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General Remarks Analysis generally involves the laws of reflection and refraction Analysis uses the procedures of geometrical optics To explain certain phenomena the phenomena, wave nature of light must be used g

C apte ChapterOptical Instruments

Dr. G. Mirjalili, Physics Dept. Yazd University

Dr. G. Mirjalili, Physics Dept. Yazd University

25.1 25 1 The Camera The Camera The single-lens photographic camera i h t hi is an optical instrument Components Light-tight box Converging lens Produces a real image

Film behind the lens Receives the imageDr. G. Mirjalili, Physics Dept. Yazd University Dr. G. Mirjalili, Physics Dept. Yazd University

Photography lenses g p yPhotography lenses are complex! Especially zoom lenses lenses.

Photography lensesModern lenses can have up to 20 p elements!Canon 17-85mm f/3.5-4.5 zoom Canon EF 600mm f/4L IS USM Super Telephoto Lens 17 elements in 13 groups $12,000

Double Gauss

Petzval

These are older designs designs.Dr. G. Mirjalili, Physics Dept. Yazd University Dr. G. Mirjalili, Physics Dept. Yazd University

f-number of lensD U'

The F-number, f / #, of a lens is the ratio of its focal length and its diameter.

Fnumber

f - number =f

f Dd1

f

f

The f-number describes the cone angle of the rays that form an image. The f-number of a lens determines four important parameters f i f i The brightness of the image The depth of field The resolution of the lens

fFast

d2

f

A lens with a low f-number is a fast lens Simple cameras usually have a fixed focal length and a fixed aperture size, with an number of about 11 (large depth of field)

f/# =1

f/# =2Dr. G. Mirjalili, Physics Dept. Yazd University

Dr. G. Mirjalili, Physics Dept. Yazd University

small f-number lenses collect more light but are harder to engineer.

Numeric ApertureThe numeric aperture (N.A.) is the product of the index of refraction (in image space) with the sine of the half-angle of the cone of illumination

Optical devices: CameraMultiMulti-element lens

N.A. = n sin U D U U'

fThe f-number of a lens, f/#, is the ratio of the focal length, f, of a lens system to the diameter d of its entrance pupil. F/# is inversely proportional to twice the diameter, d, pupil Numerical Aperture, NADr. G. Mirjalili, Physics Dept. Yazd University

AS=Iris Diaphragm

Film: edges constitute field stop

Dr. G. Mirjalili, Physics Dept. Yazd University

CameraMost common camera is the so-called 35 mm socamera ( refers to the film size) Object s = 27 mm

CameraObject s = 1 m Image s 5.25 cm Image s = 5.0 cm Thus to focus object between s = 1 m and infinity, j y, 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

34 mm Multi element lens usually has a focal length of f =50 mmDr. G. Mirjalili, Physics Dept. Yazd University

Dr. G. Mirjalili, Physics Dept. Yazd University

Brightness of image is determined by the amount of light falling on the film. film Each point on the film subtends a solid angle

Camera: Brightness of image

f-number of a lens numberDefine f-number, f,A= f = F# D

dA D 2 D 2 d = 2 = = r 4 s '2 4f2

D D

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

Irradiance at any point I di t i t on film is proportional to (D/f)2f =A D

1 Ip 2 f A

f-number

s f

d2F# =1 1Dr. G. Mirjalili, Physics Dept. Yazd University

fF# =1.2 12

I p

1 A2

Dr. G. Mirjalili, Physics Dept. Yazd University

Standard settings on camera lenses

Aperture - F # F# = f/d Amount of light proportional to 1/(F#)2 Usual Description , , 1.2, 1.8, 2.8, 4, 5.6, 8, 11, 16, , Fractional F Stop

f# = f/D1.2 12 1.8 2.8 28 4.0 5.6 56 8 11 16 22 Good lenses, f# =

(f#)21.5 15 3.2 7.8 78 16 31.5 31 5 64 121 256 484 1.2 or 1.8 (very fast) Difficult to get f/1 f/1Dr. G. Mirjalili, Physics Dept. Yazd University

Dr. G. Mirjalili, Physics Dept. Yazd University

Total exposure on Filmlight

Photo imaging with a camera lensIn ordinary 35 mm camera, the image is very small (i.e. reduced many times compared with the object Also, the lens is limited in the distance it can move relative to the film film exposure Telephoto and wide angle lens are used in camera 2 large, h2 small g , Wide-angle system 2 small, h2 large Telephoto systemDr. G. Mirjalili, Physics Dept. Yazd University

watts E = I 2 t (exp osuretime) m J = 2 mExposure time is varied by the shutter which has settings, 1/1000, 1/500, 1/250, 1/100, 1/1000 1/500 1/250 1/100 1/50 Again in steps of factor of 2

n1h11= n2h22

Dr. G. Mirjalili, Physics Dept. Yazd University

Wide angle and Telephoto images

Telephoto lensL1 L2

A larger image can be achieved with a telephoto lens Choose back focal length (bfl 50 mm) Then l Th lenses can be interchanged (easier to design) b i h d( i d i ) The idea is to increase the effective focal length (and hence image distance) of the camera lens. g )Dr. G. Mirjalili, Physics Dept. Yazd University Dr. G. Mirjalili, Physics Dept. Yazd University

d

50 mm

Example (telephoto) Assume that the f A h h front l lens h +50 mm f has 50 focal l l length and the second h d h d lens -25 mm focal length. The distance between both is 30mm determine. (a) the focal length. (b) the actual physical length of the system.f1=+50mm f2=-25mm H2

Solutionfor this telephoto lens the focal length is:

F=

f f (+50)(25) = = +250mm f + f d + 50 25 301 2 1 2

film 250 mm

30mm

film

The f Th focal length of the system is the di t ll th f th t i th distance from the f th second principal plane, H2 of the system to the filme in the camera.Dr. G. Mirjalili, Physics Dept. Yazd University

Dr. G. Mirjalili, Physics Dept. Yazd University

Solution Physical length of the systemP=2

Depth of FieldOnly one plane is imaged (i.e., is in focus) at a time. But wed like objects near this p j plane to at least be almost in focus. The range of g distances in acceptable focus is called the depth of field.P1=1/(+50)x10 -2)=+20 P2=1/(-25X10 -2) =- 40 Object Out of focus Out-of-focus plane Image Size of blur in out-of-focus plane

P1

1

1 (+20)(0.03) 1 1 a = = = 0.1m = 100mm P 102 2

P=

d 1 P( ) + 20 n

+P

It depends on how much of the lens is used, that is, the aperture. p p

2

+ ( 40) = 10

fFocal plane

The physical length is: It is acceptable.

2

30+100 = 130 mm = 13 cm

Aperture

Dr. G. Mirjalili, Physics Dept. Yazd University

The smaller the aperture, the more the depth of field.Dr. G. Mirjalili, Physics Dept. Yazd University

Depth of fieldThe range of distances in acceptable focus is called the depth of field

Depth of field example p p .

A large depth of field isnt always desirable.

f/32 (very small aperture; large depth of field)

D b = f + f f f f D b = f f fb f = D

D f f f/5 (relatively large aperture; small depth of field)

D fDr. G. Mirjalili, Physics Dept. Yazd University

b

f

A small depth of field is also p desirable for portraits.Dr. G. Mirjalili, Physics Dept. Yazd University

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

Depth of Fields2 s1 s1

Depth of Field (DOF)S`1=S`0+X

s2

x=d x x

dso ' D) )D

A=f/D A f/D

s1 = s2 =

s o f ( f + Ad f 2 + Ads o

s o f ( f Ad f 2 Ads o

x

x

d

so

soDr. G. Mirjalili, Physics Dept. Yazd University

soDr. G. Mirjalili, Physics Dept. Yazd University

Depth of field2 Adso ( so f ) f 2 DOF = s2 s1 = 2 f 4 A 2 d 2 soe.g. d = 1 m, f# = A = 4, f = 5 cm, so = 6 m DOF = 0.114 m i.e. so = 6 0. 06 mDr. G. Mirjalili, Physics Dept. Yazd University

Depth of fieldStrongly dependent on the f# of the lens gy Suppose, so = 4m, f = 5 cm, d = 40 m

s f ( f + Ad ) 10,000 s1 = o 2 f + Adso 25 + 1.6 A

1200 1000 800

DOF = s2 s1

s1,s2 (cm) (

s2Depth f fi ld (f D th of field (focus) )

600 400 200

s2 =

so f ( f Ad ) 10,000 2 f Adso 25 1.6 A

s110 12 14 16

0 0 2 4 6 8 Dr. G. Mirjalili, Physics Dept. Yazd University

f#

Aperture

Aperture have an image in the optical systemExample E li=14

Other effects and usage of apertures

F=9cm Entrance E t pupil

Exit pupil

A stop 8 mm in diameter is placed halfway between image and lens. What is the diameter and where is the place of the exit pupil?.Dr. G. Mirjalili, Physics Dept. Yazd University Dr. G. Mirjalili, Physics Dept. Yazd University

Solutiono = if (14 )( 9 ) = = 25 . 2 cm f i 9 14Place of entrance pupil

Do the exit pupil and entrance pupil lie on the same side? Yes!If the stop is moved even closer To the lens (with in the focal length) The exit pupil is virtual p p and lie on the entrance sidef

25 . 2 = 12 . 6 cm 2 o f ( 12 . 6 )( 9 ) = i = = 31 . 6 cm o + f ( 12 . 6 ) + 9 DXP i = DEP o o =

Place of Exit pupil

Entrance pupil Exit pupil

D =XP

D i (0.8)(31.5) = = 2cm o 12.6EP

Diameter of Exit pupilDr. G. Mirjalili, Physics Dept. Yazd University

Dr. G. Mirjalili, Physics Dept. Yazd U