Improving the resolution of lock-in measurements by tailoring the modulation

Phase-sensitive detection with a lock-in amplifier is a powerful, general measurement scheme finding widespread applications in science and technology. In several cases, however, its performance is limited by the modulation broadening, i.e. the resolution loss due to the finite amplitude of the modulation that, in this technique, is applied to the system under study. We demonstrate that this broadening can be reduced by employing a modulation function different from the commonly used sinusoid, which is non-optimal in this respect. On the basis of a mathematical analysis of the lock-in output, we provide a modulation function optimized for the detection at twice its frequency, testing the resulting performance in an STM–IETS experiment. Our findings can be directly applied whenever a lock-in is used to measure a second derivative, and are easily extendible to other derivatives as well.