Speckle imaging of annular Hermite Gaussian laser beam

Fourier transform (FT) corresponding to the diffuser has a comb function realised from uniform illumination, and hence the speckle image is nearly equal to comb point spread function (PSF). Consequently, the resulted distribution permits computation of the speckle size from the FWHM corresponding to the PSF of the HGnm annular aperture. In the second method, the numerical autocorrelation of the speckle images using new apertures are computed and the speckle sizes are obtained. The results in both methods are compared with the speckle images obtained using circular aperture. It is noted that, the maximum number of spots produced in the HGnm modes given by combinations m, n is an element of [0, 5] is (m+1) (n+1)=36 and all images and plots are obtained using Mat-Lab codes.