Mode imaging with Hermite-Gauss beams
Any beam may be expressed as a weighted sum of Laguerre-Gauss modes, which is also known as its spiral spectrum. This spectrum is deformed when the beam is partially blocked by an object of a certain geometry. Torner et al. [Opt. Express 13, 873 (2005)] originally proposed this as digital spiral imaging. We propose that the spectrum of a mode may also be expresssed in terms of Hermite-Gauss modes. By following the same original theoretical framework proposed by Torner et al., we explore the possibility of using HG modes to measure the spectra for two different objects. The first is a diagonal knife edge and the second is an off-center circle. We show that the measured spectra are unique to the test object. We also use these spectra to reconstruct the original wavefront. Though our reconstructions do not fully resemble the original beams, they still hold promising insights into future extensions of digital spiral imaging.