The Lens

The Pinhole camera

• Ideally have infinite depth of focus and no distortion.
• Projects light on to image plane from the pinhole lens
• Problem- light gathering ability is poor and exposure time needed is long.

Solution- The LENS

Optical axis- Connects center of image plane through the center of lens (focal point).

Focal length- Distance of the image plane from the optical origin (center of lens) when parallel rays are focused onto a single point in the image plane.

The Lens Law: 1/u + 1/v = 1/f                       where v= distance to image pnt P' and                            u= distance to world point P

Lens Properties..................

Depth of Field = is determined by the distance from the nearest object plane in focus to that of the farthest plane also simultaneously in focus.     
  

The Equation:              r= Depth of field = 2cn(m+1)/(m*m)

• n = f-stop
  n = f/d
• f = fixed focal length
• d = diameter of aperture
• c = constant
• m = v/u
• As d decreases, r increases

Perspective Projection

How 3D points project into their 2D coordinates on the image plane.

• Line of sight- line connecting object point in 3D through the focal point.
  
  
• Corresponding Image Point- Where the line of sight hits the image plane.
  
  
• The further away the object is, the smaller it will be projected onto the image plane.
  
  
• The closer the object is, the larger the projection into the image plane.
  
  
• A point in the world (3D) projects into a single point on the image.
  
  
• A point in the image can be the result of any world point (3D).