1

Stops in optical systems (5.3)

Hecht 5.3

Monday September 30, 2002

2

Stops in Optical SystemsIn any optical system, one is concerned with a number of things

including:

1. The brightness of the image

S S’

Two lenses of the same Two lenses of the same focal length (focal length (f)f), but , but diameter (D) differsdiameter (D) differs

More light collected More light collected from S by larger from S by larger lenslens

Bundle of Bundle of rays from S, rays from S, imaged at S’ imaged at S’ is larger for is larger for larger lenslarger lens

Image of S Image of S formed at formed at the same the same place by place by both lensesboth lenses

3

Stops in Optical Systems Brightness of the image is determined primarily by

the size of the bundle of rays collected by the system (from each object point)

Stops can be used to reduce aberrations

4

Stops in Optical SystemsHow much of the object we see is determined by:How much of the object we see is determined by:

(b) The field of View(b) The field of View

QQ

Q’Q’(not seen)(not seen)

Rays from Q do not pass through systemRays from Q do not pass through system

We can only see object points closer to the axis of the systemWe can only see object points closer to the axis of the system

Field of view is limited by the systemField of view is limited by the system

5

Theory of Stops

We wish to develop an understanding of how and where the bundle of rays are limited by a given optical system

6

Aperture Stop

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 or diaphragm

Aperture stop: that element of the optical system that limits the cone of light from any particular object point on the axis of the system

7

Aperture Stop (AS)

OO

8

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

OO

LL11EE

EE

E’E’

E’E’

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

EEnnP – defines the P – defines the

cone of rays cone of rays accepted by the accepted by the systemsystem

FF11’’

E’E’ = EE’E’ = EnnPP

9

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

E’’E’’

E’’E’’

FF22’’

E”E” = EE”E” = ExxPP

10

Location of Aperture Stop (AS) In a complex system, the AS can be found by

considering each element in the system The element which gives the entrance pupil

subtending the smallest angle at the object point O is the AS

Example, TelescopeExample, Telescope

eyepieceeyepieceObjective=AS=EObjective=AS=EnnPP

11

Example: Eyepiece

EE

EE

9 cm9 cm

ФФ11 = 1 cm = 1 cm ФФ22 = 2 cm = 2 cm

ff11’ = 6 cm’ = 6 cm ff22’ = 2 cm’ = 2 cm

ФФDD = 1 cm = 1 cm

1 cm1 cm 3 cm3 cm

OO

12

Example: EyepieceFind aperture stop for s = 9 cm in front of Find aperture stop for s = 9 cm in front of LL11..

To do so, treat each element in turn – To do so, treat each element in turn –

find Efind EnnP for eachP for each

(a) Lens 1(a) Lens 1 – no elements to the left – no elements to the left

tan tan µµ11 = 1/9 = 1/9

defines cone of rays defines cone of rays acceptedaccepted

9 cm9 cm

1 cm1 cm

OOµµ11

13

Example: Eyepiece

cmss

2.1'6

1

'

1

1

1

Find aperture stop for s = 9 cm in front of Find aperture stop for s = 9 cm in front of Diaphragm. Diaphragm. Find EFind EnnP P

(b) Diaphragm(b) Diaphragm – lens 1 to the left – lens 1 to the left

EE

EE

9 cm9 cm 1 cm1 cm

2.1'

s

sM

ФФDD’ = 1.2 cm’ = 1.2 cm

E’E’

E’E’

1.2 cm1.2 cm

Look at the system Look at the system from behind the slidefrom behind the slide

OO

14

Example: Eyepiece

Calculate maximum angle of cone of rays accepted by entrance Calculate maximum angle of cone of rays accepted by entrance pupil of diaphragmpupil of diaphragm

E’E’

E’E’

OO0.6 cm0.6 cm

9 + 1.2 cm9 + 1.2 cm

µµ22

tan tan µµ22 = 0.6/10.2 ≈ 1/17 = 0.6/10.2 ≈ 1/17

15

Example: Eyepiece(c) Lens 2(c) Lens 2 – 4 cm to the left of lens 1 – 4 cm to the left of lens 1

cmss12'

6

1

'

1

4

1

34

12'

s

sM

ФФ22’ = 6 cm’ = 6 cm

Look at the system Look at the system from behind the slidefrom behind the slide

9 cm9 cm 4 cm4 cm

OO

ФФ22 = 2 cm = 2 cm

16

Example: EyepieceCalculate maximum angle of cone of rays accepted by entrance Calculate maximum angle of cone of rays accepted by entrance pupil of lens 2.pupil of lens 2.

OO

3 cm3 cm

9 + 12 cm9 + 12 cm

µµ33

tan tan µµ33 = 3/21 = 1/7 = 3/21 = 1/7

17

Example: Eyepiece

Component Entrance pupil Acceptance cone angle

(degrees)

Lens 1 tan µ1 = 1/9 6.3

Diaphragm tan µ2 = 1/17 3.4

Lens 2 tan µ3 = 1/7 8.1

Thus Thus µµ22 is the smallest angle is the smallest angle

The diaphragm is the element that limits the cone of rays The diaphragm is the element that limits the cone of rays from Ofrom O

Diaphragm = Aperture StopDiaphragm = Aperture Stop

18

Example: EyepieceEntrance pupil is the image of the diaphragm in LEntrance pupil is the image of the diaphragm in L11..

9 cm9 cm

E’E’

E’E’

1.2 cm1.2 cm

OOµµ22 = tan = tan-1-1 (1/17) (1/17)

ФФDD’ = 1.2 cm’ = 1.2 cm

EEnnPP

19

Example: EyepieceExit pupil is the image of the aperture stop (diaphragm) in LExit pupil is the image of the aperture stop (diaphragm) in L22..

EE

EE

9 cm9 cm

ff22’ = 2 cm’ = 2 cm

ФФDD = 1 cm = 1 cm

1 cm1 cm 3 cm3 cm

OO

cmss6'

2

1

'

1

3

1

23

6'

s

sM

ФФ22’ = 2 cm’ = 2 cm

20

Example: Eyepiece

EE

EE

ff22’ = 2 cm’ = 2 cm

ФФDD = 1 cm = 1 cm

3 cm3 cm

OO

ФФEExxPP’ = 2 cm’ = 2 cm

E’E’

E’E’6 cm6 cm

EExxPP

21

Chief Ray

for each bundle of rays, the light ray which passes through the centre of the aperture stop is the chief ray

after refraction, the chief ray must also pass through the centre of the exit and entrance pupils since they are conjugate to the aperture stop

EnP and ExP are also conjugate planes of the complete system

22

Marginal Ray

Those rays (for a given object point) that pass through the edge of the entrance and exit pupils (and aperture stop).

23

Ray tracing with pupils and stops

P’P’

Q’Q’

OO

EEnnPP

Q’’Q’’

P’’P’’

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 to pass through

edge of ASedge of AS

•Refracted at LRefracted at L22 to pass (exit) to pass (exit)

through Ethrough ExxP.P.

LL11

LL22

Chief Ray from TChief Ray from T

•Proceed toward centre of Proceed toward centre of EEnnPP

•Refracted at LRefracted at L11 to pass to pass

though centre of ASthough centre of AS

•Refracted at LRefracted at L22 to pass (exit) to pass (exit)

through centre of Ethrough centre of ExxPP

T’T’

O’O’

24

Exit PupilDefines the bundle of rays at the imageDefines the bundle of rays at the image

OO

Q’’Q’’

P’’P’’

TT

T’T’

O’O’ αα’’

25

Field Stop

That component of the optical system that limits the field of view

θθAA

ddθθ = angular field of = angular field of viewviewA = field of view at distance dA = field of view at distance d