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Challenges for a data-driven society




             The LED Array               The Lens  The Imaging Plane              1
                                                                                                      The Measured Data
                                                                                 0.9                  The Fitting PSF Curve
                    (x 0 , y n-1 )
                                                                                 Normalizated Gray Value of The LED Image  0.6 0.5
           (x 0 , y 0)                                                           0.8 0.7
                (x i , y i)                                                      0.4
                    (x n-1 , y n-1)                                              0.3 0.2
           (x n-1 , y 0 )                                                        0.1
                                                                                  0
                                                                                         126   225   328     450
                              u                 v                                            Position of Pixels
                                                                                     (a)
          Fig. 3: The optical path of the imaging light in MIMO-IS-
          VLC system. 1 
 Diffraction light at the edge of the grating.           1                   The Measured Data
                                                                                  0.9                 The Fitting PSF Curve
           2 
 Refraction light from the lens. 3 
 Reflection light on the         0.8
                                                                                 Normalizated Gray Value of The LED Image  0.5
          inner wall of the lens’ tube.                                           0.7 0.6
          described as the Kirk model. Establish the rectangular co-              0.4 0.3
          ordinate system based on one of four corners’ LED and set               0.2
                                                                                  0.1
          (x 0 , y 0 ) as the original point as is shown in Fig.3. Then the
                                                                                  0
                                                                                        101    225     353   450
          point spread function (PSF) of the stray light is written as                       Position of Pixels
                                                                                     (b)
                                           2
                                1         r i
                       s(r i ) =  √  exp −  2           (2)                       1
                              σ 2π        2σ                                      0.9                 The Measured Data
                                                                                                      The Fitting PSF Curve
                                                                                  0.8
                    p
                        2
                            2
          Where r i =  x + y is the distance from the point (x i , y i )          0.7
                        i   i
          to the original point. σ is the intensity coefficient of the stray       0.6 0.5
          light distribution. Assuming P(x 0 , y 0 ) is the light intensity      Normalizated Gray Value of The LED Image  0.4
          of the original point. Thus, to a certain area based on the cen-        0.3
          ter coordinate of (x i , y i ), the stray light intensity is written    0.2
                                                                                  0.1
          as                                                                      0      107   225     359   450
                                                                                              Position of Pixels
                         ZZ
                                                                                     (c)
           S(x i , y i ) = K +  P(x 0 , y 0 )·s(x−x i , y−y i ) dx dy (3)
                                                             Fig. 4: The imaging results of three different lenses under
          When calculating the influence of stray light in the imaging
                                                             the same photography condition.
          system, the exposure time t e is ought to be considered. The
          total exposure value P v is the time integral of the instanta-
                                                     R
          neous light intensity P and is expressed as P v =  P dt.
          Because the stray light distribution function is not a time  To evaluate the degree of concentration of the light inten-
          correlation function, the total exposure energy can be simply  sity distribution, set 0.2 as a threshold of the normalized gray
          written as P v = P · t e .                         value and define the range that the gray value of the pixels
                                                             exceed 0.2. The narrower range the pixels distribution is,
                                                             the more concentrated the light intensity distribution will be.
          Fig.4 shows imaging results of three different lens and the
                                                             In Fig.4(a), the range of horizontal coordinate is (126, 328)
          fitting curve of the stray light intensity distribution. In the
                                                             that the normalized gray-value is higher than 0.2. It means
          experiment, the LED and the lens of image sensor is kept
                                                             that 80% of the pixels formed by the incident light is concen-
          parallel as possible to eliminate the aberrations. Analyze the
                                                             trated on around 45% pixels of the whole image. However,
          pixels on image’s transversal line. For the purpose of in-
          creasing accuracy, select the transversal line from different  the range is (101, 353) and the proportion is around 56% in
          angles and averaging. As is shown in Fig.4, he horizontal  Fig.4(b) while in Fig.4c the range is (107, 359) and the pro-
          coordinate is the pixels position from 0 to 450 and the ver-  portion is 56% as well. It demonstrates that imaging light of
          tical coordinate is the normalized gray value. A industrial  the LED is more concentrative in Fig.4(a) than the other two.
          CMOS camera is utilized in the experiment. The 3W white  With the purpose of obtaining the parameter σ in equation
          LED is at rated illumination status. The three lenses are from  (2), the least square method is used to get the fitting curve of
          different manufacturers with the same parameter. The diam-  the light intensity distribution. As a result, the obtained σ of
          eter of the three lenses is 40mm. In the experiment, the focal  the curve from Fig.4(a) is 86.2 while it is 95.1 of the Fig.4(b)
          length of lenses is set as 20mm and the aperture is F1.6. The  and 90.2 of the Fig.4(c) (The adjusted R-square value of the
          exposure time t e is 10ms and the distance from the LED to  fitting curve in three images is 0.984, 0.980 and 0.985 cor-
          the image sensor is 1m. The pixel size of the original image  respondingly). A smaller σ value of the equation (2) leads
          is 450 × 450.                                      to a narrower distribution range of the stray light, thus it is
          It can be seen that under the same photograph condition,  proofed that the imaging pixel of the LED is more concen-
          three lenses show difference on the imaging performance.  trative in Fig.4(a). It also come to the conclusion that under



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