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In many fields (e.g., spectroscopy, imaging spectroscopy, photoacoustic imaging, coded aperture imaging) binary bit patterns known as m sequences are used to encode (by multiplexing) a series of measurements in order to obtain a larger throughput. The observed measurements must be decoded to obtain the desired spectrum (or image in the case of coded aperture imaging). Decoding in the past has used a technique called the fast Hadamard transform (FHT) whose chief advantage is that it can reduce the computational effort from N(2) multiplies to N log(2) N additions or subtractions. However, the FHT has the disadvantage that it does not readily allow one to sample more finely than the number of bits used in the m sequence. This can limit the obtainable resolution and cause confusion near the sample boundaries (phasing errors). We have developed both 1-D and 2-D methods (called fast delta Hadamard transforms, FDHT) which overcome both of the above limitations. Applications of the FDHT are discussed in the context of Hadamard spectroscopy and coded aperture imaging with uniformly redundant arrays. Special emphasis has been placed on how the FDHT can unite techniques used by both of these fields into the same mathematical basis.

We report new cross-section and analyzing-power data for the excitation by 498-MeV protons of all narrow normal-parity states of ' 0 below 12.1-MeV excitation. In addition, spin-rotation measurements for elastic scattering and depolarization measurements for the 1&, 2&, and 3& states of ' 0 have been performed. These data are used in conjunction with existing data for Ca to study medium corrections to the effective interaction for nucleon-nucleus scattering at 500 MeV. Systematic differences between the data and nonrelativistic impulse approximation calculations based upon either the free t matrix or a recent density-dependent effective interaction are interpreted within the framework of the local-density approximation. An empirical effective interaction has been constructed which parametrizes the density dependence of the medium modifications in a simple form amenable to phenomenological analysis of data. The parameters of the interaction are adjusted by fitting to data from many transitions simultaneously, including inelastic transitions sensitive to both the surface and the interior of the nucleus. We find that the empirical effective interaction provides a good description of both the fitted inelastic-scattering observables and elasticscattering observables not included in the fit. Furthermore, we find that the empirical effective interaction fitted to inelastic-scattering data for ' 0 provides an excellent description of both elasticand inelastic-scattering data for Ca at 500 MeV. The most significant difference between the empirical interaction and the theoretical interaction is that absorption is enhanced at higher density, contrary to expectations based upon Pauli blocking. We find also that the empirical interaction has a stronger repulsive core than expected in nonrelativistic models of the effective interaction.Nevertheless, the optical potentials are very similar to the Schrodinger-equivalent potentials from a relativistic impulse approximation model, showing that the empirical density dependence is comparable to the equivalent density dependence due to elimination of lower components from this relativistic model of the nucleon-nucleus interaction. These results are also compared with global optical potentials from Dirac phenomenology, which suggest even stronger repulsion in the real central interaction.

The first complete measurement of the polarization-transfer observables in the (p $ p') reaction at intermediate energies is reported. Data are presented for the reaction i2 C(p,p') 12 C to the 1 + , T = 0 (12.71-MeV) and 1 + , T = l (15.11-MeV) states at 500 MeV for laboratory scattering angles of 3.5°, 5.5°, 7.5°, and 12.0°. Linear combinations of these observables are shown to exhibit a very selective dependence on the isoscalar and isovector spin-dependent components of the nucleon-nucleon interaction.