We have analyzed the spatial structure in Saturn's B and A rings for regional variations in characteristic spatial scales. To do this, we obtained radial scans of the reflectivity of the rings from the highest resolution full radial scan of the lit face of the rings in the Voyager image data set. The images were obtained in the Voyager 2 narrow angle camera, clear filter and have a resolution of approximately 5 km/pixel in the radial direction (the scans are slightly oversampled to 3.5 km). The radial scans were analyzed using a Burg maximum entropy technique to obtain spatial frequency spectra as a function of radial location in the B ring, Comparisons were made of the Burg technique and FFT techniques, and estimates of the limitations of the method were made. We find that the main rings display characteristic structure on several scales that vary with location. In the inner B ring (between the inner edge and around 99,000 km), a characteristic scale of 80-100 km is found. Between 99,000 and 103,500 ion, the 80-100 km scale vanishes and a strong preference for a longer wavelength (200-300 km) is seen. In this region, finer scale structure (20-40 km scale) is seen in abundance. This scale structure is absent in the inner B ring. The region between 103,500 and 116,000 ion has a very strong preference for 200-300 km scale structure and is practically devoid of fine scale structure except for a handful of isolated bursts. None of these bursts correspond to known strong resonances, Outside of 116,000 km, fine scale structure again appears in abundance, on top of the 200-300 km scale, and covers the ring to its outer edge. The Mimas 4:2 bending wave is clearly seen, but is responsible for only a very small fraction of the observed fine structure. (C) 1996 Academic Press, Inc.