It has been known for more than 30 years that most of the geometric content of a digital image is encoded in the phase of its Fourier transform. This has led to several works that exploit the global (Fourier) or local (Wavelet) phase information of an image to achieve quality assessment, edge detection, and, more recently, blind deblurring. We here propose a deeper insight into three recent sharpness metrics (Global Phase Coherence, Sharpness Index and a simplified version of it), that all measure in a probabilistic sense the surprisingly small total variation of an image compared to that of certain associated random-phase fields. We exhibit several theoretical connections between these indices, and study their behavior on a general class of stationary random fields. We also use experiments to highlight the behavior of these metrics with respect to blur, noise and deconvolution artifacts (ringing). Finally, we propose an application to isotropic blind deblurring and illustrate its efficiency on several examples.