CN103712781B - The multiple angles of incidence polarization interference measurement mechanism of birefringent wedge optical axis direction and method - Google Patents

Abstract

The invention discloses a device and method for multi-incident angle polarization interferometry in the direction of the optical axis of a birefringent optical wedge. The device includes a laser light source (1), an optical attenuator (2), a beam expander (3), and a polarizer (4), birefringence wedge (5), sample test bench (6), analyzer (7), area array detector (8) and signal processing system (9). Compared with the existing technology, by collecting three polarization interferograms under different incident angles, the three-dimensional direction measurement of the optical axis of the birefringent wedge can be quickly realized, which overcomes the lack of systems and methods for measuring the optical axis of the birefringent wedge in the past. Difficulties; the measurement accuracy can be further improved by increasing the number of incident angle adjustments; it is also suitable for traditional birefringent specimens with parallel incident planes and exit planes, and the error range is small to ensure measurement accuracy, so it is widely applicable.

Description

Multi-incident angle polarization interferometry device and method for birefringent wedge optical axis direction

technical field

The invention relates to the field of birefringent crystal parameter detection, in particular to a multi-incident angle polarization interferometry device in the optical axis direction of a birefringent light wedge.

Background technique

The optical axis of the crystal is an important optical parameter of the crystal. The difference in the three-dimensional direction relative to the incident surface of the crystal device will affect the performance of the crystal device. Therefore, the detection technology for the three-dimensional direction of the crystal optical axis is very important.

There are already some measurement methods for determining the direction of the crystal optical axis. M.Laue (FriedrichW, KnippingP, LaueM.Interferenceappearancesinx-rays[J].Ann.Phys.(Berlin), 1913,41:971-988.) Proposed crystal optical axis direction X-ray diffraction method, the measurement accuracy is high, but The method is complicated, and it is necessary to know the structural parameters of the crystal and the corresponding relationship between the crystal plane and the diffraction peak; Zhang Yi et al. (Zhang Yi, Shen Weimin. Theoretical and experimental research on uniaxial crystal conoscopic interference[J]. Acta Scientia Sinica), 2005,32(4):403-406.) Use the polarized light interferogram of the crystal to determine the direction of the crystal optical axis. The crystal polarized light interferogram is collected by a polarizing microscope. The corresponding point of the refracted light in the interferogram in the axial direction, that is, the black cross intersection) is used to measure the optical axis direction relative to the center of the field of view; D.Su (SuDC, HsuCC.Method for determining the optical axis and (no, ne) of abirefringent crystal[J] .Appliedoptics, 2002, 41(19): 3936-3940.) etc. used a common optical path interference heterodyne method to measure the direction of the optical axis; Duan Cunli et al. (Duan Cunli, Han Jun, Lu Shaojun, etc. Principle research on a new method to determine the direction of the optical axis of a uniaxial crystal [J]. Optical Instruments, 2008, 30(4): 55-59.) Using the Huygens principle to analyze the direction of light wave propagation, according to the relationship between the optical axis and the normal of the crystal surface Relational formula to realize the measurement of the optical axis direction of the crystal; Shen Weimin et al. Determining the normal line of the crystal surface to measure the direction of the optical axis; Xing Jinhua et al. -50.) Determine the direction of the optical axis of a uniaxial crystal by measuring the Brewster's angles on three surfaces of the crystal sample.

The above method is usually to measure the direction of the optical axis of the standard test piece. It is required that the incident surface and the outgoing surface of the test piece are parallel to each other to ensure that the two outgoing directions of the o light and the e light are parallel to each other, and the o light and the e light of the test piece are required to be parallel to each other. Light has a large refractive index difference. However, there is an angle between the incident surface and the exit surface of the birefringent wedge, which causes the two outgoing lights (o light and e light) to be non-parallel, and the difference in refractive index between the two beams of light is small, and it is difficult to distinguish them. The measurement of the three-dimensional direction of the wedge optical axis brings difficulties. The present invention aims to overcome the above-mentioned difficulties and realize the precise measurement of the three-dimensional direction of the optical axis of the birefringence wedge.

Contents of the invention

In order to overcome the problems existing in the prior art, the present invention aims at the above deficiencies, and proposes a multi-incident angle polarization interferometry device and method in the direction of the optical axis of the birefringent optical wedge, which is used for the measurement of the three-dimensional direction of the optical axis of the birefringent optical wedge, and at the same time It can also be used to measure the optical axis orientation of other birefringent devices.

The invention proposes a multi-incident angle polarization interferometry device in the direction of the optical axis of a birefringent wedge, which includes a laser light source (1), an optical attenuator (2), a beam expander (3), and a polarizer (4 ), birefringent wedge (5), sample test bench (6), analyzer (7), area array detector (8) and signal processing system (9) where:

The laser light source (1) is used to provide the input light source of the device, using visible light band lasers with good spatial coherence, including He-Ne lasers and semiconductor lasers;

The optical attenuator (2) is used to reduce the laser energy, control the power of the laser light source to be stable, and avoid saturation of the area array detector;

The beam expander (3) is used for laser beam expansion to ensure that the laser light source exits in parallel to obtain a spatially coherent laser spot covering the transverse dimension of the birefringent wedge;

The polarizer (4) is used for polarizing the laser beam, and the direction of the light transmission axis is 45° to the horizontal reference;

The sample test table (6) is used to place the birefringent light wedge (5) to be tested and to control the incident angle of the birefringent light wedge. Birefringent wedge surface produces polarization interference;

The analyzer (7) is used to realize polarization interference, and the direction of the light transmission axis is 45° to the horizontal reference, and is perpendicular or parallel to the polarizer at the same time;

An area array detector (8), including a CCD and a CMOS detector, is used to receive polarization interferogram signals; and

The signal processing system (9), including an image acquisition card and a computer, is used to collect the polarization interferogram signal, and the computer processes it according to the measurement algorithm to calculate the three-dimensional direction of the optical axis of the birefringent wedge;

The laser light source (1) outputs the laser beam in parallel, and when the laser energy is reduced by the optical attenuator (2), the laser power is controlled to be stable to avoid detector saturation; the beam expander (3) expands the laser beam to obtain a lateral coverage of the birefringent wedge The spatially coherent laser spot of the size is polarized by the polarizer (4), and the direction of the light transmission axis is 45° to the horizontal reference. The birefringent wedge 5 to be tested is placed on the sample test platform (6). By adjusting the sample test platform ( 6), rotate the birefringent wedge (5), so as to realize polarization interference on the surface of the incident wedge at different angles, and the beam passing through the birefringent wedge (5) realizes polarized light interference after the analyzer (7). The array detector (8) receives the polarization interferogram and transmits it to the signal processing system 9.

The present invention also proposes a multi-incident angle polarization interferometry method in the optical axis direction of a birefringent optical wedge, the method comprising the following steps:

The laser light source (1) outputs the laser beam in parallel, and when the laser energy is reduced by the optical attenuator (2), the laser power is controlled to be stable to avoid detector saturation; the beam expander (3) expands the laser beam to obtain a lateral coverage of the birefringent wedge The spatially coherent laser spot of the size is polarized by the polarizer (4), and the direction of the light transmission axis is 45° to the horizontal reference. The birefringent wedge (5) to be tested is placed on the sample test platform (6), and the sample is tested by adjusting the The stage (6) rotates the birefringent wedge (5), so as to realize polarization interference on the surface of the incident wedge at different angles, and the beam passing through the birefringent wedge (5) realizes polarization interference after the analyzer (7), The polarization interferogram is received by the area array detector (8) and transmitted to the signal processing system (9); at each incident angle, a polarization interferogram is recorded, and when three polarization interferograms at different incident angles are collected , in the signal processing system (9), the polarization interference signal is processed by grayscale transformation and hough transformation, the bright fringes of the polarization interferogram are extracted, the interference fringe spacing is calculated, and the simultaneous optical path difference equations composed of three incident angles , to solve the three-dimensional direction of the optical axis of the birefringent wedge;

The process of forming the simultaneous optical path difference equations through three incident angles of the birefringent wedge is as follows:

Establish the corresponding relationship between the adjacent bright fringe spacing h and the crystal wedge thickness t:

The optical path difference of adjacent bright fringes in polarization interference δΔ=λ, thus the formula of optical path difference δΔ between adjacent fringes of polarized interference light is obtained:

$\mathrm{<span\; class="notranslate">\; \&delta;\&Delta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&delta;d</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; re</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ro</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ro</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In formula (1), θ is the incident angle, n _re is the refractive index of the e-ray in its propagation direction; θ _ro is the angle between the o-ray and the normal of the crystal surface; δd is the birefringence of the adjacent e-ray The path difference propagated in the optical wedge; δx _e is the propagation path difference of adjacent e light in the x-axis direction; δz _e is the propagation path difference of adjacent e light in the z-axis direction;

When the incident angle θ remains unchanged, n _re and θ _ro remain unchanged, and only δd, δx _e and δz _e change.

Select three different incident angles of 0°, 30°, and 45° to obtain the equations:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&delta;\&Delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; re</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\\ {\mathrm{<span\; class="notranslate">\; \&delta;\&Delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; re</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.39</span>}{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\\ {\mathrm{<span\; class="notranslate">\; \&delta;\&Delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; re</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.514</span>}{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

and

In formula (3), are the angles between the wedge plane and the x, y, z axes respectively, α, β, γ are the angles between the birefringent wedge optical axis and the x, y, z axes, θ _ke is the e-ray light wave vector and the crystal surface For the included angle of the normal line, M ₁ and M ₂ are the corresponding coefficients.

Compared with the prior art, the present invention has the following positive effects:

1. A multi-incident angle polarization interferometry device and method for the direction of the optical axis of the birefringent wedge is proposed. By collecting three polarization interferograms at different incident angles, the three-dimensional direction measurement of the optical axis of the birefringent wedge can be quickly realized. Overcome the problem of no birefringent wedge optical axis measurement system and method in the past;

2. Proposed a multi-incident angle polarization interferometry device and method in the direction of the birefringent wedge optical axis, which can further improve the measurement accuracy by increasing the number of incident angle adjustments;

3. The proposed measurement device and method are also suitable for the traditional birefringent specimens whose incident plane and exit plane are parallel, so it can be widely used.

Description of drawings

Fig. 1 is the schematic diagram of the measurement system of the optical axis direction of the birefringent optical wedge in the present invention;

Figure 2 is a comparison diagram of acquisition polarization interference and restoration polarization interference;

Fig. 3 is a schematic diagram of the polarization direction of the polarization interference produced by the birefringent optical wedge;

Figure 4 is a schematic diagram of the comparison of the two-beam interference intensity distribution;

In the figure, 1. He-Ne laser, 2. Optical attenuator, 3. Beam expander, 4. Polarizer, 5. Birefringent wedge, 6. Sample test bench, 7. Analyzer, 8. Surface Array detector, 9. Signal processing system, 10 Collect polarization interferogram, 11, Restore polarization interferogram, 12, Polarizer light transmission axis direction, 13, Birefringence wedge optical axis direction, 14, Analyzer light transmission Axial direction, 15, amplitude of o light after incident light wedge, 16, projection amplitude of o light passing through analyzer, 17, amplitude of incident light, 18, amplitude of e light after incident light wedge, 19, e light passing through analyzer 20, the angle of the optical axis of the birefringent wedge from the y-axis, 21, the origin of the coordinates of the intersection point of the two polarizers, 22, the angle between the direction of the optical axis of the polarizer and the coordinate axis x, 23, the detector Angle between polarizer optical axis direction and coordinate axis x, 24 polarization interference normalized intensity variation ΔI, 25, variation Δx of optical wedge position corresponding to low coherence interference fringe peak.

detailed description

The specific implementation manner of the present invention will be further described in detail below in conjunction with the accompanying drawings and examples.

Embodiment 1: Implementation process of multi-incident angle polarization interferometry device and method in the direction of birefringent wedge optical axis

As shown in Figure 1, the present invention adopts multi-incident angle polarization interferogram to realize the measurement of the direction of the optical axis of the birefringent wedge. The measuring device consists of a laser light source (1), an optical attenuator (2), a beam expander (3), and Polarizer (4), sample test bench (6), analyzer (7), area detector (8) and signal processing system (9).

He-Ne laser (1) outputs laser light, and when the laser energy is reduced through the optical attenuator (2) in parallel, the laser power is controlled to be stable to avoid detector saturation; the beam expander (3) expands the laser beam to obtain covered birefringent light The spatially coherent laser spot of wedge lateral size is polarized by the polarizer (4), and the polarization direction is 45° to the horizontal direction. The measured birefringence wedge (5) is placed on the sample test platform (6). By adjusting the sample test The birefringent wedge is rotated to achieve polarization interference on the surface of the wedge at different angles, and the beam passing through the birefringent wedge achieves polarization interference after the analyzer (7), and is received by an area array detector (8) The polarization interferogram is transmitted to the signal processing system (9). Under each incident angle, a polarization interferogram is recorded. When three polarization interferograms with different incident angles are collected, the polarization interference signal is processed in the signal processing system. Perform grayscale transformation and hough transformation processing to extract the bright fringes of the polarization interferogram, calculate the fringe spacing of the interferogram, and solve the three-dimensional direction of the optical axis of the birefringent wedge through the simultaneous optical path difference equations composed of three incident angles .

Example 2: Specific implementation of the fringe spacing extraction process of the polarization interferogram

Three different angles of 0°, 30°, and 45° are incident on the surface of the birefringent wedge, and the polarization interference signal is collected by the area array detector (8) to extract the interferogram fringe spacing. The extraction process is as follows: firstly, the grayscale transformation is performed on the polarization interferogram to obtain the grayscale image; then the hough transformation is performed on the grayscale image to extract the bright fringes of the polarization interferogram. After hough transformation, read the pixel value difference p=p1-p2 between the number of bright fringes N. According to the size ε of each pixel of the area array detector, the interference fringe spacing is calculated as h=ε·p/N=ε·(p ₁ -p ₂ )/N.

Example 3: The specific process of solving the direction of the optical axis of the birefringent wedge

After the interference fringe spacing is extracted, theoretically analyze the expression of the incident optical path difference at different angles. The corresponding relationship between the adjacent bright fringe spacing h and the crystal wedge thickness difference t is as follows: The optical path difference between adjacent bright fringes is δΔ=λ; therefore, the formula for the optical path difference between adjacent fringes of the polarization interference signal is:

$\mathrm{<span\; class="notranslate">\; \&delta;\&Delta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&delta;d</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; re</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ro</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; ro</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, θ is the incident angle, n _re is the refractive index of the e-ray in its propagation direction; θ _ro is the angle between the o-ray and the normal of the crystal surface; δd is the birefringent wedge of the adjacent e-ray Propagation path difference; δx _e is the propagation path difference of adjacent e light in the x-axis direction; δz _e is the propagation path difference of adjacent e light in the z-axis direction;

When the incident angle θ remains unchanged, n _re and θ _ro remain unchanged, and only δd, δx _e and δz _e change.

Select three different incident angles of 0°, 30°, and 45° to obtain the equations:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&delta;\&Delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;d</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; re</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\\ {\mathrm{<span\; class="notranslate">\; \&delta;\&Delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;d</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; re</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.39</span>}{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\\ {\mathrm{<span\; class="notranslate">\; \&delta;\&Delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&delta;d</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; re</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.514</span>}{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}{\mathrm{<span\; class="notranslate">\; \&delta;z</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

and

In formula (3), are the angles between the wedge plane and the x, y, z axes respectively, α, β, γ are the angles between the birefringent wedge optical axis and the x, y, z axes, θ _ke is the e-ray light wave vector and the crystal surface The included angle of the normal line, M ₁ and M ₂ are the corresponding coefficients.

Solve the equations to obtain the solution of the equations, that is, the three-dimensional direction angles (α, β, γ) of the optical axis of the birefringent wedge.

Compared with the ideal optical axis direction, the angle error of the optical axis direction is controlled within 0.5°, which ensures the measurement accuracy. Fig. 3 is a schematic diagram of a comparison between acquisition polarization interference and restoration polarization interference. Among them, the three-dimensional direction angles α, β, and γ of the optical axis obtained by the restoration polarization interference are substituted into the expression of the optical path difference δΔ, and the restoration polarization interference light is obtained according to the optical path difference between the o light and the e light during the propagation process The intensity distribution is compared with the acquisition polarization interference, which shows that the measurement error range is small and the measurement accuracy is guaranteed.

Example 4: Analysis of the impact on the pressure demodulation system

In actual situations, when the direction of the optical axis is not ideal (parallel to the y-axis direction), there will be a certain deflection angle β. At this time, the polarized light interference diagram is shown in Figure 4.

At this time, the projected amplitude of e light and o light on the analyzer is obtained and where the interference strength is:

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; *</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; E.</span>}}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; sin</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; c</span>}{\mathrm{<span\; class="notranslate">\; os</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

The relevant parameters are as follows: β=0.4°

Central wavelength: λ ₀ =580nm, ν ₀ =5.1724×10 ¹⁴ Hz

The wavelength corresponding to the bandwidth is: λ ₁ =530nm, λ ₂ =633nm, Δν=0.92167×10 ¹⁴ Hz

Optical wedge parameters: wedge angle Length L=25mm, width d ₁ =3mm, d ₂ =6.51mm

Only considering the comparison between the actual and ideal conditions of the mutually coherent interference part in the two-beam interference, the interference light intensity diagram received by the area array detector under the two conditions is obtained, which is shown in Figure 4 after normalization.

Among them, the change amount Δx25 of the wedge position corresponding to the peak value of the mutual interference fringes:

$\mathrm{<span\; class="notranslate">\; \&Delta;x</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.776</span>}\mathrm{<span\; class="notranslate">\; \&mu;m</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In formula (5), l is the corresponding cavity length, ideally the coefficient The actual situation k' has light with the deviation angle.

Corresponding intensity variation ΔI24 of mutual interference peak:

$\mathrm{<span\; class="notranslate">\; \&Delta;I</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1.9996</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

In formula (6), $m={\sin }^{2}2\mathrm{\&beta;}+\frac{1}{2}{\cos }^{2}2\mathrm{\&beta;},$ $\mathrm{no}=\frac{1}{2}{\cos }^{2}2\mathrm{\&beta;},$ S is the sensitivity of the two-beam interference fringes. According to the analysis, the variation of the wedge position corresponding to the peak of the mutual interference fringe and the variation of the intensity corresponding to the peak are both small, so when the range of the deviation angle β is controlled within 0.5°, its effect on the demodulation of the birefringent wedge can be ignored The influence can be ignored in the pressure regulation system.

Claims (2)

1. the multiple angles of incidence polarization interference measurement mechanism of a birefringent wedge optical axis direction, it is characterized in that, this device comprises LASER Light Source (1), optical attenuator (2), beam expanding lens (3), the polarizer (4), birefringent wedge (5), sample test platform (6), analyzer (7), planar array detector (8) and signal processing system (9); Wherein:

LASER Light Source (1), for providing the input light source of this device, adopting the visible light wave range laser instrument that spatial coherence is good, comprising He-Ne laser instrument and semiconductor laser;

Optical attenuator (2), for reducing laser energy, controls laser light source power and stablizes, avoid planar array detector saturated;

Beam expanding lens (3), for laser beam expanding, ensures LASER Light Source exiting parallel, obtains the spatial coherence laser facula covering birefringent wedge lateral dimension;

The polarizer (4), does up partially for laser light, light transmission shaft direction and horizontal reference at 45 °;

Sample test platform (6), for placing birefringent wedge (5) to be measured and controlling birefringent wedge incident angle, test board can rotate around with the axle placing its plane orthogonal, realizes at least three kinds of different angles and is incident to birefringent wedge surface generation polarization interference;

Analyzer (7), for realizing polarization interference, light transmission shaft direction and horizontal reference at 45 °, simultaneously perpendicular with the polarizer or parallel;

Planar array detector (8), comprises CCD and cmos detector, for receiving polarization interference figure signal;

Signal processing system (9), comprises image pick-up card and computing machine, and for gathering polarization interference figure signal, computing machine processes according to Measurement Algorithm, calculates birefringent wedge optical axis three-dimensional;

The parallel incidence of LASER Light Source (1) Output of laser, when optical attenuator (2) reduces laser energy, controls laser power stability and avoids detector saturated, beam expanding lens (3) expands laser, obtain the spatial coherence laser facula covering birefringent wedge lateral dimension, rise partially through the polarizer (4), light transmission shaft direction and horizontal reference at 45 °, at sample test platform (6) the tested birefringent wedge of upper placement (5), by regulating sample test platform (6), rotating birefringence penetrates wedge (5), thus realize different angles incident wedge surface generation polarization interference, after analyzer (7), polarized light interference is realized by the light beam after birefringent wedge (5), planar array detector (8) is adopted to receive polarization interference figure and be passed in signal processing system (9).

2. a multiple angles of incidence polarization interference measuring method for birefringent wedge optical axis direction, it is characterized in that, the method comprises the following steps:

The parallel incidence of LASER Light Source (1) Output of laser, when optical attenuator (2) reduces laser energy, controls laser power stability and avoids detector saturated, beam expanding lens (3) expands laser, obtain the spatial coherence laser facula covering birefringent wedge lateral dimension, rise partially through the polarizer (4), light transmission shaft direction and horizontal reference at 45 °, at sample test platform (6) the tested birefringent wedge of upper placement (5), by regulating sample test platform (6), rotating birefringence penetrates wedge (5), thus realize different angles incident wedge surface generation polarization interference, after analyzer (7), polarized light interference is realized by the light beam after birefringent wedge (5), planar array detector (8) is adopted to receive polarization interference figure and be passed in signal processing system (9), under each incident angle, record a width polarization interference figure, when collecting the polarization interference figure of three different incidence angles, in signal processing system (9), greyscale transformation and hough conversion process are carried out to polarization interference signal, extract the bright fringes of polarization interference figure, calculate interference fringe spacing, the simultaneous optical path difference system of equations consisted of three angle incidences, solves the three-dimensional of birefringent wedge optical axis,

The process that described birefringent wedge forms simultaneous optical path difference system of equations by three angle incidences is as follows:

Set up adjacent bright fringe spacing h and crystal wedge surface thickness difference δ t corresponding relation formula:

In formula, for the angle of wedge;

Adjacent bright striped optical path difference δ Δ=λ in polarization interference, thus obtain polarization interference light adjacent stripes optical path difference δ Δ formula:

In formula (1), θ is incident angle, n _refor the refractive index of e light light on its direction of propagation; θ _rofor the angle of o light light and plane of crystal normal; δ d is the path length difference that adjacent e light is propagated in birefringent wedge; δ x _efor adjacent e light propagation difference in the direction of the x axis; δ z _efor adjacent e light propagation difference in the z-axis direction; n _ofor the refractive index of o light light on its direction of propagation;

When incidence angle θ is constant, n _re, θ _roconstant, only have δ d, δ x _e, δ z _echange;

Choose 0 °, 30 °, 45 ° three different incidence angles, obtain system of equations:

And

In formula (3), be respectively wedge surface and x, y, z axle angle, α, β, γ be birefringent wedge optical axis and x, y, z axle angle, θ _kefor the angle of e light light wave vector and plane of crystal normal, M ₁, M ₂for corresponding coefficient, n _ofor the refractive index of o light light on its direction of propagation.