We present a method based on a combination of temporal and spatial Fourier image analysis, involving the incorporation of a time-reversed acoustic propagation component, that can be used to obtain the angular dispersion or general dispersion relations of multiple surface acoustic modes excited by a localized pulsed source. The method is applied to the study of acoustic propagation at the surface of the highly anisotropic single-crystal TeO 2 coated with a thin gold film. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1602151͔ Surface acoustic wave propagation on bulk materials and thin film structures has proved of fundamental and practical interest for studying anisotropy and measuring film thicknesses or elastic properties. 1-6 A common method for such investigations is to use plane acoustic wave fronts, and to repeat the experiment for each propagation direction sequentially. However, the imaging of acoustic waves emanating from a point source is very useful for materials characterization because phenomena dependent on propagation direction, such as surface phonon focusing, can be effectively and immediately recorded with an omnidirectional acoustic wave vector distribution. [7][8][9][10][11] For surface acoustic imaging with impulsive point sources, the group velocity is readily measured from the wave front shape. However, it is the phase velocity-or its reciprocal, the slowness-that is more directly related to material elastic properties. 12 Impulsive point-source acoustic excitation of anisotropic samples by nature involves the generation of several surface and bulk acoustic modes that can produce complex overlapping wave fronts; no general method for the direct and automatic extraction of the individual dispersion relations ͑and hence the phase velocities͒ from such experimental images involving multiple propagating modes traveling parallel to the surface has been proposed. Previous methods can only be applied to images where only one acoustic mode propagates in any particular direction. 9 In this letter we present a general technique for analysis in time-resolved acoustic imaging at surfaces in the two lateral spatial dimensions that allows the extraction of the full set of dispersion relations for all excited modes simultaneously.We demonstrate the method with experiments on the transparent tetragonal crystal TeO 2 cut in the ͑001͒ orientation and coated with a thin polycrystalline gold film of thickness ͑40 nm͒ small enough to avoid significant thin film dispersion here and thus simplify comparison with theory. This crystal is strongly anisotropic in this cut and results in a complex phonon focusing pattern, ideal for evaluating techniques for acoustic mode analysis. 9, 13 We use an ultrafast optical pump and probe technique based on a common-path interferometer. 14 Acoustic waves are thermoelastically excited at a ϳ4 m Gaussian spot ͑full width at half maximum intensity͒ in the sample using optical pulses normally incident from the substrate side at wavelength 415 nm, repetition rate 80 MHz, du...