1 / 27

Matrix methods, aberrations & optical systems

Matrix methods, aberrations & optical systems. Friday September 27, 2002. System matrix. System matrix: Special Cases. (a) D = 0   f = Cy o (independent of  o ).  f. y o. Input plane is the first focal plane. y f.  o. System matrix: Special Cases.

blue
Download Presentation

Matrix methods, aberrations & optical systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Matrix methods, aberrations & optical systems Friday September 27, 2002

  2. System matrix

  3. System matrix: Special Cases (a) D = 0  f = Cyo (independent of o) f yo Input plane is the first focal plane

  4. yf o System matrix: Special Cases (b) A = 0  yf = Bo (independent of yo) Output plane is the second focal plane

  5. yf System matrix: Special Cases (c) B = 0  yf = Ayo yo Input and output plane are conjugate – A = magnification

  6. o f System matrix: Special Cases (d) C = 0  f = Do (independent of yo) Telescopic system – parallel rays in : parallel rays out

  7. Examples: Thin lens Recall that for a thick lens For a thin lens, d=0 

  8. Examples: Thin lens Recall that for a thick lens For a thin lens, d=0  In air, n=n’=1

  9. Imaging with thin lens in air ’ o yo y’ Input plane Output plane s s’

  10. Imaging with thin lens in air For thin lens: A=1B=0D=1 C=-1/f y’ = A’yo + B’o

  11. Imaging with thin lens in air For thin lens: A=1B=0D=1 C=-1/f y’ = A’yo + B’o For imaging, y’ must be independent of o  B’ = 0 B’ = As + B + Css’ + Ds’ = 0 s + 0 + (-1/f)ss’ + s’ = 0

  12. Examples: Thick Lens H’ ’ yo y’ f’ n nf n’ x’ h’ h’ = - ( f’ - x’ )

  13. Cardinal points of a thick lens

  14. Cardinal points of a thick lens

  15. Cardinal points of a thick lens Recall that for a thick lens As we have found before h can be recovered in a similar manner, along with other cardinal points

  16. Aberrations Monochromatic Chromatic • A mathematical treatment can be developed by expanding the sine and tangent terms used in the paraxial approximation Unclear image Deformation of image n (λ) Spherical Coma astigmatism Distortion Curvature

  17. Aberrations: Chromatic • Because the focal length of a lens depends on the refractive index (n), and this in turn depends on the wavelength, n = n(λ), light of different colors emanating from an object will come to a focus at different points. • A white object will therefore not give rise to a white image. It will be distorted and have rainbow edges

  18. Aberrations: Spherical • This effect is related to rays which make large angles relative to the optical axis of the system • Mathematically, can be shown to arise from the fact that a lens has a spherical surface and not a parabolic one • Rays making significantly large angles with respect to the optic axis are brought to different foci

  19. Aberrations: Coma • An off-axis effect which appears when a bundle of incident rays all make the same angle with respect to the optical axis (source at ∞) • Rays are brought to a focus at different points on the focal plane • Found in lenses with large spherical aberrations • An off-axis object produces a comet-shaped image f

  20. Aberrations: Astigmatism and curvature of field Yields elliptically distorted images

  21. Aberrations: Pincushion and Barrel Distortion • This effect results from the difference in lateral magnification of the lens. • If f differs for different parts of the lens, will differ also M on axis less than off axis (positive lens) M on axis greater than off axis (negative lens) fi>0 fi<0 object Pincushion image Barrel image

  22. Stops in Optical Systems • In any optical system, one is concerned with a number of things including: • The brightness of the image Two lenses of the same focal length (f), but diameter (D) differs Image of S formed at the same place by both lenses S S’ Bundle of rays from S, imaged at S’ is larger for larger lens More light collected from S by larger lens

  23. Stops in Optical Systems • Brightness of the image is determined primarily by the size of the bundle of rays collected by the system (from each object point) • Stops can be used to reduce aberrations

  24. Stops in Optical Systems How much of the object we see is determined by: (b) The field of View Q Q’ (not seen) Rays from Q do not pass through system We can only see object points closer to the axis of the system Field of view is limited by the system

  25. Theory of Stops • We wish to develop an understanding of how and where the bundle of rays are limited by a given optical system Theory of Stops

  26. Aperture Stop • A stop is an opening (despite its name) in a series of lenses, mirrors, diaphragms, etc. • The stop itself is the boundary of the lens or diaphragm • Aperture stop: that element of the optical system that limits the cone of light from any particular object point on the axis of the system

  27. Aperture Stop: Example O AS

More Related