CN202648799U - Light beam Stokes parameter measuring device - Google Patents

Abstract

A light beam Stokes parameter measuring device is provided. The polarization measuring device comprises a beam splitter prism group, a phase delay device array, an analyzer, a photoelectric detector array and a signal processing system. Units of the photoelectric detector array are corresponding to units of the phase delay device array in a one-to-one manner. The light beam Stokes parameter measuring device can measure light beam Stokes parameters in real time, reduces the influence of the phase delay amount error and the fast axis direction error of the phase delay device and the transmission axis detection error and the extinction ratio error of the analyzer on the light beam polarization measurement accuracy.

Description

Light beam stokes parameter measurement mechanism

Technical field

The present invention relates to the measurement of light beam stokes parameter, particularly a kind of light beam stokes parameter measurement mechanism.

Background technology

The 193nm liquid immersion lithography is 32nm node main flow photoetching technique.In immersion lithography, adopt certain liquid filling between the photoresist on the last a slice eyeglass of object lens and the silicon chip, so that projection objective and data aperture have obtained significant raising, when the numerical aperture of projection objective near 1 or when larger, the polarization state of illumination light can't be ignored on the impact of optical patterning.Adopt suitable polarized illumination can in the large-numerical aperture etching system, effectively improve image contrast.Along with the numerical aperture of immersed photoetching machine projection objective constantly increases, adopt polarized illumination to become the effective way that improves photoetching resolution, improves the optical patterning quality in conjunction with resolution enhance technology.

In the polarized illumination technology, owing to the needs of Polarization Control, should detect in real time the polarization information of illumination light.At present, the most frequently used light polarization detection technique is by measurement realizes to the light beam stokes parameter, and the measuring accuracy that improves the light beam stokes parameter is most important.

Formerly technology 1 is (referring to D.Sabatke, M.R.Descour, E.I.Dereniak, W.C.Sweatt, S.A.Kemme, and G.S.Phipps, " Optimization of retardance for a complete Stokes polarimeter; " Opt.Lett.25 (11), 802 – 804 (2000)) the light beam stokes parameter measurement mechanism based on discrete rotating wave plate method is optimized, adopt the fast shaft angle degree of wave plate of four optimizations, thereby improved the signal to noise ratio (S/N ratio) of detection system.The method must be rotated wave plate four times at least in order to measure whole four stokes parameters that obtain light beam, therefore can't realize the real-time measurement of stokes parameter.

Formerly technology 2(is referring to T.Hamamoto, H.Toyota, and H.Kikuta, " Microretarder array for imaging polarimetry in the visible wavelength region; " in Lithographic and Micromachining Techniques for Optical Component Fabrication, E.-B.Kley and H.P.Herzig, eds., Proc.SPIE 4440,293-300 (2001) .) the light beam stokes parameter measurement mechanism based on phase delay array proposed.Wherein the quick shaft direction of each phase delay device has adopted the fast shaft angle degree of optimizing in the technology 1 formerly in the phase delay array, has improved the signal to noise ratio (S/N ratio) of detection system.Realized that the stokes parameter of light beam measures in real time owing to adopted phase delay device array, this device.Simultaneously, because the required phase delay device array of this device is sub-wave length grating, adopt electron beam lithography; Because etching technics, though the quick shaft direction of phase delay device energy accurate etching, phase delay can't be precisely controlled, thereby there is the phase delay error in this device, brings certain error for the stokes parameter measuring system.

Summary of the invention

The objective of the invention is in order to solve above-mentioned the deficiencies in the prior art, a kind of light beam stokes parameter measurement mechanism is provided, to realize the real-time measurement of light beam stokes parameter, reduce the light transmission shaft deflection error, extinction ratio error of phase-delay quantity error, quick shaft direction error and the analyzer of phase delay device in the light beam stokes parameter measurement mechanism to the impact of light polarization measuring accuracy.

Technical solution of the present invention is as follows:

A kind of light beam stokes parameter measurement mechanism, its characteristics are that the formation of this device comprises and set gradually along systematic optical axis: the Amici prism group, the phase delay device array, analyzer and photodetector array, the output termination signal processing system of described photodetector array, each unit of described photodetector array is corresponding one by one with each unit of described phase delay device array, and according to described polarisation of light direction to be measured, adjust the light transmission shaft direction of described analyzer parallel with the polarization direction of described light beam to be measured and vertical after, carry out again respectively the polarization parameter measurement of light beam to be measured.

Described Amici prism group is the combination of the known Amici prism of splitting ratio, and a branch of incident light is formed a plurality of outgoing beamlets.

Described phase delay device array is to be rearranged by four-quadrant in same plane by four identical phase delay devices, is respectively the first phase delay device, the second phase delay device, third phase position delayer, the 4th phase delay device; The quick shaft direction of described the first phase delay device, the second phase delay device, third phase position delayer, the 4th phase delay device and the light transmission shaft angular separation θ of described analyzer _i(i=1,2,3,4) are respectively-45 °, 0 °, 30 ° and 60 °, and described phase delay device produces 90 ° of phase-delay quantities.

Described photodetector array is the assembly that a plurality of photodetectors form, or be the two-dimensional array detector, each unit of described photodetector array is corresponding one by one with each unit of described phase delay device array, is comprised of identical the first photodetector, the second photodetector, the 3rd photodetector, the 4th photodetector arranged by four-quadrant in same plane.

Utilize described light beam stokes parameter measurement mechanism to carry out the method that the light beam stokes parameter is measured, it is characterized in that: when the polarization azimuth of known light beam to be measured is

The time, the method comprises the following steps:

1. the light transmission shaft direction of adjusting described analyzer is vertical with the polarization direction of described light beam to be measured, adjusts described phase delay device array and makes the quick shaft direction of its first phase delay device, the second phase delay device, third phase position delayer, the 4th phase delay device and the light transmission shaft angular separation θ of described analyzer _i(i=1,2,3,4) are respectively-45 °, 0 °, 30 ° and 60 °, and press the inverse matrix A of following formula computing system matrix A ^-1Value:

$A^{-1}={\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\\ a_{41}& a_{42}& a_{43}& a_{44}\end{array}\right]}^{-1}$

Wherein each element of matrix is respectively:

a _i1＝1

i＝1,2,3,4;

2. utilize light beam stokes parameter measurement mechanism to treat photometry Shu Jinhang and measure, the intensity signal that described the first photodetector, the second photodetector, the 3rd photodetector, the 4th photodetector obtain respectively light beam to be measured is And calculate for the first time stokes parameter by following formula:

$\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}\\ {\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1^{90}\\ S_2^{90}\\ S_3^{90}\end{array}\right]=A^{-1}\left[\begin{array}{c}{I}_1^{90}\\ I_2^{90}\\ I_3^{90}\\ I_4^{90}\end{array}\right];$

3. the light transmission shaft direction of adjusting described analyzer is parallel with the polarization direction of described light beam to be measured, adjusts quick shaft direction and the axial angle theta of analyzer printing opacity that described phase delay device array makes the first phase delay device, the second phase delay device, third phase position delayer, the 4th phase delay device _i(i=1,2,3,4) are respectively-45 °, 0 °, 30 ° and 60 °, calculate the inverse matrix A of system matrix A by following formula ^-1Value:

$A^{-1}{=\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\\ a_{41}& a_{42}& a_{43}& a_{44}\end{array}\right]}^{-1}$

Wherein each element of matrix is respectively:

a _i1＝1

i＝1,2,3,4;

4. recycle light beam stokes parameter measurement mechanism and treat photometry Shu Jinhang measurement, the intensity signal that described the first photodetector (501), the second photodetector (502), the 3rd photodetector (503), the 4th photodetector (504) obtain respectively light beam to be measured is

And calculate for the second time stokes parameter by following formula:

$\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^0\\ {\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1^0\\ S_2^0\\ S_3^0\end{array}\right]=A^{-1}\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="I"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">I</figure-callout>}}_1^0\\ I_2^0\\ I_3^0\\ I_4^0\end{array}\right];$

5. to described

With

Calculate by following formula, obtain the final stokes parameter of described light beam to be measured:

${\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0=\frac{1}{2}({\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^0+{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90})$ ${\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1=\frac{{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1^{90}}{{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}}{S}_0$ $S_2=\frac{S_2^{90}}{{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}}{S}_0$ $S_3=\frac{S_3^{90}+{S_3}^0}{{2\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}}{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0.$

Utilize described light beam stokes parameter measurement mechanism to carry out the method that the light beam stokes parameter is measured, it is characterized in that: when the polarization direction of the unknown light beam to be measured, its concrete measuring process is as follows:

1. utilize described light beam stokes parameter measurement mechanism to measure the roughly polarization azimuth of light beam to be measured

2. the light transmission shaft direction of adjusting described analyzer is vertical with the polarization direction of described light beam to be measured, adjust described phase delay device array, make the quick shaft direction of the first phase delay device, the second phase delay device, third phase position delayer, the 4th phase delay device and the light transmission shaft angular separation θ of described analyzer _i(i=1,2,3,4) are respectively-45 °, 0 °, 30 ° and 60 °, calculate the inverse matrix A of system matrix A by following formula ^-1Value:

$A^{-1}{=\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\\ a_{41}& a_{42}& a_{43}& a_{44}\end{array}\right]}^{-1}$

Wherein each element of matrix is respectively:

a _i1＝1

i＝1,2,3,4;

3. recycle light beam stokes parameter measurement mechanism and treat photometry Shu Jinhang measurement, the intensity signal that described the first photodetector (501), the second photodetector (502), the 3rd photodetector (503), the 4th photodetector (504) obtain respectively light beam to be measured is

And calculate for the first time stokes parameter by following formula:

$\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}\\ {\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1^{90}\\ S_2^{90}\\ S_3^{90}\end{array}\right]=A^{-1}\left[\begin{array}{c}{I}_1^{90}\\ I_2^{90}\\ I_3^{90}\\ I_4^{90}\end{array}\right];$

4. the light transmission shaft direction of adjusting described analyzer is parallel with the polarization direction of described light beam to be measured, adjusts quick shaft direction and the axial angle theta of analyzer printing opacity that described phase delay device array makes the first phase delay device, the second phase delay device, third phase position delayer, the 4th phase delay device _i(i=1,2,3,4) are respectively-45 °, 0 °, 30 ° and 60 °, calculate the inverse matrix A of system matrix A by following formula ^-1Value:

$A^{-1}{=\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\\ a_{41}& a_{42}& a_{43}& a_{44}\end{array}\right]}^{-1}$

Wherein each element of matrix is respectively:

a _i1＝1

i＝1,2,3,4;

5. recycle light beam stokes parameter measurement mechanism and treat photometry Shu Jinhang measurement, described the first photodetector, the second photodetector, the 3rd photodetector, the 4th photodetector obtain respectively the intensity signal of light beam to be measured

And calculate for the second time stokes parameter by following formula:

$\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^0\\ {\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1^0\\ S_2^0\\ S_3^0\end{array}\right]=A^{-1}\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="I"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">I</figure-callout>}}_1^0\\ I_2^0\\ I_3^0\\ I_4^0\end{array}\right];$

6. to described

With

Calculate by following formula, obtain the final stokes parameter of described light beam to be measured:

${\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0=\frac{1}{2}({\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^0+{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90})$ ${\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1=\frac{{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1^{90}}{{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}}{S}_0$ $S_2=\frac{S_2^{90}}{{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}}{S}_0$ $S_3=\frac{S_3^{90}+{S_3}^0}{{2\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}}{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0.$

The present invention compares with technology formerly, has the following advantages and good effect:

1, light beam stokes parameter measurement mechanism of the present invention has adopted the phase inversion position delayer that the phase delay device array replaces tradition to revolve, photodetector array has replaced traditional single photodetector, each unit of photodetector array is corresponding one by one with each unit of phase delay device array, adopts in real time whole four stokes parameters of measuring beam of this device.

2, owing to reasons, the retardation of phase delay device array is more difficult to get accurate control.And in the polarimeter, the error of the parameters such as the light transmission shaft direction of the retardation of phase delay device array, quick shaft direction and analyzer, extinction ratio will affect the measuring accuracy of stokes parameter.Utilize detection method of the present invention, be adjusted to when perpendicular or parallel with the polarization direction of light beam to be measured by the light transmission shaft direction with analyzer, measure respectively again, obtain the stokes parameter of light beam by the processing to data, this method can effectively reduce above-mentioned foozle to the impact of stokes parameter measuring accuracy, realizes the measurement of high precision stokes parameter.

Description of drawings

Fig. 1 is light beam stokes parameter measurement mechanism synoptic diagram of the present invention;

Fig. 2 is the structural drawing of phase delay array in the embodiment of the invention;

Fig. 3 is the structural drawing of photodetector array in the embodiment of the invention;

Fig. 4 be for when existing the phase-delay quantity error delta δ of phase delay device=2 °, when quick shaft direction error delta θ=0.1 °, analyzer light transmission shaft deflection error Δ α=0.1 °, and normalization stokes parameter S ₁₀Error is with the variation of incident light polarization direction.

Fig. 5 be for when existing the phase-delay quantity error delta δ of phase delay device=2 °, when quick shaft direction error delta θ=0.1 °, analyzer light transmission shaft deflection error Δ α=0.1 °, and normalization stokes parameter S ₂₀Error is with the variation of incident light polarization direction.

Fig. 6 be for when existing the phase-delay quantity error delta δ of phase delay device=2 °, when quick shaft direction error delta θ=0.1 °, analyzer light transmission shaft deflection error Δ α=0.1 °, and normalization stokes parameter S ₃₀Error is with the variation of incident light polarization direction.

Embodiment

The invention will be further described below in conjunction with embodiment and accompanying drawing, but should not limit the scope that comprises of the present invention with this.

The synoptic diagram of light beam stokes parameter measurement mechanism embodiment of the present invention as shown in Figure 1, be followed successively by along the apparatus system optical axis: Amici prism group 2, phase delay device array 3, analyzer 4, photodetector array 5, the output signal of this photodetector array connects signal processing system 6; Each unit of photodetector array is corresponding one by one with each unit of phase delay device array; Light beam 1 to be measured is incident to described Amici prism group 2, phase delay device array 3 and analyzer 4 along systematic optical axis, survey light intensity by described photodetector array 5, the electric signal of these photodetector array 5 outputs is sent into described signal processing system 6 and is carried out the data processing.

Described Amici prism group is the combination of the known Amici prism of splitting ratio, and a branch of incident light is formed a plurality of outgoing beamlets.

Described phase delay device array is to be rearranged by four-quadrant in same plane by four the first identical phase delay devices 301, the second phase delay device 302, third phase position delayer 303, the 4th phase delay devices 304, phase delay device produces 90 ° of phase-delay quantities, is quarter-wave plate or liquid crystal modulator; The quick shaft direction of described the first phase delay device, the second phase delay device, third phase position delayer, the 4th phase delay device and the light transmission shaft direction angulation of described analyzer 4 are respectively-45 °, 0 °, 30 ° and 60 °.

Described photodetector array is the assembly that a plurality of photodetectors form, or is the two-dimensional array detector, and described photodetector is photodiode, phototriode, photomultiplier or photoelectric cell.Described photodetector array structure is corresponding with the structure of described phase delay device array, is comprised of identical the first photodetector, the second photodetector, the 3rd photodetector, the 4th photodetector arranged by four-quadrant in same plane.

It is as follows to utilize light beam stokes parameter measurement mechanism of the present invention to treat the concrete measuring process of the measuring method of the stokes parameter of photometry bundle (present embodiment is the polarization direction of unknown light beam to be measured 1):

1. utilize light beam stokes parameter measurement mechanism of the present invention to measure the roughly polarization azimuth of light beam 1 to be measured

2. the light transmission shaft direction of adjusting described analyzer 4 is vertical with the polarization direction of described light beam 1 to be measured, adjust described phase delay device array 3, make the quick shaft direction of the first phase delay device 301, the second phase delay device 302, third phase position delayer 303, the 4th phase delay device 304 and the light transmission shaft angular separation θ of described analyzer 4 _i(i=1,2,3,4) are respectively-45 °, 0 °, 30 ° and 60 °, calculate the inverse matrix A of system matrix A by following formula ^-1Value:

$A^{-1}={\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\\ a_{41}& a_{42}& a_{43}& a_{44}\end{array}\right]}^{-1}$

Wherein each element of matrix is respectively:

a _i1＝1

i＝1,2,3,4;

3. recycle light beam stokes parameter measurement mechanism and treat photometry Shu Jinhang and measure, the intensity signal that described the first photodetector 501, the second photodetector 502, the 3rd photodetector 503, the 4th photodetector 504 obtain respectively light beam to be measured is

And calculate for the first time stokes parameter by following formula:

$\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}\\ {\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1^{90}\\ S_2^{90}\\ S_3^{90}\end{array}\right]=A^{-1}\left[\begin{array}{c}{I}_1^{90}\\ I_2^{90}\\ I_3^{90}\\ I_4^{90}\end{array}\right];$

4. the light transmission shaft direction of adjusting described analyzer 4 is parallel with the polarization direction of described light beam 1 to be measured, adjust described phase delay device array 3, make quick shaft direction and the axial angle theta of analyzer printing opacity of described the first phase delay device 301, the second phase delay device 302, third phase position delayer 303, the 4th phase delay device 304 _i(i=1,2,3,4) are respectively-45 °, 0 °, 30 ° and 60 °, calculate the inverse matrix A of system matrix A by following formula ^-1Value:

$A^{-1}={\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\\ a_{41}& a_{42}& a_{43}& a_{44}\end{array}\right]}^{-1}$

Wherein each element of matrix is respectively:

a _i1＝1

i＝1,2,3,4;

5. recycle light beam stokes parameter measurement mechanism and treat photometry Shu Jinhang measurement, the intensity signal that described the first photodetector 501, the second photodetector 502, the 3rd photodetector 503, the 4th photodetector 504 obtain respectively light beam to be measured is

And calculate for the second time stokes parameter by following formula:

$\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^0\\ {\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1^0\\ S_2^0\\ S_3^0\end{array}\right]=A^{-1}\left[\begin{array}{c}{I}_1^0\\ I_2^0\\ I_3^0\\ I_4^0\end{array}\right];$

6. to described

With

Calculate by following formula, obtain the final stokes parameter of described light beam to be measured:

${\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0=\frac{1}{2}({\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^0+{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90})$ ${\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1=\frac{{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">S</figure-callout>}}_1^{90}}{{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}}{S}_0$ $S_2=\frac{S_2^{90}}{{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}}{S}_0$ $S_3=\frac{S_3^{90}+{S_3}^0}{{2\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0^{90}}{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0.$

Ultimate principle of the present invention is as follows:

Definition xyz coordinate system, wherein the z axle is the optical axis direction of described light beam stokes parameter measurement mechanism, the xy plane is the plane vertical with optical axis.If the Stokes vector of light beam 1 to be measured is S=[S ₀, S ₁, S ₂, S ₃] ^T(upper right corner " T " representing matrix transposition).Angle between the polarization direction of definition wires polarized light and the x axle positive dirction is polarization azimuth Its scope is

Defining the quick shaft direction of the first phase delay device, the second phase delay device, third phase position delayer and the 4th phase delay device in the described phase delay device array and the angle between the x axle positive dirction is fast shaft angle degree, is followed successively by θ _i, its scope is-90 °≤θ _i≤ 90 °, i=1,2,3,4; Definition and the light transmission shaft direction of analyzer and the angle between the x axle positive dirction are the light transmission shaft angle [alpha], and its scope is-90 °≤α≤90 °.

The Mueller matrix of i phase delay device is in the described phase delay device array:

$M\left({\mathrm{\&theta;}}_i\right)=\left[\begin{array}{cccc}1,& 0,& 0,& 0,\\ 0,& {\cos }^2{2\mathrm{\&theta;}}_i+{\sin }^2{2\mathrm{\&theta;}}_i\cos \mathrm{\&delta;},& {\sin 2\mathrm{\&theta;}}_i{\cos 2\mathrm{\&theta;}}_i-{\sin 2\mathrm{\&theta;}}_i{\cos 2\mathrm{\&theta;}}_i\cos \mathrm{\&delta;},& -{\sin 2\mathrm{\&theta;}}_i\sin \mathrm{\&delta;}\\ 0,& {\sin 2\mathrm{\&theta;}}_i{\cos 2\mathrm{\&theta;}}_i-{\sin 2\mathrm{\&theta;}}_i{\cos 2\mathrm{\&theta;}}_i\cos \mathrm{\&delta;},& {\sin }^2{2\mathrm{\&theta;}}_i+{\cos }^2{2\mathrm{\&theta;}}_i\cos \mathrm{\&delta;},& {\cos 2\mathrm{\&theta;}}_i\sin \mathrm{\&delta;}\\ 0,& {\sin 2\mathrm{\&theta;}}_i\sin \mathrm{\&delta;},& -{\cos 2\mathrm{\&theta;}}_i\sin \mathrm{\&delta;},& \cos \mathrm{\&delta;}\end{array}\right]$

(1)

Wherein, δ is the phase-delay quantity of phase delay device, θ _iIt is the fast shaft angle degree of i phase delay device.

The Mueller matrix of described analyzer is:

$P\left(\mathrm{\&alpha;}\right)=\left[\begin{array}{cccc}1,& \frac{p-1}{p+1}\cos 2\mathrm{\&alpha;},& \frac{p-1}{p+1}\sin 2\mathrm{\&alpha;},& 0\\ \frac{p-1}{p+1}\cos 2\mathrm{\&alpha;},& {\cos }^{2}2\mathrm{\&alpha;}+\frac{2\sqrt{p}}{p+1}{\sin }^{2}2\mathrm{\&alpha;},& \sin 2\mathrm{\&alpha;}\cos 2\mathrm{\&alpha;}-\frac{2\sqrt{p}}{p+1}\sin 2\mathrm{\&alpha;}\cos 2\mathrm{\&alpha;},& 0\\ \frac{p-1}{p+1}\sin 2\mathrm{\&alpha;},& \sin 2\mathrm{\&alpha;}\cos 2\mathrm{\&alpha;}-\frac{2\sqrt{p}}{p+1}\sin 2\mathrm{\&alpha;}\cos 2\mathrm{\&alpha;},& {\sin }^{2}2\mathrm{\&alpha;}+\frac{2\sqrt{p}}{p+1}{\cos }^{2}2\mathrm{\&alpha;},& 0\\ 0,& 0,& 0,& \frac{2\sqrt{p}}{p+1}\end{array}\right]---\left(2\right)$

Wherein, p is that extinction ratio, the α of analyzer are analyzer light transmission shaft angle.

Form four bundle outgoing beamlets after the light beam 1 process Amici prism group to be measured, by behind the first phase delay device, the second phase delay device, third phase position delayer and the 4th phase delay device and the analyzer in the phase delay device array, the Stokes vector of i bundle light is S '=P (α) M (θ respectively _i) S.Because the first row of Stokes vector represents the total intensity of light wave, the light intensity that photodetector can detect i.e. intensity level for this reason, so only be concerned about the first row numerical value of Stokes vector herein.For the ease of understanding, describe as an example of i bundle light example.

In the ideal case, can measure about S ₀, S ₁, S ₂, S ₃The quaternary linear function be:

${{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0}^{\&prime;}\left({\mathrm{\&theta;}}_i\right)=$

${\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0+S_1\frac{p-1}{p+1}\left\{\cos 2\mathrm{\&alpha;}\right[{\cos }^{2}2\left({\mathrm{\&theta;}}_i\right)+{\sin }^{2}2\left({\mathrm{\&theta;}}_i\right)\cos \mathrm{\&delta;}]+\sin 2\mathrm{\&alpha;}\sin 2\left({\mathrm{\&theta;}}_i\right)\cos 2\left({\mathrm{\&theta;}}_i\right)(1-\cos \mathrm{\&delta;})\}$

$+S_2\frac{p-1}{p+1}\{\cos 2\mathrm{\&alpha;}\sin 2\left({\mathrm{\&theta;}}_i\right)\cos 2\left({\mathrm{\&theta;}}_i\right)(1-\cos \mathrm{\&delta;})+\sin 2\mathrm{\&alpha;}[{\sin }^{2}2\left({\mathrm{\&theta;}}_i\right){+\cos }^{2}2\left({\mathrm{\&theta;}}_i\right)\cos \mathrm{\&delta;}\left]\right\}$

$+S_3\frac{p-1}{p+1}[\sin 2\mathrm{\&alpha;}\cos 2\left({\mathrm{\&theta;}}_i\right)-\cos 2\mathrm{\&alpha;}\sin 2\left({\mathrm{\&theta;}}_i\right)]\sin \mathrm{\&delta;}---\left(3\right)$

Wherein we make

$a_{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA00001690962300011.png"\; state="\{\{state\}\}">i</figure-callout>}1}=1$

$a_{i2}=\frac{p-1}{p+1}\left\{\cos 2\mathrm{\&alpha;}\right[{\cos }^{2}2\left({\mathrm{\&theta;}}_i\right)+{\sin }^{2}2\left({\mathrm{\&theta;}}_i\right)\cos \mathrm{\&delta;}]+\sin 2\mathrm{\&alpha;}\sin 2\left({\mathrm{\&theta;}}_i\right)\cos 2\left({\mathrm{\&theta;}}_i\right)(1-\cos \mathrm{\&delta;})\}$

$a_{i3}=\frac{p-1}{p+1}\{\cos 2\mathrm{\&alpha;}\sin 2\left({\mathrm{\&theta;}}_i\right)\cos 2\left({\mathrm{\&theta;}}_i\right)(1-\cos \mathrm{\&delta;})+\sin 2\mathrm{\&alpha;}[{\sin }^{2}2\left({\mathrm{\&theta;}}_i\right){+\cos }^{2}2\left({\mathrm{\&theta;}}_i\right)\cos \mathrm{\&delta;}\left]\right\}$

$a_{i4}=\frac{p-1}{p+1}[\sin 2\mathrm{\&alpha;}\cos 2\left({\mathrm{\&theta;}}_i\right)-\cos 2\mathrm{\&alpha;}\sin 2\left({\mathrm{\&theta;}}_i\right)]\sin \mathrm{\&delta;}$

Then (3) formula can be written as

$I_i={{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0}^{\&prime;}=\left[\begin{array}{cccc}{a}_{i1}& a_{i2}& a_{i3}& a_{i4}\end{array}\right]\left[\begin{array}{c}{S}_0\\ S_1\\ S_2\\ S_3\end{array}\right]---\left(4\right)$

Adopt so described detector array that the four bundle outgoing beamlets that described Amici prism group produces are measured simultaneously,

We can obtain equation:

$\left[\begin{array}{c}{I}_1\\ I_2\\ I_3\\ I_4\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\\ a_{41}& a_{42}& a_{43}& {\text{a}}_{44}\end{array}\right]\left[\begin{array}{c}{S}_0\\ S_1\\ S_2\\ S_3\end{array}\right]---\left(5\right)$

Following formula is I=AS (6)

Wherein $A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& a_{14}\\ a_{21}& a_{22}& a_{23}& a_{24}\\ a_{31}& a_{32}& a_{33}& a_{34}\\ a_{41}& a_{42}& a_{43}& a_{44}\end{array}\right]---\left(7\right)$

Here we claim that A is system matrix.

When there is inverse matrix A in system matrix A ^-1The time, we can obtain treating the photometry stokes parameter by (6) formula:

S＝A ^-1I （8）

But when actual measurement, owing in device manufacturing and measuring process, may have various errors, such as fast shaft angle degree error, phase-delay quantity error and polarizing prism light transmission shaft angular error, the extinction ratio error etc. of quarter-wave plate, this moment we obtain about S ₀, S ₁, S ₂, S ₃The quaternary linear function be:

${{\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0}^{\&prime;}\left(\mathrm{\&theta;}\right)=$

${\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HDA00001690962300021.png,HDA00001690962300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_0+S_1\frac{p-1}{p+1}\left\{\cos 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})\right[{\cos }^{2}2({\mathrm{\&theta;}}_i+\mathrm{\&Delta;\&theta;})+{\sin }^{2}2({\mathrm{\&theta;}}_i+\mathrm{\&Delta;\&theta;})\cos (\mathrm{\&delta;}+\mathrm{\&Delta;\&delta;})]$

$+\sin 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})\sin 2({\mathrm{\&theta;}}_i+\mathrm{\&Delta;\&theta;})\cos 2({\mathrm{\&theta;}}_i+\mathrm{\&Delta;\&theta;})(1-\cos (\mathrm{\&delta;}+\mathrm{\&Delta;\&delta;}))\}$

$+S_2\frac{p-1}{p+1}\{\cos 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})\sin 2({\mathrm{\&theta;}}_i+\mathrm{\&Delta;\&theta;})\cos 2({\mathrm{\&theta;}}_i+\mathrm{\&Delta;\&theta;})(1-\cos (\mathrm{\&delta;}+\mathrm{\&Delta;\&delta;}))$

$+\sin 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})[{\sin }^{2}2({\mathrm{\&theta;}}_i+\mathrm{\&Delta;\&theta;})+{\cos }^{2}2({\mathrm{\&theta;}}_i+\mathrm{\&Delta;\&theta;})\cos (\mathrm{\&delta;}+\mathrm{\&Delta;\&delta;})]\}$

$+S_3\frac{p-1}{p+1}[\sin 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})\cos 2({\mathrm{\&theta;}}_i+\mathrm{\&Delta;\&theta;})-\cos 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})\sin 2({\mathrm{\&theta;}}_i+\mathrm{\&Delta;\&theta;})]\sin (\mathrm{\&delta;}+\mathrm{\&Delta;\&delta;})$

（9）

Wherein: Δ δ is the phase delay error of phase delay device, and Δ θ is the fast shaft angle degree error of phase delay device, and Δ α is the light transmission shaft angular error of analyzer.

Because in actual measurement, have above-mentioned error, the light intensity that is detected by photodetector should adopt (9) formula to represent, and calculating stokes parameter S ₀, S ₁, S ₂, S ₃The time we use is (3) formula, calculate resulting stokes parameter and have error thereby lead.

The linear polarization degree that we have simulated the different polarization direction is the error of 95% incident light gained stokes parameter under corresponding error condition, wherein corresponding error is: phase-delay quantity error delta δ=2 °, quick shaft direction error delta θ=0.1 °, analyzer light transmission shaft deflection error Δ α=0.1 °.

Normalized stokes parameter error delta S ₁₀, Δ S ₂₀, Δ S ₃₀With change of polarization such as Fig. 4, Fig. 5, shown in Figure 6 of linearly polarized light, classic method is shown in fine rule, and the inventive method is shown in thick line.Classic method places 0 ° with analyzer light transmission shaft direction, the inventive method with analyzer light transmission shaft direction be adjusted to respectively become with the polarization direction of light beam to be measured 0 ° with 90 ° after measure again, and carry out data and process.From Fig. 4,5,6 we can find out, in the classic method, normalization stokes parameter error is larger with the change of polarization of light beam to be measured, such as normalization stokes parameter S10 error, be that 0 ° of light beam to be measured is 90 ° of light beams to be measured much larger than the polarization direction for the polarization direction, its error amount differs 0.07.And adopting method of the present invention, normalization stokes parameter error is less with the change of polarization of light beam to be measured, effectively in the situation of Δ δ=2 °, Δ θ=0.1 °, Δ α=0.1 °, with normalization stokes parameter S ₁₀, S ₂₀, S ₃₀Error is reduced in 0.005, thereby has realized the high-acruracy survey of light beam stokes parameter to be measured.

Claims (4)

1. light beam stokes parameter measurement mechanism, the formation that it is characterized in that this device comprises and setting gradually along systematic optical axis: Amici prism group (2), phase delay device array (3), analyzer (4) and photodetector array (5), the output termination signal processing system (6) of described photodetector array (5), each unit of described photodetector array (5) is corresponding one by one with each unit of described phase delay device array (3), and according to described polarisation of light direction to be measured, adjust the light transmission shaft direction of described analyzer (4) parallel with the polarization direction of described light beam to be measured and vertical after, carry out again respectively the polarization parameter measurement of light beam to be measured.

2. light beam stokes parameter measurement mechanism according to claim 1 is characterized in that: described Amici prism group (2) forms a plurality of outgoing beamlets for the combination of the known Amici prism of splitting ratio with a branch of incident light.

3. light beam stokes parameter measurement mechanism according to claim 1, it is characterized in that: described phase delay device array (3) is to be rearranged by four-quadrant in same plane by four identical phase delay devices, is respectively the first phase delay device (301), the second phase delay device (302), third phase position delayer (303), the 4th phase delay device (304); The quick shaft direction of described the first phase delay device (301), the second phase delay device (302), third phase position delayer (303), the 4th phase delay device (304) and the light transmission shaft angular separation θ of described analyzer (4) _i(i=1,2,3,4) are respectively-45 °, 0 °, 30 ° and 60 °, and described phase delay device produces 90 ° of phase-delay quantities.

4. light beam stokes parameter measurement mechanism according to claim 1, it is characterized in that: the assembly that described photodetector array (5) forms for a plurality of photodetectors, or be the two-dimensional array detector, by identical the first photodetector (501) of in same plane, pressing the four-quadrant arrangement, the second photodetector (502), the 3rd photodetector (503), the 4th photodetector (504) forms, and with first phase delay device (301) of described phase delay device array (3), the second phase delay device (302), third phase position delayer (303), the 4th phase delay device (304) is corresponding one by one.

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