Last lecture

3. Optical instrumentation 3. Optical instrumentation

Last lecture

¾

This lecture

¾

¾ Field stop, Entrance window, Exit window

¾ Depth of field, Depth of focus

¾ Brief look at aberrations

¾ prism and dispersion

¾ Camera

¾ Magnifier and eyepiece

¾ Microscope

¾ Telescope

Aperture effects on image

Optical instruments

3-1. Stops, Pupils, and Windows 3-1. Stops, Pupils, and Windows

Iris (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 (E_nP) & Exit pupil (E_xP) : AS의 image

Entrance window (E_nW) & Exit window (E_xW) : FS의 image

Stops in Optical Systems Stops 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.

Stops Stops

• Brightness

– Aperture stop: The real aperture in an optical system that limits the size of the 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 system Assume that the Diaphragm is the AS of the system

Diaphragm (조리개)

Entrance Pupil (E

P) Entrance Pupil (E

P)

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

LL₁₁ EE

EE

EE’’

EE’’

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

EE_nnPP –– defines defines the cone of rays the cone of rays accepted by the accepted by the system

system FF₁₁’’

E’E’E’E’ = E= E_nnPP

Exit Pupil (E _x P) Exit Pupil (E _x P)

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

LL₁₁ EE

EE

E’’E’’

EE’’’’

FF₂₂’’

EE””EE”” = = EE_xxPP

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 = E_nP

(b) AS = E_xP

Aperture Stop and Pupils Aperture Stop and Pupils

Figure 3-1.

(a) AS = E_nP

(c) AS = E_nP

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 stops Ray tracing with pupils and stops

PP’’

QQ’’ OO

EE_nnPP

Q’’Q’’

P’’P’’

EE_xxPP PP

QQ ASAS TT

Marginal Rays from T,O Marginal Rays from T,O

•Must proceed towards edges of •Must proceed towards edges of EE_nnPP

•Refracted at L•Refracted at L₁₁to pass through edge of ASto pass through edge of AS

•Refracted at L•Refracted at L₂₂to pass (exit) through Eto pass (exit) through E_xxP.P.

LL₁₁ LL₂₂

Chief Ray from T Chief Ray from T

•Proceed toward centre of •Proceed toward centre of EE_nnPP

•Refracted at L•Refracted at L₁₁to pass though to pass though centre of AS

centre of AS

•Refracted at L•Refracted at L₂₂to pass (exit) to pass (exit) through centre of

through centre of EE_xxPP

TT’’ OO’’

Field of view: Field Stops & Windows Field of view: Field Stops & Windows

The field stop (FS) limits the field of view.

θθ AA

dd

θθ = angular field of view= angular field of view A = field of view at distance d

A = field of view at distance d

FS

Field Stop Field Stop

The 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 (EE_nnPP), ), 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 (E

W) Entrance Window (E

W)

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

Example: Camera Example: Camera

AS AS FS FS

Where is the Where is the entrance entrance window?

window?

Exit Window (E

W) Exit Window (E

W)

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 viewed Defines the lateral dimension of the image that will be viewed Example: Camera

Example: Camera

AS AS FS FS

Where is the Where is the exit window?

exit window?

Field of a positive thin lens Field of a positive thin lens

Eye pupil Eye pupil

AS= AS= E E

P P P P

Q Q P P ’ ’

Q’ Q ’

Entrance pupil Entrance pupil

(small) (small)

Ob jec t fi eld

Ob jec t fi eld Image Image field field F F

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 seen

αα = field of view in object space= field of view in object space αα’’ = field of view in image space= field of view in image space

FS= FS= E E

W W

α α α α ’ ’

Stops, pupils and windows in an optical system

Stops, pupils and windows in an optical system

AS AS

FS FS E E

P P

E E

W W E E

W W

E E

P P

α α ’ ’

α α

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

Chromatic Chromatic aberration aberration

Monochromatic Monochromatic

aberrations aberrations

Unclear Unclear

image image

Deformation Deformation of image

of image

Spherical Spherical ComaComa

astigmatism astigmatism

Distortion Distortion Curvature Curvature

n ( n ( λ λ ) )

Aberrations: Chromatic Aberrations: 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 ( λ λ ) )

Aberrations: Spherical Aberrations: 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. Prisms

3-3. Prisms

Angular deviation of a prism Angular deviation of a prism

1 2

δ δ δ = +

Minimum deviation from a prism Minimum deviation from a prism

Occurs when the light ray passes symmetrically through the prism.

A useful method of determining

the refractive index

of the prism

Dispersion Dispersion

Normal dispersion

Anomalous dispersion

Reflecting Prisms Reflecting Prisms

Figure 3-18.

α O

B

u v

lens adjustable aperture stop

adjustable barrel

shutter

M film

I

3-4. Camera

3-4. Camera

Object _Image

Pinhole

Camera

Pinhole Camera Pinhole 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

Camera Camera

Multi

Multi--element lenselement lens

AS=Iris Diaphragm AS=Iris Diaphragm

Film: edges Film: edges

constitute field stop constitute field stop

Most common camera is the so

Most 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 mm 34 mm

27 mm 27 mm

Object (s = 1 m) Image (s

Object (s = 1 m) Image (s’’≈≈5.25 cm) ; Object (s = ∞5.25 cm) ; Object (s = ∞)) Image (s’Image (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 = 2.5mm For most cameras, this is about the limit and it is difficult to

For most cameras, this is about the limit and it is difficult tofocus 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-number Camera: Brightness and f-number

Brightness of image is determined by the amount of light falling

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

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

2 2 2

2

2

4 ' 4 f

D s

D r

d _{Ω =} dA ₌ π ₌ π

D D ’ ’

s s ’ ’ ≈ ≈ f f D D

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

D A = f

Define f

Define f--number, number,

2

1 E

∝ A

This is a measure of the

This is a measure of the speed of the lensspeed of the lens Small f# (big aperture)

Small f# (big aperture) EE large , tlarge , t shortshort Large f# (small aperture)

Large f# (small aperture) EE small, tsmall, t longlong

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

2 (exposure time) 2 e

watts J

Energy E t

m 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 ( )

depth of field

o

Ads s f f s s

f 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 Eyepieces 3-5. 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 the near point of the eye s cm

The angle subtended by the object is h

Then use the magnifier Angular magnification h s

h s

α

α α

=

=

= =

( )

0

0

:

/ 25 25

/ 25

25 :

25 25

25 1

M

M

Viewing the image at s s f we find M h s

h s f

Viewing the image at s cm we find

s f M

f f

α α

α α

′ = ∞ =

= = = =

′ = −

= = = +

+

Eyepieces

Eyepieces

Objective (대물렌즈)

Field lens Eye lens

Eyepiece Eyepiece

Huygens eyepiece

Ramsden eyepiece

s

1

1 2

2 ( )

s = f + f

3-6. Microscopes 3-6. Microscopes

• In most microscopes, L = 16 cm

• “—” means inverted image

Eyepiece Objective

Eyepiece

Objective

Magnification : 25

e o

cm L

M f f

⎛ ⎞⎛ ⎞

= −⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠

L

• Two-Step Magnification

– Objective Makes a Real Image

– Eyepiece Used as a Simple Magnifier

F F’

A’

A

F F’

Objective

Eyepiece

FF_oo FF_oo

FF_ee

FF_ee LL

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

s’s’ ≈≈ ff_oo + L+ L xx

s = x +

s = x + ff_{oo o}

o

o

x f

f L

s s h

M h

+

− +

≅

−

=

= ' '

Recall xx

Recall xx’’ = = ff_oo²² x’x’

x’x’ ≈≈ LL x = fx = f_oo²²/L/L

o

o

f

M = − L

S S’

Magnification of the Objective Magnification 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 f

M = 25cm FF_oo FF_oo

FF_ee

FF_ee LL

hh

h’h’ h”h”

25 +1

=

e

e f

M cm

Magnification of the Eyepiece

Magnification of the Eyepiece

⎟⎟ ⎠

⎜⎜ ⎞

⎝

− ⎛

=

=

e o

e

o

f

cm f

M L M

M 25

(Image at infinity) (Image at infinity)

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ +

−

=

= 25 1

e o

e

o f

cm f

M L M

M (Image at near point)(Image at near point)

Total magnification of the microscope Total magnification of the microscope

o

o

f

M = − L

Objective :

Objective : Eyepiece :Eyepiece : 10 X, 20 X, 40 X etc

40X ⇒

( L = 16 cm )

40

0.4

o

L f cm

f = → =

e

e

f

M 25 cm

=

f

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

M_e = 10X

(at ∞)

When we use a microscope ….

When we use a microscope ….

FF_oo FF_oo

FF_ee

FF_ee LL

AS

E_nP

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

Where should the eye be located to view the image?

Optimum viewing Optimum viewing ––

9Place eye near 9Place eye near EE_xxPP (moving eye away decreases illumination and F.O.V.)(moving eye away decreases illumination and F.O.V.) 9Ensure that exit pupil ~ same size as eye pupil!9Ensure that exit pupil ~ same size as eye pupil!

Numerical Aperture Numerical Aperture

Measure of light gathering power Measure of light gathering power

Cover Glass Cover Glass

αα_gg

αα_aa AirAir

OilOil

αα_gg’’ αα_oo

nn_gg

N. A. = n sin N. A. = n sin α α

LensLens

OO nn_oo

Numerical Aperture Numerical Aperture

( ) _a

g

n g

A

N . . = sin α = 1 sin α

If cover glass in air If cover glass in air

o o

o g

g

n

n A

N . . = sin α ' = sin α = 1 . 5 sin α

If cover glass immersed in oil (n

If cover glass immersed in oil (n_oo = 1.516) –= 1.516) – between glassbetween glass and oil there is essentially no refraction since

and oil there is essentially no refraction since nn_gg = 1.5= 1.5

Increases the light gathering power by about 1.5 Increases 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 telescope

o e

d = f + f

{ f

< ⁰ }

{ f

> ⁰ }

Refracting Telescope Refracting Telescope

hh_TT=f=f_eyeeyeθ’θ’ ff_oo ff_ee

Objective

Objective EyepieceEyepiece

ss’’ h”h”

hh’’ θ’θ’

θ’θ’ θθ

A.S.

E_nP

E_xP

Telescope Telescope

ShowShow

e o

f

M = − f

M

D _exit = D ^o

Reflecting Telescopes Reflecting Telescopes

Newtonian telescope Cassegrain telescope

Gregorian telescope

Schmidt telescope, Schmidt camera Schmidt telescope, Schmidt camera

Schmidt correcting plate

Reducing the aberrations

The Hubble Space Telescope The Hubble Space Telescope

2.4 m primary 2.4 m primary curved mirror curved mirror 0.3 m secondary 0.3 m secondary curved mirror curved mirror

Binoculars Binoculars

Two telescopes side

Two telescopes side--byby--sideside Prisms used to erect images

Prisms used to erect images

Eyepiece Eyepiece

Objective Objective