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Long-baseline interferometry is an important technique to spatially resolvebinary or multiple systems in close orbits. By combining several telescopestogether and spectrally dispersing the light, it is possible to detect faintcomponents around bright stars. Aims. We provide a rigorous and detailed methodto search for high-contrast companions around stars, determine the detectionlevel, and estimate the dynamic range from interferometric observations. Wedeveloped the code CANDID (Companion Analysis and Non-Detection inInterferometric Data), a set of Python tools that allows us to searchsystematically for point-source, high-contrast companions and estimate thedetection limit. The search pro- cedure is made on a N x N grid of fit, whoseminimum needed resolution is estimated a posteriori. It includes a tool toestimate the detection level of the companion in the number of sigmas. The codeCANDID also incorporates a robust method to set a 3{\sigma} detection limit onthe flux ratio, which is based on an analytical injection of a fake companionat each point in the grid. We used CANDID to search for the companions aroundthe binary Cepheids V1334 Cyg, AX Cir, RT Aur, AW Per, SU Cas, and T Vul.First, we showed that our previous discoveries of the components orbiting V1334Cyg and AX Cir were detected at > 13 sigmas. The companion around AW Per isdetected at more than 15 sigmas with a flux ratio of f = 1.22 +/- 0.30 %. Wemade a possible detection of the companion orbiting RT Aur with f = 0.22 +/-0.11 %. It was detected at 3.8{\sigma} using the closure phases only, and somore observations are needed to confirm the detection. We also set thedetection limit for possible undetected companions. We found that there is nocompanion with a spectral type earlier than B7V, A5V, F0V, B9V, A0V, and B9Vorbiting V1334 Cyg, AX Cir, RT Aur, AW Per, SU Cas, and T Vul, respectively.

Robust high-contrast companion detection from interferometric observations. The CANDID algorithm and an application to six binary Cepheids