Astronomical Light Optical Hybrid Analysis (ALOHA@3.39 µm) is a new instrumental concept designed for high angular resolution astronomical imaging in the L Band. The originality of our experimental device is to include a frequency conversion process in each arm of the interferometer that frequency shifts the mid infrared signal to the near infrared domain. This method relaxes the stringent limitations due to the thermal noise background radiated by the instrument itself. The aim of this paper is to estimate the current sensitivity limit of the instrument and validate the ability to provide calibrated contrasts with a quasi monochromatic signal. We demonstrate the possibility to measure fringe contrasts greater than 94.5% with a signal-to-noise ratio close to 7. The flux level at the input of each arm of the interferometer is then equal to 100 fW. This would correspond to a zero magnitude star in the L Band for a 1 m 2 telescope surface and a 3 nm converted spectral bandwidth.