CN113092387A - Method for measuring crystal optical axis orientation - Google Patents

Method for measuring crystal optical axis orientation Download PDF

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CN113092387A
CN113092387A CN202110321113.1A CN202110321113A CN113092387A CN 113092387 A CN113092387 A CN 113092387A CN 202110321113 A CN202110321113 A CN 202110321113A CN 113092387 A CN113092387 A CN 113092387A
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crystal
crystal sample
mueller matrix
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optical axis
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王楚慧
何倩
李方
秦培武
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Shenzhen International Graduate School of Tsinghua University
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Abstract

The invention discloses a method for measuring the optical axis orientation of a crystal, which comprises the following steps: the method comprises the following steps that a crystal sample is placed on a first plane, incident light is incident to the surface of the crystal sample along a first direction, and a first Mueller matrix of the crystal sample at the moment is measured by a Mueller matrix measuring system; rotating the crystal sample or the incident light by an angle omega around the first rotating direction to enable the incident light to be incident to the surface of the crystal sample at an incident angle omega, and measuring a second Mueller matrix of the crystal sample at the moment by adopting a Mueller matrix measuring system; rotating the crystal sample or the incident light by a rotation angle of 2 omega around the second rotation direction so that the incident light is incident on the surface of the crystal sample with the incident angle as-omega, and measuring a third Mueller matrix of the crystal sample by using a Mueller matrix measuring system; and calculating according to the first Mueller matrix, the second Mueller matrix and the third Mueller matrix to obtain the optical axis orientation of the crystal sample. The invention can realize the rapid and accurate measurement of the optical axis orientation of the uniaxial crystal.

Description

Method for measuring crystal optical axis orientation
Technical Field
The invention relates to the technical field of optics, in particular to a method for measuring the optical axis orientation of a crystal.
Background
In nonlinear optics, the optical axis orientation of a uniaxial crystal plays an important role in researching the dispersion of ordinary rays (o rays) and extraordinary rays (e rays) in the phenomenon of crystal birefringence and the quantitative analysis of the change rule of the dispersion. In addition, detection using polarized light as a light source is an important method in the field of information optics research, and generation of polarized light generally uses an optical element made of a crystal (generally, a uniaxial crystal), and the principle is related to anisotropy of the crystal, so that determination of the direction of the optical axis of the crystal is very important for researching the optical properties of the crystal.
Currently known methods of determining the orientation of the optical axis of a crystal include: an X-ray diffraction method, which adopts an X-ray diffractometer to measure the diffraction pattern of the crystal so as to determine the optical axis orientation of the crystal; obtaining a polarized light interference pattern of the crystal by utilizing polarized light interference of the crystal and adopting a polarized light microscope to assist in determining the optical axis orientation of the crystal; the method derives a relational expression between the optical axis position of the crystal and the birefringent emergent ray under the condition of light wave vertical incidence according to a Wheatstone refractive index ellipsoid theory, and calculates the optical axis position of the crystal through experiments. Regarding the existing method for measuring the crystal optical axis orientation, the precision of the X-ray diffraction method is 0.1 degrees, which is more accurate, but the experiment needs to know the structural parameters of the measured crystal and the specific corresponding relation between the crystal face and the diffraction peak in advance, the used equipment is expensive, and the process needs specific inspection and protection measures, so the method is more complex to implement, and the measured crystal range is limited; the polarized light interference method has larger error (3-5 degrees); the detection method based on the huygens principle needs to accurately measure the thickness of a sample and the radius of a birefringent emergent ray track circle, and for a sample with a thin thickness, such as a nanocrystal film with the thickness of hundreds of microns, the method fails when emergent rays are indistinguishable macroscopically.
The above background disclosure is only for the purpose of assisting understanding of the concept and technical solution of the present invention and does not necessarily belong to the prior art of the present patent application, and should not be used for evaluating the novelty and inventive step of the present application in the case that there is no clear evidence that the above content is disclosed at the filing date of the present patent application.
Disclosure of Invention
In order to solve the technical problem, the invention provides a method for measuring the optical axis orientation of a crystal, which can realize the rapid and accurate measurement of the optical axis orientation of a single-axis crystal based on Mueller matrix polarization imaging.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention discloses a method for measuring the optical axis orientation of a crystal, which comprises the following steps:
s1: placing a crystal sample on a first plane, making incident light incident on the surface of the crystal sample along a first direction, and measuring a first Mueller matrix of the crystal sample by using a Mueller matrix measuring system, wherein the first direction is vertical to the first plane;
s2: then rotating the crystal sample or the incident light around a first rotating direction to enable the incident light to be incident to the surface of the crystal sample at an incident angle of omega, and measuring a second Mueller matrix of the crystal sample at the moment by using a Mueller matrix measuring system, wherein a plane where the first rotating direction is located is perpendicular to the first plane;
s3: rotating the crystal sample or the incident light around a second rotation direction so that the incident light is incident on the surface of the crystal sample with an incident angle of-omega, and measuring a third Mueller matrix of the crystal sample by using a Mueller matrix measuring system, wherein the second rotation direction is opposite to the first rotation direction;
s4: and calculating according to the first Mueller matrix, the second Mueller matrix and the third Mueller matrix to obtain the optical axis orientation of the crystal sample.
Preferably, step S4 includes:
calculating and obtaining the phase delay delta generated after the incident light passes through the crystal sample in the step S1 according to the first Mueller matrixVComprises the following steps: deltaV＝δ0sin2θ0(ii) a Calculating according to the second Mueller matrix to obtain the incident light in the step S2Phase delay delta generated after passing through the crystal sample1Comprises the following steps:
Figure BDA0002992875070000021
calculating and obtaining the phase delay delta generated after the incident light passes through the crystal sample in the step S3 according to the third Mueller matrix2Comprises the following steps:
Figure BDA0002992875070000022
wherein, delta0Is the intrinsic phase retardation, theta, of the crystal sample0Is the angle between the optical axis of the crystal sample and the refracted ray, theta, in step S11Is the angle between the optical axis of the crystal sample and the refracted ray, theta, in step S22γ is an angle between the optical axis of the crystal sample and the refracted ray in step S3, and γ is an angle of refraction of the refracted ray in the crystal sample in steps S2 and S3.
Preferably, the formula for calculating γ is:
Figure BDA0002992875070000031
wherein n is the average refractive index of birefringence of the crystal sample.
Preferably, wherein θ1、θ2The calculation formula of (2) is as follows:
Figure BDA0002992875070000032
Figure BDA0002992875070000033
in the formula (I), the compound is shown in the specification,
Figure BDA0002992875070000034
and an angle between the projection of the optical axis of the crystal sample on the first plane in the step S1 and the positive direction of the coordinate axes on the first plane.
Preferably, wherein
Figure BDA0002992875070000035
And calculating according to the first Mueller matrix to obtain:
when the crystal sample is a positive uniaxial crystal,
Figure BDA0002992875070000036
when the crystal sample is a negative uniaxial crystal,
Figure BDA0002992875070000037
in the formula, M24Is an array element of the 2 nd row and the 4 th column of the first Mueller matrix, M43The array element is the 4 th row and the 3 rd column of the first Mueller matrix.
Preferably, the expression of the first mueller matrix is:
Figure BDA0002992875070000038
wherein the content of the first and second substances,
Figure BDA0002992875070000039
for fast axis angles, when the crystal sample is a positive uniaxial crystal,
Figure BDA00029928750700000310
and
Figure BDA00029928750700000311
90 degrees apart; when the crystal sample is a negative uniaxial crystal,
Figure BDA00029928750700000312
and
Figure BDA00029928750700000313
are equal.
Preferably, step S4 specifically includes:
when the crystal sample is a positive uniaxial crystal, solving a mathematical model of the optical axis orientation of the crystal sample as follows:
Figure BDA0002992875070000041
when the crystal sample is a negative uniaxial crystal, solving a mathematical model of the optical axis orientation of the crystal sample as follows:
Figure BDA0002992875070000042
preferably, the thickness of the crystal sample is 1mm or less.
Preferably, the mueller matrix measuring system includes a light source, a polarization state generating module, a polarization state analyzing module, and a signal light detector, light emitted by the light source passes through the crystal sample after passing through the polarization state generating module to generate polarized light of different polarization states, and reaches the signal light detector after passing through the polarization state analyzing module, and the signal light detector performs discrete fourier transform processing on the received signal to obtain the mueller matrix of the crystal sample.
Preferably, the polarization state generation module includes a first linear polarizer and a first quarter-wave plate, the polarization state analysis module includes a second linear polarizer and a second quarter-wave plate, wherein the light transmission directions of the first linear polarizer and the second linear polarizer are both parallel to a second direction, and the fast axis directions of the first quarter-wave plate and the second quarter-wave plate are parallel to the second direction at an initial time, during an experiment, the first quarter-wave plate and the second quarter-wave plate rotate in the same direction, and the angular velocity of the second quarter-wave plate is 5 times that of the first quarter-wave plate.
Compared with the prior art, the invention has the beneficial effects that: the method for measuring the crystal optical axis orientation is based on the Mueller matrix polarization imaging, and can be suitable for uniaxial crystal samples with very thin thickness, so that the scale range of the samples measured by the crystal optical axis can be expanded to a microscopic level (such as nano porous alumina crystals), the experimental operation is convenient and quick, and the rapid and accurate measurement of the uniaxial crystal optical axis orientation can be realized without destroying the samples. Meanwhile, due to the diversity of the mueller matrix measuring devices (a forward device for measuring transparent samples, a backward device for measuring non-transparent samples, and the capability of being integrated in a microscope), the method has certain guiding significance for exploring the anisotropy of samples such as biological tissues with birefringence properties.
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FIG. 1 is a schematic flow chart of a method for measuring the orientation of the optical axis of a crystal according to a preferred embodiment of the present invention;
FIG. 2 is a schematic diagram of a Mueller matrix of a sample measured by a dual slide rotation method;
FIG. 3a is a graph of the geometry of incident and refracted rays as they are directed at the surface of a sample;
FIG. 3b is a graph of the geometry of incident and refracted rays when the rays are obliquely incident on the surface of the sample;
FIG. 4 is a schematic representation of a uniaxial crystal sample lying in the XOY plane and its optical axis orientation in a three-dimensional coordinate system;
fig. 5 is a schematic diagram of the rotation angle ω of the uniaxial crystal sample in the first rotational direction about the Y axis (rotational axis) in the XOY plane.
Detailed Description
In order to make the technical problems, technical solutions and advantageous effects to be solved by the embodiments of the present invention more clearly apparent, the present invention is further described in detail below with reference to the accompanying drawings and the embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
It will be understood that when an element is referred to as being "secured to" or "disposed on" another element, it can be directly on the other element or be indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or be indirectly connected to the other element. In addition, the connection may be for either a fixing function or a circuit connection function.
It is to be understood that the terms "length," "width," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in an orientation or positional relationship indicated in the drawings for convenience in describing the embodiments of the present invention and to simplify the description, and are not intended to indicate or imply that the referenced device or element must have a particular orientation, be constructed in a particular orientation, and be in any way limiting of the present invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the embodiments of the present invention, "a plurality" means two or more unless specifically limited otherwise.
As shown in fig. 1, a preferred embodiment of the present invention provides a method for measuring crystal orientation based on mueller matrix polarization imaging, including the following steps:
s1: the method comprises the steps that a crystal sample is placed on a first plane, incident light is incident to the surface of the crystal sample along a first direction, a first Mueller matrix of the crystal sample at the moment is measured by a Mueller matrix measuring system, and the first direction is perpendicular to the first plane;
s2: then rotating the crystal sample or the incident light around a first rotating direction to enable the incident light to be incident to the surface of the crystal sample with an incident angle of omega, and measuring a second Mueller matrix of the crystal sample by using a Mueller matrix measuring system, wherein a plane where the first rotating direction is located is perpendicular to a first plane;
s3: rotating the crystal sample or the incident light around a second rotating direction to enable the incident light to be incident to the surface of the crystal sample with the incident angle being-omega, and measuring a third Mueller matrix of the crystal sample by adopting a Mueller matrix measuring system, wherein the second rotating direction is opposite to the first rotating direction;
s4: and calculating according to the first Mueller matrix, the second Mueller matrix and the third Mueller matrix to obtain the optical axis orientation of the crystal sample.
The method for measuring the crystal orientation based on mueller matrix polarization imaging according to the preferred embodiment of the present invention is described below with specific examples.
The method for measuring the optical axis orientation of a uniaxial crystal based on the Polarization imaging method of the Mueller matrix is provided by the invention, wherein the optical path for measuring the Mueller matrix of a sample is based on a dual-wave plate rotation method, a schematic diagram is shown in FIG. 2, L is a light source, P and A are two linear polarizers, C and C 'are two quarter wave plates, S is a sample, D is a signal light detector, wherein P and C are called Polarization State Generators (PSG), and C' and A are called Polarization State Analyzers (PSA). The light passing directions of P and A are set to be parallel to the x axis, the fast axis directions of initial moments C and C ' are parallel to the x axis, two quarter-wave plates C and C ' are rotated along the same direction in the experiment process, the angular speed of C ' is 5 times that of C (C is omega t, C is 5 omega t), polarized light in different polarization states can be generated to pass through a sample and reach an optical signal detector through a polarization state analysis module, and Discrete Fourier Transform (DFT) processing is carried out on the received signal, so that a Mueller matrix of the sample can be obtained. The Mueller matrix measuring light path is convenient and fast to build, and is high in mobility and integration degree, and the relative error of multiple experiments verified by a standard sample true zero-order wave plate is below 1% in a forward Mueller matrix measuring light path built in a laboratory, so that the rapid and accurate measurement of the optical axis orientation of the uniaxial crystal can be realized.
The birefringence effect of light passing through the crystal is an important feature of the crystal and also an important proof of the anisotropy of the crystal. The result of the birefringence effect is that light is split in the crystal into two beams that differ in the direction of vibration and propagation: the refractive indexes of the propagation directions of the two lights are generally different when the two lights propagate in the crystal, so that the propagation speeds of the two lights are different, and the two lights are out of phase difference when the two lights exit from the crystal. A conventional phase retarder is manufactured according to a birefringence effect of a crystal, and performs phase modulation on light passing through the crystal by the birefringence effect to change a polarization state of the light, and controls a change in a phase of the light to obtain a desired polarized light.
The polarization state of linearly polarized light passing through the crystal is changed, the crystal is equivalent to a linear phase retarder, and the Mueller matrix of pure linear phase retardation is represented as follows:
Figure BDA0002992875070000071
wherein the mueller matrix comprises only two parameters,
Figure BDA0002992875070000072
an angle parameter representing birefringence orientation, namely a fast axis angle, namely an included angle between a fast axis direction (which refers to a light vector direction with high propagation speed in the crystal, and a corresponding slow axis direction which refers to a light vector direction with low propagation speed in the crystal, wherein the fast axis and the slow axis are mutually vertical) of the crystal and a horizontal direction; δ represents the phase delay of the line phase retarder. It should be noted that, in the same crystal device, the phase retardation is related to the incident angle of light, and the phase retardation generated when light is normally incident on the crystal is different from the phase retardation generated when light is obliquely incident on the crystal, and formula (1) is used as a mueller matrix formula of a standard phase retarder and is generally commonly used in the case of normal incidence of light on the surface of a sample.
The geometrical relationship between incident rays and refracted rays when the rays are incident on the sample surface normally is shown in FIG. 3a, and the geometrical relationship between incident rays and refracted rays when the rays are incident on the sample surface obliquely is shown in FIG. 3b, where opt represents the optical axis orientation of the uniaxial crystal, and S represents the optical axis orientation of the uniaxial crystalinDenotes the incident ray, d is the sample thickness, γ1And gamma2Two refraction angles representing birefringence.
When the optical axis of the wave plate lies on the surface, the calculation formula of the phase delay generated by the light passing through the uniaxial crystal wave plate is as follows:
Figure BDA0002992875070000073
in the above formula, δintThe phase delay generated by the normal incidence of light passing through the wave plate, namely the intrinsic phase delay of the wave plate, d is the effective optical path of the light passing through the crystal, the thickness of the crystal wave plate when the light is normal incidence, neDenotes the corresponding refractive index of e-ray on the principal axis of the crystal, noDenotes the refractive index of the crystal with respect to o light, and λ denotes the wavelength of incident light, (note: formula (2) is represented by ne＞noFor example, in the case of a negative uniaxial crystal, n ise＜noThe difference between the refractive indices in the formula is no-ne)。
At this time, if the wave plate is inclined or the incident light is inclined, the phase delay generated after the light passes through the wave plate is no longer the intrinsic phase delay of the wave plate, and the phase delay at this time is measured by the phase delay deltameaTo show that:
Figure BDA0002992875070000081
in the above formula, l represents the actual effective optical path of light passing through the sample, and when the light is obliquely incident on the sample, l is usually not equal to the thickness of the sample; n'eRepresenting the actual refractive index of e-light.
Wherein, deltaintAnd deltameaThere is an approximate relationship between:
Figure BDA0002992875070000082
in the above formula, θ represents an angle between a wave normal direction of a refracted ray in the crystal (here, the direction of the refracted ray takes a refraction angle γ) and an optical axis direction of the crystal, and γ is a refraction angle γ in fig. 3b1And gamma2Average value of (a). It should be noted that in a uniaxial crystal, the refracted ray of o-light is co-directional with its wave normal, while the wave normal of e-light is at an angle, called the walk-off angle,generally denoted by α, which is calculated by the formula:
Figure BDA0002992875070000083
when tan theta is equal to ne/noWhen, α takes the maximum value. By aligning some neAnd noThe known uniaxial crystals perform numerical calculations, the maximum value of α is typically less than 0.5 °, so here the direction of the e-wave normal is taken to be approximately the direction of the e-refracted ray. At the same time, since neAnd noThe phase difference is small (so when the thickness of the crystal sheet is small, the separation of two outgoing rays with double refraction is difficult to observe macroscopically after the light passes through the sheet, which is also a disadvantage of the direction of the optical axis by the Wheatstone principle method), so that the refraction angle is gamma in the subsequent calculation1And gamma2Average value of (a).
As shown in FIG. 4, when an incident light ray perpendicularly enters the surface of the uniaxial crystal sheet, the incident point is used as the origin, the propagation direction of the incident light ray is the Z-axis direction, the X-direction and the Y-direction are positioned in the sample plane to establish a coordinate system as shown in the figure, the uniaxial crystal has arbitrary optical axis orientation, and the included angle between the optical axis direction and the refracted light ray (wave normal), namely the Z-axis, is recorded as theta0The projection of the optical axis on the XOY surface forms an included angle with the positive direction of the X axis
Figure BDA0002992875070000084
The unit vector in the optical axis direction can be expressed as:
Figure BDA0002992875070000091
determining theta0And
Figure BDA0002992875070000092
the optical axis orientation of the sample is obtained.
The following describes specific steps of measuring the optical axis orientation of a uniaxial crystal by using a mueller matrix polarization imaging method, where the coordinate system shown in fig. 4 is adopted, and the incident light is always along the Z-axis (first direction) (in other embodiments, the sample may be always kept different, and the incident angle of the rotating incident light reaches the measurement conditions of each step):
(1) placing a sample slice on an XOY plane (a first plane), enabling light to be normally incident to the surface of the sample, testing the Mueller matrix of the sample by adopting a Mueller matrix forward measurement system, wherein the included angle between the optical axis of the sample and the refracted light ray is theta0；
(2) As shown in fig. 5, the sample is rotated around the Y axis from the Z direction to the X direction (the first rotation direction) by an angle ω, that is, the incident angle of the light is ω, and the mueller matrix of the sample is measured, and the included angle between the optical axis of the sample and the refracted light is θ1；
(3) Rotating the sample by 2 omega from the X direction to the Z direction (second rotation direction) around the Y axis, namely the incident angle of the light is-omega, measuring the Mueller matrix of the sample at the moment, wherein the included angle between the optical axis of the sample and the refracted light is theta2。
The intrinsic phase retardation of the sample is noted as delta0In the above three cases, the phase retardation generated after the incident light enters the sample sheet is deltaV，δ1，δ2After determining the Mueller matrix of the sample, deltaV，δ1，δ2A Mueller Matrix Decomposition (MMD) can be used to obtain specific values. According to equation (4), the following relationship holds:
Figure BDA0002992875070000093
where γ can be derived from the law of refraction:
Figure BDA0002992875070000094
the optical axis vector in the step (2) can be obtained by multiplying the original vector by a rotation matrix:
Figure BDA0002992875070000095
the refracted ray vector is:
Figure BDA0002992875070000101
then using the vector inner product, one can calculate:
Figure BDA0002992875070000102
then:
Figure BDA00029928750700001011
from formulas (7) and (11):
Figure BDA0002992875070000103
similarly, for the case where the incident angle is- ω in step (3), the optical axis vector is:
Figure BDA0002992875070000104
the refracted ray vector is:
Figure BDA0002992875070000105
it is possible to obtain:
Figure BDA0002992875070000106
from formulas (7) and (14):
Figure BDA0002992875070000107
the equations (12) and (15) can be combined to form an equation system containing 3 unknowns, θ0，
Figure BDA0002992875070000108
And the average refractive index n of the birefringence of the sample, the third equation being based on the Mueller matrix equation (1) for a phase-only retarder
Figure BDA0002992875070000109
The parameters are listed and need to be modified according to the crystal type.
In formula (1)
Figure BDA00029928750700001010
Is the angle between the fast axis direction of the crystal and the horizontal direction (X direction in fig. 4). When the sample of the thin slice is very thin (millimeter magnitude or thinner), the normal direction of the light wave propagating in the sample can be assumed to be coincident with the light direction, and then the relation between the projection of the optical axis on the sample surface and the fast axis of the sample thin slice can be found according to the propagation rule of the plane monochromatic wave in the crystal and the Maxwell equation system. When light is normally incident on the surface of the crystal sheet, the projection of the optical axis on the surface of the crystal sheet is the vibration direction of the e-ray light vector as viewed in the index ellipsoid. For a positive uniaxial crystal (n)o<ne) The fast axis direction is the vibration direction of the o light vector and is always vertical to the optical axis, and the vibration direction of the e light vector is the slow axis direction, namely when the assumed condition is met, the projection of the optical axis on the surface of the crystal slice corresponds to the slow axis direction of the crystal, and the fast axis angle is
Figure BDA0002992875070000111
The positive included angle between the projection of the optical axis on the XOY plane and the X axis
Figure BDA0002992875070000112
90 degrees apart; for negative uniaxial crystal, the fast axis direction is the vibration direction of e-ray light vector, namely the projection of the optical axis on the surface of the crystal slice is the fast axis direction at the moment, and the fast axis angle
Figure BDA0002992875070000113
Included angle between projection of optical axis on XOY plane and positive direction of X axis
Figure BDA0002992875070000114
Are equal.
Considering the situation that the light is normally incident to the surface of the sample in the step (1), the Mueller matrix array element M in the formula (1)24And M34(or M)43And M42) Angle of fast axis
Figure BDA0002992875070000115
Can be expressed as:
Figure BDA0002992875070000116
in summary, the mathematical model for determining the orientation of the optical axis of a uniaxial crystal of known crystal lamella type by measuring the mueller matrix of a crystal sample at normal incidence and two symmetric rotations can be summarized as:
positive uniaxial crystal:
Figure BDA0002992875070000117
negative uniaxial crystal:
Figure BDA0002992875070000118
the unknowns in the formulae (17) and (18) are 3, θ0，
Figure BDA0002992875070000119
And n, solving the equation system to obtain an angle parameter theta representing the optical axis orientation0，
Figure BDA00029928750700001110
The preferred embodiment of the invention provides a method for measuring the crystal optical axis orientation by using Mueller matrix polarization imaging, starting from the essence that the crystal birefringence is influenced by the optical axis orientation, a reasonable assumption is provided by using a standard Mueller matrix formula and a basic formula of birefringence of a birefringence device under the condition that a sample per se meets specific conditions, namely when the thickness of a uniaxial crystal sample is very thin (less than or equal to 1mm), the light ray direction of light propagating in the crystal is superposed with the light wave normal direction, and a mathematical model capable of solving the crystal optical axis orientation by using limited measurement is constructed; in addition, the model is concise in form, is combined with a mature Mueller matrix decomposition method, and is more accurate when being discussed according to different crystal types in different cases.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several equivalent substitutions or obvious modifications can be made without departing from the spirit of the invention, and all the properties or uses are considered to be within the scope of the invention.

Claims (10)

1. A method for measuring the optical axis orientation of a crystal is characterized by comprising the following steps:
s1: placing a crystal sample on a first plane, making incident light incident on the surface of the crystal sample along a first direction, and measuring a first Mueller matrix of the crystal sample by using a Mueller matrix measuring system, wherein the first direction is vertical to the first plane;
s2: then rotating the crystal sample or the incident light around a first rotating direction to enable the incident light to be incident to the surface of the crystal sample at an incident angle of omega, and measuring a second Mueller matrix of the crystal sample at the moment by using a Mueller matrix measuring system, wherein a plane where the first rotating direction is located is perpendicular to the first plane;
s3: rotating the crystal sample or the incident light around a second rotation direction so that the incident light is incident on the surface of the crystal sample with an incident angle of-omega, and measuring a third Mueller matrix of the crystal sample by using a Mueller matrix measuring system, wherein the second rotation direction is opposite to the first rotation direction;
s4: and calculating according to the first Mueller matrix, the second Mueller matrix and the third Mueller matrix to obtain the optical axis orientation of the crystal sample.
2. The measuring method according to claim 1, wherein step S4 includes:
calculating and obtaining the phase delay delta generated after the incident light passes through the crystal sample in the step S1 according to the first Mueller matrixVComprises the following steps: deltaV＝δ0sin2θ0(ii) a Calculating and obtaining the phase delay delta generated after the incident light passes through the crystal sample in the step S2 according to the second Mueller matrix1Comprises the following steps:
Figure FDA0002992875060000011
calculating and obtaining the phase delay delta generated after the incident light passes through the crystal sample in the step S3 according to the third Mueller matrix2Comprises the following steps:
Figure FDA0002992875060000012
wherein, delta0Is the intrinsic phase retardation, theta, of the crystal sample0Is the angle between the optical axis of the crystal sample and the refracted ray, theta, in step S11Is the angle between the optical axis of the crystal sample and the refracted ray, theta, in step S22γ is an angle between the optical axis of the crystal sample and the refracted ray in step S3, and γ is an angle of refraction of the refracted ray in the crystal sample in steps S2 and S3.
3. The method of claim 2, wherein γ is calculated by the formula:
Figure FDA0002992875060000013
wherein n is the average refractive index of birefringence of the crystal sample.
4. The method of claim 2, wherein θ1、θ2The calculation formula of (2) is as follows:
Figure FDA0002992875060000021
Figure FDA0002992875060000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002992875060000023
and an angle between the projection of the optical axis of the crystal sample on the first plane in the step S1 and the positive direction of the coordinate axes on the first plane.
5. The measuring method according to claim 4, wherein
Figure FDA0002992875060000024
And calculating according to the first Mueller matrix to obtain:
when the crystal sample is a positive uniaxial crystal,
Figure FDA0002992875060000025
when the crystal sample is a negative uniaxial crystal,
Figure FDA0002992875060000026
in the formula, M24Is an array element of the 2 nd row and the 4 th column of the first Mueller matrix, M43The array element is the 4 th row and the 3 rd column of the first Mueller matrix.
6. The measurement method according to claim 5,
the expression of the first mueller matrix is:
Figure FDA0002992875060000027
wherein the content of the first and second substances,
Figure FDA0002992875060000028
for fast axis angles, when the crystal sample is a positive uniaxial crystal,
Figure FDA0002992875060000029
and
Figure FDA00029928750600000210
90 degrees apart; when the crystal sample is a negative uniaxial crystal,
Figure FDA00029928750600000211
and
Figure FDA00029928750600000212
are equal.
7. The measurement method according to claim 5, wherein step S4 specifically includes:
when the crystal sample is a positive uniaxial crystal, solving a mathematical model of the optical axis orientation of the crystal sample as follows:
Figure FDA0002992875060000031
when the crystal sample is a negative uniaxial crystal, solving a mathematical model of the optical axis orientation of the crystal sample as follows:
Figure FDA0002992875060000032
8. the measurement method according to any one of claims 1 to 7, wherein the thickness of the crystal sample is 1mm or less.
9. The measurement method according to any one of claims 1 to 7, wherein the mueller matrix measurement system includes a light source, a polarization state generation module, a polarization state analysis module, and a signal light detector, light emitted by the light source passes through the crystal sample after passing through the polarization state generation module to generate polarized light of different polarization states, and reaches the signal light detector after passing through the polarization state analysis module, and the signal light detector performs discrete Fourier transform processing on the received signal to obtain the mueller matrix of the crystal sample.
10. The measurement method according to claim 9, wherein the polarization state generation module comprises a first linear polarizer and a first quarter-wave plate, the polarization state analysis module comprises a second linear polarizer and a second quarter-wave plate, wherein the light transmission directions of the first linear polarizer and the second linear polarizer are both parallel to a second direction, and the fast axis directions of the first quarter-wave plate and the second quarter-wave plate are parallel to the second direction at an initial moment, the first quarter-wave plate and the second quarter-wave plate rotate in the same direction during an experiment, and the angular velocity of the second quarter-wave plate is 5 times that of the first quarter-wave plate.
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