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Optical systems: Cameras and the eye

Optical systems: Cameras and the eye. Hecht 5.7 Friday October 4, 2002. Optical devices: Camera. Multi-element lens. Film: edges constitute field stop. AS=Iris Diaphragm. Camera. Most common camera is the so-called 35 mm camera ( refers to the film size). 27 mm. 34 mm.

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Optical systems: Cameras and the eye

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  1. Optical systems:Cameras and the eye Hecht 5.7 Friday October 4, 2002

  2. Optical devices: Camera Multi-element lens Film: edges constitute field stop AS=Iris Diaphragm

  3. Camera Most common camera is the so-called 35 mm camera ( refers to the film size) 27 mm 34 mm Multi element lens usually has a focal length of f =50 mm

  4. Camera Object s = 1 m Image s’ ≈ 5.25 cm Object s = ∞ Image s’ = 5.0 cm Thus to focus object between s = 1 m and infinity, we only have to move the lens about 0.25 cm = 2.5mm For most cameras, this is about the limit and it is difficult to focus on objects with s < 1 m

  5. Camera AS=EnP=ExP Why?

  6. Camera: Light Gathering Power D = diameter of entrance pupil L = object distance (L>> d) D l

  7. Camera: Brightness of image Brightness of image is determined by the amount of light falling on the film. Each point on the film subtends a solid angle D D’ Irradiance at any point on film is proportional to (D/f)2 s’ ≈ f

  8. f-number of a lens Define f-number, This is a measure of the speed of the lens Small f# (big aperture) I large , t short Large f# (small aperture) I small, t long

  9. Standard settings on camera lenses Good lenses, f# = 1.2 or 1.8 (very fast) Difficult to get f/1

  10. Total exposure on Film Exposure time is varied by the shutter which has settings, 1/1000, 1/500, 1/250, 1/100, 1/50 Again in steps of factor of 2

  11. Photo imaging with a camera lens In ordinary 35 mm camera, the image is very small (i.e. reduced many times compared with the object An airplane 1000 m in the air will be imaged with a magnification, Thus a 30 m airplane will be a 2 mm speck on film (same as a 2 m woman, 50 m) Also, the lens is limited in the distance it can move relative to the film

  12. Telephoto lens L1 L2 50 mm d A larger image can be achieved with a telephoto lens Choose back focal length (bfl ≈ 50 mm) Then lenses can be interchanged (easier to design) The idea is to increase the effective focal length (and hence image distance) of the camera lens.

  13. Telephoto Lens, Example Suppose d = 9.0 cm, f2=-1.25 cm f1 = 10 cm Then for this telephoto lens Choose f = |h’| + bfl Now the principal planes are located at

  14. Telephoto Lens, Example H’ h’ = - 45 cm 9 cm 5 cm f’= s’TP = 50 cm Airplane now 1 cm long instead of 1 mm !!!!

  15. Depth of Field s2 s2’ s1 s1’ d x x so so’ If d is small enough (e.g. less than grain size of film emulsion ~ 1 µm) then the image of these points will be acceptable

  16. Depth of Field (DOF) α α d D x x so’

  17. Depth of field E.g. d = 1 µm, f# = A = 4, f = 5 cm, so = 6 m DOF = 0.114 m i.e. so = 6 ± 0. 06 m

  18. Depth of field Strongly dependent on the f# of the lens Suppose, so = 4m, f = 5 cm, d = 40 µm DOF = s2 – s1

  19. Human Eye, Relaxed 20 mm 15 mm n’ = 1.33 F H H’ F’ 3.6 mm P = 66.7 D 7.2 mm

  20. Accommodation • Refers to changes undergone by lens to enable imaging of closer objects • Power of lens must increase • There is a limit to such accommodation however and objects inside one’s “near point” cannot be imaged clearly • Near point of normal eye = 25 cm • Fully accommodated eye P = 70.7 for s = 25 cm, s’ = 2 cm

  21. Myopia: Near Sightedness Eyeball too large ( or power of lens too large)

  22. Myopia – Near Sightedness Far point of the eye is much less than ∞, e.g. lf Must move object closer to eye to obtain a clear image Normal N.P. Myopic F.P. Myopic N.P.

  23. Myopia e.g. lf = 2m How will the near point be affected? 0.5 + 66.7 = 67.2 D is relaxed power of eye – too large! To move far point to ∞, must decrease power to 66.7 Use negative lens with P = -0.5 D

  24. Laser Eye surgery Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeball Usually use the 10.6 µm line of a CO2 laser for almost 100% absorption by the corneal tissue Blurred vision Front view

  25. Laser Eye surgery Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeball Usually use the 10.6 µm line of a CO2 laser for almost 100% absorption by the corneal tissue Distinct vision Front view Flattening

  26. Hyperopia – Far Sightedness Eyeball too small – or lens of eye can’t fully accommodate Image of close objects formed behind retina

  27. Hyperopia – Far Sightedness Suppose near point = 1m Recall that for a near point of 25 cm, we need 70.7D Use a positive lens with 3 D power to correct this person’s vision (e.g. to enable them to read) Usually means they can no longer see distant objects - Need bifocals

  28. Correction lenses for myopia and hyperopia http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/V/Vision.html

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