We report a comprehensive approach to analysing continuous-output photon detectors. We employ principal component analysis to maximize the information extracted from output signals, followed by a novel noise-tolerant parameterized approach to the tomography of photon-number resolving detectors. We further propose a measure for rigorously quantifying a detector's photon-number-resolving capability. Our approach applies to all detectors with continuous-output signals. We illustrate our methods by applying them to experimental data obtained from a transition-edge sensor detector.