Context. Wide-field spectrometers are needed to deal with current astrophysical challenges that require multiband observations at millimeter wavelengths. An example of these is the KIDs Interferometer Spectrum Survey (KISS), which uses two arrays of kinetic inductance detectors (KIDs) coupled to a Martin-Puplett interferometer (MPI). KISS has a wide instantaneous field of view (1 deg in diameter) and a spectral resolution up to 1.45 GHz in the 120-180 GHz electromagnetic band. The instrument is installed on the 2.25 m Q-U-I JOint TEnerife telescope in Teide Observatory (Tenerife, Canary Islands), at an altitude of 2395 m above sea level. Aims. This work presents an original readout modulation method developed to improve the sky signal reconstruction accuracy for types of instruments for which a fast sampling frequency is required both to remove atmospheric fluctuations and to perform full spectroscopic measurements on each sampled sky position. Methods. We first demonstrate the feasibility of this technique using simulations. Then, we apply such a scheme to on-sky calibration. Results. We show that the sky signal can be reconstructed to better than 0.5% for astrophysical sources, and to better than 2% for large background variations such as in skydip, in an ideal noiseless scenario. The readout modulation method is validated by observations on-sky during the KISS commissioning campaign. Conclusions. We conclude that accurate photometry can be obtained for future KID-based MPI.
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