Coherence quantifies the statistical fluctuations in an optical field and has been extensively studied in the space, time, and polarization degrees of freedom. In the context of space, coherence theory has been formulated between two transverse positions as well as between two azimuthal positions, referred to as transverse spatial coherence and angular coherence, respectively. In this paper, we formulate the theory of coherence for optical fields in the radial degree of freedom and discuss the associated concepts of coherence radial width, radial quasi-homogeneity, and radial stationarity with some physically realizable examples of radially partially coherent fields. Furthermore, we propose an interferometric scheme for measuring radial coherence.