Context : Long-baseline interferometry is an important technique to spatially resolve binary or multiple systems in close orbits .
By combining several telescopes together and spectrally dispersing the light , it is possible to detect faint components around bright stars in a few hours of observations .

Aims : We provide a rigorous and detailed method to search for high-contrast companions around stars , determine the detection level , and estimate the dynamic range from interferometric observations .

Methods : We developed the code CANDID ( Companion Analysis and Non-Detection in Interferometric Data ) , a set of Python tools that allows us to search systematically for point-source , high-contrast companions and estimate the detection limit using all interferometric observables , i.e. , the squared visibilities , closure phases and bispectrum amplitudes .
The search procedure is made on a N \times N grid of fit , whose minimum needed resolution is estimated a posteriori .
It includes a tool to estimate the detection level of the companion in the number of sigmas .
The code CANDID also incorporates a robust method to set a 3 \sigma detection limit on the flux ratio , which is based on an analytical injection of a fake companion at each point in the grid .
Our injection method also allows us to analytically remove a detected component to 1 ) search for a second companion ; and 2 ) set an unbiased detection limit .

Results : We used CANDID to search for the companions around the 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 V1334 Cyg and AX Cir were detected at > 25 \sigma and > 13 \sigma , respectively .
The astrometric positions and flux ratios provided by CANDID for these two stars are in good agreement with our previously published values .
The companion around AW Per is detected at more than 15 \sigma with a flux ratio of f = 1.22 \pm 0.30 % , and it is located at \rho = 32.16 \pm 0.29 mas and PA = 67.1 \pm 0.3 ^ { \circ } .
We made a possible detection of the companion orbiting RT Aur with f = 0.22 \pm 0.11 % , and at \rho = 2.10 \pm 0.23 mas and PA = -136 \pm 6 ^ { \circ } .
It was detected at 3.8 \sigma using the closure phases only , and so more observations are needed to confirm the detection .
No companions were detected around SU Cas and T Vul .
We also set the detection limit for possible undetected companions around these stars .
We found that there is no companion with a spectral type earlier than B7V , A5V , F0V , B9V , A0V , and B9V orbiting the Cepheids V1334 Cyg , AX Cir , RT Aur , AW Per , SU Cas , and T Vul , respectively .
This work also demonstrates the capabilities of the MIRC and PIONIER instruments , which can reach a dynamic range of 1:200 , depending on the angular distance of the companion and the ( u,v ) plane coverage .
In the future , we plan to work on improving the sensitivity limits for realistic data through better handling of the correlations .

Conclusions :