This paper reports on a near-infrared survey of early-type galaxies designed to provide information on bar strengths, bulges, disks, and bar parameters in a statistically well-defined sample of S0-Sa galaxies. Early-type galaxies have the advantage that their bars are relatively free of the effects of dust, star formation, and spiral structure that complicate bar studies in later type galaxies. We describe the survey and present results on a detailed analysis of the relative Fourier intensity amplitudes of bars in 26 early-type galaxies. We also evaluate the ``symmetry assumption'' of these amplitudes with radius, used recently for bar-spiral separation in later type galaxies. The results show a wide variety of radial Fourier profiles of bars, ranging from simple symmetric profiles that can be represented in terms of a single Gaussian component to both symmetric and asymmetric profiles that can be represented by two overlapping Gaussian components. More complicated profiles than these are also found, often due to multiple barlike features including extended ovals or lenses. Based on the gravitational bar torque indicator Qb, double-Gaussian bars are stronger on average than single-Gaussian bars, at least for our small sample. We show that published numerical simulations in which the bar transfers a large amount of angular momentum to the halo can account for many of the observed profiles. The range of possibilities encountered in models seems well-represented in the observed systems.