CN101936774B - Method for measuring device error in polarization detection device - Google Patents

Abstract

A method for measuring device error in a polarization detection device comprises a phase delay device, an analyzer and a photoelectric detector which are sequentially arranged along the optical axis of the device system, wherein the output of the photoelectric detector is connected with a signal processing system; and setting an initial state of the second measurement and measuring, wherein the initial state of the second measurement is that the phase delay device and the analyzer are respectively rotated by certain angles on the basis of the initial state of the first measurement, the rotation angle of the analyzer is 2 times that of the phase delay device, the rotation directions are the same, and data processing is carried out on the measurement to obtain the error of the device. The invention can quickly measure various errors of the phase delay device and the analyzer without disassembling the polarization detection device.

Description

The measuring method of device error in the device for testing polarization

Technical field

The present invention relates to device for testing polarization, the measuring method of device error in particularly a kind of device for testing polarization.

Background technology

The progress of semiconductor fabrication is always with the power that is reduced to of the increase of the reducing of exposure wavelength, projection objective numerical aperture and photoetching process factor k1.Recent years, immersion lithography has obtained fast development.In immersion lithography, adopt certain liquid filling between the photoresist on last a slice eyeglass of object lens and the silicon chip, the numerical aperture of projection objective is significantly improved.When the numerical aperture of projection objective near 0.8 or when bigger, the illumination polarization state of light is very important to the influence of optical patterning.Adopting suitable polarized illumination is a kind of strong method that improves image contrast under the large-numerical aperture situation.For different lighting systems, polarization illumination requires to form different linear polarization, as x direction polarized light, y direction polarized light, radial polarisation light, tangential polarization light etc.

When using polarized illumination, there are all multifactor impact polarization state of light in the illuminator of projection aligner.Most importantly the intrinsic birefringence of optical material and stress birefrin reduce the polarisation of light degree.In addition, the polarization characteristic of optical thin film, light also can influence polarization state of light in the reflection and the refraction at interface.Therefore, in the polarized illumination system, because the needs of Polarization Control should detect the illumination polarization state of light in real time, and the rotating wave plate in the FEEDBACK CONTROL illuminator, guarantee the linearly polarized light output of high-polarization.In addition, also need to carry out polarization illumination and detect dress school and the maintenance that is used for litho machine.Formerly technology 1 (Jap.P.: Te Open 2005-005521) has proposed a kind of polarization parameter pick-up unit that utilizes the rotatable phase delayer.Fig. 7 is the synoptic diagram of illumination iris polarization parameter pick-up unit in the projection aligner that proposes of technology 1 formerly.As shown in Figure 7, this polarization parameter pick-up unit comprises pinhole mask 10, transform lens group 20, phase delay device 2 and driver 6 thereof, analyzer 3, photodetector 4 and signal processing system 5.Illuminating bundle by the pin hole 101 on the pinhole mask 10 after, become parallel beam through transform lens group 20.This parallel beam is surveyed by photodetector 4 by phase delay device 2 and analyzer 3 backs successively as incident beam 1.

Described pinhole mask 10 place projection aligner the mask face or near, perhaps with the plane of mask face conjugation or neighbouring (the silicon chip face or near, perhaps with the plane of silicon chip face conjugation or near).

When utilizing device in the technology 1 formerly to measure, the systematic optical axis rotation of phase delay device 2 winding apparatus, utilize technology 1 formerly and formerly the data processing method in the technology 2 (Jap.P.: Te Open 2006-179660) electric signal of photodetector output is handled, can obtain the Stokes' parameter of incident beam, and then obtain the polarization state distribution.But the phase delay device of this device and analyzer all are operated in the deep ultraviolet wave band, are difficult to make desirable device according to design objective at this wave band, therefore can produce Stokes' parameter and degree of polarization measuring error.

For this reason, formerly technology 2 has proposed not to be subjected to the method that the influence of phase delay device and analyzer correlated error, high-precision measurement polarization state distribute.This method is to measure the polarization characteristic of each device before constituting device for testing polarization with wave plate and analyzer, comprises that light transmission shaft direction, the extinction ratio of the interior distribution of face, quick shaft direction and the analyzer of wave plate phase-delay quantity distributes.But this method still not energy measurement be installed in the positioning error of the direction of the quick shaft direction of phase delay device of device for testing polarization and analyzer light transmission shaft, can't eliminate of the influence of the angle orientation error of the device that constitutes device for testing polarization to polarimetry.

Summary of the invention

The objective of the invention is to replenish above-mentioned the deficiencies in the prior art, the measuring method of device error in a kind of device for testing polarization is provided, or rather, is the measuring method of phase delay device and all kinds of errors of analyzer in a kind of device for testing polarization.By the phase-delay quantity error of measuring the phase delay device to obtain in the manufacture process and to occur when constituting device for testing polarization, the light transmission shaft deflection error of quick shaft direction sum of errors analyzer.

Technical solution of the present invention is as follows:

The measuring method of device error in a kind of device for testing polarization, the formation of described device for testing polarization comprises phase delay device, analyzer and the photodetector that sets gradually along the apparatus system optical axis, the output of this photodetector connects signal processing system, it is characterized in that:

The Stokes' parameter of described incident beam is known;

Original state when measuring for the first time is that the fast shaft angle degree of described phase delay device is θ ₁, described analyzer the light transmission shaft angle be α ₁, and carry out the first time and measure;

Original state when measuring for the second time is to measure on the basis of original state for the first time, rotating the angle of described phase delay device and described analyzer again along same direction, and making the fast shaft angle degree of phase delay device is θ ₁+ β, the axis of homology angle of analyzer is α ₁+ 2 β carry out the second time and measure;

Described signal processing system is handled measurement data, obtains the device error after as calculated.

The concrete measuring process of the measuring method of device error is as follows in the described device for testing polarization:

1. the original state of measuring for the first time is set: the system optical axis of setting up departments is the z axle of enlightening card coordinate, the forward of z axle is the light beam working direction, the plane vertical with the z axle is the xy plane, earlier selected arbitrary x direction of principal axis in the xy plane, and the angle between the polarization direction of the linearly polarized light of definition x axle positive dirction and incident is the polarization position angle

Angle between the fast axle of x axle positive dirction and phase delay device is fast shaft angle degree θ, angle between x axle positive dirction and the analyzer light transmission shaft is the light transmission shaft angle [alpha], design parameter with described phase delay device and analyzer is a benchmark, and the fast shaft angle degree of adjusting described phase delay device is θ ₁, described analyzer the light transmission shaft angle be α ₁, and set the original state of this state for measuring for the first time;

2. measure for the first time: utilize the described phase delay device rotation of driver drives, described photodetector is surveyed light signal and is exported electric signal, described electric signal obtains the Stokes' parameter (s of incident beam after described signal processing system data processing _E10, s _E11, s _E12, s _E13), utilize following formula to calculate corresponding degree of polarization V _E1With the polarization position angle

Degree of polarization V _E1For:

$V_{e1}=\sqrt{\frac{s_{e11}^2+s_{e12}^2+s_{e13}^2}{s_{e10}^2}},$

The polarization position angle

Polarization azimuth angle error then

The degree of polarization error is Δ V ₁=V _E1-V=m ₁, Δ θ wherein ₁Be the fast shaft angle degree error of described phase delay device, Δ α ₁Be the axis of homology angular error of analyzer, V is the degree of polarization of incident beam,

Polarization position angle for incident beam;

3. the original state of measuring for the second time is set: the original state when described phase delay device of recovery and analyzer are extremely measured for the first time earlier, along same direction described phase delay device is rotated the β angle again, described analyzer is rotated 2 β angles, wherein β＜5 °;

4. measure for the second time: the described phase delay device rotation of described driver drives, described photodetector is surveyed light signal and is exported electric signal, described electric signal carries out data processing through described signal processing system to described electric signal, the fast shaft angle degree θ when still measuring with the first time during data processing ₁With the light transmission shaft angle [alpha] ₁Be initial angle, obviously, during second measurement, the error of described fast shaft angle degree is Δ θ ₂=Δ θ ₁+ β, the error of described axis of homology angle is Δ α ₂=Δ α ₁+ 2 β, and phase-delay quantity error delta δ and extinction coefficient p remain unchanged, and obtain the Stokes' parameter of incident beam after the data processing, calculate corresponding degree of polarization V _E2With the polarization position angle Polarization azimuth angle error then The degree of polarization error is Δ V ₂=V _E2-V=m ₂

5. obtain gross data: the light transmission shaft angular error satisfies Δ α-2 Δ θ=q with fast shaft angle degree error, obtain the gross data of the degree of polarization error delta V of the known linearly polarized light of Stokes' parameter with fast shaft angle degree error delta θ and phase-delay quantity error delta δ variation by emulation, obtain a theoretical curved surface Δ V=f (Δ θ, Δ δ);

6. determine error: in described theoretical curved surface, degree of polarization error delta V=m ₁Pairing coordinate is (Δ θ _1i, Δ δ _1i), degree of polarization error delta V=m ₂Corresponding coordinate is (Δ θ _2i, Δ δ _2i), i=1 wherein, 2,3 ..., fast shaft angle degree error delta θ when measuring according to twice ₂=Δ θ ₁The relation of+β is at coordinate (Δ θ _1i, Δ δ _1i) and (Δ θ _2i, Δ δ _2i) in find and satisfy Δ θ _2c=Δ θ _1c+ β and Δ δ _2c=Δ δ _1cCoordinate (Δ θ _1c, Δ δ _1c), then fast shaft angle degree error delta θ=Δ θ _1c, phase-delay quantity error delta δ=Δ δ _1c, ask axis of homology angular error Δ α=2 Δ θ according to Δ α=2 Δ θ+q again _1c+ q.

Described phase delay device is for producing quarter-wave plate, electrooptic modulator or the light ball modulator of 90 ° of phase delays.

The described phase delay device system for winding of described driver drives optical axis at the uniform velocity rotates or the angle of fixed interval is repeatedly rotated, perhaps by driving the position of at least four different angles between fast axle that the phase delay device rotation can be provided with phase delay device and the described analyzer light transmission shaft.

Described photodetector is two-dimensional array detector or point probe.

The present invention has been owing to adopted technique scheme, compares with technology formerly, has the following advantages and good effect:

Formerly technology 2 is distinguished the foozle of Measurement Phase delay device and analyzer before constituting device for testing polarization, and measuring process is more loaded down with trivial details; And formerly technology 2 can't be measured the positioning error that constitutes device behind the device for testing polarization, makes measurement result still be subjected to affect positioning.Compare with technology 2 formerly, the present invention need not to dismantle under the situation of device for testing polarization device, only by measuring the polarization position angle and the degree of polarization of incident beam for twice, and can Measurement Phase delay device and the manufacturing of analyzer and the error that the location forms.

Description of drawings

Fig. 1 is the related device for testing polarization synoptic diagram of the method for the measurement of device error in the device for testing polarization of the present invention.

Fig. 2 is when there are error-3 °≤Δ θ≤3 ° in the fast shaft angle degree θ of quarter-wave plate, the azimuthal error of Computer Simulation polarization

Change curve with Δ θ.

Fig. 3 is the light transmission shaft angle [alpha] when polarizing prism when having error-4 °≤Δ α≤4 °, the azimuthal error of Computer Simulation polarization Change curve with Δ α.

Fig. 4 is when there are error-3 °≤Δ δ≤3 ° in the phase-delay quantity δ of quarter-wave plate, the azimuthal error of Computer Simulation polarization

Change curve with Δ δ.

Fig. 5 a, 5b be respectively the extinction ratio p of polarizing prism have error, when 1000≤p≤10000, Stokes' parameter is s=[s ₀, s ₁, s ₂, s ₃] ^T=[1.031,0.8,0.6] ^TThe degree of polarization error delta V and the polarization azimuth angle error of the Computer Simulation linearly polarized light of (upper right corner " T " representing matrix transposition)

Change curve with p.

Fig. 6 is a process flow diagram of determining all kinds of errors.

Fig. 7 is the synoptic diagram of illumination iris polarization parameter pick-up unit in the existing projection aligner.

Embodiment

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

See also Fig. 1 earlier, Fig. 1 is the related device for testing polarization synoptic diagram of the method for the measurement of device error in the device for testing polarization of the present invention.As seen from the figure, the formation of the device for testing polarization that the present invention relates to comprises the phase delay device 2 that sets gradually along the apparatus system optical axis, analyzer 3 and photodetector 4, the output of this photodetector 4 connects signal processing system 5, but described phase delay device 2 is the rotation of winding apparatus systematic optical axis under the driving of driver 6, parallel beam is incident to described phase delay device 2 and analyzer 3 in systematic optical axis, and by described photodetector 4 detections, the electric signal of these photodetector 4 outputs is sent into described signal processing system 5 and is carried out data processing, obtain the Stokes' parameter of incident beam 1, and then obtain polarization state.

The characteristics of the method for the measurement of device error are in the device for testing polarization of the present invention:

The Stokes' parameter of described incident beam 1 is known;

Original state when measuring for the first time is that the fast shaft angle degree of described phase delay device 2 is θ ₁, described analyzer 3 the light transmission shaft angle be α ₁

Original state when measuring for the second time is to measure on the basis of original state for the first time, rotates the certain angle of described phase delay device 2, and the angle of rotating described analyzer 3 is 2 times of the anglec of rotation of phase delay device 2, and sense of rotation is identical;

Data processing is carried out in twice measurement, obtain the device error.

For the ease of the understanding of the present invention, about key concept of the present invention with according to being explained as follows:

All kinds of device errors in the described device for testing polarization comprise: the positioning error of quick shaft direction can be summed up as fast shaft angle degree error when foozle between phase delay device 2 quick shaft directions and the design parameter and formation device for testing polarization; Quick shaft direction and the caused phase-delay quantity error of systematic optical axis off plumb positioning error can be summed up as the phase-delay quantity error when phase-delay quantity of phase delay device 2 and the foozle between the design parameter and formation device for testing polarization; The axial positioning error of printing opacity can be summed up as the light transmission shaft angular error when light transmission shaft direction of analyzer 3 and the foozle between the design parameter and formation device for testing polarization; The extinction ratio of analyzer 3 and the foozle between the design parameter are the extinction ratio error.

Original state during described the measurement is before rotatable phase delay device 2 is measured, the fast axle of phase delay device 2 and the residing position of light transmission shaft of analyzer 3.

Described phase delay device 2 is for producing quarter-wave plate, electrooptic modulator or the light ball modulator of 90 ° of phase delays.Phase delay device 2 is a quarter-wave plate in the present embodiment.

Described driver 6 drives that described phase delay device 2 system for winding optical axises at the uniform velocity rotate or the angle of fixed interval is repeatedly rotated, perhaps by driving the position of at least four different angles between fast axle that phase delay device 2 rotations can be provided with phase delay device 2 and described analyzer 3 light transmission shafts.Driver 6 can drive phase delay device 2 system for winding optical axises and at the uniform velocity rotates in the present embodiment.

Analyzer 3 in the described device for testing polarization is 100% for the transmitance of the polarization direction linearly polarized light parallel with light transmission shaft in the ideal case; And the transmitance of the linearly polarized light vertical with this light transmission shaft direction is 0.Definition is parallel to the light transmission shaft direction and is extinction coefficient p perpendicular to the ratio of the axial linear polarization light intensity of printing opacity transmitance, and ideally p be an infinity.Analyzer 3 is a polarizing prism in the present embodiment.

Described photodetector 4 is two-dimensional array detector or point probe.Photodetector 4 is two-dimensional array CCD in the present embodiment, with the polarization state distribution of measuring beam.

Described signal processing system 5 utilize technology 1 formerly and formerly the data processing method in the technology 2 electric signal of photodetector 4 outputs is handled, obtain the Stokes' parameter of incident beam 1, and then obtain degree of polarization and polarization position angle.

Xyz coordinate system shown in definition Fig. 1, wherein the z axle is a systematic optical axis, and the positive dirction of z axle is the light beam working direction, and the xy plane is the plane vertical with systematic optical axis.If the Stokes' parameter of incident beam is s=[s ₀, s ₁, s ₂, s ₃] ^T(upper right corner " T " representing matrix transposition), its degree of polarization is:

$V=\sqrt{\frac{{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HSA00000250681000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1^2+{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">s</figure-callout>}}_2^2+{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">s</figure-callout>}}_3^2}{s_0^2}},---\left(1\right)$

Angle between definition x axle positive dirction and the linearly polarized light polarization direction is the polarization position angle

And utilize the polarization position angle Characterize the polarization direction of linearly polarized light, and have:

Utilize degree of polarization V and polarization position angle

Can characterize the polarization characteristic of linearly polarized light.As the foundation of estimating the measuring polarization state result, the measuring error of incident beam polarization state is discussed with these two indexs.

Angle between definition x axle positive dirction and the quarter-wave plate fast axis is fast shaft angle degree θ, and its scope is-90 °≤θ≤90 °; Angle between definition x axle positive dirction and the polarizing prism light transmission shaft is the light transmission shaft angle [alpha], and its scope is-90 °≤α≤90 °.

The Muller matrix of the quarter-wave plate of described systematic optical axis rotation around device for testing polarization is:

$M\left(\mathrm{\&theta;}\right)=\left[\begin{array}{cccc}1,& 0,& 0,& 0\\ 0,& {\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}}^{2}2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}}^{2}2\mathrm{\&theta;}\cos \mathrm{\&delta;},& \mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}-\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}\cos \mathrm{\&delta;},& -\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\sin \mathrm{\&delta;}\\ 0,& \mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}-\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}\cos \mathrm{\&delta;},& {\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}}^{2}2\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}}^{2}2\mathrm{\&theta;}\cos \mathrm{\&delta;},& \mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}\sin \mathrm{\&delta;}\\ 0,& \mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&theta;}\sin \mathrm{\&delta;},& -\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&theta;}\sin \mathrm{\&delta;},& \cos \mathrm{\&delta;}\end{array}\right],---\left(3\right)$

Wherein, δ is the phase-delay quantity of quarter-wave plate, ideally δ=pi/2.

The light transmission shaft angle is that the Muller matrix of the polarizing prism of α is:

$P\left(\mathrm{\&alpha;}\right)=\left[\begin{array}{cccc}1,& \frac{p-1}{p+1}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;},& \frac{p-1}{p+1}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;},& 0\\ \frac{p-1}{p+1}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;},& {\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}}^{2}2\mathrm{\&alpha;}+\frac{2\sqrt{p}}{p+1}{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}}^{2}2\mathrm{\&alpha;},& \mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;}-\frac{2\sqrt{p}}{p+1}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;},& 0\\ \frac{p-1}{p+1}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;},& \mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;}-\frac{2\sqrt{p}}{p+1}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;}\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;},& {\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}}^{2}2\mathrm{\&alpha;}+\frac{2\sqrt{p}}{p+1}{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}}^{2}2\mathrm{\&alpha;},& 0\\ 0,& 0,& 0,& \frac{2\sqrt{p}}{p+1}\end{array}\right].---\left(4\right)$

Behind incident beam 1 process quarter-wave plate and the polarizing prism, Stokes' parameter is s '=P (α) M (θ) s.Because the total intensity of first expression light wave of Stokes' parameter, the light intensity that photodetector 4 can detect i.e. intensity level for this reason, so only be concerned about first numerical value of Stokes' parameter herein.Photodetector 4 is an area array CCD in the present embodiment, and its each pixel all obtains the relevant data of light intensity, the data of each pixel is handled the Stokes' parameter that obtains this pixel place incident beam 1.For the ease of understanding, existing is that example describes with a pixel.

In the ideal case, when promptly δ=pi/2, p are infinitely great, have:

s ₀′(θ)＝s ₀+s ₁[cos2αcos ²2θ+sin2αsin2θcos2θ]，(5)

+s ₂[cos2αsin2θcos2θ+sin2αsin ²2θ]+s ₃(sin2αcos2θ-cos2αsin2θ)

During measurement, rotate quarter-wave plate and change θ.(5) formula is carried out following processing obtain 4 Stokes' parameter s ₀, s ₁, s ₂, s ₃:

s ₀' as the function of θ, it is carried out fourier expansion:

${{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HSA00000250681000021.png,HSA00000250681000023.png"\; state="\{\{state\}\}">s</figure-callout>}}_0}^{\&prime;}\left(\mathrm{\&theta;}\right)=\frac{a_0}{2}+\underset{n}{\mathrm{\&Sigma;}}(a_n\cos \mathrm{n\&theta;}+b_n\sin \mathrm{n\&theta;}),---\left(6\right)$

By s ₀' (θ) obtain coefficient a _nAnd b _n:

$a_n=\frac{1}{\mathrm{\&pi;}}\underset{-\mathrm{\&pi;}}{\overset{\mathrm{\&pi;}}{\&Integral;}}{{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HSA00000250681000021.png,HSA00000250681000023.png"\; state="\{\{state\}\}">s</figure-callout>}}_0}^{\&prime;}\left(\mathrm{\&theta;}\right)\cos \mathrm{n\&theta;d\&theta;},---\left(7\right)$

$b_n=\frac{1}{\mathrm{\&pi;}}\underset{-\mathrm{\&pi;}}{\overset{\mathrm{\&pi;}}{\&Integral;}}{{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HSA00000250681000021.png,HSA00000250681000023.png"\; state="\{\{state\}\}">s</figure-callout>}}_0}^{\&prime;}\left(\mathrm{\&theta;}\right)\sin \mathrm{n\&theta;d\&theta;}.---\left(8\right)$

Obtain a shown in the formula of following (9)～(13) so respectively ₀, a ₂, b ₂, a ₄And b ₄:

$\frac{a_0}{2}={\mathrm{<figure-callout\; id="0"\; label="S"\; filenames="HSA00000250681000021.png,HSA00000250681000023.png"\; state="\{\{state\}\}">S</figure-callout>}}_0+\frac{p-1}{2(p+1)}({\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HSA00000250681000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;}+{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">s</figure-callout>}}_2\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;}),---\left(9\right)$

$a_2=\frac{p-1}{p+1}{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">s</figure-callout>}}_3\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;},---\left(10\right)$

${\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">b</figure-callout>}}_2=-\frac{p-1}{p+1}{s}_3\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;},---\left(11\right)$

$a_4=\frac{p-1}{2(p+1)}({\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HSA00000250681000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;}-{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">s</figure-callout>}}_2\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;}),---\left(12\right)$

${\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="HSA00000250681000011.png"\; state="\{\{state\}\}">b</figure-callout>}}_4=\frac{p-1}{2(p+1)}({\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HSA00000250681000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;}+s_2\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;}).---\left(13\right)$

The a that utilization obtains ₀, a ₂, b ₂, a ₄And b ₄, calculate 4 the Stokes' parameter ss corresponding with the polarization state of incident beam 1 ₀, s ₁, s ₂, s ₃:

${\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HSA00000250681000021.png,HSA00000250681000023.png"\; state="\{\{state\}\}">s</figure-callout>}}_0=\frac{a_0}{2}-(a_4\mathrm{<figure-callout\; id="4"\; label="cos"\; filenames="HSA00000250681000011.png"\; state="\{\{state\}\}">cos</figure-callout>}4\mathrm{\&alpha;}+{\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="HSA00000250681000011.png"\; state="\{\{state\}\}">b</figure-callout>}}_4\mathrm{<figure-callout\; id="4"\; label="sin"\; filenames="HSA00000250681000011.png"\; state="\{\{state\}\}">sin</figure-callout>}4\mathrm{\&alpha;}),---\left(14\right)$

${\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HSA00000250681000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1=\frac{2(p+1)}{(p-1)}(a_4\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;}+{\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="HSA00000250681000011.png"\; state="\{\{state\}\}">b</figure-callout>}}_4\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;}),---\left(15\right)$

${\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">s</figure-callout>}}_2=\frac{2(p+1)}{(p-1)}({\mathrm{<figure-callout\; id="4"\; label="b"\; filenames="HSA00000250681000011.png"\; state="\{\{state\}\}">b</figure-callout>}}_4\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;}-a_4\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;}),---\left(16\right)$

${\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">s</figure-callout>}}_3=\frac{-(p+1)b_2}{(p-1)\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&alpha;}}=\frac{(p+1)a_2}{(p-1)\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&alpha;}}.---\left(17\right)$

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

${{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HSA00000250681000021.png,HSA00000250681000023.png"\; state="\{\{state\}\}">s</figure-callout>}}_0}^{\&prime;}\left(\mathrm{\&theta;}\right)=$

${\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HSA00000250681000021.png,HSA00000250681000023.png"\; state="\{\{state\}\}">s</figure-callout>}}_0+s_1\frac{p-1}{p+1}\{\cos 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})+[{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}}^{2}2(\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})+{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}}^{2}2(\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})\cos \mathrm{\&delta;}]+\sin 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})\sin 2(\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})\cos 2(\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})(1-\cos \mathrm{\&delta;})\}$

$+s_2\frac{p-1}{p+1}\{\cos 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})\sin 2(\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})\cos 2(\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})(1-\cos \mathrm{\&delta;})+\sin 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})[{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">sin</figure-callout>}}^{2}2(\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})+{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HSA00000250681000011.png,HSA00000250681000012.png"\; state="\{\{state\}\}">cos</figure-callout>}}^{2}2(\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})\cos \mathrm{\&delta;}\left]\right\}$

$+s_3\frac{p-1}{p+1}[\sin 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})\cos 2(\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})-\cos 2(\mathrm{\&alpha;}+\mathrm{\&Delta;\&alpha;})\sin 2(\mathrm{\&theta;}+\mathrm{\&Delta;\&theta;})]\sin \mathrm{\&delta;},---\left(18\right)$

Wherein: Δ α is the angular error of polarizing prism light transmission shaft, and Δ θ is initial (being the original state of quarter-wave plate when not rotating) fast shaft angle degree error of quarter-wave plate.

When having above-mentioned error, the pixel actual detection of CCD to light intensity represent by (18) formula, and calculate Stokes' parameter s ₀, s ₁, s ₂, s ₃The time light intensity used be (5) formula, thereby there is error in the Stokes' parameter that causes obtaining, polarisation-affecting degree V and polarization position angle

Result of calculation.

To degree of polarization is that V, polarization position angle are

Known linearly polarized light measure, when having error delta θ, Δ α, Δ δ and p, with (18) formula carry out with the same processing of (5) formula, the Stokes' parameter s when obtaining having error delta θ, Δ α, Δ δ and p _E0, s _E1, s _E2, s _E3, utilize (1) formula and (2) formula, the degree of polarization V when obtaining having error delta θ, Δ α, Δ δ and p again _eWith the polarization position angle

Calculate degree of polarization error delta V=V _e-V and polarization azimuth angle error

Consider the foozle and the positioning error of device, think that the fast shaft angle degree error range of quarter-wave plate is-4 °≤Δ δ≤4 ° for-3 °≤Δ θ≤3 °, phase-delay quantity error range, the axis of homology angular error scope of polarizing prism is that-3 °≤Δ α≤3 °, extinction coefficient scope are 1000≤p≤10000.We theoretically emulation in above-mentioned scope under the different errors, degree of polarization V and polarization position angle

Error.Simulation result such as Fig. 2～shown in Figure 5.

When there are error-3 °≤Δ θ≤3 ° in the fast shaft angle degree θ of quarter-wave plate, the azimuthal error of the polarization that Δ θ causes

With the change curve of Δ θ as shown in Figure 2.As seen from the figure, polarization azimuth angle error

With the pass of Δ θ be

When there are error-4 °≤Δ α≤4 ° in the light transmission shaft angle [alpha] of polarizing prism, the azimuthal error of the polarization that Δ α causes

With the change curve of Δ α as shown in Figure 3.As seen from the figure, polarization azimuth angle error

With the pass of Δ α be

When there are error-3 °≤Δ δ≤3 ° in the phase-delay quantity of quarter-wave plate, the azimuthal error of the polarization that Δ δ causes

With the change curve of Δ δ as shown in Figure 4.As seen from the figure, polarization position angle Be not subjected to the influence of phase-delay quantity error,

When there is error in the extinction ratio of polarizing prism, as 1000≤p≤10000 o'clock, the azimuthal error of the polarization that p causes With the change curve of p respectively shown in Fig. 5 a.As seen from the figure, polarization position angle

Be not subjected to the influence of extinction coefficient error,

With the Stokes' parameter is s=[s ₀, s ₁, s ₂, s ₃] ^T=[1.031,0.8,0.6] ^TLinearly polarized light be example, the error delta V of the degree of polarization that p causes _pWith the change curve of p respectively shown in Fig. 5 b.As seen from the figure, degree of polarization error delta V _pBe-0.002＜Δ V _p＜0, can ignore.And, for the degree of polarization that uses in the projection aligner near 1 linearly polarized light, when 1000≤p≤10000, degree of polarization error delta V _pAll can ignore.

By The above results as can be known, when having error delta θ, Δ α, Δ δ and p, the polarization azimuth angle error

Degree of polarization is that V, polarization position angle are

Known linearly polarized light when being incident to device for testing polarization, according to above-mentioned Δ θ, Δ α, Δ δ and p to degree of polarization error delta V and polarization azimuth angle error

Influence, can measure all kinds of errors fast according to process flow diagram shown in Figure 6, concrete steps are as follows:

1, the original state of measuring for the first time is set: setting the z axle is systematic optical axis, the forward of z axle is the light beam working direction, the plane vertical with the z axle is the xy plane, earlier selected arbitrary x direction of principal axis in the xy plane, the angle between the polarization direction of the linearly polarized light of definition x axle positive dirction and incident is the polarization position angle

Angle between x axle positive dirction and the quarter-wave plate fast axis is fast shaft angle degree θ, angle between x axle positive dirction and the polarizing prism light transmission shaft is the light transmission shaft angle [alpha], the design parameter of described quarter-wave plate and polarizing prism is a benchmark, and the fast shaft angle degree of adjusting described quarter-wave plate is θ ₁, described polarizing prism the light transmission shaft angle be α ₁

2, measure for the first time: driver 6 drives described quarter-wave plate rotation, described photodetector 4 recording light signals are also exported electric signal, 5 pairs of described electric signal of described signal processing system carry out data processing, obtain the Stokes' parameter of incident beam 1, calculate corresponding degree of polarization V _E1With the polarization position angle

Polarization azimuth angle error then

The degree of polarization error is Δ V=V _E1-V=m ₁, Δ θ wherein ₁Be the fast shaft angle degree error of described quarter-wave plate, Δ α ₁Be the axis of homology angular error of polarizing prism, V is the degree of polarization of known incident beam 1,

Polarization position angle for known incident beam 1;

3, the original state of measuring for the second time is set: recover described quarter-wave plate and the polarizing prism original state when measuring for the first time, rotate quarter-wave plate β and polarizing prism 2 β respectively along same direction again, wherein β＜5 °;

4, measure for the second time: driver 6 drives described quarter-wave plate rotation, during data processing still with fast shaft angle degree θ ₁With the light transmission shaft angle [alpha] ₁Be initial angle, then the error of the sum of errors axis of homology angle of fast shaft angle degree is respectively Δ θ ₂=Δ θ ₁+ β and Δ α ₂=Δ α ₁+ 2 β have Δ α ₂-2 Δ θ ₂=q, and phase-delay quantity error delta δ and extinction coefficient p remain unchanged, and described photodetector 4 recording light signals are also exported electric signal, and 5 pairs of described electric signal of described signal processing system carry out data processing, obtain the Stokes' parameter of incident beam 1, calculate corresponding degree of polarization V _E2With the polarization position angle

Polarization azimuth angle error then

The degree of polarization error is Δ V=V _E2-V=m ₂

5, obtain gross data: degree of polarization error delta V changes with Δ θ, Δ α, Δ δ and p, the error of the degree of polarization that p causes can be ignored, when light transmission shaft angular error and fast shaft angle degree error satisfy Δ α-2 Δ θ=q, obtain the gross data of the degree of polarization error delta V of the known linearly polarized light of Stokes' parameter with fast shaft angle degree error delta θ and phase-delay quantity error delta δ variation by emulation, obtain a theoretical curved surface Δ V=f (Δ θ, Δ δ);

6, determine error: in described theoretical curved surface, degree of polarization error delta V=m ₁Pairing coordinate is (Δ θ _1i, Δ δ _1i), degree of polarization error delta V=m ₂Corresponding coordinate is (Δ θ _2i, Δ δ _2i), i=1 wherein, 2,3 ..., according to the fast shaft angle degree error delta θ that measures for twice that implements ₂=Δ θ ₁The relation of+β is at coordinate (Δ θ _1i, Δ δ _1i) and (Δ θ _2i, Δ δ _2i) in find and satisfy Δ θ _2c=Δ θ _1c+ β and Δ δ _2c=Δ δ _1cCoordinate (Δ θ _1c, Δ δ _1c), then fast shaft angle degree error delta θ=Δ θ _1c, phase-delay quantity error delta δ=Δ δ _1c, try to achieve axis of homology angular error Δ α=2 Δ θ according to Δ α=2 Δ θ+q again _1c+ q.

Be the feasibility of device error measurement method in the checking polarimetry device, under the situation of known device error delta θ=2 °, Δ α=1 °, Δ δ=1.5 °, p=9999, utilize method of the present invention to determine all kinds of error process with following example explanation.

If after pinhole mask and transform lens group, the Stokes' parameter of the known linearly polarized light of incident is s=[s ₀, s ₁, s ₂, s ₃] ^T=[1.031,0.8,0.6] ^T, its polarization position angle then

Degree of polarization is 0.9699.Measure according to the following steps:

1, the original state of measuring for the first time is set: the fast shaft angle degree of setting quarter-wave plate is θ ₁=0 °, the light transmission shaft angle of polarizing prism are α ₁=0 °;

2, measure for the first time: obtain the Stokes' parameter of incident beam 1 after the data processing, calculate degree of polarization V _E1=1.03634, the position angle shakes

The polarization azimuth angle error

Promptly

The degree of polarization error is Δ V ₁=V _E1-V=1.0363-0.97=0.0663, i.e. m ₁=0.0663;

3, the original state of measuring for the second time is set: the original state when recovering to measure described quarter-wave plate and polarizing prism to the first time, i.e. θ ₁=0 °, α ₁=0 °, rotate quarter-wave plate β=1 ° and polarizing prism 2 β=2 ° respectively along same direction again;

4, measure for the second time: the θ when still measuring during data processing with the first time ₁=0 °, α ₁=0 ° is initial angle, and the error of then fast shaft angle degree and axis of homology angle is respectively Δ θ ₂=Δ θ ₁+ β=Δ θ ₁+ 1 ° and Δ α ₂=Δ α ₁+ 2 β=Δ α ₁+ 2 ° are satisfied Δ α ₂-2 Δ θ ₂=-3 °=q, and phase-delay quantity error delta δ and extinction coefficient p remain unchanged, and obtain the Stokes' parameter of incident beam 1 after the data processing, calculate degree of polarization V _E2=1.0174, the polarization position angle

Polarization azimuth angle error then

Promptly

The degree of polarization error is Δ V=V _E2-V=1.0174-0.97=0.0474, i.e. m ₂=0.0474;

5, obtain gross data: the light transmission shaft angular error satisfies θ=q=-3 ° of Δ α-2 Δ with fast shaft angle degree error, and obtaining Stokes' parameter by emulation is s=[s ₀, s ₁, s ₂, s ₃] ^T=[1.031,0.8,0.6] ^TThe degree of polarization error delta V of linearly polarized light with the gross data that fast shaft angle degree error delta θ and phase-delay quantity error delta δ change, obtain theoretical curved surface Δ V=f (Δ θ, Δ δ);

6, determine error: being the example explanation herein, is to reduce data volume, with 0.1 ° of interval Δ θ and Δ δ is carried out value in-3 °≤Δ θ≤3 ° ,-3 °≤Δ δ≤3 ° scope, then in described theoretical curved surface, and degree of polarization error delta V=m ₁=0.0663 pairing coordinate is (Δ θ _1i, Δ δ _1i) be (2.2 ° ,-1.8 °), (2.1 ° ,-1.7 °), (2.0 °,-1.6 °), (1.9 °,-1.5 °), (1.8 ° ,-1.4 °), (1.1 ° ,-0.8 °), (1.0 °,-0.7 °), (0.5 °,-0.3 °), (0.4 ° ,-0.2 °), (0 °, 0.1 °), (0.4 °, 0.4 °), (0.8 °, 0.7 °), (1.1 °, 0.9 °), (1.4 °, 1.1 °), (1.7 °, 1.3 °), (2 °, 1.5 °), (2.2 °, 1.6 °), (2.5 °, 1.8 °), (2.7 °, 1.9 °), degree of polarization error delta V=m ₂The coordinate of=0.0474 correspondence is (Δ θ _2i, Δ δ _2i) be (1.8 °,-2.0 °), (1.7 °,-1.9 °), (1.6 ° ,-1.8 °), (1.0 ° ,-1.3 °), (0.9 °,-1.2 °), (0.4 °,-0.8 °), (0.3 ° ,-0.7 °), (0.1 ° ,-0.4 °), (0.5 °,-0.1 °), (0.9 °, 0.2 °), (1.2 °, 0.4 °), (1.5 °, 0.6 °), (1.8 °, 0.8 °), (2.0 °, 0.9 °), (2.3 °, 1.1 °), (2.5 °, 1.2 °), (3 °, 1.5 °), according to the fast shaft angle degree error delta θ that measures for twice ₂=Δ θ ₁+ 1 ° relation is at coordinate (Δ θ _1i, Δ δ _1i) and (Δ θ _2i, Δ δ _2i) in find and satisfy Δ θ _2c=Δ θ _1c+ 1 ° and Δ δ _2c=Δ δ _1cCoordinate be (Δ θ _1c, Δ δ _1c2 ° of)=(, 1.5 °), then fast shaft angle degree error delta θ=Δ θ _1c=2 °, phase-delay quantity error delta δ=δ _1c=1.5 °, try to achieve axis of homology angular error Δ α=2 Δ θ according to Δ α=2 Δ θ+q again _1c-3 °=1 °.

The result who calculates and known error Δ θ=2 °, Δ α=1 °, Δ δ=1.5 are ° consistent.Therefore, the feasibility of device error measurement method has obtained checking in the polarimetry device.

Figure 7 shows that the synoptic diagram of illumination iris polarization parameter pick-up unit in the projection aligner that technology formerly 1 proposes.

The light beam of transform lens group 20 outgoing in the described device for testing polarization is a parallel beam, and is the lens combination of polarization irrelevant or low-birefringence.When the transform lens group of polarization parameter pick-up unit is polarization irrelevant, the degree of polarization V that records _eWith the polarization position angle

Be net result; When there is birefringence in the transform lens group, need its birefringent influence from V as a result _eWith

The middle removal.

The measuring method of device error is applicable to this polarization parameter pick-up unit in the polarimetry device of the present invention.After determining error delta θ, Δ α, Δ δ, angle that can be by adjusting phase delay device and analyzer or in computation process, parameter θ, α, δ are revised, eliminate of the influence of all kinds of errors, thereby realize the high-acruracy survey of incident beam polarization state device for testing polarization.

Claims (4)

1. the measuring method of device error in the device for testing polarization, described device for testing polarization comprises phase delay device, analyzer and the photodetector that sets gradually along the apparatus system optical axis, the output of this photodetector connects signal processing system, it is characterized in that:

The Stokes' parameter of incident beam is known;

Concrete measuring process is as follows:

1. the original state of measuring for the first time is set: the system optical axis of setting up departments is the z axle of enlightening card coordinate, the forward of z axle is the light beam working direction, the plane vertical with the z axle is the xy plane, earlier selected arbitrary x direction of principal axis in the xy plane, and the angle between the polarization direction of the linearly polarized light of definition x axle positive dirction and incident is the polarization position angle Angle between the fast axle of x axle positive dirction and phase delay device is fast shaft angle degree θ, angle between x axle positive dirction and the analyzer light transmission shaft is the light transmission shaft angle [alpha], design parameter with described phase delay device and analyzer is a benchmark, and the fast shaft angle degree of adjusting described phase delay device is θ ₁, described analyzer the light transmission shaft angle be α ₁, and set the original state of this state for measuring for the first time;

2. measure for the first time: utilize the described phase delay device rotation of driver drives, described photodetector is surveyed light signal and is exported electric signal, described electric signal obtains the Stokes' parameter (s of incident beam after described signal processing system data processing _E10, s _E11, s _E12, s _E13), utilize following formula to calculate corresponding degree of polarization V _E1With the polarization position angle

Degree of polarization V _E1For:

$V_{e1}=\sqrt{\frac{s_{e11}^2+s_{e12}^2+s_{e13}^2}{s_{e10}^2}},$

The polarization position angle

The polarization azimuth angle error

The degree of polarization error is Δ V ₁=V _E1-V=m ₁, Δ θ wherein ₁Be the fast shaft angle degree error of described phase delay device, Δ α ₁Be the light transmission shaft angular error of analyzer, V is the degree of polarization of incident beam,

Polarization position angle for incident beam;

3. the original state of measuring for the second time is set: the original state when described phase delay device of recovery and analyzer are extremely measured for the first time earlier, along same direction described phase delay device is rotated the β angle again, described analyzer is rotated 2 β angles, wherein β＜5 °;

4. measure for the second time: the described phase delay device rotation of described driver drives, described photodetector is surveyed light signal and is exported electric signal, described electric signal carries out data processing through described signal processing system to described electric signal, the fast shaft angle degree θ when still measuring with the first time during data processing ₁With the light transmission shaft angle [alpha] ₁Be initial angle, obviously, during second measurement, the error of described fast shaft angle degree is Δ θ ₂=Δ θ ₁+ β, the error of described light transmission shaft angle is Δ α ₂=Δ α ₁+ 2 β, and phase-delay quantity error delta δ and extinction coefficient p remain unchanged, and obtain the Stokes' parameter of incident beam after the data processing, calculate corresponding degree of polarization V _E2With the polarization position angle

Polarization azimuth angle error then

The degree of polarization error is Δ V ₂=V _E2-V=m ₂

5. obtain gross data: the light transmission shaft angular error satisfies Δ α-2 Δ θ=q with fast shaft angle degree error, obtain the gross data of the degree of polarization error delta V of the known linearly polarized light of Stokes' parameter with fast shaft angle degree error delta θ and phase-delay quantity error delta δ variation by emulation, obtain a theoretical curved surface Δ V=f (Δ θ, Δ δ);

6. determine error: in described theoretical curved surface, degree of polarization error delta V=m ₁Pairing coordinate is (Δ θ _1i, Δ δ _1i), degree of polarization error delta V=m ₂Corresponding coordinate is (Δ θ _2i, Δ δ _2i), i=1 wherein, 2,3 ..., fast shaft angle degree error delta θ when measuring according to twice ₂=Δ θ ₁The relation of+β is at coordinate (Δ θ _1i, Δ δ _1i) and (Δ θ _2i, Δ δ _2i) in find and satisfy Δ θ _2c=Δ θ _1c+ β and Δ δ _2c=Δ δ _1cCoordinate (Δ θ _1c, Δ δ _1c), then fast shaft angle degree error delta θ=θ _1c, phase-delay quantity error delta δ=Δ δ _1c, ask light transmission shaft angular error Δ α=2 Δ θ according to Δ α=2 Δ θ+q again _1c+ q.

2. the measuring method of device error in the device for testing polarization according to claim 1 is characterized in that described phase delay device is for producing quarter-wave plate, electrooptic modulator or the light ball modulator of 90 ° of phase delays.

3. the measuring method of device error in the device for testing polarization according to claim 1, it is characterized in that the described phase delay device system for winding of described driver drives optical axis at the uniform velocity rotates or the angle of fixed interval is repeatedly rotated, perhaps by driving the position of at least four different angles between fast axle that the phase delay device rotation can be provided with phase delay device and the described analyzer light transmission shaft.

4. the measuring method of device error in the device for testing polarization according to claim 1 is characterized in that described photodetector is two-dimensional array detector or point probe.

Images