Noise asaresolution limiting factor ingroupdelay dispersion measurements withspectrally integrated white light interferometers

A detailed theoretical andexperimental analysis oftherelationship between spectral resolution andinaccuracy ofgroupdelay dispersion determination ispresented. Therequired measurement timescales withthesixth poweroftheinverse spectral resolution. Manyultrafast processes, forexample ultrashort pulse generation andcharacterization, ultrabroadband compression, supercontinuum generation infibers etc., rely onknowing thegroup delay dispersion (GDD)ofoptical components. Thestandard technique tomeasure thedispersion overabroadband spectral range iswhite light interferometry. Spectral resolution, inaccuracy ofGDD determination andthemeasurement timearethekeyparameters ofanydispersion measurement. Thespectral resolution ofa Fourier transform spectrometer (scanning Michelson whitelight interferometer (1)) isdetermined bytheinverse ofthetotal scanning range overwhichthedataarerecorded. Thedata areaffected bynoise fromthelight source andfromthedetection electronics, causing arandominaccuracy inthe measured GDD;this inaccuracy canbereduced byproperly averaging theresults ofrepeated measurements. By increasing thescanning range, onecanachieve afiner spectral resolution, but, asweshow, this strongly increases the sensitivity tonoise. Therefore, foracertain specified accuracy oftheGDD measurement, therequired measurement timedepends critically onthespectral resolution. Hence, there isapractical limit fortheachievable spectral resolution. Ananalytical relationship between thespectral resolution, aninaccuracy ofGDD determination, themeasurement time andthebrightness ofthelight source hasbeenestablished. A keyresult isthat thestandard deviation ofGDD determination scales withthethird poweroftheinverse spectral resolution foragiven measurement time, andthe measurement timeforagiven GDD inaccuracy scales with thesixth poweroftheinverse spectral resolution. Different measurement regimes andtheinfluence ofrelevant experimental parameters arediscussed. Theestablished relationship hasbeenexperimentally verified withaspecially constructed fiber-coupled scanning white light (around 1550nm,50nmFWHM)Michelson interferometer. Animproved datacollection algorithm eliminates mechanical noise uptoseveral 100kHz.Ahighupdate rate ofseveral Hzsimplifies thealignment procedure.