In fluorescence correlation spectroscopy (FCS) analysis it is generally assumed that molecular species diffuse freely in volumes much larger than the three-dimensional FCS observation volume. However, this standard assumption is not valid in many measurement conditions, particularly in tubular structures with diameters in the micrometer range, such as those found in living cells (organelles, dendrites) and microfluidic devices (capillaries, reaction chambers). As a result the measured autocorrelation functions (ACFs) deviate from those predicted for free diffusion, and this can shift the measured diffusion coefficient by as much as ~50% when the tube diameter is comparable with the axial extension of the FCS observation volume. We show that the range of validity of the FCS measurements can be drastically improved if the tubular structures are located in the close vicinity of a mirror on which FCS is performed. In this case a new fluctuation time in the ACF, arising from the diffusion of fluorescent probes in optical fringes, permits measurement of the real diffusion coefficient within the tubular structure without assumptions about either the confined geometry or the FCS observation volume geometry. We show that such a measurement can be done when the tubular structure contains at least one pair of dark and bright fringes resulting from interference between the incoming and the reflected excitation beams on the mirror surface. Measurement of the diffusion coefficient of the enhanced green fluorescent protein (EGFP) and IscS-EGFP in the cytoplasm of living Escherichia coli illustrates the capabilities of the technique.