Phase retrieval of gyrotron beams based on irradiance moments

Abstract

Abstract--We present the formulation of the moment method applied to the determination of phase profiles of microwave beams from known amplitudes. While traditional approaches to this problem employ an iterative error-reduction algorithm, the irradiance moment technique calculates a two-dimensional polynomial phasefront based on the moments of weighted intensity measurements. This novel formulation has the very important advantage of quantifying measurement error, thus allowing for its possible reduction. The validity of the irradiance moment approach is tested and confirmed by examining a simple case of an ideal Gaussian beam with and without measurement errors.The effectiveness of this approach is further demonstrated by applying intensity measurements from cold-test gyrotron data to produce a phasefront solution calculated via the irradiance moment technique. The accuracy of these results is shown to be comparable with that obtained from the previously developed iteration method.

Theoretical Investigation of Iterative Phase Retrieval Algorithm for Quasi-Optical Millimeter-Wave RF Beams

“…Therefore, it is required to have knowledge of the RF field properties in terms of determining the amplitude and phase profiles. Since the phase measurements are not available in such high-power applications, one has to rely on intensity measurements to calculate the phase profile [1]- [7]. The intensity measurements can be performed using an infrared thermography technique by irradiating a target material with the high-power microwave beam and measuring the spatial temperature elevation (which is proportional to the spatial RF power profile of the microwave beam) on the material using an infrared camera.…”

“…The intensity measurements can be performed using an infrared thermography technique by irradiating a target material with the high-power microwave beam and measuring the spatial temperature elevation (which is proportional to the spatial RF power profile of the microwave beam) on the material using an infrared camera. Although a number of methods [2], [7]- [9] have been studied for phase reconstruction, the error reduction approach seems to be most accurate in general and in particular for high-power gyrotrons. Other methods, such as the transport of intensity equation (TIE) [9], solve the real part of the wave equation, considering it as an elliptic partial differential equation.…”

“…Furthermore, in TIE, an accurate estimate of the intensity derivative along the direction of propagation needs closely spaced intensity measurements (no specific criterion for the separation between the planes is defined, and at millimeter wavelength, there is no significant difference between very closely spaced planes). The moment irradiance approach [7] works well only if the beam pattern contains a minimal fraction of higher order modes.…”

Numerical Modeling of Millimeter-Wave Transmission Lines

“…A phase reconstruction for plane apertures that are perpendicular to the beam can also be achieved with the method of irradiance moments [24]. It relies on the Fresnel approximation of the diffraction integral, which is justified if the apertures are not too close to each other.…”

Analysis of iterative phase retrieval approach to optimize amplitude measurement parameters

“…The moment irradiance approach [3] works well only if the beam pattern contains a minimal fraction of higher order modes.…”