We have developed a scanning superconducting quantum interference device ͑SQUID͒ microscope system with interchangeable sensor configurations for imaging magnetic fields of room-temperature ͑RT͒ samples with submillimeter resolution. The low-critical-temperature ͑T c ͒ niobium-based monolithic SQUID sensors are mounted on the tip of a sapphire and thermally anchored to the helium reservoir. A 25 m sapphire window separates the vacuum space from the RT sample. A positioning mechanism allows us to adjust the sample-to-sensor spacing from the top of the Dewar. We achieved a sensor-to-sample spacing of 100 m, which could be maintained for periods of up to four weeks. Different SQUID sensor designs are necessary to achieve the best combination of spatial resolution and field sensitivity for a given source configuration. For imaging thin sections of geological samples, we used a custom-designed monolithic low-T c niobium bare SQUID sensor, with an effective diameter of 80 m, and achieved a field sensitivity of 1.5 pT/ Hz 1/2 and a magnetic moment sensitivity of 5.4ϫ 10 −18 A m 2 /Hz 1/2 at a sensor-to-sample spacing of 100 m in the white noise region for frequencies above 100 Hz. Imaging action currents in cardiac tissue requires a higher field sensitivity, which can only be achieved by compromising spatial resolution. We developed a monolithic low-T c niobium multiloop SQUID sensor, with sensor sizes ranging from 250 m to 1 mm, and achieved sensitivities of 480-180 fT/ Hz 1/2 in the white noise region for frequencies above 100 Hz, respectively. For all sensor configurations, the spatial resolution was comparable to the effective diameter and limited by the sensor-to-sample spacing. Spatial registration allowed us to compare high-resolution images of magnetic fields associated with action currents and optical recordings of transmembrane potentials to study the bidomain nature of cardiac tissue or to match petrography to magnetic field maps in thin sections of geological samples.

We have developed a monolithic low-temperature superconducting quantum interference device (SQUID) magnetometer and incorporated the device in a scanning microscope for imaging magnetic fields of room temperature samples. The instrument has a ∼100 μm spatial resolution and a 1.4 pT/Hz1/2 field sensitivity above a few hertz. We discuss design constraints on and potential applications of the SQUID microscope.

We magnetically imaged the magnetic action field and optically imaged the transmembrane potentials generated by planar wavefronts on the surface of the left ventricular wall of Langendorff-perfused isolated rabbit hearts. The magnetic action field images were used to produce a time series of two-dimensional action current maps. Overlaying epifluorescent images allowed us to identify a net current along the wavefront and perpendicular to gradients in the transmembrane potential. This is in contrast to a traditional uniform double-layer model where the net current flows along the gradient in the transmembrane potential. Our findings are supported by numerical simulations that treat cardiac tissue as a bidomain with unequal anisotropies in the intra- and extracellular spaces. Our measurements reveal the anisotropic bidomain nature of cardiac tissue during plane wave propagation. These bidomain effects play an important role in the generation of the whole-heart magnetocardiogram and cannot be ignored.

In recent years many groups have used Fisher, Fisher, and Huse (FFH) dynamical scaling to investigate and demonstrate details of the superconducting phase transition. Some attention has been focused on two dimensions where the phase transition is of the Kosterlitz-ThoulessBerezinskii (KTB) type. Pierson et al. used FFH dynamical scaling almost exclusively to suggest that the dynamics of the two-dimensional superconducting phase transition may be other than KTB-like. In this work we investigate the ability of scaling behavior by itself to yield useful information on the nature of the transition. We simulate current-voltage (IV) curves for two-dimensional Josephson junction arrays with and without finite-size-induced resistive tails.We find that, for the finite-size effect data, the values of the scaling parameters, specifically the transition temperature and the dynamical scaling exponent z, depend critically on the magnitude of the contribution that the resistive tails make to the IV curves. In effect, the values of the scaling parameters depend on the noise floor of the measuring system. 3

Executive SummaryThe Defense Advanced Research Projects Agency (DARPA) asked the Institute for Defense Analyses (IDA) to assemble a summary of work on gradient index optics completed under funding from the Agency. The purpose was to archive the efforts, motivation, and accomplishments that the Agency supported and to provide a reference for any future programs that explore this new area of optics.Although optical instruments, such as lenses and mirrors, dating back thousands of years ago have been unearthed, lenses were not put into practical use until the invention of eyeglasses in the thirteenth century. The microscope and the telescope were invented in the seventeenth century, but no revolutionary changes occurred in these complex lens systems for the next 200 years. Most lens systems remained homogeneous multi-element systems with spherical glass surfaces and fixed optical properties. Recently, however, new materials and lens designs have been developed, inspired by properties of biological eyes. Materials with a gradient index (GRIN) allow the development of compact systems that have high focusing power while correcting for aberration.In 2002, DARPA initiated the Bio-Optic Synthetic Systems (BOSS) program, which aimed to synthesize the components of a biologically inspired vision system and demonstrate a level of performance beyond that of standard optical imaging systems (i.e., with reduced size and complexity). Out of more than a dozen exploratory efforts, four efforts were selected for further development and demonstration: fluidic adaptive zoom lenses, foveated imaging, photon sieves, and nanolayer lenses.As an example, Case Western Reserve University (CWRU) and the Naval Research Laboratory (NRL) collaborated on the nanolayer lens effort to create a synthetic lens that would mimic the structure and capabilities of an octopus eye. The CWRU/NRL team used a forced assembly nanolayer coextrusion process to form films that had a tailored refractive index consisting of thousands of nanolayers of two different polymers that had different refractive indices. The films of various n were stacked to create a refractive index range (Δn) and formed into hemispheres, which were combined to form the synthetic bi-convex octopus lens. A zoom lens system constructed from three of these GRIN lenses was demonstrated on a small unmanned aerial vehicle (UAV).Limited manufacturing capabilities have hindered practical applications of GRIN lenses. In 2008, DARPA initiated the Manufacturable Gradient Index Optics (M-GRIN) program to address GRIN lens manufacturing issues in the development of low-cost, iii customizable GRIN-based optics for use in a variety of military systems. This effort included a significant focus on metrology, where new tools were required for monitoring the polymer nanolayer process for GRIN optics. Performers in the M-GRIN program included the following teams: