1949) the Rayleigh disc. Proc. R. Soc. A 878 (1935) 1.
85. [6] LAFFERTY A. J. and KUMAR R., Proc. of Brit. Ac. SOC.
Spring Meeting Apri! (1972).
