the present application uses the grin lens as a light polarization state detection modulation device to realize modulation and demodulation of a sop , or the grin lens is taken as a polarization state generator ( psg ) and polarization state analyzer ( psa ). the present embodiment is intended to explain a light polarization state detection apparatus and a detection method thereof using the grin lens . the grin lens is also called as a gradient index lens , is a columnar optical lens of which the refractive index is gradually changed along the radial direction and has focusing and imaging functions . when light in the air encounters other mediums , the transmission direction of light is changed due to different refractive indexes . the imaging of traditional lens is to use the generated optical length difference to condense light into one point by controlling the curvature of the surface of the lens . the grin lens differs from a classical lens in that the grin lens material can cause light propagating along the axis direction to generate refraction , and the distribution of the refraction index is gradually reduced along the radial direction , to realize the emergent light convergence to a point smoothly and continuously . fig1 a shows a side section schematic diagram of a grin lens , wherein ab is an object , and a ′ b ′ is an image . birefringence distribution of the grin lens used in the present embodiment is different from refractive index distribution , the birefringence value is gradually increased along a radial direction ( the gray level is gradually increased from the center to the periphery ), a fast axis direction 10 is along an annular direction of the grin lens ( as shown in fig1 b ), the gray level in the drawing represents the birefringence change and the birefringence is larger in the region with darker color . the present embodiment is a simultaneous stokes parameter detection instrument based on the grin lens , and as shown in fig2 , it comprises a housing , a grin lens 1 , a polarizer p ( with a fixed polarization angle ), an imaging lens l , an area array charge - coupled device ( ccd ), a data transmission line , an electronic computer , and data processing , analysis , result displaying software . the grin lens 1 , the polarizer p , the imaging lens l and the ccd are packaged in the housing . the length of the grin lens is centimeter magnitude , the whole sop detection apparatus can be made to a length of 6 cm or even shorter , a diameter of 1 . 5 mm or even shorter , and is high in portability and compatibility . a memorizer or singlechip can be stored in the sop detection apparatus and can independently work without the electronic computer . fig2 is a light path diagram used by the present embodiment , the ccd is located in the imaging plane of the front surface of grin lens , wherein ab is an object and corresponds to the front surface of the grin lens , a ′ b ′ is an image in the grin lens and a ″ b ″ is an image in the ccd . the present embodiment comprises the following measuring steps to perform polarization detection ( as shown in fig6 ): a , causing a light beam to be measured to enter the light inlet of a detection apparatus , wherein incident light has a certain sop , namely having intensity and phase distributions in x direction and y direction ; b , causing the incident light to enter a grin lens to generate spatial phase modulation of a light field ; c , causing the light emergent from the grin lens to enter a polarizer , wherein the light of different phases generates polarization interference after passing the polarizer and generate an interference pattern ; d , causing the light to enter a ccd , wherein interference fringes are projected and recorded on the ccd ; e , calculating the sop of the incident light by certain specific pattern and storing , wherein different interference pattern shapes correspond to different sops of the incident light , that is , the sops of the incident light correspond to the patterns of the ccd one to one , and such one to one relation is built by a calculating program ; f , displaying a poincare sphere representing sops and the corresponding elliptical polarization parameters in the user interface , thereby vividly displaying the polarization measuring result . the principle of the method of the sop detection apparatus is analyzed and explained as follows : the incident light with different sops is projected on the ccd after passing the grin lens and the polarizer . in the process , the change of the sop is wherein , s in is the sop of incident light , s out is the sop of exit light at the ccd surface , m p is the mueller matrix of the polarizer and m grin is the mueller matrix of the grin lens . the signal finally detected by the ccd is a light intensity signal and is only related to the first row of the mueller matrix of the polarizer . m p ( 1 ,:)=( p x 2 + p y 2 ,( p x 2 − p y 2 ) cos 2θ p ,( p x 2 − p y 2 ) sin 2θ p , 0 ) where p x and p y are extinction ratios of the exit light to the incident light in the minimal extinction direction and the maximal extinction direction of the polarizer , and θ p is the azimuth angle of the minimal extinction direction of the polarizer . when the incident beam is horizontally polarized , above formula can be simplified to be it is found in the experiment that the retardance distributions and fast axis directions of the grin lens are as shown in fig3 a and fig3 b : fig3 a is the phase retardance profile of the grin lens and fig3 b is the fast axis direction . the range of retardance is 0 ˜ 180 degrees , the range of the fast axis angle is − 90 ˜ 90 degrees , which are results obtained by the measurement of muller matrix . seen from the drawing , the birefringence distribution of the grin lens is annular symmetric . polarization properties of different positions in the aperture of the grin lens are different , namely having different mueller matrixes . for the purpose , the grin lens is divided into n micro regions , and if each micro region is small enough , the inside sop can be considered to be the same . each micro region is called as a sublens , correspondingly , the incident light is divided into n sub light beams , and each sub light beam corresponds to one sublens . the mueller matrix of the nth sublens is where δ n and θ n are the retardance and fast axis direction of the nth wave plate , respectively . m p in the formula is not required to be directly measured and can be directly used . the mueller matrix m grin is obtained by the experiment in advance and the birefringence experiment result as shown in fig3 b can be derived from the m grin . the m grin obtained by experiment is explained by m grinn in an ideal form , in implementing , m grinn can also be replaced by the element of the mueller matrix of the grin lens for following calculating . assuming the incident light beam is n sub light beams , the grin lens consists of n tiny wave plates of different retardances and fast axis directions , correspondingly , n pixel light intensity values are obtained on the ccd , and the calculating formula of the light intensity of the nth pixel is s outn 0 = p x 2 s in 0 + p x 2 ( cos 2 2θ n + sin 2 2θ n · cos δ n ) s in 1 + 0 . 5 p x 2 sin 4θ n ( 1 − cos δ n )· s in 2 − p x 2 sin 2θ n sin δ n · s in 3 , wherein , a t is transposition of a , and ( a t a ) − 1 is inverse of ( a t a ). where i is the intensity value of each pixel on the ccd , a is a 4 × n matrix , and a p − 1 is a general inverse matrix of a , which are all known quantities during the calculation progress of s in . s in has four unknown quantities , n light intensity values are obtained on the ccd , and n corresponds to the number of imaging pixels on the ccd , and is usually very large . it is equivalent to solve a linear equation system , there are four unknown numbers and n equations . in order to solve this overdetermined equation set , a solving process can refer to a pseudo - inverse algorithm , which can automatically obtained optimal solution by the least - square estimate method . through theoretical calculation , generally , the accuracy of measurement will increase with the increase of n . equally weighted variance ( ewv ) represents a measuring error tolerance of the system . the smaller the ewv , the higher the tolerance . where w + is pseudo - inverse of w , and tr means the matrix trace . of course , not all the n light intensities and n equations are all necessary . condition number ( k ( a )) of matrix is adopted to seek for an optimal instrument matrix , the minimal condition number of a matrix is 1 , and the solving of the linear equation system is more precise if the condition number is closer to 1 . two types of condition number are defined as follows by balancing the optimal ewv and condition number , an annular region of certain retardance is selected to ensure measuring precision . through formula we can obtain the sop of the incident light s in . monochrome parallel light is obtained by a method of introducing collimated led light into a narrow - band filter ( central wave length is 633 nm and full width at half maximum is 3 nm ), and then the light is introduced into a polarized polarizer and ¼ wave plate . in the present embodiment , the polarizer is fixed at a certain angle , the ¼ wave plate is rotated , the light intensity measured on the ccd is shown in fig4 ( fig4 shows a corresponding light intensity pattern on the ccd when the wave plate is rotated by 180 degrees and the polarizer in the psg is fixed ). fig4 shows a - r eighteen schematic patterns in the 180 degree rotating process of the wave plate , each pattern selects n pixels , and the light intensity of the nth pixel is s outn0 . fig5 shows sops s in1 , s in2 , s in3 of the incident light obtained by calculating the light intensity patterns on the ccd and are normalized by s in0 . fig5 shows stokes parameters of the incident derived form 54 light intensity patterns of the ccd when the polarizer in the psg is fixed and the wave plate is rotated by 180 degrees , theoretical ideal curves are s 1 , s 2 , s 3 , experimental result is that square marker is close to s 1 , circle marker is close to s 2 and triangle marker is close to s 3 , in fig5 , the transverse axis is angle θ ( degree ) and the longitudinal axis is the normalized value of the stokes parameters . measuring patterns and results of completely polarized light are listed above . partially polarized light or natural light can also be measured in a single - shot . seen from above , the present embodiment can realize the accurate measuring of the sop and has a lot of advantages : 1 , the sop of incident light can be determined by single frame picture , and simultaneous measuring requirements can be met ; 2 , the apparatus is a full static system without the need of any mechanical rotation devices ; 3 , the apparatus does not need any electrical phase modulation optical element ( which are easily affected by outside factors such as temperature and has high requirement on modulation power source ), so that the system is less influenced by electric signal , low in error and much more stable ; 4 , no excessive amplitude division or wavefront division elements are required , so that the cost is effectively reduced , the structure is compact and portable , and the apparatus can be easily applied to related systems and high in compatibility ; 5 , compared with most sop detection apparatuses at present , initial calibration of the system is rapid and accurate , parameter selection can be optimized by a built - in algorithm through one - click , thereby greatly improving easiness in use and reducing the labor of an operator in instrument debugging ; 6 , the system has simultaneous measurement , low cost , stability , universality and easiness in use and is simple in structure , stable in performance , and low in cost and can be applied to various complex occasions . there are many flexible implementing methods to demodulate sop with the grin lens , for example : 1 , above discussion aims at certain wave length , the experimental result is obtained by an led red light source with a center wave length of 633 nm and a band width of 3 nm . in fact , analysis of other specific wave lengths is similar . the sop detection apparatus has wide wave length measuring range as long as the incident light is a narrow band beam . 2 , above method is only limited to the incident light with a uniform sop , thus this is point measurement , which has one requirement that the sop of the incident light in the aperture of the grin lens is uniform . the grin lens can also realize measurement of area imaging . the diameter of the grin lens can be as small as 0 . 1 mm and massive grin lenses can constitute m × n lens system , each grin lens corresponds to one point measurement and the spatial sop distribution of the m × n size is finally obtained . 3 , the present embodiment is explained by the grin lens , its phase distribution is shown in fig3 a and covers the retardance of 0 ˜ 180 degrees and the fast axis angles of − 90 ˜ 90 degrees , and such distribution traverses all possible planar birefringence and has the largest error tolerance . but the method is not limited to the grin lens and is universal to process the sop detection apparatus with any retardance devices as long as the mueller matrix of the retardance devices is known . for example , if a thin film is designed with a larger retardance and fast axis angle range , it can also constitute the polarization measuring instrument by directly using the method in the specification . therefore , the present sop detection method is suitable for not only the grin lens but also other variable birefringence material . 4 , the sop detection apparatus can be used in various ellipsometers , mueller matrix measurement instruments , polarization remote sensing apparatuses , etc . the application of the self - focusing devices to above three aspects or similar fields also belongs to the scope of the present invention . the embodiment 1 and the flexible implements use the grin lens to demodulate sop . the inventor also finds that the grin lens can be used to modulate sop , that is , the grin lens is used to modulate sop of light in a three dimensional space to generate a polarization vector vortex field with spatial distribution , which is explained by following embodiments 2 - 5 . the grin lens is used to modulate sop to generate the polarization vector vortex field with spatial distribution . the vortex field comprises all of the possible sop , namely grin lens generates all sops on the poincare sphere . meanwhile , the grin lenses with different intercepts in the production process are used to generate different phase modulations . as above mentioned , at present some two dimensional phase modulation plates prepared by a process such as thin film processing exist in the market and have high price , while the grin lens as a phase modulator can replace the existing phase modulation plates , has a low price , and can generate three - dimensional phase modulation . considering an example , when a horizontal linear polarization light enters the grin lens , the stokes vector of exit light is where θ n and δ n range from 0 ˜ 180 degrees . thus s out can traverse all sops . it can be seen that aop relates to values of θ n and δ n , in other words , aop values are different in different positions . in the formula , the plus sign represent right - handed elliptically polarized light , the negative sign represent left - handed elliptically polarized light . the proportion values are related to θ n and δ n , which means that the proportions of circularly polarized light are different in different proportion . fig7 shows the distribution of the exit sop ( s out ) across the section when the incident beam ( s in ) is horizontal linear polarized , namely a schematic diagram of the polarization light modulated by the grin lens at certain section . it contains all possible linear polarized light , right - handed , left - handed circularly polarized light and elliptically polarized light . the uses of polarization vector vortex field with the spatial distribution include the following several aspects : ( 1 ) polarization remote sensing measuring and multichannel light information transmission in free space . as shown in fig7 , the grin lens can convert the horizontally polarized light into any possible polarized light , for example , generate the linearly polarized light in any direction in the peripheral region of the 180 degree retardance . such one - to - many manner can improve the band width of light communication ; ( 2 ) the polarization vector vortex field generated by the grin lens contains many optical singular points and can be used for singular optics research and optical orbital angular momentum research ; ( 3 ) for the simultaneous spatial polarization state generator , multichannel polarization lighting and analysis , that is , the grin lens is used to irradiate a sample to be detected , polarization light received in different positions of the sample are different , and high pass measuring can be performed ; ( 4 ) for the simultaneous spatial polarization state generator , measuring the optical axis direction of crystal in a single shot , that is , the grin lens is used to irradiate the crystal to be detected , the polarized light received by different positions of the crystal are different , and detection results of different positions are considered comprehensively to determine the optical axis direction of the crystal ; ( 5 ) for the simultaneous spatial polarization state generator , and the mueller matrix measuring of a sample can be realized in a single shot by combining the simultaneous polarization detection apparatus namely a grin lens polarization analyzer . a light path is as shown in fig8 , light from a light source is collimated by a lens group l and enters a grin lens grin 1 after passing a polarizer in a horizontal 0 degree direction ( or other directions , the horizontal direction is taken as an example herein ), thus finishing the sop modulation . the back module is a polarization analyzer consisting of a polarizer p 2 with four polarization angles of 0 , 45 , 90 and 135 degrees , and the ccd is an imaging detector , wherein the polarizer is a sop analyzer , and the wave plates with different retardance are used for assisting the optical phase modulation . by using the polarization modulation solution in fig8 , some specific distributions of polarization state can be generated . in order to visualize polarization distribution , the p 2 is rotated by four angles to record light intensity patterns on the ccd , and fig9 a , 9 b , 9 c and 9 d correspond to the situations that the p 2 is at the four polarization angles of 0 , 45 , 90 and 135 degrees , respectively . a light path is shown in fig1 , light from a light source is collimated by a lens group l and enters a grin lens grin 1 and a grin lens grin 2 after passing a polarizer in a horizontal 0 degree direction ( or other directions , the horizontal direction is taken as an example herein ), thus finishing the sop modulation . the back module is a polarization analyzer consisting of a polarizer p 2 with four polarization angles of 0 , 45 , 90 and 135 degrees , and the ccd is an imaging detector . by using the polarization modulation solution in fig1 , some specific distributions of polarization state can be generated . in order to visualize polarization distribution , the p 2 is rotated by four angles to record light intensity patterns on the ccd , and fig1 a , 11 b , 11 c and 11 d correspond to the situations that the p 2 is at the four polarization angles of 0 , 45 , 90 and 135 degrees , respectively . a light path is as shown in fig1 , light from a light source is collimated by a lens group l and enters a grin lens grin 1 after passing a polarizer in a horizontal 0 degree direction ( or other directions , the horizontal direction is taken as an example herein ) and then enters a grin lens grin 2 after passing r ( a ¼ wave plate in the embodiment ), thus finishing the sop spatial modulation . the back module is a polarization analyzer consisting of a polarizer p 2 with four polarization angles of 0 , 45 , 90 and 135 degrees , and the ccd is an imaging detector . by using the polarization modulation solution in fig1 , some specific distributions of polarization state can be generated . in order to visualize polarization distribution , the p 2 is rotated by four angles to record light intensity patterns on the ccd , and fig1 a , 13 b , 13 c and 13 d correspond to the situations that the p 2 is at the four polarization angles of 0 , 45 , 90 and 135 degrees , respectively . a light path is still as shown in fig1 , light from a light source is collimated by a lens group l and enters a grin lens grin 1 after passing a polarizer in a horizontal 0 degree direction ( or other directions , the horizontal direction is taken as an example herein ) and then enters a grin lens grin 2 after passing r ( a ½ wave plate different from that in the embodiment 4 ), thus finishing the sop spatial modulation . the back module is a polarization analyzer consisting of a polarizer p 2 with four polarization angles of 0 , 45 , 90 and 135 degrees , and the ccd is an imaging detector . by using the polarization modulation solution in fig1 , some specific distributions of polarization state can be generated . in order to visualize polarization distribution , the p 2 is rotated by four angles to record light intensity patterns on the ccd , and fig1 a , 14 b , 14 c and 14 d correspond to the situations that the p 2 is at the four polarization angles of 0 , 45 , 90 and 135 degrees , respectively . the embodiments 2 - 5 explain four different embodiments using the grin lens to perform spatial polarization modulation , and the use of more grin lenses or the grin lenses with different lengths and different wave plates can generate more different spatial polarization modulations . here cannot be exhausted . the grin lens as the spatial polarization modulation device has the characteristics of continuous modulation aperture and diverse types of modulation , and has significant performance and price advantages compared with other polarization modulation devices prepared based on micro - nano machining on the market .