Effect of spatial coherence on the focusability of annular laser beams

This paper presents a first comprehensive experimental study and theoretical analysis on the effect of spatial coherence on the focusability of annular laser beams. The circular apertures of annularity 0, 0.2, 0.4, 0.6 and 0.8 were studied experimentally for the far-field intensity distributions with three different partially coherent incident visible pulsed laser beams of spatial coherence fraction of 100%, 40% and 2% of full beam cross-section. These beams were generated from a copper vapor laser with different optical resonators. The spatial coherence fraction was computed from the interferograms recorded by a reversal shear interferometer. The resulting far-field patterns of focused annular beam were found to depend very critically on the spatial coherence of the incident beam. A theoretical analysis, based on Fourier transform of partially coherent incident light with coherent function taken as J1(r)/r, was carried out. The far-field diffraction patterns were estimated numerically for the annular beams involving correlation interval and obstruction ratio. The MATLAB based mathematical process was the Fourier transformation of the product of source autocorrelation function and correlation function across the aperture. Experimental and theoretical results are in good agreement.