Theory of double-sided flux decorations

A two-sided Bitter decoration technique was recently employed by Yao et al. to study the structure of the magnetic vortex array in high-temperature superconductors. Here we discuss the analysis of such experiments. We show that two-sided decorations can be used to infer quantitative information about the bulk properties of flux arrays, and discuss how a least-squares analysis of the lcoal density differences can be used to bring the two sides into registry. Information about the tilt, compressional and shear moduli of bulk vortex configurations can be extracted from these measurements. The experimental value for the compresssional modulus is about four order of magnitude smaller than expected from mean-field theory