Eric W. Hansen

Magnetic nanoparticle temperature estimation.

The authors present a method of measuring the temperature of magnetic nanoparticles that can be adapted to provide in vivo temperature maps. Many of the minimally invasive therapies that promise to reduce health care costs and improve patient outcomes heat tissue to very specific temperatures to be effective. Measurements are required because physiological cooling, primarily blood flow, makes the temperature difficult to predict a priori. The ratio of the fifth and third harmonics of the magnetization generated by magnetic nanoparticles in a sinusoidal field is used to generate a calibration curve and to subsequently estimate the temperature. The calibration curve is obtained by varying the amplitude of the sinusoidal field. The temperature can then be estimated from any subsequent measurement of the ratio. The accuracy was 0.3 degree K between 20 and 50 degrees C using the current apparatus and half-second measurements. The method is independent of nanoparticle concentration and nanoparticle size distribution.

Recursive methods for computing the Abel transform and its inverse

The Abel transform and its inverse appear in a wide variety of problems in which it is necessary to reconstruct axisymetric functions from line-integral projections. We present a new family of algorithms, principally for Abel inversion, that are recursive and hence computationally efficient. The methods are based on a linear, space-variant, state-variable model of the Abel transform. The model is the basis for deterministic algorithms, applicable when data are noise free, and least-squares-estimation (Kalman filter) algorithms, which accommodate the noisy data case. Both one-pass (filtering) and two-pass (smoothing) estimators are considered. In computer simulations, the new algorithms compare favorably with previous methods for Abel inversion.

Enhanced 3-D reconstruction from confocal scanning microscope images. 1: Deterministic and maximum likelihood reconstructions

Significant improvement in the longitudinal (optical axis) resolution of a microscope has previously been obtained either by posterior digital processing of optical sections collected with a conventional microscope, or by collecting sections with a confocal scanning microscope. In this paper we report the feasibility of obtaining longitudinal resolution comparable to the lateral diffraction limit by posterior processing of confocal sections. A confocal through-focus image series was simulated numerically and restored by constrained iterative deconvolution and by maximum likelihood. Several typical imaging situations were simulated. The results support the possibility of achieving equal longitudinal and lateral resolution.

Fast Hankel transform algorithm

The Hankel, or Fourier-Bessel, transform is an important computational tool for optics, acoustics, and geophysics. It may be computed by a combination of an Abel transform, Which maps an axisymmetric two-dimensional function into a line integral projection, and a one-dimensional Fourier transform. This paper presents a Hankel transform algorithm using a fast (linear time) Abel transform, followed by an FFT.

Enhanced three-dimensional reconstruction from confocal scanning microscope images. II. Depth discrimination versus signal-to-noise ratio in partially confocal images

The enhanced depth discrimination of a confocal scanning optical microscope is produced by a pinhole aperture placed in front of the detector to reject out-of-focus light. Strictly confocal behavior is impractical because an infinitesimally small aperture would collect very little light and would result in images with a poor signal-to-noise ratio (SNR), while a finite-sized partially confocal aperture provides a better SNR but reduced depth discrimination. Reconstruction algorithms, such as the expectationmaximization algorithm for maximum likelihood, can be applied to partially confocal images in order to achieve better resolution, but because they are sensitive to noise in the data, there is a practical trade-off involved. With a small aperture, fewer iterations of the reconstruction algorithm are necessary to achieve the desired resolution, but the low a priori SNR will result in a noisy reconstruction, at least when no regularization is used. With a larger aperture the a priori SNR is larger but the resolution is lower, and more iterations of the algorithm are necessary to reach the desired resolution; at some point the a posteriori SNR is lower than the a priori value. We present a theoretical analysis of the SNR-toresolution trade-off partially confocal imaging, and we present two studies that use the expectationmaximization algorithm as a postprocessor; these studies show that a for a given task there is an optimum aperture size, departures from which result in a lower a posteriori SNR.

Nanoparticle temperature estimation in combined ac and dc magnetic fields

The harmonics produced by the nonlinear magnetization of superparamagnetic nanoparticles have been utilized in a number of budding medical devices. Here we expand on an earlier technique for quantitatively measuring nanoparticle temperature in a purely ac field by including the presence of a static field. The ability to quantify nanoparticle temperature by tracking changes in the 4th/2nd harmonic ratio is presented and shown to achieve an accuracy of 0.79 K. The advantage of even harmonics, issues with odd harmonics in the presence of a static field and the potential for future incorporation into an imaging system are discussed.

Circular harmonic image reconstruction: experiments

A method of image reconstruction from projections is described which processes the data in polar rather than rectangular coordinates and which does not require back projection. It is based on the decomposition of the object and its shadow (set of projections) into circular harmonics or radial modulators of angular Fourier components. The radial modulators of the object may be reconstructed from those of the shadow using a space-variant system which becomes space-invariant under a coordinate transformation. Experiments using digital and optical implementations are described.

Advanced Technology Solar Telescope: a progress report

The four-meter Advanced Technology Solar Telescope (ATST) will be the most powerful solar telescope and the worlds leading resource for studying solar magnetism that controls the solar wind, flares, coronal mass ejections and variability in the Suns output. Development of a four-meter solar telescope presents many technical challenges (e.g., thermal control of the enclosure, telescope structure and optics). We give a status report of the ATST project (e.g., system design reviews, instrument PDR, Haleakala site environmental impact statement progress) and summarize the design of the major subsystems, including the telescope mount assembly, enclosure, mirror assemblies, wavefront correction, and instrumentation.

State variable representation of a class of linear shift-variant systems

Certain types of linear shift-variant systems are rendered shift-invariant by appropriate coordinate transformations (changes of variable). Examples occur in aerial photography, restoration of images degraded by coma, and reconstruction of two-dimensional functions from line integrals. The matrices in the continuous state variable representations of such systems may be written as constant matrices multiplied by scalar functions of the independent variables; while the discretized models do not appear to share this feature, one system discussed in this paper does have a simple discrete-time structure. Given a shift-variant impulse response and the corresponding coordinate transformations, it is shown how to construct a state variable representation. Experimental results from an application to image processing are presented.

Leaky annular pupil for improved lateral resolution in confocal fluorescence microscopy

Imaging properties of an optical system may be modified by the introduction of spatial filters at the entrance and exit pupils. A classic example of this is the annular pupil, which is known to improve lateral resolution at the expense of depth discrimination. In confocal fluorescence microscopy, previous studies have shown that a configuration with an annular pupil in the excitation path and ca circular pupil in the emission path offer little improvement. We show here that a more favorable situation results if the annular excitation pupil is design with a partially transmissive central obstruction. Our simulations show that the radii and leakage of the annulus may be adjusted to improve the point spread functions lateral resolution by 13 percent and with not degradation of the Z-axis full width at half-maximum. A slightly different pupil is shown to improve the lateral resolution by 10 percent and the Z-axis response by 5 percent.