CN104075998A - Near-infrared polarization invisible anti-fake element identification system - Google Patents

Abstract

The invention relates to a near-infrared polarization invisible anti-fake element identification system which integrates an infrared light source, a polarization sheet, a CCD (Charge Coupled Device) camera and a stepper motor into one system, so as to achieve optical, mechanical and electronic integration. The infrared light source adopts a square indirect lighting mode, infrared ray passes through a diffusion plate to be subjected to scattering to form a bidirectional highly-uniform circular symmetric light field, interference caused by slight different of the surface of an article can be filtered, the rapid gradient change characteristic can be revealed, and due to adoption of the infrared sensitive camera, light of a near-infrared waveband can be effectively identified; the rotation of a polarization rotating disc and the imaging of the camera are synchronized. After the initialization is accomplished, the detection on invisible anti-fake elements can be achieved through only one-key operation, so that the operation is very easy and rapid, the whole system has the advantages of compact structure, small size, rapidness and the like, and the system further has the functions of image filtering, confusion, storage and the like, so that the purposes that the operation is stable and reliable and labor and cost are saved are achieved.

Description

A kind of near infrared polarization concealed anti-false element identification system

Technical field

The invention belongs to Security element identification system, be specifically related to a kind of near infrared polarization concealed anti-false element identification system.

Background technology

In order to protect article; for example value document and paper; and the spare part of consumer product area, medicine, textile or other registered trademark products avoid imitated and forge and distort, and in order to detect the true and false of these article, for they have configured specific Security element.Manufacturing Security element needs some special material and pigment, because they have specific optical characteristics, therefore be not easy to be imitated.Known Security element has watermark, be combined in anti-counterfeiting line in paper, luminous or magnetic-particle etc.; Security element can be added in printing-ink or relief hologram, then be applied in the packaging of shielded article surface or article as paper tinsel element.

Also have some to utilize the Security element of infrared printing ink fabrication techniques, infrared hidden anti-fake print technology utilizes infrared band not in human eye visible range, and the invisible false proof technique of realizing.For the hiding information of needs, can will be above it upper infrared covering ink of printing, information can only just can be seen the figure or the word that cover below ink under infrared imaging device like this.If application number is " 200420071314.2 ", name is called " for the device of displaying invisible printed ink ", the element that utilizes transmission-type to utilize invisible printing ink printing or write from the back side transmitting infrared light detection of paper.

Latent image method for making based on polarization technology is mainly to rely on the image information color manifesting under polarized light and different realization of color manifesting under natural light, under white light, can distinguish hiding picture and text by polarization information.Its corresponding detection method is carried out according to polarization latent image producing principle, if application number is " 201210252363.5 ", it is by the polarization spectrum information of color filter and polaroid detecting element itself that name is called " Multi-band Polarization imaging Security element identification system ".

Near infrared polarization invisible false proof technique is the novel invisible anti-counterfeiting technology that combines infrared printing ink technology and polarization stealth technique.If application number is " 201310340065 ", name is called the patent of " near infrared polarization latent image element and preparation method thereof ", introduce a kind of method for making of the latent image that infrared hidden anti-fake print technology and polarization technology are combined, for image-text hiding.The Security element that utilizes the method to make can be used for false proof field, this Security element cannot be seen hiding picture and text under natural light, only by polarized light or only the light by near-infrared band can not the hiding picture and text of identification, only under the polarized light of near-infrared band, utilizing just can the hiding picture and text of identification to the imaging device of near-infrared band sensitivity.This recessive Security element has been strengthened the concealment effect of picture and text, has strengthened the difficulty being forged with lower cost.This kind of method is with low cost, manufacture craft simple, be easy to apply, and has very large application potential.

For near infrared polarization concealed anti-false element, only could unique true or false of determining tested Security element at near-infrared band.Although application number is " 201210252363.5 ", name is called " Multi-band Polarization imaging Security element identification system " and includes near-infrared band, but, this identification system cannot artificially determine, cannot predict wave band used, is the polarization concealed anti-false element under near-infrared band therefore cannot detect under specific band.For example, for the stealthy element of the polarization under the visible light wave range of a forgery, because application number is " 201210252363.5 ", name is called " Multi-band Polarization imaging Security element identification system " and utilizes visible light wave range to detect its hiding information, thereby judge that this element is true, obviously testing result is wrong.

For near infrared polarization concealed anti-false element, also do not have at present the feasible checkout equipment can identification.

Summary of the invention

The technical matters solving

For fear of the deficiencies in the prior art part, the present invention proposes a kind of near infrared polarization concealed anti-false element identification system, carries out false proof element for existing use near infrared polarization stealth technique, carries out effective, quick, conveniently recognized problem.The present invention near infrared polarization concealed anti-false element have or not, true and false identification.And multiple hardware modules such as integrated data acquisition and processing, the control of infrared diffused ray source, there is automatic collection and the feature such as real-time.

Technical scheme

A kind of near infrared polarization concealed anti-false element identification system, is characterized in that comprising the responsive camera image acquisition module of near infrared, image processing module, polaroid runner and control module and infrared diffusion light source module; Described infrared diffused ray source module comprises aluminum alloy casing 1, near-infrared light source 3 and diffusing panel 4; The upper surface of aluminum alloy casing 1 is provided with rectangular through-hole, and rectangular through-hole below forms tapered cavity with four diffusing panels 4 of ramp structure, and near-infrared light source is placed in the top of diffusing panel 4, and detected element is placed in the below of tapered cavity; Described polaroid runner and control module thereof comprise stepper motor 6, polaroid rotating disk 10 and are placed in polaroid; Polaroid rotating disk 10 is provided with circular hole, and polaroid is fixed in circular hole by set collar 11, and stepper motor 6 is controlled the motion of polaroid rotating disk 10 by transmission gear 7; Polaroid runner and control module thereof are placed in the top of aluminum alloy casing 1, polaroid is positioned at the rectangular through-hole position of the upper surface of aluminum alloy casing 1, infrared-sensitive camera image acquisition module is placed in the top of polaroid, and realizes electric signal with image processing module and be connected.

Adjust stepper motor 6 and be with nutating gear 7 to rotate 180 while spending, polaroid rotating disk 10 drives polaroid rotation 45 degree that are arranged on wherein.

Described near-infrared light source adopts near-infrared LED 3 as near-infrared light source.

Described near-infrared LED 3 is 850nm near-infrared LED.

Adopt Stokes parameter in described System Discrimination Security element and a method for polarization parameter, it is characterized in that step is as follows:

Step 1, initialization: the motor control module in circuit control unit carries out initialization operation to stepper motor 6, does zero correction by approach switch; And the each Rotate 180 degree of stepper motor 6 is set, corresponding polaroid runner 10 rotates 45 degree; Between every twice rotation of stepper motor, stop gathering image for the responsive camera 8 of near infrared in 1 second, stepper motor 6 rotates 4 times to be stopped after 2 weeks totally;

Step 2, image acquisition: computer terminal sends image pick-up signal and starts timing, when t=0, polaroid runner 10 rotates to 0 degree, computing machine transmission collection signal carries out the single frames storage of collected of image to responsive camera 8 image capture modules of near infrared, in the t=1s moment, the image acquisition of 0 degree is complete; Polaroid runner 10 Rotate 180 degree respectively under the control of motor control module, at moment t=(T+1) s, t=(2*T+2) s and the responsive camera 8 of t=(3*T+3) s near infrared, to gather respectively polaroid be image while spending of 45 degree, 90 degree and 135 and be sent to computer terminal;

Step 3, gathered: stepper motor rotated after 2 weeks, computer acquisition is the images of 0 degree, 45 degree, 90 degree, 135 degree to detected element 5 at polaroid, is sent and is fed back signal to circuit control unit by computing machine, and suppressed zero position, in order to detecting next time;

Step 4, calculate Stokes parameter and polarization parameter degree of polarization DoLP in infrared polarization concealed anti-false element, polarization azimuth AoP:

$\left[\begin{array}{c}I\\ Q\\ U\end{array}\right]=\left[\begin{array}{c}\frac{1}{2}(I_{\left(\mathrm{0,0}\right)}+I_{\left(\mathrm{45,0}\right)}+I_{\left(\mathrm{90,0}\right)}+I_{\left(\mathrm{135,0}\right)})\\ I_{\left(\mathrm{0,0}\right)}-I_{\left(\mathrm{90,0}\right)}\\ I_{\left(\mathrm{45,0}\right)}-I_{\left(\mathrm{135,0}\right)}\end{array}\right]=\left[\begin{array}{c}{I}_{\left(\mathrm{0,0}\right)}+I_{\left(\mathrm{90,0}\right)}\\ I_{\left(\mathrm{0,0}\right)}-I_{\left(\mathrm{90,0}\right)}\\ I_{\left(\mathrm{45,0}\right)}-I_{\left(\mathrm{135,0}\right)}\end{array}\right]$

$\mathrm{DoLP}=\frac{\sqrt{Q^2+U^2}}{I}$

$\mathrm{AoP}=\frac{1}{2}{\tan }^{-1}\frac{U}{Q}$

Wherein: I represents the total intensity of light wave, Q represents the intensity of linearly polarized light in horizontal direction, and U represents the intensity of linearly polarized light in 45 ° of directions, I _(0,0)represent that polaroid is 0 to spend time intensity of wave, I _(45,0)represent that polaroid is 45 to spend time intensity of wave, I _(90,0)represent that polaroid is 90 to spend time intensity of wave, I _(135,0)represent that polaroid is 135 to spend time intensity of wave.

Beneficial effect

A kind of near infrared polarization concealed anti-false element identification system that the present invention proposes, for the near infrared polarization latent image, the stealthy labeling etc. that use near infrared polarization invisible false proof technique to make, can effectively detect wherein hiding information, and the detection method of native system is easy to use, testing result is intuitive and reliable, be with a wide range of applications in false proof discriminating field.

The present invention has the following advantages compared with existing polarization anti-counterfeiting technology: 1) infrared light supply, polaroid, CCD camera and stepper motor are integrated in a system, have realized optical, mechanical and electronic integration; 2) infrared light supply adopts the mode of square indirect lighting, Infrared is through diffusing panel, light is formed to the symmetrical light field of two-way, high circle uniformly through scattering, the interference that body surface nuance can be caused filters out, highlight sharply variation characteristic of the gradient, and adopt infrared-sensitive camera, can carry out effective identification to the light of near-infrared band; 3) diameter of transmission gear and polaroid rotating disk is than being 1:4, and by the accurate control step motor of DSP rotational speed, and synchronous polaroid turntable rotation and camera are adopted picture.After initialization completes, only need a key operation, just can realize the detection of concealed anti-false element, operation is extremely simple, quick; 4) total system has the advantages such as compact conformation, volume are little, quick, and system also has the functions such as image filtering, fusion and storage, therefore can reach reliable and stable work, save the object of manpower and financial resources.Its overall performance is as follows:

1, the camera response time, in 20ms, is less than 10s from image acquisition to the time that calculates polarization parameter;

2, memory space: can reach 4G, in the time that image reaches memory capacity, can enable communication module and view data transfer is carried out at surface work station;

3, Data Dynamic scope: 14bit/16bit;

4, polarization resolution: can obtain linear polarization component, linear polarization degree component, polarization phase angle component image in Stokes parameter.

Brief description of the drawings

Fig. 1: infrared polarization imaging anti-counterfeiting identification system hardware structure figure

Fig. 2: infrared polarization imaging anti-counterfeiting identification system signal flow graph

Fig. 3: light path travel path and one-piece construction schematic diagram in imaging device

Fig. 4: infrared diffusion light-source structure figure

Fig. 5: rotating disk size layout

Fig. 6: turntable structure decomposing schematic representation

Fig. 7: turntable structure assembling schematic diagram

Wherein: 1, aluminum alloy casing; 2, heat sink; 3, IR LED; 4, diffusing panel; 5, detected element; 6, stepper motor; 7, transmission gear; 8, infrared-sensitive camera; 9, camera lens; 10, polaroid rotating disk; 11, set collar; 12, rotating disk fixed head; 13, rotating disk guide-rail plate; 14, trip bolt.

Embodiment

Now in conjunction with the embodiments, the invention will be further described for accompanying drawing:

In embodiments of the invention technical scheme, mainly comprise the ingredients such as infrared diffusion light source module, polaroid runner and control module thereof, the responsive camera image acquisition module of near infrared, image processing module.

Infrared diffused ray source is made up of a prescription shape structural al alloy shell 1, heat sink 2, near-infrared light source 3 and diffusing panel 4, uses 850nm near-infrared LED 3 as near-infrared light source, at the front placement diffusing panel 4 of near-infrared light source 3, as shown in Figure 3 and Figure 4.Light is after target area overlaps, and area coverage is not less than 210 × 210mm ², the uniform light that is used for realizing for Security element to be measured irradiates.

Polaroid runner and control module thereof mainly realize the accurate control that stepper motor 6 rotates polaroid rotating disk 10.Polarization deflexion disk 10 diameters are 120mm, and it is around with gear, by being arranged on the transmission gear 7 interlock transmissions on stepper motor 6.The diameter of transmission gear 7 is 30mm.Diameter is 80mm for the circular hole of polaroid is installed on polaroid rotating disk 10, to have designed one, and polaroid is fixed in circular hole by set collar 11.Polaroid rotating disk 10 drives by transmission gear 7, and in the time that stepper motor 6 is with nutating gear 7 to rotate half-turn (i.e. 180 degree), polaroid rotating disk 10 drives polaroid rotation 45 degree that are arranged on wherein.Stepper motor 6 is controlled functions such as can realizing zero point alignment, angle control, speed adjusting, braking in real time.As shown in Figure 3, Figure 5 and Figure 6.

After polaroid rotating disk 10, placing the responsive camera 8 of near infrared, the responsive camera image acquisition module of near infrared mainly completes collection and the storage of REAL TIME INFRARED THERMAL IMAGE polarization image.This module is made up of a CCD camera to near-infrared band sensitivity, and the Image Real-time Transmission of collection is to computing machine.Image is processed and is completed by computing machine.As shown in Figure 3.

The light source that this embodiment adopts is that centre wavelength is that the near-infrared LED lamp of 850nm forms by preceding method.The computing machine that this embodiment adopts comprises collected by camera software, and computer model is Lenovo Qitian M7150.The CCD camera of this embodiment adopts dimension to look MV-1300-UM, and the drive motor of runner is leadshine-1.8/4.0A stepper motor.The control module of runner is the polarization imager control system of seminar based on DSP exploitation.

The imaging process of CCD is by circuit control unit control.Circuit control unit is the core component of native system.1) initialization: the motor control module in circuit control unit carries out initialization operation to stepper motor 6, does zero correction by approach switch.The each Rotate 180 degree of stepper motor 6 is set, and corresponding polaroid runner 10 rotates 45 degree.Between every twice rotation of stepper motor, stop gathering image for the responsive camera 8 of near infrared in 1 second, stepper motor 6 rotates 4 times to be stopped after 2 circles totally.This calculates by stepper motor rotational speed is set the time T that stepper motor Rotate 180 degree needs, and it is automatic sampling pattern that the responsive camera 8 of near infrared is set, and sampling interval is (T+1) s; 2) image acquisition: first computer terminal sends image pick-up signal and starts timing.When t=0, now polaroid runner 10 rotates to 0 degree, and computing machine transmission collection signal carries out the single frames storage of collected of image to responsive camera 8 image capture modules of near infrared, and in the t=1s moment, the image acquisition of 0 degree is complete; Polaroid runner 10 is difference Rotate 180 degree under the control of motor control module, then gathers respectively 45 degree, 90 degree and 135 degree images at moment t=(T+1) s, t=(2*T+2) s and t=(3*T+3) s.When gathering image, 4 width images are sent to computer terminal; 3) gathered: after stepper motor rotates 2 weeks, computing machine has gathered 0 degree, 45 degree, 90 degree, the 135 degree images of detected element 5, is sent and is fed back signal to circuit control unit by computing machine, and suppressed zero position, in order to detecting next time; 4) calculate polarization parameter: due to 0 degree collecting, 45 degree, 90 degree, 135 degree images, met the requirement of calculating Stokes parameter, can read memory image, the operation such as the calculating of geometry correction and polarization parameter.

Referring to Fig. 3, runner control and image acquisition.Circuit control unit is integrated in DSP disposable plates, and control mode is automatically to control.Detailed process is as follows:

1, initialization: the motor control module in circuit control unit carries out initialization operation to stepper motor 6, does zero correction by approach switch.The each Rotate 180 degree of stepper motor 6 is set, and corresponding polaroid runner 10 rotates 45 degree.Between every twice rotation of stepper motor, stop gathering image for the responsive camera 8 of near infrared in 1 second, stepper motor 6 rotates 4 times to be stopped after 2 weeks totally.By stepper motor rotational speed is set, calculate the time T that stepper motor Rotate 180 degree needs, it is automatic drainage pattern that the responsive camera 8 of near infrared is set, sampling interval is (T+1) s;

2, image acquisition: first computer terminal sends image pick-up signal and starts timing.When t=0, now polaroid runner 10 rotates to 0 degree, and computing machine transmission collection signal carries out the single frames storage of collected of image to responsive camera 8 image capture modules of near infrared, and in the t=1s moment, the image acquisition of 0 degree is complete; Polaroid runner 10 Rotate 180 degree respectively under the control of motor control module, gathers respectively 45 degree, 90 degree and 135 degree images automatically at moment t=(T+1) s, t=(2*T+2) s and the responsive camera 8 of t=(3*T+3) s near infrared.When gathering image, 4 width images are sent to computer terminal;

3, gathered: after stepper motor rotates 2 weeks, computing machine has gathered 0 degree, 45 degree, 90 degree, the 135 degree images of detected element 5, is sent and is fed back signal to circuit control unit by computing machine, and suppressed zero position, in order to detecting next time;

4, calculate polarization parameter: due to 0 degree collecting, 45 degree, 90 degree, 135 degree images, met the requirement of calculating Stokes parameter, can read memory image, the operation such as the calculating of geometry correction and polarization parameter.

According to the impact of ignoring circularly polarized light intensity V in calculating degree of polarization process.Only need just can calculate polarization parameter by the image under 4 polarization angles that obtain.

Polarization parameter calculates.In polarization imaging technical applications, generally adopt the polarization state of the accurate monochromatic plane wave of Stokes vector analysis, Stokes vector can be described as: S=[I Q U V] ^t.Wherein, I represents the total intensity of light wave, and Q represents the intensity of linearly polarized light in horizontal direction, and U represents the intensity of linearly polarized light in 45 ° of directions.V represents circular polarization light intensity.In application, V is generally very little, in native system, ignores the size of V.

Axis of homology direction and the reference direction angle of supposing linear polarizer are θ, and wave plate quick shaft direction and reference direction angle are φ, and the strength formula of Stokes is:

$I(\mathrm{\θ},\mathrm{\φ})=\frac{1}{2}[I+Q\cos 2\mathrm{\θ}+U\cos \mathrm{\φ}\sin 2\mathrm{\θ}+V\sin \mathrm{\φ}\sin 2\mathrm{\θ}]$

When φ gets 0 ° of degree, θ gets four angles, during as 0 °, 45 °, 90 ° and 135 °, just obtains three independently equations.Thereby derive known Stokes parameter and polarization parameter (degree of polarization DoLP, polarization azimuth AoP) are:

$\left[\begin{array}{c}I\\ Q\\ U\end{array}\right]=\left[\begin{array}{c}\frac{1}{2}(I_{\left(\mathrm{0,0}\right)}+I_{\left(\mathrm{45,0}\right)}+I_{\left(\mathrm{90,0}\right)}+I_{\left(\mathrm{135,0}\right)})\\ I_{\left(\mathrm{0,0}\right)}-I_{\left(\mathrm{90,0}\right)}\\ I_{\left(\mathrm{45,0}\right)}-I_{\left(\mathrm{135,0}\right)}\end{array}\right]=\left[\begin{array}{c}{I}_{\left(\mathrm{0,0}\right)}+I_{\left(\mathrm{90,0}\right)}\\ I_{\left(\mathrm{0,0}\right)}-I_{\left(\mathrm{90,0}\right)}\\ I_{\left(\mathrm{45,0}\right)}-I_{\left(\mathrm{135,0}\right)}\end{array}\right]$

$\mathrm{DoLP}=\frac{\sqrt{Q^2+U^2}}{I}$

$\mathrm{AoP}=\frac{1}{2}{\tan }^{-1}\frac{U}{Q}.$

Claims (5)

1. a near infrared polarization concealed anti-false element identification system, is characterized in that comprising the responsive camera image acquisition module of near infrared, image processing module, polaroid runner and control module and infrared diffusion light source module; Described infrared diffused ray source module comprises aluminum alloy casing (1), near-infrared light source (3) and diffusing panel (4); The upper surface of aluminum alloy casing (1) is provided with rectangular through-hole, rectangular through-hole below forms tapered cavity with four diffusing panels (4) of ramp structure, near-infrared light source is placed in the top of diffusing panel (4), and detected element is placed in the below of tapered cavity; Described polaroid runner and control module thereof comprise stepper motor (6), polaroid rotating disk (10) and are placed in polaroid; Polaroid rotating disk (10) is provided with circular hole, and polaroid is fixed in circular hole by set collar (11), and stepper motor (6) is controlled the motion of polaroid rotating disk (10) by transmission gear (7); Polaroid runner and control module thereof are placed in the top of aluminum alloy casing (1), polaroid is positioned at the rectangular through-hole position of the upper surface of aluminum alloy casing (1), infrared-sensitive camera image acquisition module is placed in the top of polaroid, and realizes electric signal with image processing module and be connected.

2. near infrared polarization concealed anti-false element identification system according to claim 1, it is characterized in that: when adjustment stepper motor (6) band nutating gear (7) rotation 180 is spent, polaroid rotating disk (10) drives the polaroid rotation 45 being arranged on wherein to spend.

3. near infrared polarization concealed anti-false element identification system according to claim 1, is characterized in that: described near-infrared light source adopts near-infrared LED (3) as near-infrared light source.

4. near infrared polarization concealed anti-false element identification system according to claim 1, is characterized in that: described near-infrared LED (3) is 850nm near-infrared LED.

5. adopt the Stokes parameter in any one System Discrimination Security element and a method for polarization parameter described in claim 1～4, it is characterized in that step is as follows:

Step 1, initialization: the motor control module in circuit control unit carries out initialization operation to stepper motor (6), does zero correction by approach switch; And the each Rotate 180 degree of stepper motor (6) is set, corresponding polaroid runner (10) rotation 45 is spent; Between every twice rotation of stepper motor, stop gathering image for the responsive camera of near infrared (8) in 1 second, stepper motor (6) rotation stops after 2 weeks for 4 times totally;

Step 2, image acquisition: computer terminal sends image pick-up signal and starts timing, when t=0, polaroid runner (10) rotates to 0 degree, computing machine transmission collection signal carries out the single frames storage of collected of image to responsive camera (8) image capture module of near infrared, in the t=1s moment, the image acquisition of 0 degree is complete; Polaroid runner (10) Rotate 180 degree respectively under the control of motor control module, at moment t=(T+1) s, t=(2*T+2) s and the responsive camera of t=(3*T+3) s near infrared (8), to gather respectively polaroid be image while spending of 45 degree, 90 degree and 135 and be sent to computer terminal;

Step 3, gather: stepper motor rotated after 2 weeks, computer acquisition is the image of 0 degree, 45 degree, 90 degree, 135 degree at polaroid to detected element (5), sent and fed back signal to circuit control unit by computing machine, suppressed zero position, in order to detecting next time;

Step 4, calculate Stokes parameter and polarization parameter degree of polarization DoLP in infrared polarization concealed anti-false element, polarization azimuth AoP:

$\left[\begin{array}{c}I\\ Q\\ U\end{array}\right]=\left[\begin{array}{c}\frac{1}{2}(I_{\left(\mathrm{0,0}\right)}+I_{\left(\mathrm{45,0}\right)}+I_{\left(\mathrm{90,0}\right)}+I_{\left(\mathrm{135,0}\right)})\\ I_{\left(\mathrm{0,0}\right)}-I_{\left(\mathrm{90,0}\right)}\\ I_{\left(\mathrm{45,0}\right)}-I_{\left(\mathrm{135,0}\right)}\end{array}\right]=\left[\begin{array}{c}{I}_{\left(\mathrm{0,0}\right)}+I_{\left(\mathrm{90,0}\right)}\\ I_{\left(\mathrm{0,0}\right)}-I_{\left(\mathrm{90,0}\right)}\\ I_{\left(\mathrm{45,0}\right)}-I_{\left(\mathrm{135,0}\right)}\end{array}\right]$

$\mathrm{DoLP}=\frac{\sqrt{Q^2+U^2}}{I}$

$\mathrm{Aop}=\frac{1}{2}{\tan }^{-1}\frac{U}{Q}$

Wherein: I represents the total intensity of light wave, Q represents the intensity of linearly polarized light in horizontal direction, and U represents the intensity of linearly polarized light in 45 ° of directions, I _(0,0)represent that polaroid is 0 to spend time intensity of wave, I _(45,0)represent that polaroid is 45 to spend time intensity of wave, I _(90,0)represent that polaroid is 90 to spend time intensity of wave, I _(135,0)represent that polaroid is 135 to spend time intensity of wave.