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We study a technique to measure the radio-frequency (RF) spectrum of an optical signal based on nonlinear optics. The conventional approach, based on fast photodetection and analysis of the generated photocurrent via electronics means, is replaced by a nonlinear interaction of the source under test with a quasimonochromatic source followed by an optical spectrum measurement. Our technique has the advantage of an all-optical measurement that can provide a much larger bandwidth than electronic alternatives. The properties of this diagnostic, such as resolution and bandwidth, are studied. Typical applications to the monitoring of optical signals are presented.