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Optical systems:Cameras and the eye

Hecht 5.7

Friday October 4, 2002

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Optical devices: CameraMulti-element lensMulti-element lens

AS=Iris DiaphragmAS=Iris DiaphragmFilm: edges Film: edges constitute field stopconstitute field stop

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CameraMost common camera is the so-called 35 mm Most common camera is the so-called 35 mm camera ( refers to the film size)camera ( refers to the film size)

Multi element lens usually has a focal length of Multi element lens usually has a focal length of ff =50 mm =50 mm

34 mm34 mm

27 mm27 mm

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Camera

Object s = 1 m Image s’ Object s = 1 m Image s’ ≈ 5.25 cm≈ 5.25 cm

Object s = Object s = ∞∞ Image s’ = 5.0 cm Image s’ = 5.0 cm

Thus to focus object between s = 1 m and infinity, Thus to focus object between s = 1 m and infinity, we only have to move the lens about 0.25 cm = we only have to move the lens about 0.25 cm = 2.5mm2.5mm

For most cameras, this is about the limit and it is For most cameras, this is about the limit and it is difficult to focus on objects with s < 1 mdifficult to focus on objects with s < 1 m

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Camera

AS=EAS=EnnP=EP=ExxP Why?P Why?

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Camera: Light Gathering Power

D = diameter of entrance pupilD = diameter of entrance pupil

L = object distance (L>> d)L = object distance (L>> d)

ll

DD

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Camera: Brightness of imageBrightness of image is determined by the amount of Brightness of image is determined by the amount of light falling on the film.light falling on the film.

Each point on the film subtends a solid angleEach point on the film subtends a solid angle

2

2

2

2

2 4'4 f

D

s

D

r

dAd

D’D’

s’ s’ ≈ ≈ ff

DD

Irradiance at any pointIrradiance at any pointon film is proportional on film is proportional to (D/f)to (D/f)22

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f-number of a lens

D

fADefine f-number, Define f-number,

This is a measure of the speed of the lensThis is a measure of the speed of the lens

Small f# (big aperture) I large , t shortSmall f# (big aperture) I large , t shortLarge f# (small aperture) I small, t longLarge f# (small aperture) I small, t long

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1

AI

9Good lenses, f# = 1.2 or 1.8 (very fast) Difficult to get f/1Good lenses, f# = 1.2 or 1.8 (very fast) Difficult to get f/1

Standard settings on camera lensesStandard settings on camera lenses

f# = f/D (f#)2

1.2 1.5

1.8 3.2

2.8 7.8

4.0 16

5.6 31.5

8 64

11 121

16 256

22 484

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Total exposure on Film

2

2)(exp

m

J

osuretimetm

wattsIE

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

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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

53

2

10510

105

M

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

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Telephoto lensLL11 LL22

dd 50 mm50 mm

A larger image can be achieved with a A larger image can be achieved with a telephoto lenstelephoto lens

Choose back focal length (bfl Choose back focal length (bfl ≈ 50 mm≈ 50 mm))Then lenses can be interchanged (easier to design)Then lenses can be interchanged (easier to design)

The idea is to increase the effective focal length (andThe idea is to increase the effective focal length (andhence image distance) of the camera lens.hence image distance) of the camera lens.

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Telephoto Lens, Example

cmf

PdPPPP

502121

Suppose d = 9.0 cm, Suppose d = 9.0 cm, ff22=-1.25 cm f=-1.25 cm f11 = 10 cm = 10 cm

Then for this telephoto lensThen for this telephoto lens

Now the principal planes are located atNow the principal planes are located at

cmf

fdHHh

cmf

fdHHh

360

45'

''''

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Choose f = |h’| + bflChoose f = |h’| + bfl

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Telephoto Lens, Example

9 cm9 cm 5 cm5 cm

h’ = - 45 cmh’ = - 45 cm

ff’= s’’= s’TPTP = 50 cm = 50 cm

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55

550

5

5'

c

TPTP

s

s

M

m

Airplane now Airplane now 1 cm1 cm long longinstead of instead of 1 mm !!!!1 mm !!!!

H’H’

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Depth of Fieldss22 ss22’’

ss11 ss11’’

ssoo ssoo’’

xx xx

dd

If d is small enough (e.g. less than grain size of film emulsion ~ 1 If d is small enough (e.g. less than grain size of film emulsion ~ 1 µm)µm)then the image of these points will be acceptablethen the image of these points will be acceptable

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Depth of Field (DOF)

xx xx

ddαα ααDD

ssoo’’

D

dsx o '

o

o

o

o

Adsf

Adffss

Adsf

Adffss

22

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Depth of field

2224

2

12

)(2

o

oo

sdAf

ffsAdsssDOF

E.g. d = 1 E.g. d = 1 µm, f# = A = 4, f = 5 cm, sµm, f# = A = 4, f = 5 cm, soo = 6 m = 6 m

DOF = 0.114 mDOF = 0.114 m

i.e. si.e. soo = 6 = 6 ± 0. 06 m± 0. 06 m

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Depth of field

AAdsf

Adffss

o

o

6.125

000,1021

AAdsf

Adffss

o

o

6.125

000,1022

Strongly dependent on the f# of the lensStrongly dependent on the f# of the lens

Suppose, sSuppose, soo = 4m, = 4m, ff = 5 cm, d = 40 = 5 cm, d = 40 µµmm

DOF = s2 – s1

0 2 4 6 8 10 12 14 160

200

400

600

800

1000

1200

s1

s2

Depth of field (focus)

s 1,s 2

(cm

)

f#

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20

Human Eye, Relaxed

3.6 mm

7.2 mm

20 mm

n’ = 1.33

15 mm

F F’H H’

P = 66.7 D

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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

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Myopia: Near Sightedness

Eyeball too large ( or power of lens too large)

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Myopia – Near SightednessFar point of the eye is much less than Far point of the eye is much less than ∞, e.g. ∞, e.g. llff Must move object closer to eye to obtain a clear imageMust move object closer to eye to obtain a clear image

MyopicMyopic

F.P.F.P.

Normal N.P.Normal N.P.

MyopicMyopic

N.P.N.P.

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Myopiae.g. le.g. lff = 2m = 2m

fs

n

l f

1

'

'1

0.5 + 66.7 = 67.2 D0.5 + 66.7 = 67.2 D

is relaxed power of eye – too large!is relaxed power of eye – too large!

To move far point to To move far point to ∞, must decrease power ∞, must decrease power to 66.7to 66.7

Use negative lens with P = -0.5 DUse negative lens with P = -0.5 D

How will the How will the near point be near point be affected?affected?

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Laser Eye surgeryRadial Keratotomy – Introduce radial cuts to the Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeballcornea of the elongated, myopic eyeball

Usually use the 10.6 Usually use the 10.6 µm line of a COµm line of a CO22 laser for laser for

almost 100% absorption by the corneal tissuealmost 100% absorption by the corneal tissue

Front viewFront view

BlurredBlurredvisionvision

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Laser Eye surgeryRadial Keratotomy – Introduce radial cuts to the Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeballcornea of the elongated, myopic eyeball

Usually use the 10.6 Usually use the 10.6 µm line of a COµm line of a CO22 laser for laser for

almost 100% absorption by the corneal tissuealmost 100% absorption by the corneal tissue

Front viewFront viewFlatteningFlattening

Distinct Distinct visionvision

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Hyperopia – Far Sightedness

Eyeball too small – or lens of eye can’t fully accommodateEyeball too small – or lens of eye can’t fully accommodate

Image of close objects formed behind retinaImage of close objects formed behind retina

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Hyperopia – Far Sightedness

Suppose near point = 1mSuppose near point = 1m

Ds

n7.677.661

'

'

1

1

Recall that for a near point of 25 cm, we need 70.7DRecall that for a near point of 25 cm, we need 70.7D

Use a positive lens with 3 D power to correct this Use a positive lens with 3 D power to correct this person’s vision (e.g. to enable them to read)person’s vision (e.g. to enable them to read)

Usually means they can no longer see distant Usually means they can no longer see distant objects - objects - Need bifocalsNeed bifocals

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Correction lenses for myopia and hyperopia

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