3. Geometrical Optics

Geometric optics—process of light ray through lenses and mirrors to determine the location and size of the image from a given object. Reflection and Mirror

Image Formation by Reflection

Application of Double Reflection-Periscope

DIY Periscope

DIY Periscope (Cont’)

Law of reflection (Snell’s law)

Types of Lenses

Ray Tracing through Thin Lenses

Image Formation by thin Lenses Lens equation:

ABCD Matrix

ABCD Matrix (Cont’)

Aberrations of Lenses Primary Aberration  image deviate from the original picture/the first-order approximation Monochromatic aberrations  Spherical Aberration  Coma  Astigmatism  Curvature of field  Distortion Chromatic aberration

General Method of Reducing Aberration in Optical Systems-Multiple Lenses United States Patent

General Method of Reducing Aberration in Optical Systems-Multiple Lenses (Cont’) United States Patent

Chromatic Aberration The focal lengths of lights with distinct wavelengths are different.

Solution of Chromatic Aberration-Using Doublet, Triplet, or Diffractive Lens

Spherical Aberration (SA)

Spherical Aberration for Different Lenses (a) Simple biconvex lens (b) “Best-form” lens (c) Two lenses (d) Aspheric, almost plano-convex lens

Solutions of Spherical Aberration- Using Aspherical Lens or Stop

Coma

Coma (Cont’) (a) Negative coma (b) Postive coma

Astigmatism

Astigmatism (Cont’)

Solutions of Astigmatism-Using Multiple Lenses

Curvature of field

Solutions of Curvature of field-Using Multiple Lenses

Distortion Picture taken by a wide-angle camera in front of graph paper with square grids

Solution of Distortion-Using Multiple Lenses

Nearsightedness (Myopia) and Farsightedness (Hyperopia)

Image Formation  Camera

Camera Eg. 50 mm camera lens, aperture stop 6.25mm: F-number = 8 (f/8) F-number Exposure E: energy collected by camera lens B: brightness of object A: area of aperture d: diameter of aperture stop

Camera Lenses Wide-angle Lenses- the Aviogon and the Zeiss Orthometer lenses Standard Lenses-the Tessar and the Biotar lenses Lens of reducing the 3rd-order aberration- the Cooke triplet lens

Depth of Field (DOF) The distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image. In cinematography, a large DOF is called deep focus, and a small DOF is often called shallow focus. For a given F-number, increasing the magnification decreases the DOF; decreasing magnification increases DOF. For a given subject magnification, increasing the F-number increases the DOF; decreasing F-number decreases DOF.

Numerical Aperture (NA) The numerical aperture of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. Generally, For a multi-mode optical fiber,

Telescope

Astronomical (Keplerian) Telescope Magnification (magnifying power):  : angle subtended at input end in front of objective  ’: angle subtended at output end behind eyepiece (inverted image) For small angle: General Keplerian telescope: d=f o +f e

Galileo Telescope General Galileo telescope: d=f o -f e

Terrestrial Telescope All images are erecting

Optical Microscope

Microscope Theory Objective Overall magnification: m o : linear magnification of objective m e : angular magnification of eyepiece Linear magnification: Numerical aperture (NA)

Microscope Theory (Cont’) Angular magnification: (normal reading distance) Overall magnification of microscope: f o : focal length of objective f e : focal length of eyepiece Eyepiece

Simple Projection System

Fresnel Lens and Plates focusing point (in phase) Radius of the concentric circular: r n = [(n ) 2 +2fn ] ½, n=0, 1, 2,…. Sapce between two adjacent circular zone:  r n = r n+1  r n