In the presentation we report on novel applications of Gaussian beam mode (GBM) analysis, including in image deconvolution and Fourier grating design.
GBMs are the natural modes with which to describe propagation of quasi-collimated long-wavelength beams, with only a small number of modes required to reach adequate accuracy for many practical applications. GBMs provide a more efficient and natural basis set with which to describe propagation than for example plane wave decomposition, especially because of the limited spatial frequency content (only a few degrees of freedom are necessary to describe such beams and the degrees of freedom can be associated with component GBMs).
We discuss how GBM analysis provides a useful alternative scheme to FFT approaches for performing deconvolutions and image retrieval in long-wavelength quasi-collimated systems. The convolving beam is usually described very efficiently in terms of beam modes and an SVD approach can be used to extract the mode coefficients of the deconvolved image. We discuss in particular the novel application to mapping in astronomical telescope observations.
Another useful area of application is in the design of Fourier phase gratings. Fourier gratings can be used for beam multiplexing of local oscillator power in array imaging systems. In this case phase retrieval is often driven by an iterative approach to the solution based on FFTs and thus by implication plane waves. A GBM approach leads to a more efficient and physically more meaningful approach, especially again because of the limited spatial frequencies possible in long wavelength systems.