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

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

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 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=E n P=E x P Why?

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

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

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 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 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 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 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 Depth of Field (DOF) xx dαα D so’so’so’so’

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

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

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

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

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 Myopia e.g. l f = 2m = 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 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 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 Hyperopia – Far Sightedness Eyeball too small – or lens of eye can’t fully accommodate Image of close objects formed behind retina

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 Correction lenses for myopia and hyperopia