Spectrometer light intensity correlation Mueller matrix four-element spectrum measurement method

Abstract

The invention discloses a spectrograph light intensity correlation Mueller matrix four-element spectrum measurement method. According to the method, the relative intensity data [Iti, theta i] of light received by the ith pixel unit of the spectrometer CCD, which is obtained by a measuring device for the light intensity related Mueller matrix four-element spectrum of the spectrometer based on an angle scanning method, is substituted into a principle formula of the relative intensity of light received by the ith pixel unit of the spectrometer CCD. And traversing the range of [0, 2pi] where theta i is located, selecting four theta i values according to a certain rule, establishing an equation set with four Iti measured values corresponding to the four theta i values, solving and normalizing to obtain a Mueller matrix element related to the light intensity of the spectrograph corresponding to the wavelength lambda i. The measurement method is an external measurement method, and the spectrograph is not disassembled; all light intensity related Mueller matrix element spectrums are measured by adding a retardation curve of a 1 / 4 wave plate, and the method is not only suitable for a single spectrograph, but also suitable for a spectrograph system; the core optical device only uses the polarizer and the rotary 1 / 4 wave plate, the related hardware cost is low, and the method is simple and rapid; the environment adaptability is good.

Description

Technical Field

[0001] The present invention relates to the field of spectrometer detection and applications. Specifically, the present invention relates to a method for testing the four-element spectrum of the Mueller matrix related to the light intensity of a spectrometer. Background Art

[0002] In the measurement of polarized light spectra that combine the polarization and spectrum of light, a spectrometer is often used. However, spectrometers or spectrometer systems, such as Czerny-Turner spectrometers or fiber spectrometers combined with optical fibers, have non-negligible polarization effects. When composite light containing different polarization states is incident on the spectrometer CCD, due to the polarization effect of the spectrometer, there is a large error between the spectral power distribution of the spectral lines captured by the spectrometer and the true spectral power distribution of the incident light. Even some spectral lines will be extinguished and not captured. Atoms of substances will emit light of a specific polarization state under specific restrictions, such as the Zeeman effect; atoms of substances will absorb light of the corresponding polarization state under specific restrictions, such as magnetic circular dichroism. Therefore, the polarization effect of the spectrometer needs to be eliminated by certain methods in the spectral measurement of polarized light.

[0003] The most commonly used method is to install an integrating sphere in front of the spectrometer to depolarize the light incident on the spectrometer. This method will cause a decrease in the intensity of the incident light for absorption spectra, resulting in a decrease in the signal-to-noise ratio of the overall test. If the integrating sphere is connected to the spectrometer through an optical fiber, due to the polarization that may be brought about by the optical fiber, the polarization effect of the spectrometer is still not perfectly overcome. In addition, the performance of the integrating sphere is positively correlated with its volume, which is not conducive to simplifying and integrating the measurement optical path, and the integrating sphere brings additional device costs. Another method is to measure the matrix elements related to the light intensity of the Mueller matrix of the spectrometer or spectrometer system, and restore the spectral power distribution and polarization state of the incident light through the polarization information carried by the Mueller matrix elements of the spectrometer or spectrometer system. This method does not require adding depolarizing devices, does not lose the incident light intensity, ensures the test accuracy, and is convenient for integrating the test optical path and reducing costs.

[0004] The Mueller matrix of an optical instrument can be measured by traditional methods, such as those described in the monograph (A. Gerrard, J. M. Burch. Introduction to Matrix Methods in Optics. Dover Publications, 1975.), which require inserting appropriate polarization devices into the optical path inside the optical instrument to measure its Mueller matrix elements. Currently, commercial spectrometers, especially small spectrometers with a very high degree of integration, are not suitable for measuring their Mueller matrices using traditional methods. If the spectrometer is disassembled, its precision will be damaged, and there is not enough space in a highly integrated spectrometer to insert conventional polarization devices. Fortunately, for the spectral curve, the main purpose is to restore the spectral power distribution and the state of light polarization before entering the spectrometer based on the polarization of the spectrometer, which only involves the Mueller matrix elements related to light intensity. Thus, without disassembling the integrated spectrometer, some of the Mueller matrix elements of the spectrometer that affect light intensity can also be measured using an external polarization measurement method. The spectral line measurement of a spectrometer must involve composite light waves, and the Mueller matrix elements of the spectrometer are also related to the wavelength of the light wave. Therefore, what needs to be measured should be the spectral Mueller matrix elements related to the light intensity of the spectrometer. It should be noted that even for spectrometers of the same model, there are differences in their spectral Mueller matrix elements spectra.

[0005] There is a major category of measurement methods in polarization measurement called the sequential polarization measurement method (Russell A. Chipman. Polarized Light and Optical Systems. CRC Press, Taylor & Francis Group. 2019), that is, a series of measurements of the light flux are carried out in chronological order. Between each measurement, the polarization generator and analyzer are changed, and usually rotating polarization elements are used. This method is also narrowly referred to as the q-scan method or the angular scan method (Xiangshen, Meng, et al. Circularly polarized light to study linear magneto-optics for ferrofluids: θ-scan technique [J]. Measurement Science & Technology, 2018, 29. DOI: 10.1088 / 1361-6501 / aab0e2.). The method of the present invention is based on the principle of the angular scan method. Summary of the Invention

[0006] Objective of the Invention: To solve the deviation of the measurement results of incident light caused by the polarization effect existing in the spectrometer or the spectrometer system itself, the present invention proposes a method for measuring the light intensity-related Mueller matrix element spectrum of a spectrometer or a spectrometer system. The measured light intensity-related Mueller matrix element spectrum of the spectrometer system can be used to restore the spectral power distribution and light polarization state before entering the spectrometer.

[0007] To achieve the above objective, the present invention provides the following technical solutions:

[0008] A four-element spectrum of the light intensity-related Mueller matrix of a spectrometer. Along the light path in the direction of the optical path, the device is successively a light source (S), a lens group (L1), a diaphragm (D), a polarizer (P), a vertical rotating table (R) for installing a quarter-wave plate (W), a lens group (L2), and a spectrometer (G), which are coaxially placed in sequence; as Figure 1 shown.

[0009] The vertical rotating table (R) drives the quarter-wave plate (W) to rotate around the optical axis through mechanical transmission by a controllable stepping motor thereon, constituting the angular scanning part; the rotation angle and speed of the stepping motor on the vertical rotating table (R) are set and controlled by a test program on a host computer (PC), and the command is transmitted to a stepping motor controller (C) to drive the stepping motor to execute; the spectrometer (G) sends the collected data to the host computer (PC), and is stored by the test program on the host computer (PC) in a time-sequence manner; the angular scanning and spectral data collection are synchronously started and ended by the test program on the host computer (PC);

[0010] The angular scanning method is that the fast axis direction of the quarter-wave plate (W) rotates at a uniform angular velocity, and the CCD of the spectrometer (G) detects the relative intensity information of the light with the time-sequence change of the polarization state after passing through the rotating quarter-wave plate (W) in a time-sequence manner, and the angle θ between the fast axis direction of the quarter-wave plate (W) and the positive direction of the y-axis of the laboratory coordinate system is equal to the product of the uniform angular velocity ω of the rotation of the fast axis direction of the quarter-wave plate (W) and the time t, that is, the expression θ = ωt; the relative intensity data [I ti , t i received by the i-th pixel unit of the measured spectrometer (G) CCD obtained by the angular scanning method is converted into data [I i = ωt i into data [I ti , θ i .

[0011] The Stokes parameters of the natural light emitted by the natural light broad-spectrum light source are: T0 = [1, 0, 0, 0] T ; after being polarized by the polarizer, the Stokes parameters of the linearly polarized light with the transmission axis in the y-axis direction become T1 = [1, 1, 0, 0] T ; after passing through the rotating quarter-wave plate and reaching the spectrometer CCD, its Stokes parameters are: In the formula, is the Mueller matrix of the quarter-wave plate considering the rotation delay amount δ, and θ is the angle between the fast axis direction of the quarter-wave plate and the positive direction of the y-axis (such as Figure 1 the coordinate axes shown); is the Mueller matrix of the spectrometer; the relative light intensity of the light received by the spectrometer CCD is proportional to the first element of the Stokes parameter T t of the received light: I t = β[e 11 + e 12 (cos 2 2θ + cosδsin 2 2θ) + e 13 (1 - cosδ)cos2θsin2θ + e 14 sinδsin2θ] In the formula, β is a constant proportionality coefficient, which is the conversion coefficient of the light intensity and the spectrometer CCD count value, the relative light intensity of the light incident from the spectrometer slit opening, and the combined parameter of the constant coefficient; e 11 , e 12 , e 13 and e 14 are related to the light intensity and are called the Mueller matrix elements related to the light intensity of the spectrometer.

[0012] Substitute the relative light intensity data [I ti , θ i of the light received by the i-th pixel unit of the spectrometer CCD obtained by the measuring device of the Mueller matrix four-element spectrum of the spectrometer based on the angle scanning method into the principle formula of the relative light intensity of the light received by the i-th pixel unit of the spectrometer CCD: In the formula, the subscript i is the pixel unit number of the spectrometer CCD, the wavelength of the received light corresponding to the i-th pixel unit of the spectrometer CCD is λ i , and the parameters with the subscript i all correspond to the wavelength λ i ; β i is the proportionality coefficient; δ i is the known wavelength-related delay amount function of the quarter-wave plate; e 11i , e 12i , e 13i and e 14i are the 4 elements of the first row of the Mueller matrix elements of the spectrometer corresponding to the wavelength λ i ; θ i is the angle between the fast axis direction of the quarter-wave plate and the positive direction of the y-axis of the laboratory coordinate system.

[0013] Traverse θ i Within the range of [0, 2π] where θ is located, select 4 θ values according to certain rules i and the 4 I measured values corresponding to these 4 θ values i to form a system of equations ti Solve to obtain the normalized corresponding wavelength λ The Mueller matrix elements of the spectrometer light intensity are i In the formula, the subscript number of θ represents 4 different θ where θ i The subscript number represents 4 different θ i , θ i The subscript n represents the nth group of equations, and N represents the number of equations formed

[0014] Compared with the existing invention, the advantages of the present invention are as follows:

[0015] The present invention proposes a method for measuring the four-element spectrum of the Mueller matrix related to the light intensity of a spectrometer, which is an external measurement method and does not disassemble the spectrometer; by adding the delay curve of a quarter-wave plate, all four light intensity-related Mueller matrix element spectra can be measured, which is applicable not only to a single spectrometer but also to a spectrometer system; the core optical devices only use a polarizer and a rotating quarter-wave plate, the hardware cost involved in the test method is low, the method is simple and fast; the relative calculation amount is small and the result accuracy is high; the environmental adaptability is good Description of the Drawings

[0016] Figure 1 is a schematic diagram of the measurement device of the method of the present invention

[0017] Figure 2 is the four-element spectrum diagram of the Mueller matrix related to the light intensity of the spectrometer under test

[0018] Description of the Reference Numerals

[0019] Figure 1 Among them, natural light broad-spectrum light source (S), lens group (L1), aperture (D), polarizer (P), vertical rotating table (R) for installing a quarter-wave plate (W), lens group (L2), spectrometer (G), upper computer (PC), stepper motor controller (C) Specific Embodiments

[0020] The present invention will be further described in detail below with reference to the drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention

[0021] The present invention is applicable to various spectrometers, especially C-T type spectrometers

[0022] As Figure 1 shown, a spectrometer light intensity-related Mueller matrix element spectrum test device provided by an embodiment of the present invention is as follows: along the light travel direction in the optical path, a natural light broad-spectrum light source (S), a lens group (L1), a diaphragm (D), a polarizer (P), a vertical rotating table (R) for mounting a quarter-wave plate (W), a lens group (L2), and a spectrometer (G) are coaxially arranged in sequence;

[0023] The vertical rotating table (R) is driven by a controllable stepper motor thereon through mechanical transmission to drive the quarter-wave plate (W) to rotate around the optical axis, constituting an angular scanning part; the rotation angle and speed of the stepper motor on the vertical rotating table (R) are set and controlled by a test program on a host computer (PC), and the instruction is transmitted to the stepper motor controller (C) to drive the stepper motor to execute; the spectrometer (G) sends the collected data to the host computer (PC), and is stored by the test program on the host computer (PC) in a time-sequential manner; the angular scanning and spectral data collection are synchronously started and ended by the test program on the host computer (PC).

[0024] The angular scanning method is that the fast axis direction of the quarter-wave plate (W) rotates at a uniform angular velocity, and the CCD of the spectrometer (G) detects the relative intensity information of the light whose polarization state changes in time sequence after passing through the rotating quarter-wave plate (W) in a time-sequential manner, and the angle θ between the fast axis direction of the quarter-wave plate (W) and the positive direction of the y-axis of the laboratory coordinate system is equal to the product of the uniform angular velocity ω of the rotation of the fast axis direction of the quarter-wave plate (W) and the time t, that is, the expression θ = ωt; the relative intensity data [I ti , t i received by the i-th pixel unit of the measured spectrometer CCD obtained by the angular scanning method is converted into data [I i = ωt i , θ ti by the expression θ i .

[0025] Preferably, the light source (S) is a halogen lamp as a broad-spectrum continuous spectral light source.

[0026] Preferably, the quarter-wave plate adopts a Wuhan Youguang achromatic quarter-wave plate, corresponding to the optical band range of the spectrometer, and its retardation function is δ = (1.08×10 -13 )λ 5 - (3.93×10 -10 )λ 4 + (5.67×10 -7 )λ 3 - (4.06×10 -4 )λ 2 + 0.14λ - 18.45

[0027] Preferably, the fast axis direction of the quarter-wave plate (W) is set with a uniform angular velocity of 5° / s, the rotation angle is set to 360°, and the single sampling time of the spectrometer (G) is 0.01 s.

[0028] The Stokes parameters of the natural light emitted by the natural light broad-spectrum light source are: T0 = [1, 0, 0, 0] T ; After passing through the polarizer, it becomes linearly polarized light with the vibration direction transmitted along the y-axis, and the Stokes parameters become T1 = [1, 1, 0, 0] T ; After passing through the rotating analyzer and reaching the spectrometer CCD, its Stokes parameters are: In the formula, is the Mueller matrix of the quarter-wave plate with a known delay amount rotated, θ is the angle between the vibration direction of the analyzer and the positive y-axis direction (as shown in the coordinate axes), and the positive y-axis direction is the initial direction; Figure 1 shown coordinate axes), the positive y-axis direction is the initial direction; is the Mueller matrix of the spectrometer; the relative light intensity of the light received by the spectrometer CCD is proportional to the first element of the Stokes parameter T t of the received light: I t = β[e 11 + e 12 (cos 2 2θ + cosδsin 2 2θ) + e 13 (1 - cosδ)cos2θsin2θ + e 14 sinδsin2θ] In the formula, β is a constant proportionality coefficient, which is the conversion coefficient between the light intensity and the count value of the spectrometer CCD, the relative light intensity of the light incident from the spectrometer slit, and the combined parameter of the constant coefficient; e 11 , e 12 , e 13 and e 14 are related to the light intensity and are called the Mueller matrix elements related to the light intensity of the spectrometer.

[0029] Substitute the relative light intensity data [I ti ,, θ i of the light received by the i-th pixel unit of the spectrometer CCD obtained by the measuring device of the four-element spectrum of the Mueller matrix related to the light intensity of the spectrometer based on the angular scanning method into the principle formula of the relative light intensity of the light received by the i-th pixel unit of the spectrometer CCD: In the formula, the subscript i is the pixel unit number of the spectrometer CCD, and the wavelength of the light received by the i-th pixel unit of the spectrometer CCD is λ i,Parameters with subscript \(i\) are all related to the wavelength \(\lambda\) i ; \(\beta\) i is a proportionality coefficient; \(\delta\) i is the known wavelength-dependent retardance function of the quarter-wave plate; \(e\) 11i , \(e\) 12i , \(e\) 13i and \(e\) 14i are the 4 elements of the first row of the Mueller matrix of the spectrometer corresponding to the wavelength \(\lambda\) i ; \(\theta\) i is the angle between the transmission axis direction of the analyzer and the positive direction of the \(y\)-axis of the laboratory coordinate system.

[0030] Divide the range \([0, 2\pi]\) where \(\theta\) i is located into 12 equal parts and sort them. According to the ascending order of the \(\theta\) i value, name the regions in sequence. From the 2nd to the 5th regions, select one \(\theta\) i value in each region according to the \(i\) order, select 4 \(\theta\) i values and form a system of equations with the 4 measured \(I\) i values corresponding to these 4 \(\theta\) ti values; In the same way, select 4 \(\theta\) i values from the 8th to the 11th regions and form a system of equations with the 4 measured \(I\) i values corresponding to these 4 \(\theta\) ti values. The solved normalized Mueller matrix elements of the spectrometer light intensity corresponding to the wavelength \(\lambda\) i are In the formula, the subscript number of \(\theta\) i represents 4 different \(\theta\) i , and the subscript \(n\) of \(\theta\) i represents the \(n\)th group of equations, and \(N\) represents the number of systems of equations formed.

[0031] Through computer programming calculation, the Mueller matrix element spectrum diagram related to the spectrometer light intensity as shown in Figure 2 is obtained. It should be noted that the four-element spectrum is related to the set initial direction. When performing spectral power distribution and polarization state restoration, the same initial direction should be used.

[0032] The above is only the specific implementation manner of the present invention, but those skilled in the art should know that the present invention is not limited to the above description. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for measuring the four-element spectrum of the Mueller matrix related to the light intensity of a spectrometer, characterized in that: The relative light intensity data [I ti , θ i received by the i-th pixel unit of the spectrometer (G) CCD obtained by the measuring device for the four-element spectrum of the Mueller matrix related to the light intensity of the spectrometer based on the angular scanning method is substituted into the principle formula for the relative light intensity received by the i-th pixel unit of the spectrometer (G) CCD: In the formula, the subscript i is the pixel unit number of the CCD of the spectrometer (G), and the received optical wavelength corresponding to the i-th pixel unit of the spectrometer (G) CCD is λ i , and the parameters with the subscript i are all related to the wavelength λ i ; β i is the proportionality coefficient; δ i is the known wavelength-dependent delay function of the quarter-wave plate (W); e 11i , e 12i , e 13i and e 14i are the 4 elements of the first row of the Mueller matrix elements of the spectrometer (G) corresponding to the wavelength λ i ; θ i is the angle between the transmission axis direction of the analyzer (A) and the positive direction of the y-axis of the laboratory coordinate system; Traverse θ i In the range of [0, 2π] where it is located, select 4 θ values according to certain rules i values and the 4 I i measured values corresponding to these 4 θ ti measured values to form a system of equations The solution gives the normalized corresponding wavelength λ i The four elements of the first row of the Mueller matrix elements of the spectrometer (G) are where θ i The subscript numbers represent four different θ i , θ i The subscript n represents the nth set of equations, and N represents the number of sets of equations formed.

2. The method for measuring the four-element spectrum of the Mueller matrix related to the light intensity of a spectrometer according to claim 1, characterized in that A practical device for testing the four-element spectrum of the Mueller matrix related to the light intensity of a spectrometer is as follows: along the optical path in the direction of the optical travel, there are a natural light broad-spectrum light source (S), a lens group (L1), a diaphragm (D), a polarizer (P), a vertical rotating table (R) for mounting a quarter-wave plate (W), a lens group (L2), and a spectrometer (G), which are coaxially arranged in sequence; The vertical rotating table (R) drives the quarter-wave plate (W) to rotate around the optical axis by a controllable stepping motor thereon through mechanical transmission, constituting the angular scanning part; the rotation angle and speed of the stepping motor on the vertical rotating table (R) are set and controlled by a test program on the upper computer (PC), and the command is sent to the stepping motor controller (C) to drive the stepping motor to execute; the spectrometer (G) sends the collected data to the upper computer (PC), and is stored by the test program on the upper computer (PC) in a time-sequential manner; the angular scanning and spectral data acquisition are synchronously started and ended by the test program on the upper computer (PC).

3. A method for measuring the four-element spectrum of the Mueller matrix related to the light intensity of a spectrometer, characterized in that, In the angular scanning method, the fast axis of the quarter-wave plate (W) rotates at a uniform angular velocity. The CCD of the spectrometer (G) detects the relative intensity information of the light whose polarization state changes in sequence after passing through the rotating quarter-wave plate (W) according to the time sequence. And the angle θ between the fast axis direction of the quarter-wave plate (W) and the positive direction of the y-axis of the laboratory coordinate system is equal to the product of the uniform angular velocity ω of the rotation of the fast axis direction of the quarter-wave plate (W) and the time t, that is, the expression θ = ωt; the relative intensity data [I ti , t i received by the i-th pixel unit of the measured spectrometer CCD obtained by the angular scanning method is converted into the data [I i = ωt i to the data [I ti , θ i .

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