A new optical probing method with increased interferometric sensitivity for a low-density gas jet characterization is presented. The proposed technique employs a Michelson interferometer with a self-imaging object arm, which enables the relay imaging of the object on itself, and in this way, the phase sensitivity of the device is increased by a double propagation of the object laser beam through the gas jet. The wavelength of 405 nm was chosen to further increase the sensitivity by increasing the probe wavenumber. A low-density argon gas jet with various backing pressures was characterized by our method and by a commonly used Mach-Zehnder interferometer setup showing the expected twofold increase in the signal to noise ratio in the double pass configuration.