Three-phase spectral interferometry with improved signal retrieval

An interferometric method for determining characteristics of an input optical signal using a three-phase interferometric system, comprising:

• providing the input optical signal to a first input of a three-by-three optical splitter;
• providing a reference optical signal to a second input of the three-by-three optical splitter;
• measuring spectra associated with three interferograms produced at a first, a second and a third output of the three-by-three optical splitter using a plurality of spectrometers, each of the three interferograms being a function of a plurality of parameters including a first parameter that defines a spectral response amplitude of the reference optical signal for the corresponding interferogram and a second parameter that defines a spectral response amplitude of the input optical signal for the corresponding interferogram, and
• determining an amplitude value and a phase value of the input optical signal from information obtained from the measured spectra, wherein:
• prior to providing the input optical signal and the reference optical signal for determining characteristics of an input optical signal, performing a calibration procedure to characterize point spread functions across the plurality of spectrometers used for measuring interferograms output from the three-by-three optical splitter, the calibration operation including, for each interferometer:
• constructing a regression matrix and determining a correction factor that allow spectra of the input optical signal to be retrieved from a background subtracted image according to a linear fitting model;
• and
• determining the first and the second parameter values as part of the calibration procedure that injects a broadband source into the first and the second input of the three-by-three optical splitter one at a time and making corresponding spectral measurements, wherein the first and the second parameter values are determined based on the following relationships:
• A
• RN
• =
• R
• N
• -
• ⁢
• Measured
• /
• R
• Retrieved
• ,
• and
• A
• SN
• =
• S
• N
• -
• ⁢
• Measured
• /
• S
• Retrieved
• wherein:
• ARN represents the first parameter for the Nth spectrometer, where N has values of 1, 2 and 3,
• ASN represents the second parameter for the Nth spectrometer, where N has values of 1, 2 and 3,
• SN_Measured and RN_Measured are respectively spectra of the broadband source measured on spectrometer N at the corresponding output of the three-by-three optical splitter,
• SRetrieved is a retrieved signal spectra computed using all N spectral measurements associated with the broadband source that is injected into the first input of the three-by-three optical splitter, and
• RRetrieved is a retrieved reference signal spectra computed using all N spectral measurements associated with the broadband source that is injected into the second input of the three-by-three optical splitter.

A device for determining characteristics of an input optical signal, comprising:

• a processor and a non-transitory memory with instructions stored thereon, wherein the instructions upon execution by the processor cause the processor to:
• measure spectra associated with three interferograms produced at a first, a second and a third output of a three-by-three optical splitter using a plurality of spectrometers, wherein the three-by-three optical splitter is configured to receive a reference optical signal and the input optical signal at two different input ports thereof;
• and
• determine an amplitude value and a phase value of the input optical signal from information obtained from the measured spectra, wherein:
• prior to determining an amplitude value and a phase value of the input optical signal, the instructions upon execution by the processor configure the processor to perform a calibration procedure to characterize point spread functions across the plurality of spectrometers used for measuring interferograms output from the three-by-three optical splitter, the calibration operation including, for each interferometer:
• constructing a regression matrix and determining a correction factor that allow spectra of the input optical signal to be retrieved from a background subtracted image according to a linear fitting model, wherein the regression matrix is generated from calibration images acquired at multiple wavelengths and is configured to compensate for wavelength-dependent point spread function distortions and non-uniform spectral response of each spectrometer in retrieving spectra associated with the interferograms.