The reading of Rayleigh interference photographs produced by the ultracentrifuge ( 1) is laborious and time-consuming. To obtain data of high precision, it is necessary to measure the displacement of several fringes or to average several readings of the same fringe at thirty to fifty points along the solution column (2). Several photographs should be evaluated for each experiment, and the plate measurement and data reduction for one run usually requires several hours of concentrated effort on the part of a skilled operator.
With an automatic densitometer and the algorithm we shall describe, plate measurement can be automated. The effort needed and the skill required to make such measurements are greatly reduced. Moreover, in our hands, the data are more precise than the best data we can collect manually.
The basis of the algorithm is the Fourier transform. Since the optical density profile produced by a scan across the fringes is an amplitudemodulated sine wave, the Fourier transform provides a convenient method of calculating the averaged or smoothed sine wave profile. From the smoothed profile, the following can be obtained: the fringe displacement, the fringe interval, the fringe visibility, and the position of the fringe envelope. To obtain these data, only three points of the Fourier transform need be calculated from an optical density profile. This can be done quickly and easily.
Teller has described a semiautomated plate reading procedure based on the moire pattern obtained by projecting the image of the fringe system to be measured through a photographic transparency of a baseline fringe pattern. The light transmitted through the transparency is collected by a condensing lens and measured by a photomultiplier. The method described by Teller can be regarded in terms of the Fourier transform. The effect of the procedure is to multiply the experimental I39