CN113063495A - Interference pattern sub-sampling level alignment method and system of Fourier transform spectrometer - Google Patents
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Abstract
The invention provides a method and a system for aligning an interferogram of a Fourier transform spectrometer at a sub-sampling level, wherein the method comprises the following steps: step S1: respectively calculating the fast Fourier transform of two interferogram sequences with the same length; step S2: calculating the mutual position spectrum of the two interferograms according to the calculated fast Fourier transform of the two interferogram sequences with the same length; step S3: selecting a spectral channel participating in translation amount estimation according to a preset requirement; step S4: calculating the relative translation amount of the two interferograms based on the estimated spectral channel and the mutual position spectrum of the two interferograms; step S5: by interference pattern I1(n) relative spectral phase of the corresponding complex as a reference, and interference pattern I is mapped based on the relative translation amount2(n) performing phase compensation operation on the corresponding complex spectrum to obtain a compensated interference pattern I2(n) complex spectrum. According to the method for aligning the interferograms at the sub-sampling level, even if the interferograms are obviously asymmetric, the translation amount of the sub-sampling level between the interferograms can be obtained through the calculation of the mutual phase spectrums.
Description
Technical Field
The invention relates to the field of applied optics, in particular to a method and a system for aligning an interference pattern of a Fourier transform spectrometer at a sub-sampling level.
Background
The Fourier transform spectrometer is a common spectrometer, firstly obtains an interferogram sequence of target radiation through interference spectroscopy, and then obtains spectral component information of the target radiation by utilizing discrete Fourier transform. In the process of generating a plurality of interferograms of an actual fourier transform spectrometer, due to possible deviation of sampling positions, preprocessing of aligning sampling points is needed in spectrum calculation of many occasions, such as: 1) when a plurality of interference patterns radiated by the same target need to be superposed and averaged in order to improve the signal to noise ratio; 2) the calibration coefficient is obtained when the calibration coefficient is calibrated with actually measured interferogram data; 3) the alignment of the forward and reverse interferograms of a fourier transform spectrometer is used.
The purpose of the interference pattern sub-sampling level alignment of the Fourier transform spectrometer is to enable all the spectral patterns to be subjected to superposition, comparison and other analysis under the same phase, and the alignment precision of the interference patterns in the preprocessing directly influences the subsequent processing precision. The current interference pattern alignment method is a method based on zero optical path difference position determination, and all interference patterns are aligned to the same reference according to the zero optical path difference position. For example, in document [1] (von gorgeous, interferogram zero optical path difference position determination method, 2017), the offset of the zero optical path difference position is obtained by performing linear regression analysis on the residual phase; document [2] (jiang outline, white light interference zero optical path position pickup algorithm based on symmetry judgment, 2013) gives a fitting method of a zero optical path position based on symmetry criterion of an interference pattern.
Patent document CN1540282A (application number: 200310106893.X) discloses a method for quickly and accurately measuring the position of zero optical path difference of interference of a two-beam broadband light source. The broadband light formed by the LED (1) and the LED (2) light source enters the unidirectional coupler (3), the bidirectional coupler (4) respectively couples the light emitted by the unidirectional coupler to the optical sensor (5) and the matching arm (6), and couples the reflected light of the optical sensor and the matching arm out to the interference detector (7). The wavelength 1/4 of the interference light is used as the sampling step length, the interference light intensity of the sampling point is detected at equal intervals, the distribution of the interference modulation degree is obtained by the calculation formula, and the maximum position of the distribution is the position of the zero optical path difference of the two-beam interference. The patent uses the interferogram maximum as the zero optical path difference position. None of these methods based on zero-opd position determination are applicable to interferogram phase alignment when fourier transform spectrometers are due to the presence of significantly asymmetric interferograms.
Patent document CN108827473A (application number: 201810661557.8) discloses a fourier transform infrared spectrometer complex radiometric calibration processing method, which includes the following steps: firstly, inputting interference pattern data and blackbody emissivity data of different blackbody temperature points. And step two, the reverse interference pattern is reversely ordered and is aligned with the forward interference pattern through correlation operation. And thirdly, carrying out fast Fourier transform on the multiple groups of interferogram data of each temperature point to obtain a plurality of spectrums, and averaging results at the same temperature. And step four, calculating the theoretical target radiance according to the blackbody emissivity and a Planck formula. And fifthly, performing complex linear fitting on each wave number position in the spectral range of the Fourier transform infrared spectrometer to obtain a calibration coefficient corresponding to each wave number, wherein the calibration coefficient comprises response gain and background radiance. And step six, calibrating the complex spectral digital quantity to the input radiance according to a complex calibration equation.
Aiming at the particularity of the spectrum phase of the Fourier transform spectrometer and combining the translation characteristic of Fourier transform, the method provides a method for obtaining the sub-sampling level translation between two interferograms. The method is suitable for spectrum calculation preprocessing in various occasions.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method and a system for aligning an interferogram of a Fourier transform spectrometer at a sub-sampling level.
The invention provides a method for aligning an interference pattern of a Fourier transform spectrometer at a sub-sampling level, which comprises the following steps:
step S1: respectively calculating the fast Fourier transform of two interferogram sequences with the same length;
step S2: calculating the mutual position spectrum of the two interferograms according to the calculated fast Fourier transform of the two interferogram sequences with the same length;
step S3: selecting a spectral channel participating in translation amount estimation according to a preset requirement;
step S4: calculating the relative translation amount of the two interferograms based on the estimated spectral channel and the mutual position spectrum of the two interferograms;
step S5: by interference pattern I1(n) relative spectral phase of the corresponding complex as a reference, and interference pattern I is mapped based on the relative translation amount2(n) performing phase compensation operation on the corresponding complex spectrum to obtain a compensated interference pattern I2(n) complex spectrum.
Preferably, the step S1 includes:
when two interferogram sequences I1(n)、I2(N) are all N, the fast Fourier transforms are respectively F1(σ)、F2(σ)；
F1(σ)＝fft{I1(n)}
F2(σ)＝fft{I2(n)}
Wherein n represents the sequence number of the sampling point of the interferogram; sigma is a spectral channel; fft denotes fast fourier transform.
Preferably, the step S2 includes:
wherein R (σ) represents a mutual phase spectrum;
represents a complex number F2(σ) conjugation.
Preferably, the step S3 includes: selecting
For spectral channels greater than a threshold T, the expression for threshold T is as follows:
where max represents taking the maximum value.
Preferably, the step S4 includes: calculating the data of the estimated spectral channel by a least square method to obtain the relative translation amount of the two interferograms;
wherein | · | purple sweet2Representing the vector two-norm made up of the estimated spectral channels, δ representing the relative amount of translation, and σ representing the estimated spectral channels.
Preferably, the step S5 includes: by interference pattern I1(n) taking the corresponding complex spectral phase as a reference, and taking the interference pattern I as a reference2(n) performing phase compensation operation on the corresponding complex spectrum;
C2(σ)＝F2(σ)·ei2πδσ
wherein, C2(σ) is an interferogram I2(n) phase compensated complex spectrum.
The invention provides an interference pattern sub-sampling level alignment system of a Fourier transform spectrometer, which comprises:
module M1: respectively calculating the fast Fourier transform of two interferogram sequences with the same length;
module M2: calculating the mutual position spectrum of the two interferograms according to the calculated fast Fourier transform of the two interferogram sequences with the same length;
module M3: selecting a spectral channel participating in translation amount estimation according to a preset requirement;
module M4: calculating the relative translation amount of the two interferograms based on the estimated spectral channel and the mutual position spectrum of the two interferograms;
module M5: by interference pattern I1(n) relative spectral phase of the corresponding complex as a reference, and interference pattern I is mapped based on the relative translation amount2(n) performing phase compensation operation on the corresponding complex spectrum to obtain a compensated interference pattern I2(n) complex spectrum.
Preferably, said module M1 comprises:
when two interferogram sequences I1(n)、I2(N) are all N, the fast Fourier transforms are respectively F1(σ)、F2(σ)；
F1(σ)＝fft{I1(n)}
F2(σ)＝fft{I2(n)}
Wherein n represents the sequence number of the sampling point of the interferogram; sigma is a spectral channel; fft denotes fast fourier transform.
Preferably, said module M2 comprises:
wherein R (σ) represents a mutual phase spectrum;
represents a complex number F2(σ) conjugation;
the module M3 includes: selecting
For spectral channels greater than a threshold T, the expression for threshold T is as follows:
where max represents taking the maximum value.
Preferably, said module M4 comprises: calculating the data of the estimated spectral channel by a least square method to obtain the relative translation amount of the two interferograms;
wherein | · | purple sweet2Representing the vector two norm formed by the estimated spectral channels, delta representing the relative translation amount, and sigma representing the estimated spectral channels;
the module M5 includes: by interference pattern I1(n) taking the corresponding complex spectral phase as a reference, and taking the interference pattern I as a reference2(n) performing phase compensation operation on the corresponding complex spectrum;
C2(σ)＝F2(σ)·ei2πδσ
wherein, C2(σ) is an interferogram I2(n) phase compensated complex spectrum.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the interference pattern sub-sampling level alignment method, even if the interference patterns are obviously asymmetric, the translation amount of the sub-sampling level between the interference patterns can be obtained through the calculation of the mutual phase spectrums;
2. the method is reasonable, simple in calculation and easy to implement, and can be widely applied to spectrum calculation of the Fourier transform spectrometer.
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Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 shows two interferograms of a Fourier transform spectrometer observing different targets.
Fig. 3 shows the mutual position spectrum (phase angle) of the two interferograms.
FIG. 4 is a diagram of spectral channels involved in the estimation of translation.
Fig. 5 shows the mutual phase spectrum (phase angle) of two interferograms after phase compensation of the interferogram 2.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
Aiming at the situation that an asymmetric interferogram may exist in a Fourier transform spectrometer, the invention aims to provide an interferogram sub-sampling level alignment method of the Fourier transform spectrometer, which is universally applicable and can obtain the interferogram translation amount of a sub-sampling level.
Example 1
The invention provides a method for aligning an interference pattern of a Fourier transform spectrometer at a sub-sampling level, which comprises the following steps:
step S1: respectively calculating the fast Fourier transform of two interferogram sequences with the same length;
step S2: calculating the mutual position spectrum of the two interferograms according to the calculated fast Fourier transform of the two interferogram sequences with the same length;
step S3: selecting a spectral channel participating in translation amount estimation according to a preset requirement;
step S4: calculating the relative translation amount of the two interferograms based on the estimated spectral channel and the mutual position spectrum of the two interferograms;
step S5: by interference pattern I1(n) relative spectral phase of the corresponding complex as a reference, and interference pattern I is mapped based on the relative translation amount2(n) performing phase compensation operation on the corresponding complex spectrum to obtain a compensated interference pattern I2(n) complex spectrum.
Specifically, the step S1 includes:
when two interferogram sequences I1(n)、I2(N) are all N, the fast Fourier transforms are respectively F1(σ)、F2(σ)；
F1(σ)＝fft{I1(n)}
F2(σ)＝fft{I2(n)}
Wherein n represents the sequence number of the sampling point of the interferogram; sigma is a spectral channel; fft denotes fast fourier transform.
Specifically, the step S2 includes:
wherein R (σ) represents a mutual phase spectrum;
represents a complex number F2(σ) conjugation.
Specifically, the step S3 includes: selecting
For spectral channels greater than a threshold T, the expression for threshold T is as follows:
where max represents taking the maximum value.
Specifically, the step S4 includes: when obtaining
After the spectrum channels are larger than the threshold value T, the data of the channels can be calculated by a least square method to obtain the relative translation quantity delta of the two interferograms;
wherein | · | purple sweet2Representing the vector two-norm made up of the estimated spectral channels, δ representing the relative amount of translation, and σ representing the estimated spectral channels.
Specifically, the step S5 includes: by interference pattern I1(n) taking the corresponding complex spectral phase as a reference, and taking the interference pattern I as a reference2(n) corresponding complex spectraPerforming phase compensation operation;
C2(σ)＝F2(σ)·ei2πδσ
wherein, C2(σ) is an interferogram I2(n) phase compensated complex spectrum.
The invention provides an interference pattern sub-sampling level alignment system of a Fourier transform spectrometer, which comprises:
module M1: respectively calculating the fast Fourier transform of two interferogram sequences with the same length;
module M2: calculating the mutual position spectrum of the two interferograms according to the calculated fast Fourier transform of the two interferogram sequences with the same length;
module M3: selecting a spectral channel participating in translation amount estimation according to a preset requirement;
module M4: calculating the relative translation amount of the two interferograms based on the estimated spectral channel and the mutual position spectrum of the two interferograms;
module M5: by interference pattern I1(n) relative spectral phase of the corresponding complex as a reference, and interference pattern I is mapped based on the relative translation amount2(n) performing phase compensation operation on the corresponding complex spectrum to obtain a compensated interference pattern I2(n) complex spectrum.
Specifically, the module M1 includes:
when two interferogram sequences I1(n)、I2(N) are all N, the fast Fourier transforms are respectively F1(σ)、F2(σ)；
F1(σ)＝fft{I1(n)}
F2(σ)＝fft{I2(n)}
Wherein n represents the sequence number of the sampling point of the interferogram; sigma is a spectral channel; fft denotes fast fourier transform.
Specifically, the module M2 includes:
wherein R is(σ) represents a cross-phase spectrum;
represents a complex number F2(σ) conjugation;
the module M3 includes: selecting
For spectral channels greater than a threshold T, the expression for threshold T is as follows:
where max represents taking the maximum value.
Specifically, the module M4 includes: when obtaining
After the spectrum channels are larger than the threshold value T, the data of the channels can be calculated by a least square method to obtain the relative translation quantity delta of the two interferograms;
wherein | · | purple sweet2Representing the vector two norm formed by the estimated spectral channels, delta representing the relative translation amount, and sigma representing the estimated spectral channels;
the module M5 includes: by interference pattern I1(n) taking the corresponding complex spectral phase as a reference, and taking the interference pattern I as a reference2(n) performing phase compensation operation on the corresponding complex spectrum;
C2(σ)＝F2(σ)·ei2πδσ
wherein, C2(σ) is an interferogram I2(n) phase compensated complex spectrum.
Example 2
Example 2 is a modification of example 1
Fourier transform spectroscopyThe interferometer obtains an interferogram of target radiation by using an interference spectroscopy technology, and then obtains a spectrogram through Fourier transform calculation. Theoretically, the interferogram should be even-symmetric about the zero-optical path difference position, the spectrogram is real, and the phase spectrum is constant at 0. In the actual sampling process, due to the existence of factors such as electronic sampling delay, the actual sampling position of an interferogram sequence may have a certain offset, so that the interferogram cannot be exactly acquired at a zero optical path difference position, the interferogram is not strictly even and symmetrical, and the non-ideality of an internal optical path of the interferometer causes the asymmetry of the interferogram, so that the spectrogram is complex and has a nonlinear phase spectrum. If two interferograms are respectively marked as I1(n)、I2And (N), wherein N is the number of the sampling points of the interferogram, N is 1,2, …, and N is the total number of the sampling points of the interferogram.
F1(σ)＝fft{I1(n)} (1)
F2(σ)＝fft{I2(n)} (2)
Wherein F1(σ)、F2(σ) are interferograms I respectively1(n)、I2(n) the corresponding discrete Fourier transform spectrum is a complex value, and σ represents the spectral channel.
When in use
Then, the mutual position spectrum R (sigma) of the two interferograms satisfies
Wherein, delta is the relative translation amount of the two interferograms (interferogram I)2(n) relative to I1The amount of leftward translation of (n).
Because the radiation actually reaching the detector by the actual Fourier transform spectrometer is a signal with limited spectral bandwidth, namely, the radiation meets the requirement of
The spectrum of the condition is only of limited spectral range, taking into account in addition, if part, of the laboratory measurement or in-orbit observationThe spectral channels have strong gas (such as water vapor and carbon dioxide) absorption lines, the radiation signals of the channels are weak, and the mutual position spectrum calculated by the formula (3) can be inaccurate. In order to improve the calculation accuracy of the relative translation amount, the spectral channels in the formula (3) are screened, and the channels with strong signal amplitude are selected.
In actual operation, can choose
Spectral channels greater than a threshold T, the threshold T being determined by:
where max represents taking the maximum value.
When obtaining
After the spectral channels are larger than the threshold value T, the data of the channels can be calculated by a least square method to obtain the relative translation quantity delta of the two interferograms.
Wherein | · | purple sweet2Representing the vector two norm made up of the selected channels.
After one interferogram is selected as a reference, the translation amount of other interferograms relative to the reference interferogram can be respectively calculated. After the translation amount is obtained, if the translation amount is an integer value (integer sampling interval), all interferograms can be unified in the same phase through interferogram data shifting. But for sub-sample level shifts, the amount of shift δ is real and is typically less than 1 sample interval. For the sub-sampling level translation of the interferogram, the interferogram needs to be resampled, and the information finally required to be acquired by the Fourier transform spectrometer is the spectral information of target radiation, so that the phase compensation of the sub-sampling level can be directly performed on a complex spectrum, and the spectrograms corresponding to all the interferograms are unified under the same phase.
If it is an interference pattern I1(n) taking the corresponding complex spectral phase as a reference, and taking the interference pattern I as a reference2(n) the corresponding complex spectrum needs to be subjected to the following phase compensation operation:
C2(σ)＝F2(σ)·ei2πδσ (6)
wherein C is2(σ) is an interferogram I2(n) phase compensated complex spectrum.
The following describes an implementation of the present invention with reference to an interferogram of a fourier transform spectrometer, and fig. 2 shows the interferogram of the fourier transform spectrometer when observing different targets. It can be seen that the interferograms are asymmetric to some extent, and it is difficult to determine the zero-optical path difference positions of interferograms 1 and 2 by conventional methods.
The calculation results of the mutual phase spectra of all the spectral channels are shown in fig. 3 (the mutual phase spectra are complex numbers with a modulus of 1, and fig. 3 shows the corresponding phase angles of the complex number mutual phase spectra). The spectral channels involved in the estimation of the translation amount are obtained by threshold control as shown in fig. 4.
The translation estimation by least squares was-7.8366 e-05cm, corresponding to 0.5055 times the interferogram sampling interval. After the phase compensation of the sub-sampling stage is performed on the interferogram 2 through the step five, the mutual phase-spectrum angle of the two interferograms is shown in fig. 5. As can be seen from fig. 5, the mutual phase spectrum is close to 0.
Those skilled in the art will appreciate that, in addition to implementing the systems, apparatus, and various modules thereof provided by the present invention in purely computer readable program code, the same procedures can be implemented entirely by logically programming method steps such that the systems, apparatus, and various modules thereof are provided in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system, the device and the modules thereof provided by the present invention can be considered as a hardware component, and the modules included in the system, the device and the modules thereof for implementing various programs can also be considered as structures in the hardware component; modules for performing various functions may also be considered to be both software programs for performing the methods and structures within hardware components.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.
Claims (10)
1. A method for aligning an interferogram at a sub-sampling level of a fourier transform spectrometer, comprising:
step S1: respectively calculating the fast Fourier transform of two interferogram sequences with the same length;
step S2: calculating the mutual position spectrum of the two interferograms according to the calculated fast Fourier transform of the two interferogram sequences with the same length;
step S3: selecting a spectral channel participating in translation amount estimation according to a preset requirement;
step S4: calculating the relative translation amount of the two interferograms based on the estimated spectral channel and the mutual position spectrum of the two interferograms;
step S5: by interference pattern I1(n) relative spectral phase of the corresponding complex as a reference, and interference pattern I is mapped based on the relative translation amount2(n) performing phase compensation operation on the corresponding complex spectrum to obtain a compensated interference pattern I2(n) complex spectrum.
2. The method for aligning the sub-sampling level of the interferogram of the fourier transform spectrometer as recited in claim 1, wherein the step S1 comprises:
when two interferogram sequences I1(n)、I2(N) are all N, the fast Fourier transforms are respectively F1(σ)、F2(σ)；
F1(σ)＝fft{I1(n)}
F2(σ)＝fft{I2(n)}
Wherein n represents the sequence number of the sampling point of the interferogram; sigma is a spectral channel; fft denotes fast fourier transform.
3. The method for aligning the sub-sampling level of the interferogram of the fourier transform spectrometer as recited in claim 1, wherein the step S2 comprises:
wherein R (σ) represents a mutual phase spectrum;
represents a complex number F2(σ) conjugation.
4. The method for aligning the sub-sampling level of the interferogram of the fourier transform spectrometer as recited in claim 1, wherein the step S3 comprises: selecting
For spectral channels greater than a threshold T, the expression for threshold T is as follows:
where max represents taking the maximum value.
5. The method for aligning the sub-sampling level of the interferogram of the fourier transform spectrometer as recited in claim 1, wherein the step S4 comprises: calculating the data of the estimated spectral channel by a least square method to obtain the relative translation amount of the two interferograms;
wherein | andi·||2Representing the vector two-norm made up of the estimated spectral channels, δ representing the relative amount of translation, and σ representing the estimated spectral channels.
6. The method for aligning the sub-sampling level of the interferogram of the fourier transform spectrometer as recited in claim 1, wherein the step S5 comprises: by interference pattern I1(n) taking the corresponding complex spectral phase as a reference, and taking the interference pattern I as a reference2(n) performing phase compensation operation on the corresponding complex spectrum;
C2(σ)＝F2(σ)·ei2πδσ
wherein, C2(σ) is an interferogram I2(n) phase compensated complex spectrum.
7. An interferogram sub-sampling level alignment system for a fourier transform spectrometer comprising:
module M1: respectively calculating the fast Fourier transform of two interferogram sequences with the same length;
module M2: calculating the mutual position spectrum of the two interferograms according to the calculated fast Fourier transform of the two interferogram sequences with the same length;
module M3: selecting a spectral channel participating in translation amount estimation according to a preset requirement;
module M4: calculating the relative translation amount of the two interferograms based on the estimated spectral channel and the mutual position spectrum of the two interferograms;
module M5: by interference pattern I1(n) relative spectral phase of the corresponding complex as a reference, and interference pattern I is mapped based on the relative translation amount2(n) performing phase compensation operation on the corresponding complex spectrum to obtain a compensated interference pattern I2(n) complex spectrum.
8. The system for alignment of an interferogram at a sub-sampling level of a fourier transform spectrometer as claimed in claim 7, wherein the module M1 comprises:
when two interferogram sequences I1(n)、I2(N) the lengths are N, then the fast Fourier transformAre transformed into F1(σ)、F2(σ)；
F1(σ)＝fft{I1(n)}
F2(σ)＝fft{I2(n)}
Wherein n represents the sequence number of the sampling point of the interferogram; sigma is a spectral channel; fft denotes fast fourier transform.
9. The system for alignment of an interferogram at a sub-sampling level of a fourier transform spectrometer as claimed in claim 7, wherein the module M2 comprises:
wherein R (σ) represents a mutual phase spectrum;
represents a complex number F2(σ) conjugation;
the module M3 includes: selecting
For spectral channels greater than a threshold T, the expression for threshold T is as follows:
where max represents taking the maximum value.
10. The system for alignment of an interferogram at a sub-sampling level of a fourier transform spectrometer as claimed in claim 7, wherein the module M4 comprises: calculating the data of the estimated spectral channel by a least square method to obtain the relative translation amount of the two interferograms;
wherein | · | purple sweet2Representing the vector two norm formed by the estimated spectral channels, delta representing the relative translation amount, and sigma representing the estimated spectral channels;
the module M5 includes: by interference pattern I1(n) taking the corresponding complex spectral phase as a reference, and taking the interference pattern I as a reference2(n) performing phase compensation operation on the corresponding complex spectrum;
C2(σ)＝F2(σ)·ei2πδσ
wherein, C2(σ) is an interferogram I2(n) phase compensated complex spectrum.
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