CN105628343B - A kind of wave plate detection device and method - Google Patents

A kind of wave plate detection device and method Download PDF

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CN105628343B
CN105628343B CN201610029435.8A CN201610029435A CN105628343B CN 105628343 B CN105628343 B CN 105628343B CN 201610029435 A CN201610029435 A CN 201610029435A CN 105628343 B CN105628343 B CN 105628343B
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CN105628343A (en
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刘世元
张传维
谷洪刚
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WUHAN INDUSTRIAL INSTITUTE FOR OPTOELECTRONICS Co Ltd
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Abstract

The invention discloses wave plate detection device, which includes light source, is polarized arm, for placing the sample stage of wave plate to be detected, analyzing arm and detector；The center for being polarized arm, wave plate to be detected and analyzing arm is on same straight line, the light that light source is sent obtains modulated polarized light after being polarized arm and being polarized and modulate, modulated polarized light modulation and analyzing after analyzing arm after the information of wave plate to be detected coupling wave plate, are finally received by a detector.The present invention establishes relation between wave plate characteristic parameter and Muller matrix element using Muller matrix, using the Muller matrix spectroscopic data of Muller matrix ellipsometer measurement wave plate to be detected, further obtains the characteristic parameter spectroscopic data of wave plate to be detected.The present invention can obtain all characteristic parameter spectroscopic datas of any wave plate in one-shot measurement, including phase-delay quantity, phase retardation, angle of rotation, fast and slow axis transmitance Amplitude Ration angle, depolarization index.

Description

A kind of wave plate detection device and method
Technical field
The invention belongs to optical element detection field, more particularly, to a kind of wave plate detection device and method.
Background technology
Wave plate is Optical Instrument Designing and common optical element in field of optical measurements, it enables to the two of polarised light A vertical component generates additional light path (or phase difference), which is known as the phase-delay quantity of wave plate.The phase of wave plate is prolonged The polarization state that slow characteristic can be used for changing light wave (such as becomes circularly polarized light, it is inclined to become line from elliptically polarized light from linearly polarized light Shake light etc.) or check light wave polarization state.Wave plate is usually made by birefringece crystal, common birefringece crystal bag Include mica, gypsum, magnesium fluoride, sapphire, crystal quartz etc..
The optical characteristics of wave plate includes phase-delay quantity, phase retardation, angle of rotation, dichroism, depolarization index etc., this A little optical characteristics can all influence the performance of optical system, in actual use, it is necessary to carry out essence to the optical characteristics of wave plate True detection and calibration.
At present, there are many kinds of the detection of wave plate and calibration techniques, including interferometry, laser frequency mode split method, phase bit comparison Method, phase compensation method, spectroscopic methodology and time domain method etc..These prior arts can carry out essence to some optical property parameters of wave plate True detection and calibration, but there is the deficiencies of the following aspects：(1) prior art be typically only capable to characterization one of wave plate or Two characteristic parameters such as phase-delay quantity or phase retardation, and are difficult to that wave plate is carried out comprehensively to detect and characterize；(2) have A little technologies are typically only capable to provide the parameter of some wavelength points of wave plate, and then using the dispersion equation of material, other ripples are calculated Long parameter value or the spectroscopic data that wave plate is provided by scanning wavelength, it is also difficult to wave plate is directly detected in one-shot measurement Spectrum parameter；(3) some technology accuracy of detection are very high, if laser frequency mode split method is (present retardation of wave plate detects National standard is based on this method), but detection process and data processing are all complex, it is more demanding to operating personnel's technology.
The content of the invention
It is an object of the invention to provide a kind of wave plate detection device and method, this method characterizes wave plate using Muller matrix Any wave plate by establishing the equivalent model of wave plate, is equivalent to a phase with dichroic attenuation characteristic by optical characteristics The cascade system of delayer, a polarization apparatus and a depolarizer composition, with phase-delay quantity δ, phase retardation θ, fast and slow axis Transmitance Amplitude Ration angle ψ, angle of rotation ρ and five parameter characterizations of depolarization index D.The invention device utilizes Muller matrix ellipsometer The Muller matrix spectrum of wave plate can be provided, thus this method and its device can obtain any wave plate in one-shot measurement Institute there are five characteristic parameter spectrum, and this method and its device operation easily, data processing it is simple.
The object of the invention is realized the technical solution adopted is that a kind of wave plate detection device, the device include light source, be polarized arm, For placing the sample stage of wave plate to be detected, analyzing arm and detector；The center for being polarized arm, wave plate to be detected and analyzing arm On same straight line, the light that light source is sent obtains modulated polarized light, modulated polarized light warp after being polarized arm and being polarized and modulate Modulation and analyzing after analyzing arm after the information of wave plate to be detected coupling wave plate are crossed, is finally received by a detector.
The method that wave plate detection is realized by above-mentioned wave plate detection device, comprises the following steps：
S100, light source is opened, adjustment is polarized arm and analyzing arm, makes its center on same straight line；
S200, wave plate to be detected is placed on sample stage, adjusts the height and orientation of sample stage, guarantee is put in sample stage With the center of analyzing arm and analyzing arm on same straight line, the beam orthogonal of light source, which incides into, to be treated at the center of upper wave plate to be detected Wave plate is detected, and beam and focus can all pass through wave plate to be detected；
S300, the Muller matrix spectrum M using detector measurement wave plate to be detectedc, wave plate to be detected wavelength be λ when Measure Muller matrix Mc(λ) is：
Wherein, Γ is the spectral region of the wave plate of being detected characteristic parameter, and Γ is provided wave plate detection device Muller square A subset in the available band scope of battle array ellipsometer, λ are any one wavelength points in wavelength band Γ, are mij(λ)(i =1,2,3,4；J=1,2,3,4 it is) that wave plate measures Muller matrix M when wavelength is λcThe normalization element of (λ)；
The measurement Muller matrix M of S400, the wave plate to be detected obtained according to measurementcObtain the characteristic parameter of wave plate to be detected Spectrum θ, δ, ψ, ρ and D, θ is the phase retardation of wave plate to be detected, δ is phase-delay quantity, ψ is fast and slow axis transmitance Amplitude Ration Angle ψ (λ), ρ are angle of rotation, D is depolarization index.
Compared with prior art, the present invention has following technical advantage：
(1) wave plate detection device and method provided by the present invention can detect the characteristic parameter of any wave plate, including appointing The single wave plate for the arbitrary center phase retardation of material of anticipating, composite wave plate；
(2) wave plate detection device and method provided by the present invention can provide the institute of wave plate to be detected in one-shot measurement There is characteristic parameter, including phase-delay quantity, phase retardation, angle of rotation, fast and slow axis transmitance reproduction ratio angle, depolarization index；
(3) wave plate detection device and method provided by the present invention it is special can to provide wave plate to be detected in one-shot measurement Parameter phase retardation, phase retardation, angle of rotation, fast and slow axis transmitance reproduction ratio angle, depolarization index spectrum are levied, including selected Select the characteristic ginseng value of all wavelengths point in wavelength band.
Description of the drawings
Fig. 1 is single wave plate structure diagram.
Fig. 2 is the composite wave plate structure diagram to be formed an angle by n single wave plate according to optical axis.
Fig. 3 is wave plate structure of the detecting device schematic diagram proposed by the invention.
Fig. 4 is that there are the 532nm quarter-waves quartz compound zero of optical axis alignment error involved by the embodiment of the present invention Grade wave plate structure diagram.
Fig. 5 is utilizes the present invention to put forward the 532nm a quarters there are optical axis alignment error that wave plate detection device obtains The Muller matrix spectrogram of the compound zero-th order waveplates of wavelength quartz.
Fig. 6 is utilizes the present invention to put forward the 532nm a quarters there are optical axis alignment error that wave plate detection device obtains The characteristic parameter spectrogram of the compound zero-th order waveplates of wavelength quartz.
Specific embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, below in conjunction with attached drawing, to the present invention into Row is further described.If described herein as be related to being only used to explain the present invention during specific example, the present invention is not limited.
In the present invention, any wave plate refers to be composed of into arbitrary angle according to its optical axis the single wafer of any number Wave plate, wherein being known as single wave plate by the wave plate that single single-chip forms, the wave plate being made of multiple single-chips is known as complex wave Piece.
For the structure diagram of single wave plate as shown in Figure 1, light is propagated along z-axis negative direction, wave plate is parallel with x-o-y planes It places, the angle theta of the fast axle (F) of wave plate between x is known as the phase retardation of wave plate.Multiple single wave plates are according to optical axis into certain Angle be composed, be known as composite wave plate, as shown in Fig. 2, light is propagated along z-axis negative direction, according to the light direction of propagation, appoint Each single wave plate of meaning composite wave plate be referred to as wave plate 1, wave plate 2 ..., wave plate n, the fast axle of each single wave plate is expressed as F1、 F2、…、F3, θ1、θ2、…、θ3Angle between the fast axle and x-axis of respectively each single wave plate is known as the fast axis direction of each single wave plate Angle.
Wave plate Muller matrix is expressed as in the present invention：
Wherein M be wave plate Muller matrix, Mij(i=1,2,3,4；J=1,2,3,4 16) for wave plate Muller matrix are non- Normalize element, mij(i=1,2,3,4；J=1,2,3,4) for wave plate Muller matrix compared with M11Normalized Muller matrix member Element.
As present invention further optimization, phase delay device, polarization apparatus and depolarizer with dichroic attenuation characteristic Muller matrix can be expressed as
Wherein, M (θ, δ, ψ), R (ρ) and M (D) be respectively with the phase delay device of dichroic attenuation characteristic, polarization apparatus, The Muller matrix of depolarizer, θ are the phase retardation of phase delay device, and δ is the phase-delay quantity of phase delay device, and ψ is phase The fast and slow axis transmitance Amplitude Ration angle of delayer, ρ are the angle of rotation of polarization apparatus, and D is the depolarization index of depolarizer, and wherein D can be with By dividing depolarization index da、dbAnd dcIt is calculated,
The equivalent model of any wave plate is described with Muller matrix form
M=R (ρ) R (- θ) M (δ, ψ) R (θ) M (D) (6)
Wherein, M is the Muller matrix of any wave plate, and M (θ, δ, ψ), R (ρ) and M (D) are respectively to have dichroic attenuation spy Phase delay device, polarization apparatus, the Muller matrix of depolarizer of property.
The optical characteristics of any wave plate can be represented with a Muller matrix as shown in formula (1).Ideally, by more The composite wave plate that a single wave plate is formed according to optical axis into certain optical axis included angle can optically be equivalent to an optical phase Delayer and a polarization apparatus are represented with three phase-delay quantity, phase retardation and angle of rotation characteristic parameters.Actual conditions Under, the wave plate dichroic attenuation characteristic certain since the factors such as fault in material, manufacturing deficiency can generate and depolarization characteristic, at this point, The composite wave plate of one reality can be equivalent to phase delay device, a polarization apparatus and one with dichroic attenuation characteristic A depolarizer, with phase-delay quantity δ, phase retardation θ, fast and slow axis transmitance Amplitude Ration angle ψ, angle of rotation ρ and depolarization index D Five parameter characterizations, as shown in formula (6).Wave plate detection method provided by the present invention is based on the above-mentioned wave plate principle of equal effects.
Wave plate detection device of the present invention is Muller matrix ellipsometer, as shown in figure 3, the Muller matrix ellipsometer includes one Light source 1, one is polarized arm PSG2,3, analyzing arm PSA4 of a sample stage, a detector 5, wherein wave plate to be detected 6 is put It puts on sample stage, wherein sample stage 3 can move up and down and horizontally rotate to adjust the height and orientation of wave plate 6 to be measured, It is polarized arm PSG2 and analyzing arm PSA4 and can adjust the angle so that light beam can be to treat on different incident angles to sample stage 3 Detect wave plate 6.Arm PSG2, wave plate to be detected 6, the center of analyzing arm PSA4 three are polarized on same straight line, light source 1 is sent Light after being polarized arm PSG2 and being polarized and modulate be known as modulated polarized light, modulated polarized light pass through wave plate to be detected, polarised light Polarization state certain variation occurs, so as to couple the information of wave plate, then after analyzing arm PSA4, polarised light is by into one Step system and analyzing are finally received by detector 5, and processing is carried out to the signal that detector 5 receives and can obtain wave plate 6 to be detected Muller matrix, further using wave plate detection method provided by the present invention obtain wave plate all characteristic parameters.
All characteristic parameters realized the detection process of any wave plate and obtain wave plate are implemented in accordance with the following steps：
S100, the light source for opening wave plate detection device Muller matrix ellipsometer provided by the present invention, adjustment Muller matrix are ellipse Inclined instrument is polarized arm PSG and analyzing arm PSA, makes its center on same straight line, ensures that the light beam sent from light source can be according to Secondary process is polarized arm PSG and analyzing arm PSA, and the light intensity signal that detector receives reaches most strong.
S200, wave plate to be detected is placed on the sample stage of Muller matrix ellipsometer, adjusts height of specimen and orientation, protected The center of wave plate and the center of Muller matrix ellipsometer analyzing arm PSG and analyzing arm PSA are demonstrate,proved on same straight line, beam orthogonal Wave plate to be detected is incided into, and beam and focus can all pass through wave plate to be detected.
S300, using wave plate detection device provided by the present invention Muller matrix ellipsometer measurement wave plate to be detected Muller Matrix spectrum Mc, measurement Muller matrix M of the wave plate to be detected when wavelength is λc(λ) is：
Wherein, Γ is the spectral region of the wave plate of being detected characteristic parameter, and Γ is provided wave plate detection device Muller square A subset in the available band scope of battle array ellipsometer, λ are any one wavelength points in wavelength band Γ, are mij(λ)(i =1,2,3,4；J=1,2,3,4 it is) that wave plate measures Muller matrix M when wavelength is λcThe normalization element of (λ).
The measurement Muller matrix M of S400, the wave plate to be detected obtained according to Muller matrix ellipsometer measurementcIt obtains to be detected The characteristic parameter spectrum (θ, δ, ψ, ρ, D) of wave plate, can specifically follow the steps below.
S401, wave plate when according to wavelength being λ measure Muller matrix Mc(λ), it is λ that wave plate to be detected, which is calculated, in wavelength When depolarization index D (λ), it is as follows
Wherein, the mark of Tr representing matrixes, the transposition of T representing matrixes.
S402, wave plate when according to wavelength being λ measure Muller matrix McThe wave plate to be detected that (λ) and step 1 obtain is in ripple Depolarization index D (λ) during a length of λ calculates the Muller matrix M that wave plate to be detected does not include depolarization parameterc' (λ), it can be obtained by following formula
Wherein, M-1[D (λ)] represents the inverse matrix that depolarization index is D (λ) depolarizer Muller matrix, mij' (λ) (i=1,2, 3,4；J=1,2,3,4) represent that wave plate to be detected does not include the Muller matrix M of depolarization parameterc' (λ) normalization element.
S403, the Muller matrix M that wave plate to be detected when wavelength is λ does not include depolarization parameter is obtained according to step 2c' (λ), Phase retardation θ (λ), phase-delay quantity δ (λ), the speed of to be detected wave plate of the wave plate to be detected when wavelength is λ is calculated Axis transmitance Amplitude Ration angle ψ (λ), angle of rotation ρ (λ).There is following relation at this time
Mc' (λ)=R [ρ (λ)] R [- θ (λ)] M [δ (λ), ψ (λ)] R [θ (λ)] (10)
Wherein, it is form as follows that R [ρ (λ)], R [- θ (λ)], R [θ (λ)] and M [δ (λ), ψ (λ)] have respectively
Simultaneous formula (9)-(14) can obtain the phase retardation of the wave plate to be detected when wavelength is λ of wave plate to be detected θ (λ), phase-delay quantity δ (λ), fast and slow axis transmitance Amplitude Ration angle ψ (λ), angle of rotation ρ (λ).
S404, conversion wavelength, repeat step S401~S403, obtain the fast axle of the wave plate to be detected under another wavelength Azimuth angle theta (λ), phase-delay quantity δ (λ), fast and slow axis transmitance Amplitude Ration angle ψ (λ), angle of rotation ρ (λ) and depolarization index D (λ).
S405, constantly repeat step S404, until in selected wavelength band Γ under all wavelengths wave plate to be detected it is fast Axis azimuth, phase-delay quantity, fast and slow axis transmitance Amplitude Ration angle, angle of rotation and depolarization index, obtain the institute of wave plate to be detected There is characteristic parameter spectrum.
In the present embodiment, wave plate detection side provided by the present invention is illustrated with a homemade Muller matrix ellipsometer The implementation process of method and device, but wave plate detection method provided by the present invention and its device are not limited thereto.The present invention is implemented The wavelength available scope of self-control Muller matrix ellipsometer in example is 200-1000nm.
In order to further illustrate the implementation process and effect of wave plate detection method provided by the present invention and its device, on State in embodiment using optical axis there are certain alignment error the compound zero-th order waveplates of 532nm quarter-waves quartz as ripple to be detected Piece.It as shown in figure 4, the composite wave plate includes two single wave plates, is placed in parallel respectively at x-o-y planes, light is along z-axis negative direction It propagates, according to the light direction of propagation, two single wave plates are referred to as wave plate 1, wave plate 2, and fast axle is expressed as F1、F2, θ1、 θ2Angle between the fast axle and x-axis of respectively two single wave plates is known as its phase retardation, S1For the slow axis of wave plate 1, unicast The fast axle and slow axis of piece are orthogonal, therefore F1⊥S1.To the compound zero-th order waveplates of ideal design, fast axle and the wave plate 1 of wave plate 2 Fast axle between be mutually perpendicular to, therefore have F1⊥F2Or F2∥S1.In actual processing, it will not be managed between the fast axle of two wave plates Think it is vertical, can be there are certain alignment error α, therefore F2And S1Between angle be α.The alignment error can make the phase of composite wave plate There is certain fluctuation in the parameters spectrum such as position retardation, phase retardation and angle of rotation.
The wave plate detection method of the present embodiment and its operating procedure of device is described in detail with reference to specific implementation process：
(1) light source of wave plate detection device Muller matrix ellipsometer provided by the present invention is opened, adjustment Muller matrix is ellipse partially Instrument is polarized arm PSG and analyzing arm PSA, and Muller matrix ellipsometer is made to be in straight-through measurement pattern, that is, is polarized arm PSG and analyzing arm The center of PSA on same straight line, ensure the light beam sent from light source can successively by being polarized arm PSG and analyzing arm PSA, The light intensity signal that detector receives reaches most strong.
(2) the compound zero-th order waveplates of quartz to be detected are placed on the sample stage of Muller matrix ellipsometer, adjustment sample is high Degree and orientation ensure the center of wave plate with the center of Muller matrix ellipsometer analyzing arm PSG and analyzing arm PSA in same straight line On, beam orthogonal incides into wave plate to be detected, and beam and focus can all pass through wave plate to be detected.
(3) the Muller square of the Muller matrix ellipsometer measurement wave plate to be detected of wave plate detection device provided by the present invention is utilized Battle array spectrum Mc, wherein, wavelength detecting wavelength Γ elects the available spectrum scope of the self-control Muller matrix ellipsometer as, i.e. and Γ= [200nm, 1000nm], the Muller matrix spectroscopic data of the compound zero-th order waveplates of embodiment 532nm quarter-waves quartz is such as Shown in Fig. 5.
(4) the measurement Muller matrix M of the wave plate to be detected obtained according to Muller matrix ellipsometer measurementcWith formula (8)-(14) The process shown obtains the characteristic parameter spectrum (θ, δ, ψ, ρ, D) of wave plate to be detected, embodiment 532nm quarter-waves The characteristic parameter spectroscopic datas of the compound zero-th order waveplates of quartz as shown in fig. 6, including phase-delay quantity, phase retardation, angle of rotation, Fast and slow axis transmitance Amplitude Ration angle, depolarization index.
By above example, it is seen that wave plate detection method provided by the present invention and its device can provide in one-shot measurement Whole characteristic parameter spectroscopic datas of wave plate, including phase-delay quantity, phase retardation, angle of rotation, fast and slow axis transmitance amplitude Than angle, depolarization index, this is that existing wave plate detection technique is difficult to realize.
Self-control Muller matrix when describing specific implementation process only using wavelength available scope as 200-1000nm above Ellipsometer is to detection process of the optical axis there are the compound zero-th order waveplates of 532nm quarter-waves quartz of certain alignment error Example, but the present invention is not only limited to above-mentioned specific embodiment, persons skilled in the art disclosed design according to the present invention Method may be employed other a variety of specific embodiments and implement the present invention, such as select different Muller matrix ellipsometer, different Wave plate to be detected etc., therefore, the thinking of every wave plate detection method using the present invention and its device does some simple variations Or the design of change, both fall within the scope of protection of the invention.

Claims (1)

  1. A kind of 1. method for realizing wave plate detection, which is characterized in that including：
    S100, light source is opened, adjustment is polarized arm and analyzing arm, makes its center on same straight line；
    S200, wave plate to be detected is placed on sample stage, adjusts the height and orientation of sample stage, guarantee, which is put on sample stage, to be treated Center and the analyzing arm of wave plate and the center of analyzing arm are detected on same straight line, the beam orthogonal of light source incides into be detected Wave plate, and beam and focus can all pass through wave plate to be detected；
    S300, the Muller matrix spectrum M using detector measurement wave plate to be detectedc, measurement of the wave plate to be detected when wavelength is λ Muller matrix Mc(λ) is：
    <mrow> <msub> <mi>M</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>14</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>22</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>23</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>24</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>31</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>32</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>33</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>34</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>41</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>42</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>43</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>m</mi> <mn>44</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mrow> <mi>&amp;lambda;</mi> <mo>&amp;Element;</mo> <mi>&amp;Gamma;</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, Γ is the spectral region of the wave plate of being detected characteristic parameter, and Γ is that provided wave plate detection device Muller matrix is ellipse A subset in the available band scope of inclined instrument, λ are any one wavelength points in wavelength band Γ, are mij(λ) (i=1, 2,3,4；J=1,2,3,4 it is) that wave plate measures Muller matrix M when wavelength is λcThe normalization element of (λ)；
    The measurement Muller matrix M of S400, the wave plate to be detected obtained according to measurementcObtain the characteristic parameter spectrum of wave plate to be detected θ, δ, ψ, ρ and D, θ is the phase retardation of wave plate to be detected, δ is phase-delay quantity, ψ is fast and slow axis transmitance Amplitude Ration angle ψ (λ), ρ are angle of rotation, D is depolarization index；It specifically includes：
    S401, wave plate when according to wavelength being λ measure Muller matrix Mc(λ), be calculated wave plate to be detected wavelength be λ when Depolarization index D (λ) is as follows
    <mrow> <mi>D</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>{</mo> <mfrac> <mrow> <mi>T</mi> <mi>r</mi> <mo>&amp;lsqb;</mo> <msub> <mi>M</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <msubsup> <mi>M</mi> <mi>c</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mn>1</mn> </mrow> <mn>3</mn> </mfrac> <mo>}</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, the mark of Tr representing matrixes, the transposition of T representing matrixes；
    S402, wave plate when according to wavelength being λ measure Muller matrix McThe wave plate to be detected that (λ) and step S401 are obtained is in wavelength For λ when depolarization index D (λ), calculate wave plate to be detected do not include depolarization parameter Muller matrix Mc' (λ), it can be obtained by following formula
    <mrow> <msubsup> <mi>M</mi> <mi>c</mi> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>M</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <msup> <mi>M</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&amp;lsqb;</mo> <mi>D</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>12</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>13</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>14</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>21</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>22</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>23</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>24</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>31</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>32</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>33</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>34</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>41</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>42</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>43</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>m</mi> <mn>44</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, M-1[D (λ)] represents the inverse matrix that depolarization index is D (λ) depolarizer Muller matrix, mij' (λ) (i=1,2,3,4；j =1,2,3,4) represent that wave plate to be detected does not include the Muller matrix M of depolarization parameterc' (λ) normalization element；
    S403, the Muller matrix M that wave plate to be detected when wavelength is λ does not include depolarization parameter is obtained according to step S402c' (λ), meter It calculates and obtains phase retardation θ (λ), phase-delay quantity δ (λ), the fast and slow axis of to be detected wave plate of the wave plate to be detected when wavelength is λ Transmitance Amplitude Ration angle ψ (λ), angle of rotation ρ (λ), there is following relation at this time
    M′c(λ)=R [ρ (λ)] R [- θ (λ)] M [δ (λ), ψ (λ)] R [θ (λ)] (10)
    Wherein, it is form as follows that R [ρ (λ)], R [- θ (λ)], R [θ (λ)] and M [δ (λ), ψ (λ)] have respectively
    <mrow> <mi>R</mi> <mo>&amp;lsqb;</mo> <mi>&amp;rho;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;rho;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>sin</mi> <mn>2</mn> <mi>&amp;rho;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mn>2</mn> <mi>&amp;rho;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;rho;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>R</mi> <mo>&amp;lsqb;</mo> <mo>-</mo> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mn>2</mn> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>sin</mi> <mn>2</mn> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>cos</mi> <mn>2</mn> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>R</mi> <mo>&amp;lsqb;</mo> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>sin</mi> <mn>2</mn> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>M</mi> <mo>&amp;lsqb;</mo> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>&amp;psi;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>cos</mi> <mn>2</mn> <mi>&amp;psi;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>cos</mi> <mn>2</mn> <mi>&amp;psi;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>sin</mi> <mn>2</mn> <mi>&amp;psi;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>sin</mi> <mn>2</mn> <mi>&amp;psi;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mn>2</mn> <mi>&amp;psi;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>sin</mi> <mn>2</mn> <mi>&amp;psi;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <mi>&amp;lambda;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
    Simultaneous formula (9)-(14) can obtain the phase retardation θ of the wave plate to be detected when wavelength is λ of wave plate to be detected (λ), phase-delay quantity δ (λ), fast and slow axis transmitance Amplitude Ration angle ψ (λ), angle of rotation ρ (λ)；
    S404, conversion wavelength, repeat step S401-S403, obtain the fast axis direction of the wave plate to be detected under another wavelength Angle θ (λ), phase-delay quantity δ (λ), fast and slow axis transmitance Amplitude Ration angle ψ (λ), angle of rotation ρ (λ) and depolarization index D (λ)；
    S405, step S404 is constantly repeated, up to the fast axle side of wave plate to be detected under all wavelengths in selected wavelength band Γ Parallactic angle, phase-delay quantity, fast and slow axis transmitance Amplitude Ration angle, angle of rotation and depolarization index, obtain all spies of wave plate to be detected Levy parameter spectrum.
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