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We present the first demonstration of shot-noise limited supercontinuum-based spectral domain optical coherence tomography (SD-OCT) with axial resolution of 5.9 $\mu$m at a center wavelength of 1370 nm. Current supercontinuum-based SD-OCT systems cannot be operated in the shot-noise limited detection regime because of severe pulse-to-pulse relative intensity noise of the supercontinuum source. To overcome this disadvantage we have developed a low-noise supercontinuum source based on an all-normal dispersion (ANDi) fiber, pumped by a femtosecond laser. The noise performance of our 90 MHz ANDi supercontinuum source is compared to that of two commercial sources operating at 80 and 320 MHz repetition rate. We show that the low noise of the ANDi supercontinuum source improves the OCT images significantly in terms of both higher contrast, better sensitivity, and improved penetration. From SD-OCT imaging of skin, retina, and multi-layer stacks we conclude that supercontinuum-based SD-OCT can enter the domain of shot-noise limited detection., Comment: 14 pages, 6 combined images