Spectrograph stabilization using a single-delay interferometer
View Patent ↗Methods, systems and devices are described that improve optical spectroscopic techniques and particularly those that involve externally dispersed interferometer (EDI) techniques that result in an output spectrum having improved stability characteristics. The output spectrum minimizes the unwanted shifts in wavelength when the spectrograph component of the EDI instrument is under stresses that would otherwise shift or distort the wavelength positions of the spectrum.
1 . A method for improving spectrograph results obtained by an externally dispersed interferometer, the method comprising:
receiving information representing measured optical signals produced by the externally dispersed interferometer;
determining a nonfringing component from the received information;
obtaining an adjusted fringing component from the received information by at least:
determining a fringing component from the received information, the fringing component having a range of frequencies;
upshifting frequencies of the fringing component to reverse an interferometer heterodyning;
removing frequency components in an upper section of the range of frequencies of the fringing component, and
adjusting magnitudes of frequency components in a lower section of the range of frequencies of the fringing component based on one or more weights;
combining the nonfringing component with the adjusted fringing component to produce a combined output spectrum; and
performing an equalization operation to modify a shape of the combined output spectrum to produce an improved output spectrum with improved tolerance to wavelength shifts or distortions compared to output spectra obtained solely based on the received information representing the measured optical signals produced by the externally dispersed interferometer.
2 . The method of claim 1 , wherein determining the nonfringing component includes adding a plurality of signals contained in the received information associated with a plurality of phase shifts.
3 . The method of claim 2 , wherein adding the plurality of signals includes adding signals that correspond to a zero-degree, a 90-degree, a 180-degree and a 270-degree phase shift.
4 . The method of claim 1 , wherein determining the fringing component includes subtracting one or more signals associated with one or more phase shifts from one or more additional signals associated with one or more additional phase shifts.
5 . The method of claim 4 , wherein subtracting the one or more signals includes:
subtracting a first signal that corresponds to a 180-degree phase shift from a second signal that corresponds to a zero-degree phase shift, and
subtracting a third signal that corresponds to a 270-degree phase shift from a fourth signal that corresponds to a 90-degree phase shift.
6 . The method of claim 1 , wherein removing the frequency components comprises filtering out frequencies in an upper half of the range of frequencies.
7 . The method of claim 1 , wherein:
the nonfringing component is a representative of interferometer's spectral response,
spectral contents of the fringing component and the nonfringing component overlap, and
a separation between a peak of the fringing component and a peak of the nonfringing component is equal to a delay implemented in the interferometer.
8 . The method of claim 7 , wherein a contribution of the nonfringing component to the combined output spectrum is substantially zero at a spectral location of the peak of the fringing component.
9 . The method of claim 1 , wherein the adjusted fringing component is a counteracting component against the fringing component's movements due to an insult, thereby enabling correction of errors in the measured optical signals due to the insult.
10 . The method of claim 1 , wherein adjusting the magnitudes of the frequency components in the lower section of the range of frequencies includes:
determining a set of weights as a function of frequency such that upon combination of the nonfringing component with the adjusted fringing component, the combined output spectrum has a substantially zero phase up to a frequency that corresponds to a delay implemented in the interferometer, and
applying the determined weights to the frequency components in the lower section of the range frequencies.
11 . The method of claim 1 , wherein the equalization operation modifies the shape of the combined output spectrum to resemble a Gaussian profile.
12 . The method of claim 1 , further comprising, prior to performing the equalization operation, adding the frequency components in the upper section of the range of frequencies to obtain a boost in resolution.
13 . The method of claim 1 , further comprising:
(a) determining an estimate of the insult associated interferometer measurements,
(b) using the estimate of the insult to conduct a further determination of the nonfringing component and the adjusted fringing component; and
(c) obtaining a revised combined output spectrum.
14 . The method of claim 13 , further comprising repeating operations (a) through (c) a plurality of times.
15 . The method of claim 1 , further comprising producing interpolated weights obtained from a first spectral region and applying the interpolated weights to a second spectral region that is larger than the first spectral region after determining the nonfringing and the fringing components.
16 . The method of claim 1 , wherein the frequencies are a function of wavenumbers.
17 . The method of claim 1 , wherein upshifting frequencies of the fringing component includes, in wavenumber space, multiplying the fringing component spectrum by an imaginary Euler exponential that includes a frequency dependent delay, obtaining a real part of a resulting product for combination or comparison with the nonfringing component.
18 . An externally dispersed interferometric system, comprising:
an interferometer configured to receive light from an object, the interferometer having a single fixed-valued delay;
a spectrograph positioned to receive optical signals output from the interferometer and to produce spectrally dispersed optical signals;
a detector positioned to receive the spectrally dispersed optical signals from the spectrograph and to produce information representing signals detected thereon; and
a processor and a memory including instructions that are stored thereon, wherein the instructions when executed by the processor configure the processor to:
receive information representing measured optical signals produced by the detector,
determine a nonfringing component from the received information,
obtain an adjusted fringing component from the received information by at least:
determining a fringing component from the received information, the fringing component having a range of frequencies;
upshifting frequencies of the fringing component to reverse an interferometer heterodyning;
removing spatial frequency components in an upper section of the range of frequencies of the fringing component, and
adjusting magnitudes of frequency components in a lower section of the range of frequencies of the fringing component based on one or more weights;
combine the nonfringing component with the adjusted fringing component to produce a combined output spectrum; and
perform an equalization operation to modify a shape of the combined output spectrum to produce an improved output spectrum with improved tolerance to wavelength shifts or distortions compared to an output spectrum obtained solely based on the received information representing the measured optical signals produced by the detector.
19 . The system of claim 18 , wherein the instructions when executed by the processor configure the processor to determine the nonfringing component by operations that include adding a plurality of signals contained in the received information associated with a plurality of phase shifts, and determine the fringing component by operations that include subtracting one or more signals associated with one or more phase shifts from one or more additional signals associated with one or more additional phase shifts.
20 . The system of claim 18 , wherein:
the nonfringing component is a representative of interferometer's spectral response,
spectral contents of the fringing component and the nonfringing component overlap, and
a separation between a peak of the fringing component and a peak of the nonfringing component is equal to a delay implemented in the interferometer.
21 . The system of claim 18 , wherein adjusting the magnitudes of the frequency components in the lower section of the range of frequencies includes:
determining a set of weights as a function of frequency such that upon combination of the nonfringing component with the adjusted fringing component, the combined output spectrum has a substantially zero phase up to a frequency that corresponds to the delay implemented in the interferometer, and
applying the determined weights to the frequency components in the lower section of the range frequencies.
22 . The system of claim 18 , wherein the instructions when executed by the processor further configure the processor to, prior to performing the equalization operation, add the frequency components in the upper section of the range of frequencies to obtain a boost in resolution.
23 . The system of claim 18 , wherein the instructions when executed by the processor further configure the processor to:
(a) determine an estimate of an insult associated interferometer measurements,
(b) use the estimate of the insult to conduct a further determination of the nonfringing component and the adjusted fringing component; and
(c) obtain a revised combined output spectrum.
24 . The system of claim 18 , wherein the instructions when executed by the processor further configure the processor to produce interpolated weights obtained from a first spectral region and apply the interpolated weights to a second spectral region that is larger than the first spectral region after determining the nonfringing and the fringing components.