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Stops in optical systems (5.3)

Stops in optical systems (5.3)

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Stops in optical systems (5.3)

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  1. Stops in optical systems (5.3) Hecht 5.3 Monday September 30, 2002

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. Aperture Stop (AS) O

  8. Entrance Pupil (EnP) is defined to be the image of the aperture stop in all the lenses preceding it (i.e. to the left of AS - if light travels left to right) E’ How big does the aperture stop look to someone at O E L1 E’E’ = EnP O F1’ EnP – defines the cone of rays accepted by the system E E’

  9. Exit Pupil (ExP) The exit pupil is the image of the aperture stop in the lenses coming after it (i.e. to the right of the AS) E’’ E L1 E”E” = ExP F2’ O E E’’

  10. Location of Aperture Stop (AS) • In a complex system, the AS can be found by considering each element in the system • The element which gives the entrance pupil subtending the smallest angle at the object point O is the AS Example, Telescope eyepiece Objective=AS=EnP

  11. Example: Eyepiece f1’ = 6 cm f2’ = 2 cm E O E 9 cm 1 cm 3 cm Ф1 = 1 cm ФD = 1 cm Ф2 = 2 cm

  12. Example: Eyepiece Find aperture stop for s = 9 cm in front of L1. To do so, treat each element in turn – find EnP for each (a) Lens 1 – no elements to the left tan µ1 = 1/9 defines cone of rays accepted 1 cm µ1 O 9 cm

  13. Example: Eyepiece Find aperture stop for s = 9 cm in front of Diaphragm. Find EnP (b) Diaphragm – lens 1 to the left Look at the system from behind the slide E E’ O E E’ 9 cm 1 cm ФD’ = 1.2 cm 1.2 cm

  14. Example: Eyepiece Calculate maximum angle of cone of rays accepted by entrance pupil of diaphragm E’ 0.6 cm O µ2 9 + 1.2 cm tan µ2 = 0.6/10.2 ≈ 1/17 E’

  15. Example: Eyepiece (c) Lens 2 – 4 cm to the left of lens 1 Look at the system from behind the slide O Ф2’ = 6 cm 9 cm 4 cm Ф2 = 2 cm

  16. Example: Eyepiece Calculate maximum angle of cone of rays accepted by entrance pupil of lens 2. 3 cm O µ3 9 + 12 cm tan µ3 = 3/21 = 1/7

  17. Example: Eyepiece Thus µ2 is the smallest angle The diaphragm is the element that limits the cone of rays from O Diaphragm = Aperture Stop

  18. Example: Eyepiece Entrance pupil is the image of the diaphragm in L1. E’ µ2 = tan-1 (1/17) O E’ EnP 9 cm ФD’ = 1.2 cm 1.2 cm

  19. Example: Eyepiece Exit pupil is the image of the aperture stop (diaphragm) in L2. f2’ = 2 cm E O E Ф2’ = 2 cm 9 cm 1 cm 3 cm ФD = 1 cm

  20. Example: Eyepiece E’ f2’ = 2 cm E ФExP’ = 2 cm O ExP E E’ 3 cm 6 cm ФD = 1 cm

  21. Chief Ray • for each bundle of rays, the light ray which passes through the centre of the aperture stop is the chief ray • after refraction, the chief ray must also pass through the centre of the exit and entrance pupils since they are conjugate to the aperture stop • EnP and ExP are also conjugate planes of the complete system

  22. Marginal Ray • Those rays (for a given object point) that pass through the edge of the entrance and exit pupils (and aperture stop).

  23. Chief Ray from T • Proceed toward centre of EnP • Refracted at L1 to pass though centre of AS • Refracted at L2 to pass (exit) through centre of ExP Ray tracing with pupils and stops L2 L1 Q’’ P’ T P O’ O Q T’ • Marginal Rays from T,O • Must proceed towards edges of EnP • Refracted at L1 to pass through edge of AS • Refracted at L2 to pass (exit) through ExP. Q’ P’’ AS EnP ExP

  24. Exit Pupil Defines the bundle of rays at the image Q’’ T O’ α’ O T’ P’’

  25. Field Stop • That component of the optical system that limits the field of view A θ d θ = angular field of view A = field of view at distance d