Douglas H. Strope

Time-Average Holographic Interferometry of a Circular Plate Vibrating Simultaneously in Two Rationally Related Modes*

This paper presents the results of time-average holographic interferometry of a circular metal plate vibrating simultaneously in two unique modes whose frequencies are rationally related. Rational and irrational frequency ratios are presented for comparison. The rational and irrational results differ significantly, and these differences are explained by use of their respective characteristic functions.

Holographic Interferometry Applied to Motion Studies of Ultrasonic Bonders

case, for an aperture of 100wavelengths; the loss will be smaller for a narrower aperture. It seems that a reasonable upper figure for the contribution to the insertionloss from non-standard irradiation of the ouput transducer may be as much as 1.3 dB. Richardson and Kino (8) used a path-length of 3.05 cm and an aperture of 38 wavelengths. The value of ‘p is reduced by a factor of 38/100,as compared with the value of 1.097 used in Section IV. The insertion loss for 0.1’ tilt is then found to be 0.063 dB, and the insertion loss for misalignment due to a 0.1” divergence of the beam direction from the line joining the center-points of the two transducers is found to be 0.384 dB. From Fig. 3 of Richardson’s and Kino’s paper, a / /and b/l can be taken as 0.2, and bearing in mind that there is little contribution to the loss from the amplitude and phase ripples, Eqns. (17) and (1 8) give a contribution toE of 0.294 dB. The loss due to power in the side lobes is about 0.1 dB, according to observations by Richardson and Kino (8 ) , Kharusi and Farnell (12), and Williamson (private communication). The predicted loss due to inefficiency is thus about 0.85 dB, and the error in the calculation, due to the ideal forms of the various defects that were assumed to simplify the calculation, is probably substantially less than 0.1 dB. The loss observed by Richardson and Kino and not accounted for was about 0.9 _+ 0.2 dB. The agreement is good, and it appears that the effects discussed in this paper can account for the residual observedlosses not previously accounted for. These residual losses do not form part of the transmission coefficient T , but contribute to the efficiency factorE. Only T can be affected by an electrical network connected between the transducer and the load. Thus the residual losses cannot be reduced by changing the parameters of such a circuit.