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

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

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

4. 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. 5 Camera AS=E n P=E x P Why?

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

7. 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’ s’ ≈ f D Irradiance at any point on film is proportional to (D/f) 2

8. 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. 9 Good lenses, f# = 1.2 or 1.8 (very fast) Difficult to get f/1 Standard settings on camera lenses f# = f/D(f#) 2 1.21.5 1.83.2 2.87.8 4.016 5.631.5 864 11121 16256 22484

10. 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. 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. 12 Telephoto lens L1L1L1L1 L2L2L2L2 d 50 mm 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. 13 Telephoto Lens, Example Suppose d = 9.0 cm, f 2 =-1.25 cm f 1 = 10 cm Then for this telephoto lens Now the principal planes are located at Choose f = |h’| + bfl

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

15. 15 Depth of Field s2s2s2s2 s2’s2’s2’s2’ s1s1s1s1 s1’s1’s1’s1’ sosososo so’so’so’so’ xx d 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. 16 Depth of Field (DOF) xx dαα D so’so’so’so’

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

18. 18 Depth of field Strongly dependent on the f# of the lens Suppose, s o = 4m, f = 5 cm, d = 40 µm DOF = s 2 – s 1

19. 19

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

21. 21 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

22. 22 Myopia: Near Sightedness Eyeball too large ( or power of lens too large)

23. 23 Myopia – Near Sightedness Far point of the eye is much less than ∞, e.g. l f Must move object closer to eye to obtain a clear image Myopic F.P. F.P. Normal N.P. MyopicN.P.

24. 24 Myopia e.g. l f = 2m 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 How will the near point be affected?

25. 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 CO 2 laser for almost 100% absorption by the corneal tissue Front view Blurredvision

26. 26 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 CO 2 laser for almost 100% absorption by the corneal tissue Front view Flattening Distinctvision

27. 27 Hyperopia – Far Sightedness Eyeball too small – or lens of eye can’t fully accommodate Image of close objects formed behind retina

28. 28 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

29. 29 Correction lenses for myopia and hyperopia http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/V/Vision.html