A simple image domain ray tube integration formula is presented to efficiently compute the inverse synthetic aperture radar (ISAR) image of a complex target by the shooting and bouncing ray (SBR) technique. Contrary to the conventional approach where the ISAR image is obtained by inverse Fourier transforming the computed scattered field data over frequency and aspect, this image domain formula gives the contribution of each ray to the overall ISAR image directly. Under the small angle approximation and utilizing the bistatic-monostatic equivalence, the image domain ray tube integration formula is determined in closed form. Simulation results using the SBR-based code “Xpatch” show that the direct image domain method results in good image quality and superior time performance when compared to the conventional frequency aspect approach.

Image domain ray tube integration formula for the shooting and bouncing ray technique

We present a fast simulation algorithm for generating the range profiles and inverse synthetic aperture radar (ISAR) images of complex targets using the shooting and bouncing ray (SBR) technique. Starting with the time-domain and image-domain ray-tube integration formulas we derived previously, we cast these formulas into a convolution form. The convolution consists of a nonuniformly sampled signal and a closed-form time-domain or image-domain ray spread function. Using a fast scheme proposed by Sullivan (1990), the nonuniformly sampled function is first interpolated onto a uniform grid before the convolution is performed by the fast Fourier transform (FFT) algorithm. Results for several complex targets are presented to demonstrate the tremendous computation time savings and excellent fidelity of the scheme. Using the fast scheme, a speed gain of a factor of 30 is achieved in performing the ray summation as compared to the direct convolution in range profile computation and a factor of 180 in ISAR image formation for a typical aircraft at S-band. >

A fast algorithm for signature prediction and image formation using the shooting and bouncing ray technique

A shooting and bouncing ray (SBR) formulation is presented for treating the electromagnetic scattering from electrically large, inhomogeneous objects. A dense grid of rays representing the incident plane wave is shot toward the inhomogeneous objects. At the scatterer boundary, reflected rays and refracted rays are generated due to the discontinuity of the medium parameters. The trajectory, amplitude, phase and polarization of the rays inside the inhomogeneous object are traced based on geometrical optics. Whenever the rays cross the scatterer surface, additional reflected/refracted rays are generated and are tracked. This is repeated until the intensities of the refracted/reflected rays become negligible. The contributions of the existing rays to the total scattered field are calculated using the equivalence principle in conjunction with a ray-tube integration scheme. The ray formulation is applied to calculate the backscattering from cylinders and spheres and good agreement with the exact series solutions is observed in the high-frequency range. In addition, the backscattering mechanisms in penetrable objects are interpreted in terms of simple ray pictures. >

Electromagnetic scattering from an inhomogeneous object by ray tracing

Plasmas alter high-frequency electromagnetic signals primarily through strong electron density gradients or electron densities approaching the critical plasma density. A plasma can potentially degrade electromagnetic systems through signal attenuation as well as increased amplitude or phase noise. This paper reviews the physical mechanisms of a plasma which cause phase shift, attenuation, phase modulation, and amplitude modulation. To make predictions of these effects, a general ray-tracing method is also reviewed and then applied to the localized high-speed plasma flow of a stationary plasma thruster (SPT). The SPT is currently being tested and considered for use aboard next-generation spacecraft, where careful consideration must be given to possible interactions with satellite electromagnetic systems such as for communication, navigation, and remote sensing. The study also models the rather significant plume impact to phase and amplitude for a range of frequencies. A summary is provided of ray-tracing simulations characterizing both phase and amplitude effects at frequencies from 0.5 to 17 GHz and thruster axial positions from 0.25 m to 1.5 m. The results correlate well with known data.

Electromagnetic signal modification in a localized high-speed plasma flow: Simulations and experimental validation of a stationary plasma thruster

Reported is the use of a microwave interferometric technique for making nonintrusive measurements of plasma electron number density in the plume of a space electric propulsion thruster. The technique is capable of providing good sensitivity and accuracy as well as resolution using modern microwave network analyzer technology. Density profiles were obtained throughout the plume of a 1 kW hydrogen arcjet based on accurate microwave differential phase measurements. Spatially resolved integrated phase shifts for a 17.5 GHz signal radiated through the plume at various radial positions were Abel inverted to calculate radial electron density profiles. All measurements were taken in the University of Michigan's Large Chamber Plasma Facility, a 6 m by 9 m vacuum chamber, at pressures of 2/spl middot/10/sup -4/ Torr or less. The interferometer measured electron densities as low as 1/spl middot/10/sup 15/ m/sup -3/ with a predicted capability to measure peak densities as high as 3/spl middot/10/sup 18/ m/sup -3/. The accuracy of this technique is estimated to be on the order of /spl plusmn/10%. Comparison with Langmuir probe electron number density measurements demonstrate relative agreement between the two methods. Further, a previously reported tendency for the Langmuir probe to underpredict electron number density was consistent with our measurements. It is postulated that this underprediction may be due to small Langmuir probe perturbations in the local plasma of the far-field plume and errors in estimation of the probe collection area. >

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Nonintrusive electron number density measurements in the plume of a 1 kW arcjet using a modern microwave interferometer

The effect of an arcjet plume on the performance of satellite reflector antennas is studied. The arcjet plume is modeled as a weakly ionized plasma. The spatial permittivity distribution of the plume is approximated using the measured electron density profile and a cold plasma model. Geometrical optics is applied to determine the ray paths as well as the transmitted fields through the inhomogeneous plume. The ray optics results are compared against several exact solutions for scattering from inhomogeneous dielectrics, and good agreement is observed for sufficiently large scatterer size. The far-field antenna patterns of the reflector in the presence of the plume are calculated from the transmitted ray fields using a ray-tube integration scheme. For arcjet prototypes in the 1-kW class, the plume effect on the antenna performance is small. As the electron density increases, the main beam and sidelobe level gradually degrade. The main beam also tends to squint away from the plume region. >

B.W. Birkner

Papers

Effect of an arcjet plume on satellite reflector performance