Rays and wavefronts
Rays and wavefronts

In optics a ray is an idealized geometrical model of light, obtained by choosing a curve that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow.[1][2] Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. Ray optics or geometrical optics does not describe phenomena such as diffraction, which require wave optics theory. Some wave phenomena such as interference can be modeled in limited circumstances by adding phase to the ray model.

Definition

A light ray is a line (straight or curved) that is perpendicular to the light's wavefronts; its tangent is collinear with the wave vector. Light rays in homogeneous media are straight. They bend at the interface between two dissimilar media and may be curved in a medium in which the refractive index changes. Geometric optics describes how rays propagate through an optical system. Objects to be imaged are treated as collections of independent point sources, each producing spherical wavefronts and corresponding outward rays. Rays from each object point can be mathematically propagated to locate the corresponding point on the image.

A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.[3]

Special rays

There are many special rays that are used in optical modelling to analyze an optical system. These are defined and described below, grouped by the type of system they are used to model.

Interaction with surfaces

Diagram of rays at a surface, where 
  
    
      
        
          θ
          
            
              i
            
          
        
      
    
    {\displaystyle \theta _{\mathrm {i} ))
  
 is the angle of incidence, 
  
    
      
        
          θ
          
            
              r
            
          
        
      
    
    {\displaystyle \theta _{\mathrm {r} ))
  
 is the angle of reflection, and 
  
    
      
        
          θ
          
            
              R
            
          
        
      
    
    {\displaystyle \theta _{\mathrm {R} ))
  
 is the angle of refraction.
Diagram of rays at a surface, where is the angle of incidence, is the angle of reflection, and is the angle of refraction.

See also: Reflection (physics), Refraction, Absorption (optics), Birefringence, Specular reflection, and Plane of incidence

Optical systems

Simple ray diagram showing typical chief and marginal rays
Simple ray diagram showing typical chief and marginal rays

Fiber optics

See also: Numerical aperture

Geometrical optics

Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometric optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances.

The simplifying assumptions of geometrical optics include that light rays:

  • propagate in straight-line paths as they travel in a homogeneous medium
  • bend, and in particular circumstances may split in two, at the interface between two dissimilar media
  • follow curved paths in a medium in which the refractive index changes
  • may be absorbed or reflected.
Geometrical optics does not account for certain optical effects such as diffraction and interference. This simplification is useful in practice; it is an excellent approximation when the wavelength is small compared to the size of structures with which the light interacts. The techniques are particularly useful in describing geometrical aspects of imaging, including optical aberrations.

Ray tracing

In physics, ray tracing is a method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces. Under these circumstances, wavefronts may bend, change direction, or reflect off surfaces, complicating analysis. Ray tracing solves the problem by repeatedly advancing idealized narrow beams called rays through the medium by discrete amounts. Simple problems can be analyzed by propagating a few rays using simple mathematics. More detailed analysis can be performed by using a computer to propagate many rays.

When applied to problems of electromagnetic radiation, ray tracing often relies on approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. Ray theory does not describe phenomena such as interference and diffraction, which require wave theory (involving the phase of the wave).

See also

References

  1. ^ Moore, Ken (25 July 2005). "What is a ray?". ZEMAX Users' Knowledge Base. Retrieved 30 May 2008.
  2. ^ Greivenkamp, John E. (2004). Field Guide to Geometric Optics. SPIE Field Guides. p. 2. ISBN 0819452947.
  3. ^ Arthur Schuster, An Introduction to the Theory of Optics, London: Edward Arnold, 1904 online.
  4. ^ a b c d Stewart, James E. (1996). Optical Principles and Technology for Engineers. CRC. p. 57. ISBN 978-0-8247-9705-8.
  5. ^ a b Greivenkamp, John E. (2004). Field Guide to Geometrical Optics. SPIE Field Guides vol. FG01. SPIE. ISBN 0-8194-5294-7., p. 25 [1].
  6. ^ a b Riedl, Max J. (2001). Optical Design Fundamentals for Infrared Systems. Tutorial texts in optical engineering. Vol. 48. SPIE. p. 1. ISBN 978-0-8194-4051-8.
  7. ^ Malacara, Daniel and Zacarias (2003). Handbook of Optical Design (2nd ed.). CRC. p. 25. ISBN 978-0-8247-4613-1.
  8. ^ Greivenkamp (2004), p. 28 [2].
  9. ^ Greivenkamp (2004), pp. 19–20 [3].
  10. ^ Nicholson, Mark (21 July 2005). "Understanding Paraxial Ray-Tracing". ZEMAX Users' Knowledge Base. Retrieved 17 August 2009.
  11. ^ a b Atchison, David A.; Smith, George (2000). "A1: Paraxial optics". Optics of the Human Eye. Elsevier Health Sciences. p. 237. ISBN 978-0-7506-3775-6.
  12. ^ Welford, W. T. (1986). "4: Finite Raytracing". Aberrations of Optical Systems. Adam Hilger series on optics and optoelectronics. CRC Press. p. 50. ISBN 978-0-85274-564-9.
  13. ^ Buchdahl, H. A. (1993). An Introduction to Hamiltonian Optics. Dover. p. 26. ISBN 978-0-486-67597-8.
  14. ^ Nicholson, Mark (21 July 2005). "Understanding Paraxial Ray-Tracing". ZEMAX Users' Knowledge Base. p. 2. Retrieved 17 August 2009.