An arrangement (1; 10; 40; 60) for measuring frequency differences in a frequency interval in order to measure an observable comprising: at least one light source (2; 11, 12; 41, 42; 62, 63, 64) for generating a first light component of a first frequency comprising a first mode and a second light component of a second frequency comprising a second mode orthogonal to said first mode; an optical resonator (4; 17; 45; 69) having differing optical path lengths for the first and second modes within a frequency interval including the first and second frequencies, at least one of the optical path lengths being variable depending on the observable and a dependence of the respective optical path length on the observable being different for said first and second modes, wherein the at least one light source is optically coupled to the optical resonator for feeding the first and second light components into the optical resonator, and the at least one light source comprises a first light source (11; 41; 63) for generating the first light component and a second light source (12; 42; 64) for generating the second light component, the first and second light source being coupled to the optical resonator and being tunable independently of each other through said frequency interval; a detector unit (6; 23 52; 74) being coupled to the optical resonator for coupling out the light components and being configured for detecting a frequency difference between a resonance frequency of the optical resonator for the first mode and a resonance frequency of the optical resonator for the second mode; a mode converter (20; 50; 72) arrangement situated between the optical resonator and the detector unit, the mode converter arrangement configured to rotate the first and/or second mode such that the modes comprise components in a matching direction; and a control unit for controlling the at least one light source and the optical resonator, the control unit configured such that a scan time through the frequency interval is different for the first and second light sources, and the scan time of the first light source at least five times the scan time of the second light source. at least one light source (2; 11, 12; 41, 42; 62, 63, 64) for generating a first light component of a first frequency comprising a first mode and a second light component of a second frequency comprising a second mode orthogonal to said first mode; an optical resonator (4; 17; 45; 69) having differing optical path lengths for the first and second modes within a frequency interval including the first and second frequencies, at least one of the optical path lengths being variable depending on the observable and a dependence of the respective optical path length on the observable being different for said first and second modes, wherein the at least one light source is optically coupled to the optical resonator for feeding the first and second light components into the optical resonator, and the at least one light source comprises a first light source (11; 41; 63) for generating the first light component and a second light source (12; 42; 64) for generating the second light component, the first and second light source being coupled to the optical resonator and being tunable independently of each other through said frequency interval; a detector unit (6; 23 52; 74) being coupled to the optical resonator for coupling out the light components and being configured for detecting a frequency difference between a resonance frequency of the optical resonator for the first mode and a resonance frequency of the optical resonator for the second mode; a mode converter (20; 50; 72) arrangement situated between the optical resonator and the detector unit, the mode converter arrangement configured to rotate the first and/or second mode such that the modes comprise components in a matching direction; and a control unit for controlling the at least one light source and the optical resonator, the control unit configured such that a scan time through the frequency interval is different for the first and second light sources, and the scan time of the first light source at least five times the scan time of the second light source.