An ultrafast pulse analysis apparatus, comprising: a sampling system (16, 20, 106, 108) configured to receive at least one pulse under test, the sampling system (16, 20, 106, 108) is configured to define a plurality of sampling bins each spanning a frequency range of the at least one pulse under test, the plurality of sampling bins arranged over different frequency ranges so that the plurality of sampling bins define a continuous frequency range over at least a portion of a total frequency range of the at least one pulse under test, adjacent ones of the sampling bins overlapping in frequency ranges; collection optics (26, 112, 114, 118) configured to receive a plurality of pulse portions, each pulse portion derived from the at least one pulse under test and having a frequency range corresponding to at least one of the sampling bins; one or more detectors (14, 120) configured to receive the plurality of pulse portions from the collection optics (26, 112, 114, 118) and to output an electrical pulse signal corresponding to each of the plurality of pulse portions; and analysis electronics (30, 98, 124) configured to receive and digitize the electrical pulse signal, the analysis electronics configured to store a sonogram corresponding to the at least one pulse under test wherein the sonogram comprises sequences of digitized values of the electrical pulse signal at a plurality of time intervals, the digitized values within a sequence corresponding to the pulse portion defined by the at least one sampling bin, wherein the analysis electronics (30, 98, 124) is configured to perform phase retrieval on the sonogram, wherein the sonogram is defined so that spacing of the time intervals is independent of spacing of the plurality of sampling bins. a sampling system (16, 20, 106, 108) configured to receive at least one pulse under test, the sampling system (16, 20, 106, 108) is configured to define a plurality of sampling bins each spanning a frequency range of the at least one pulse under test, the plurality of sampling bins arranged over different frequency ranges so that the plurality of sampling bins define a continuous frequency range over at least a portion of a total frequency range of the at least one pulse under test, adjacent ones of the sampling bins overlapping in frequency ranges; collection optics (26, 112, 114, 118) configured to receive a plurality of pulse portions, each pulse portion derived from the at least one pulse under test and having a frequency range corresponding to at least one of the sampling bins; one or more detectors (14, 120) configured to receive the plurality of pulse portions from the collection optics (26, 112, 114, 118) and to output an electrical pulse signal corresponding to each of the plurality of pulse portions; and analysis electronics (30, 98, 124) configured to receive and digitize the electrical pulse signal, the analysis electronics configured to store a sonogram corresponding to the at least one pulse under test wherein the sonogram comprises sequences of digitized values of the electrical pulse signal at a plurality of time intervals, the digitized values within a sequence corresponding to the pulse portion defined by the at least one sampling bin, wherein the analysis electronics (30, 98, 124) is configured to perform phase retrieval on the sonogram,