3.5.1 Time-average holography

The kind of holographic image illustrated here is made by taking a long exposure of the object while it is being driven in steady sinusoidal oscillation at the resonant frequency of a vibration mode. A laser beam is split in two: one beam illuminates the vibrating object, while the other is sent by a different route to act as a reference beam. The hologram is formed on a piece of photographic emulsion coated on glass, where the two beams are brought back together. The image is formed as an interference pattern between the light reflected from the object and light from the reference beam: when the two beams are in phase, the combination is bright, but when they are exactly in opposite phase, cancellation occurs and the combination is dark.

Figure 1. Laboratory set-up for making a time-average holography image of a vibrating object: a violin plate in this image. The laser (on the left) generates the green light beam, which is split in two. One proceeds directly to the photographic recording plate (front right), while the other reflects off the vibrating object first. Image copyright Bernard Richardson, reproduced by permission.

The recording period covers many cycles of the object, so the holographic image involves a collection of all the object positions between the two extremes of its motion — a sort of “blur”. However, the object spends most of its time at the two extremities of its motion, and it is these two positions which contribute the greatest to the holographic image and it is essentially these which create the interference patterns (the “fringes”) observed in the final image. The fringe contrast (and hence visibility) falls off for higher- order fringes because of the “blur” (the fringe intensities are actually described by the square of the zero-order Bessel function $J_0$, which we will meet in section 3.6.1 in connection with vibration modes of a drum: see Fig. 2 in that section). The fringes map out contours of equal vibration amplitude with adjacent bright (or dark) fringes representing a further (approximately) quarter-wavelength amplitude change. Nodal lines stand out as very intense fringes: they are brighter than others because there is no “blurring” in these positions.