3. Optical instrumentation3. Optical instrumentationLast lecture

This lecture Aperture stop, Entrance pupil, Exit pupilField stop, Entrance window, Exit windowDepth of field, Depth of focusBrief look at aberrationsprism and dispersionCameraMagnifier and eyepieceMicroscopeTelescope

Aperture effectson image

Optical instruments

3-1. Stops, Pupils, and Windows3-1. Stops, Pupils, and WindowsIris

(조리개)

aperture stop(AS)

film

field stop(FS)

AS (aperture stop) : 상의 밝기를 결정하는 실제로 설치된 aperture

FS (field stop) : 상의 크기를 조절하기 위해 실제로 설치된 aperture

Entrance pupil (EnP) & Exit pupil (ExP) : AS의 image

Entrance window (EnW) & Exit window (ExW) : FS의 image

Stops in Optical SystemsStops in Optical Systems

• Brightness and Field-of-view of the image are determined by the Stops

• Stops can be used to reduce aberrations

• A stop is an opening (despite its name) in a series of lenses, mirrors, diaphragms, etc.

• The stop itself is the boundary of the lens, diaphragm, or film.

StopsStops• Brightness

– Aperture stop: The real aperture in an optical system that limits the size ofthe cone of the rays accepted by the system from an axial object point

– Entrance pupil: The image of the aperture stop formed by the optical elements (if any) that precede it.

– Exit pupil: The image of the aperture stop formed by the optical elements (if any) that follow it.

– The aperture stop also is used to control the depth of field and depth of focus for an optical system, and to reduce the effect of optical aberrations.

• Field of view– Field stop: The real aperture that limits the angular field of view formed by

an optical system– Entrance window: The image of the field stop formed by the optical

elements (if any) that precede it.– Exit window: The image of the field stop formed by the optical elements (if

any) that follow it.– The field stops are used to control the field of view (the extent of the object

plane that is imaged in the image plane) and to control aberrations.

Aperture Stop and Field Stop Aperture Stop and Field Stop Optics, E. Hecht, p. 149

FS

Aperture Stop (AS)Aperture Stop (AS)

OO

EE

EE

Assume that the Diaphragm is the AS of the systemAssume that the Diaphragm is the AS of the system

Diaphragm (조리개)

Entrance Pupil (EnP)Entrance Pupil (EnP)The entrance pupil is defined to be the image of the aperture The entrance pupil is defined to be the image of the aperture stop in all the lenses preceding it stop in all the lenses preceding it (i.e. to the left of AS (i.e. to the left of AS -- if light if light travels left to right)travels left to right)

OO

LL11EE

EE

EE’’

EE’’

How big does the How big does the aperture stop look aperture stop look to someone at Oto someone at O

EEnnPP –– defines defines the cone of rays the cone of rays accepted by the accepted by the systemsystem

FF11’’

EE’’EE’’ = = EEnnPP

Exit Pupil (ExP)Exit Pupil (ExP)

The exit pupil is the image of the aperture stop in the lenses The exit pupil is the image of the aperture stop in the lenses coming after it coming after it (i.e. to the right of the AS)(i.e. to the right of the AS)

OO

LL11EE

EE

EE’’’’

EE’’’’

FF22’’EE””EE”” = = EExxPP

Aperture Stop and Pupils Aperture Stop and Pupils

Here is an aperture stop (AS) in a three-lens system. Ray traces are shown for the chief ray from an object point at the top of the bulb and for a marginal ray from an axial object point.

Optics, E. Hecht, p. 151

Aperture Stop and Pupils Aperture Stop and Pupils

Figure 3-1.

(a) AS = EnP

(b) AS = ExP

Aperture Stop and Pupils Aperture Stop and Pupils

Figure 3-1.

(a) AS = EnP

(c) AS = EnP

Chief Ray and Marginal Ray Chief Ray and Marginal Ray The chief ray is directed from the object point to the center of the Entrance Pupil. The chief ray will thus always pass through the center of AS and Exit Pupil.

-> conjugate planes

The marginal ray is directed to the edge of Entrance Pupil.The marginal ray will thus always pass through the edge of AS and Exit Pupil.

-> conjugate planes

Figure 3-2.

Chief ray

marginal ray

Ray tracing with pupils and stopsRay tracing with pupils and stops

PP’’

QQ’’

OO

EEnnPP

QQ’’’’

PP’’’’

EExxPP

PP

QQ

ASAS

TT

Marginal Rays from T,OMarginal Rays from T,O

••Must proceed towards edges of Must proceed towards edges of EEnnPP

••Refracted at LRefracted at L11 to pass through edge of ASto pass through edge of AS

••Refracted at LRefracted at L22 to pass (exit) through to pass (exit) through EExxPP..

LL11LL22

Chief Ray from TChief Ray from T••Proceed toward centre of Proceed toward centre of EEnnPP

••Refracted at LRefracted at L11 to pass though to pass though centre of AScentre of AS

••Refracted at LRefracted at L22 to pass (exit) to pass (exit) through centre of through centre of EExxPP

TT’’

OO’’

Field of view: Field Stops & WindowsField of view: Field Stops & WindowsThe field stop (FS) limits the field of view.

θθAA

dd

θθ = angular field of view= angular field of viewA = field of view at distance dA = field of view at distance d

FS

Field StopField StopThe aperture that controls the field of view by limiting The aperture that controls the field of view by limiting the solid angle formed by the solid angle formed by chief rayschief rays

As seen from the centre of the entrance pupil (As seen from the centre of the entrance pupil (EEnnPP), ), the field stop (or its image) subtends the largest angle.the field stop (or its image) subtends the largest angle.

Figure 3-3.

Entrance Window (EnW)Entrance Window (EnW)

The image of the field stop in all elements The image of the field stop in all elements precedingpreceding itit

Defines the lateral dimension of the object that will be viewedDefines the lateral dimension of the object that will be viewed

Example: CameraExample: Camera

ASAS FSFS

Where is the Where is the entrance entrance window?window?

Exit Window (ExW)Exit Window (ExW)

The image of the field stop in all elements The image of the field stop in all elements following following itit

Defines the lateral dimension of the image that will be viewedDefines the lateral dimension of the image that will be viewed

Example: CameraExample: Camera

ASAS FSFS

Where is the Where is the exit window?exit window?

Field of a positive thin lensField of a positive thin lens

Eye pupilEye pupil

AS=AS=EExxPP

PP

QQPP’’

QQ’’

Entrance pupilEntrance pupil(small)(small)

Object field

Object field Image field

Image field

FF

Object point must be within cone Object point must be within cone (to left of lens) to be seen(to left of lens) to be seenαα = field of view in object space= field of view in object spaceαα’’ = field of view in image space= field of view in image space

FS=FS=EEnnWW

αα αα’’

Stops, pupils and windowsin an optical system

Stops, pupils and windowsin an optical system

ASASFSFS

EExxPPEExxWW

EEnnWWEEnnPP

αα’’αα

3-2. A Brief look at aberrations 3-2. A Brief look at aberrations

ChromaticChromaticaberrationaberration

MonochromaticMonochromaticaberrationsaberrations

Unclear Unclear imageimage

Deformation Deformation of imageof image

SphericalSpherical

ComaComa

astigmatismastigmatism

DistortionDistortion

CurvatureCurvature

n (n (λλ))

Aberrations: ChromaticAberrations: Chromatic• Because the focal length of a lens depends on the

refractive index (n), and this in turn depends on the wavelength, n = n(λ), light of different colors emanating from an object will come to a focus at different points.

• A white object will therefore not give rise to a white image. It will be distorted and have rainbow edges

n (n (λλ))

Aberrations: SphericalAberrations: Spherical• This effect is related to rays which make large angles

relative to the optical axis of the system• Mathematically, can be shown to arise from the fact that

a lens has a spherical surface and not a parabolic one• Rays making significantly large angles with respect to

the optic axis are brought to different foci

3-3. Prisms3-3. Prisms

Angular deviation of a prismAngular deviation of a prism

1 2δ δ δ= +

Minimum deviation from a prismMinimum deviation from a prismOccurs when the light ray passes symmetrically through the prism.

A useful method of determining

the refractive index of the prism

DispersionDispersion

Normaldispersion

Anomalousdispersion

Reflecting PrismsReflecting PrismsFigure 3-18.

αO

B

u v

lens adjustableaperture stop

adjustablebarrel

shutter

filmM

I

3-4. Camera3-4. Camera

Object Image

Pinhole

Camera

Pinhole CameraPinhole Camera

• Simplest form of camera

• Consist of box with a hole in it– Low light levels with small hole

– Increasing size of hole blurs image

CameraCamera

MultiMulti--element lenselement lens

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

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

Object (s = 1 m) Image (sObject (s = 1 m) Image (s’’ ≈≈ 5.25 cm) ; Object (s = 5.25 cm) ; Object (s = ∞∞)) Image (sImage (s’’ = 5.0 cm)= 5.0 cm)Thus to focus object between s = 1 m and infinity, we only move Thus to focus object between s = 1 m and infinity, we only move the lens about 0.25 cm = 2.5mmthe lens about 0.25 cm = 2.5mmFor most cameras, this is about the limit and it is difficult toFor most cameras, this is about the limit and it is difficult to focus on objects with s < 1 mfocus on objects with s < 1 m

The f-number The f-number The f/# or f-number is the ratio of the lens focal length to the diameter of the aperture stop: f/# = f/D.

Optics, E. Hecht, p. 152

D

f

Camera: Brightness and f-numberCamera: Brightness and f-number

Brightness of image is determined by the amount of light fallingBrightness of image is determined by the amount of light falling on the film.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 fD

sD

rdAd ππ

===Ω

DD’’

ss’’ ≈≈ ff

DD

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

DfA =Define fDefine f--number, number,

2

1eE

A∝

This is a measure of the This is a measure of the speed of the lensspeed of the lensSmall f# (big aperture) Small f# (big aperture) EE large , large , tt shortshortLarge f# (small aperture) Large f# (small aperture) EE small, small, tt longlong

Good 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

2 2(exposure time)ewatts JEnergy E tm m

⎛ ⎞= • =⎜ ⎟⎝ ⎠

Exposure time is varied by the shutter which has settings,1/1000, 1/500, 1/250, 1/100, 1/50

Depth of Field Depth of Field Consider a fixed image plane. The distance in the object space over which object points are in acceptable focus at the image plane (the allowable blurring parameter, d) is termed the depth of field.

Figure 3-22.

{ }2

2 1 4 2 2 2

2 ( )depth of field o o

o

Ads s f fs sf A d s

−≡ − =

−

Depth of Focus Depth of Focus Consider a fixed object plane. The distance in image space over which object points are in acceptable focus at the image plane (the allowable blurring parameter, d)is termed the depth of focus.

Figure 3-22.

depth of focus 2x≡

3-5. Simple magnifiers and Eyepieces3-5. Simple magnifiers and Eyepieces

Figure 3-24. A simple magnifier

0

0

( 25 ).

/ 25.

. :/ 25

/ 25

near pt

M

A small object of height h is held at thenear point of the eye s cm

The angle subtended by the object ish

Then use the magnifier Angular magnificationh s

h s

α

αα

=

=

= =

( )

0

0

:/ 25 25

/ 25

25 :25 25 1

25

M

M

Viewing the image at s s f we findh sMh s f

Viewing the image at s cm we findfs Mf f

αα

αα

′ = ∞ =

= = = =

′ = −

= = = ++

EyepiecesEyepiecesEyepiece(접안렌즈)

Objective(대물렌즈)

Field lens

Eye lens

Eyepiece Eyepiece

Huygenseyepiece

Ramsdeneyepiece

s

11 22 ( )s f f= +

3-6. Microscopes 3-6. Microscopes

• In most microscopes, L = 16 cm• “—” means inverted image

EyepieceObjective

Eyepiece

ObjectiveMagnification : 25

e o

cm LMf f

⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠

L

• Two-Step Magnification

– Objective Makes a Real Image

– Eyepiece Used as a Simple Magnifier

F’F

A’A

F’F

ObjectiveEyepiece

FFoo FFoo

FFee

FFee

LL

Wish to have intermediate image (hWish to have intermediate image (h’’) ) just inside the focus of the eyepiecejust inside the focus of the eyepiece

ss’’ ≈≈ ffoo + L+ L

xx

s = x + s = x + ffoo o

oo fx

fLss

hhM

++

−≅−==''

Recall xxRecall xx’’ = = ffoo22

xx’’

xx’’ ≈≈ LL

x = x = ffoo22/L/L

oo f

LM −=

S S’

Magnification of the ObjectiveMagnification of the Objective

(Newtonian equation – Eq. 2.36)

Recall: The magnification of an image formed Recall: The magnification of an image formed by a magnifier (eyepiece)by a magnifier (eyepiece)

(a)(a) at the near point isat the near point is

(b)(b)at infinity at infinity e

e fcmM 25

=

FFoo FFoo

FFee

FFee

LL

hh

hh’’

hh””

125+=

ee f

cmM

Magnification of the EyepieceMagnification of the Eyepiece

⎟⎟⎠

⎞⎜⎜⎝

⎛−==

eoeo f

cmfLMMM 25

(Image at infinity)(Image at infinity)

⎟⎟⎠

⎞⎜⎜⎝

⎛+−== 125

eoeo f

cmfLMMM (Image at near point)(Image at near point)

Total magnification of the microscopeTotal magnification of the microscope

oo f

LM −=Objective :Objective : Eyepiece :Eyepiece :

10 X, 20 X, 40 X etc

40X ⇒

( L = 16 cm )

40 0.4oo

L f cmf= → =

ee f

cmM 25=

fe = 2.5 cm

Total magnification M = 40 X 10 = 400Total magnification M = 40 X 10 = 400

Me = 10X

(at ∞)

When we use a microscope ….When we use a microscope ….

FFoo FFoo

FFee

FFee

LLAS

EnP

ExP

Where should the eye be located to view the image?Where should the eye be located to view the image?

Optimum viewing Optimum viewing ––Place eye near Place eye near EExxPP (moving eye away decreases illumination and F.O.V.)(moving eye away decreases illumination and F.O.V.)Ensure that exit pupil ~ same size as eye pupil!Ensure that exit pupil ~ same size as eye pupil!

Numerical ApertureNumerical Aperture

Measure of light gathering powerMeasure of light gathering power

Cover GlassCover Glass

ααgg

ααaa

AirAirOilOil

ααgg’’ααoo

nngg

N. A. = n sin N. A. = n sin αα

LensLens

OO

nnoo

Numerical ApertureNumerical Aperture

( ) aggnAN αα sin1sin.. ==If cover glass in airIf cover glass in air

ooogg nnAN ααα sin5.1sin'sin.. ===

If cover glass immersed in oil (nIf cover glass immersed in oil (noo = 1.516) = 1.516) –– between glassbetween glassand oil there is essentially no refraction since and oil there is essentially no refraction since nngg = 1.5= 1.5

Increases the light gathering power by about 1.5Increases the light gathering power by about 1.5

(N.A. roughly analogous to f# of a lens)(N.A. roughly analogous to f# of a lens)

3-7. Telescopes 3-7. Telescopes Astronomical telescope

Galilean telescopeo ed f f= +

{ }0ef <

{ }0ef >

Refracting TelescopeRefracting Telescope

hhTT==ffeyeeyeθθ’’

ffoo ffee

ObjectiveObjective EyepieceEyepiece

ss’’

hh””

hh’’

θθ’’

θθ’’θθ

A.S.

EnP

ExP

TelescopeTelescope

ShowShow

e

o

ffM −= (magnification of the telescope)(magnification of the telescope)

MDD o

exit =(diameter of the exit pupil)(diameter of the exit pupil)

Diameter of objective lens, Do

Reflecting TelescopesReflecting Telescopes

Newtonian telescope Cassegrain telescope

Gregorian telescope

Schmidt telescope, Schmidt cameraSchmidt telescope, Schmidt camera

Schmidt correcting plate

Reducing the aberrations

The Hubble Space TelescopeThe Hubble Space Telescope

2.4 m primary2.4 m primarycurved mirrorcurved mirror

0.3 m secondary0.3 m secondarycurved mirrorcurved mirror

BinocularsBinoculars

Two telescopes sideTwo telescopes side--byby--sideside

Prisms used to erect imagesPrisms used to erect images

EyepieceEyepiece

ObjectiveObjective