Image Formation Lens Optics Photometry Geometric Optics Prof

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Image Formation Lens Optics, Photometry, Geometric Optics Prof. Dr. Elli Angelopoulou Chair of Pattern

Image Formation Lens Optics, Photometry, Geometric Optics Prof. Dr. Elli Angelopoulou Chair of Pattern Recognition (Computer Science 5) Friedrich-Alexander-University Erlangen-Nuremberg

Page 2 Thin Lens Center of projection (COP): center of lens Optic axis: axis

Page 2 Thin Lens Center of projection (COP): center of lens Optic axis: axis perpendicular to the lens that passes through the COP Focus of the lens, Fr: point on the optic axis where all the parallel rays incident on the lens converge. Focal length, f: the perpendicular distance between the lens and the focus point of the lens Fr Elli Angelopoulou Image Formation

Page 3 Imaging with Thin Lens From the similar triangles P Fl S and

Page 3 Imaging with Thin Lens From the similar triangles P Fl S and R Fl O => and the similar triangles p Fr s and Q Fl O => But and => Let and . Then Elli Angelopoulou Thin Lens Law Image Formation

Page 4 Lens-related definitions n More definitions: n Effective diameter of a lens, d:

Page 4 Lens-related definitions n More definitions: n Effective diameter of a lens, d: diameter of the lens reachable by light rays (an adjustable iris changes the effective diameter of a lens. n Field of view w: the half-angle subtended by the effective lens diameter, d, on the focus, F: n Depth of field: range of depth values that appear in- focus in an image. n F-stop number: the ratio of the focal length over the effective diameter, Elli Angelopoulou Image Formation

Page 5 Light-surface-camera Elli Angelopoulou Image Formation

Page 5 Light-surface-camera Elli Angelopoulou Image Formation

Page 6 Radiometry n Questions: § how “bright” will surfaces be? § what is

Page 6 Radiometry n Questions: § how “bright” will surfaces be? § what is “brightness”? § measuring light § interactions between light and surfaces n Core idea - think about light arriving at a surface n Around any point is a hemisphere of directions n Simplest problems can be dealt with by reasoning about this hemisphere Elli Angelopoulou Image Formation

Page 7 Solid Angle Elli Angelopoulou Image Formation

Page 7 Solid Angle Elli Angelopoulou Image Formation

Page 8 Lens and Solid Angles Elli Angelopoulou Image Formation

Page 8 Lens and Solid Angles Elli Angelopoulou Image Formation

Page 9 Camera Coords Elli Angelopoulou Image Formation

Page 9 Camera Coords Elli Angelopoulou Image Formation

Page 10 Radial Distortion n A pin-hole image of a square grid. n A

Page 10 Radial Distortion n A pin-hole image of a square grid. n A lens-system image of the same square grid Image courtesy of VIPBase Elli Angelopoulou Image Formation