camera by cuiliqing

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									Camera Simulation

                            Effect           Cause

                            Field of view    Film size,
                                             stops and pupils
                            Depth of field   Aperture,
                                             focal length
                            Motion blur      Shutter
                            Exposure Film speed,
                                            aperture, shutter


References
       Photography, B. London and J. Upton
       Optics in Photography, R. Kingslake
       The Camera, The Negative, The Print, A. Adams
CS348B Lecture 7                                   Pat Hanrahan, 2005
Topics

Ray tracing lenses
Focus
Field of view
Depth of focus / depth of field
Exposure




CS348B Lecture 7                  Pat Hanrahan, 2005
Lenses
Refraction

    Snell’s Law

       n sin I   n sin I   N
                              I

                                           I
                                  n   n




CS348B Lecture 7                                Pat Hanrahan, 2005
Paraxial Approximation

                           e0
  sinU  u

  tanU  u

                   U



                   z

  Rays deviate only
  slightly from the axis
CS348B Lecture 7                 Pat Hanrahan, 2005
Incident Ray

                   Angles: ccw is positive; cw is negative



                           I

                    U                    



            I U 

  The sum of the interior angles is equal to the exterior angle.
CS348B Lecture 7                                      Pat Hanrahan, 2005
Refracted Ray




                               I
                                       U 

                           ( )  I   (U )

            I   U  


CS348B Lecture 7                        Pat Hanrahan, 2005
Derivation

Paraxial approximation

        I U   i  u
        I   U     i   u  




CS348B Lecture 7                       Pat Hanrahan, 2005
Derivation

Paraxial approximation

        I U   i  u
        I   U     i   u  

Snell’s Law
       n sin I   n sin I  ni   ni
        n(u  )  n(u  )



CS348B Lecture 7                           Pat Hanrahan, 2005
Ray Coordinates
    h                h         h
 u           u         
    z               z        R




                                   h
                     u                 R         u 



                     z                       z



CS348B Lecture 7                                    Pat Hanrahan, 2005
Gauss’ Formula

Paraxial approximation to Snell’s Law
    n(u  )  n(u  )
Ray coordinates
           h           h         h
    u                  u
           z          R         z
Thin lens equation
       h h       h h
    n(  )  n(  )
       z R      z R
    n n ( n  n )
                          Holds for any height, any ray!
    z z     R
CS348B Lecture 7                                Pat Hanrahan, 2005
Vergence
            Diverging                       Converging




              V 0       V 0                V 0

                             n n 1                
Vergence                 V         m  diopters 
                              r z                 
Thin lens equation       V  V  P
                                        1
Surface Power equation   P  ( n   n)
                                        R
CS348B Lecture 7                               Pat Hanrahan, 2005
Lens-makers Formula

  Refractive Power
                                   1  1 1
                   P  ( n   n)    
                                   R1 R2  f




                   Converging       Diverging


CS348B Lecture 7                                Pat Hanrahan, 2005
Conjugate Points




                                            1 1 1
                                               
                                            z z f



To focus: move lens relative to backplane
Horizontal rays converge on focal point in the focal plane
CS348B Lecture 7                                             Pat Hanrahan, 2005
Gauss’ Ray Tracing Construction



                       Parallel Ray




                   Focal Ray
                                      Chief Ray




         Object                                          Image



CS348B Lecture 7                                  Pat Hanrahan, 2005
Ray Tracing: Finite Aperture




      Focal Plane   Aperture Plane      Back Plane



CS348B Lecture 7                     Pat Hanrahan, 2005
Real Lens




            Cutaway section of a Vivitar Series 1 90mm f/2.5 lens
            Cover photo, Kingslake, Optics in Photography
CS348B Lecture 7                                           Pat Hanrahan, 2005
Double Gauss


     Data from W. Smith,
     Modern Lens Design, p 312

 Radius       Thick        nd      V-no    aperture
  (mm)        (mm)
    58.950         7.520   1.670    47.1        50.4
   169.660         0.240                        50.4
    38.550         8.050   1.670    47.1        46.0
    81.540         6.550   1.699    30.1        46.0
    25.500     11.410                           36.0
                   9.000                        34.2
   -28.990         2.360   1.603    38.0        34.0
    81.540     12.130      1.658    57.3        40.0
   -40.770         0.380                        40.0
   874.130         6.440   1.717    48.0        40.0
   -79.460     72.228                           40.0

CS348B Lecture 7                                       Pat Hanrahan, 2005
Ray Tracing Through Lenses




             200 mm telephoto               35 mm wide-angle




           50 mm double-gauss                16 mm fisheye


  From Kolb, Mitchell and Hanrahan (1995)

CS348B Lecture 7                                  Pat Hanrahan, 2005
Thick Lenses

      Equivalent Lens




         Refraction occurs at the principal planes
CS348B Lecture 7                              Pat Hanrahan, 2005
Field of View
Field of View




                   From London and Upton
CS348B Lecture 7                           Pat Hanrahan, 2005
Field of View




                   From London and Upton
CS348B Lecture 7                           Pat Hanrahan, 2005
Field of View
                                        Redrawn from Kingslake,
Field of view                           Optics in Photography


            fov filmsize
      tan      
             2      f


Types of lenses
           Normal                26º
            Film diagonal  focal length
           Wide-angle 75-90º
           Narrow-angle          10º

CS348B Lecture 7                                      Pat Hanrahan, 2005
Perspective Transformation

Thin lens equation

       1 1 1          fz
            z 
       z z f        z f
                      fx
               x 
                     z f
                      fy
               y 
                     z f

Represent transformation as a 4x4 matrix
CS348B Lecture 7                           Pat Hanrahan, 2005
Depth of Field
Depth of Field




                   From London and Upton
CS348B Lecture 7                           Pat Hanrahan, 2005
Circle of Confusion

                                 s            s
                            z            z        d

                                     a                  c



                   Focal Plane                Back Plane




  Circle of confusion proportional                 c d  s  z
                                                     
  to the size of the aperture                      a z     z

CS348B Lecture 7                                        Pat Hanrahan, 2005
Depth of Focus [Image Space]
                                          s           s
Depth of focus 
                                               a
       Equal circles of confusion
Two planes: near and far
                                     zf             z f

                   c d  s  z f
                        f
                                                                     c
                         
                   a z f   z f
                                                                d
                                                                 f
                                          zn                
                                                           zn
                   c dn zn  s 
                        
                                                                   c
                      
                   a zn     
                           zn

                                                                 
                                                                dn
CS348B Lecture 7                               Pat Hanrahan, 2005
Depth of Focus [Image Space]
                                          s           s
Depth of focus 
                                               a
       Equal circles of confusion

                                     zf             z f

 c d  s  z f
      f              1 1  c
                       1                                      c
 a z f   z f       z f s  a 
                                                                d
                                                                 f
                                          zn                
                                                           zn
  c dn zn  s
               1 1  c                                            c
                  1  
     
  a zn     
          zn     zn s   a 
                  
                                                                 
                                                                dn
CS348B Lecture 7                               Pat Hanrahan, 2005
Depth of Focus [Image Space]

Depth of focus 
       Equal circles of confusion

    1 1  c              1 1  c            z f
         1                1                       s
    z f s  a          zn s   a 
                           
                                                               c
                   1 1      1
                        2
                         
                   z f zn  s                        
                                                     zn

               1 1 2c 1
                    
                     
               z f zn a s


CS348B Lecture 7                         Pat Hanrahan, 2005
 Depth of Field [Object Space]

 Depth of field 
       Equal circles of confusion
                                     zf
1 1 1         1 1 1     1 1 1
                         
s s f         
              zn zn f   z f z f f
                                                               c
       1 1    1
          2
       zn z f s                           zn

       1 1 2c  1 1  2 c 1                                    c
             
       zn z f a  f s a f


CS348B Lecture 7                               Pat Hanrahan, 2005
Hyperfocal Distance
     1 1    1                   a
        2                  N     zf
     zn z f s                   f

     1 1 2c 1     cN    1                                     c
              2 2 2
     zn z f a f    f    H
                                         zn
  When
                                                              c
                H
    s  H  zn  , z f  
                2

   H is the hyperfocal distance



CS348B Lecture 7                              Pat Hanrahan, 2005
Depth of Field Scale




CS348B Lecture 7       Pat Hanrahan, 2005
Factors Affecting DOF
  From http://www.kodak.com/global/en/consumer/pictureTaking/cameraCare/cameCar6.shtml




 1 cN
   2
 H f




CS348B Lecture 7                                                              Pat Hanrahan, 2005
Resolving Power

 Diffraction limit
                   f
        c  1.22
                   a
                          1.22  64  .500m=0.040 mm 
 35mm film (Leica standard)

        c  0.025mm

 CCD/CMOS pixel aperture

        c  0.0116 mm (Nikon D1)



CS348B Lecture 7                                       Pat Hanrahan, 2005
Exposure
Image Irradiance



                             a

                                   f



                                                       2
                                              a
           E   L cos  d  L  sin   L
                                       2
                                                
                   
                                              4 f 


CS348B Lecture 7                               Pat Hanrahan, 2005
Relative Aperture or F-Stop



                                         f
                   a
                                      a
                       f
                                         N

                                       1
F-Number and exposure:          EL        2
                                      4N
Fstops: 1.4 2 2.8 4.0 5.6 8 11 16 22 32 45 64
      1 stop doubles exposure
CS348B Lecture 7                                Pat Hanrahan, 2005
Camera Exposure

Exposure           H  E T

Exposure overdetermined
       Aperture: f-stop - 1 stop doubles H
           Decreases depth of field
       Shutter: Doubling the open time doubles H
           Increases motion blur




CS348B Lecture 7                             Pat Hanrahan, 2005
Aperture vs Shutter




          f/16               f/4               f/2
          1/8s             1/125s            1/500s

                   From London and Upton
CS348B Lecture 7                           Pat Hanrahan, 2005
High Dynamic Range




Sixteen photographs of the Stanford Memorial Church
   taken at 1-stop increments from 30s to 1/1000s.
From Debevec and Malik, High dynamic range
   photographs.

CS348B Lecture 7                        Pat Hanrahan, 2005
Simulated Photograph




         Adaptive histogram   With glare, contrast, blur
CS348B Lecture 7                              Pat Hanrahan, 2005
Camera Simulation


                                                                      A
                       L( x, , t,  )
                                                                               L( x ,  , t,  )
                                                            


       R   P( x ,  ) S( x ,  , t ) L(T ( x ,  ,  ), t,  ) dA( x )  d  dt d
            AT 

       Sensor response                             P( x ,  )
       Lens                                        ( x,  )  T ( x ,  ,  )
       Shutter                                     S( x ,  , t )
       Scene radiance                              L( x, , t,  )
CS348B Lecture 7                                                              Pat Hanrahan, 2005

								
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