6.6. OpticalOptical instrumentationinstrumentation

Last chapter ¾ Chromatic Aberration ¾ Third-order (Seidel) Optical Aberrations ™ Spherical aberrations, Coma, Astigmatism, Curvature of Field, Distortion

This chapter ¾ Aperture stop, Entrance pupil, Exit pupil ¾ Field stop, Entrance window, Exit window Aperture effects on image ¾ Depth of field, Depth of focus ¾ prism and dispersion ¾ Camera ¾ Magnifier and eyepiece Optical instruments ¾ Microscope ¾ Telescope StopsStops inin OpticalOptical SystemsSystems

Larger lens improves the brightness of the image

Image of S Two lenses of the same formed at focal length (f), but the same diameter (D) differs place by both lenses

SS’

Bundle of rays from S, imaged at S’ More light collected is larger for from S by larger larger lens lens StopsStops inin OpticalOptical SystemsSystems • 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 StopsStops inin OpticalOptical SystemsSystems

How much of the object we see is determined by: Field of View

Q

Q’ (not seen)

Rays from Q do not pass through system We can only see object points closer to the axis of the system Thus, the Field of view is limited by the system ApertureAperture StopStop

• 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 ApertureAperture StopStop (AS)(AS)

E

O

Diaphragm E

Assume that the Diaphragm is the AS of the system Entrance Pupil (E P) Entrance Pupil (EnnP) The entrance pupil is defined to be the image of the aperture stop in all the lenses preceding it (i.e. to the left of AS - if light travels left to right) E’ How big does the aperture stop look E to someone at O L1

E’E’ = EnP O

F1’ 1 EnP – defines the cone of rays accepted by the system E E’ Exit Pupil (E P) Exit Pupil (ExxP)

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

E’’ E L1

E”E” = ExP F ’ O 2

E E’’ LocationLocation ofof ApertureAperture StopStop (AS)(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, Telescope

O

eyepiece

Objective = AS = EnP Example:Example: FindFind thethe ASAS ofof thethe EyepieceEyepiece

f1’ = 6 cm f2’ = 2 cm E

Ф2 = 2 cm Ф = 1 cm Ф1 = 1 cm AS O

E

9 cm 1 cm 3 cm Diaphragm Example:Example: EyepieceEyepiece

Find aperture stop for s = 9 cm in front of L1. To do so, treat each element in turn – find EnP for each (Lens 1, diaphragm, Lens 2)

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

tan µ1 = 1/9 defines cone of rays accepted

1 cm µ1 O 9 cm Example:Example: EyepieceEyepiece Find aperture stop for s = 9 cm in front of Diaphragm.

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

E E’

Look at the system f1’ = 6 cm from behind the slide O 1 1 1 + = 1 s' 6 s'= −1.2cm s' E M = − =1.2 E’ s

9 cm 1 cm

ФD’ = 1.2 cm 1.2 cm D Example:Example: EyepieceEyepiece

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

E’

0.6 cm O µ2

9 + 1.2 cm

tan µ = 0.6/10.2 ≈ 1/17 2 E’ Example:Example: EyepieceEyepiece

(c) EnP of Lens 2 – 4 cm to the left of lens 1

Look at the system from behind the slide 1 1 1 + = O 4 s' 6 s'= −12cm s' 12 M = − = = 3 s 4

Ф2’ = 6 cm

9 cm 4 cm

Ф2 = 2 cm Example:Example: EyepieceEyepiece

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

3 cm

O µ3

9 + 12 cm

tan µ3 = 3/21 = 1/7 Example:Example: EyepieceEyepiece

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 µ2 is the smallest angle The diaphragm is the element that limits the cone of rays from O Therefore, Diaphragm = Aperture Stop in this eyepiece Example:Example: EyepieceEyepiece

Entrance pupil is the image of the diaphragm in L1.

E’

-1 µ2 = tan (1/17) O

E’ EnP

9 cm

ФD’ = 1.2 cm 1.2 cm D Example:Example: EyepieceEyepiece

Exit pupil is the image of the aperture stop (diaphragm) in L2.

f2’ = 2 cm E

1 1 1 + = O 3 s' 2 s'= 6cm s' 6 M = − = − = −2 s 3 E Ф2’ = 2 cm

9 cm 1 cm 3 cm

ФD = 1 cm Example:Example: EyepieceEyepiece

E’ f2’ = 2 cm E Ф ’ = 2 cm ФExP’ = 2 cm

O

EE PP E x

3 cm 6 cm E’

ФD = 1 cm ChiefChief RayRay

• for each bundle of rays, the light ray which passes through the center of the aperture stop is the chief ray • after refraction, the chief ray must also pass through the center of the exit and entrance pupils since they are conjugate to the aperture stop

• EnPand ExP are also conjugate planes of the complete system MarginalMarginal RayRay

• Those rays (for a given object point) that pass through the edge of the entrance and exit pupils (and aperture stop). Chief Ray from T RayRay tracingtracing withwith pupilspupils andand stopsstops

•Proceed toward centre of EnP

•Refracted at L1 to pass though centre of AS L •Refracted at L2 to pass (exit) L2 through centre of E P L through centre of ExP L1 Q’’ T P’ P

O’

O

Q T’ Q’ P’’ Marginal Rays from T,O AS EnP •Must proceed towards edges of EnP ExP •Refracted at L1 to pass through edge of AS

•Refracted at L2 to pass (exit) through ExP. ExitExit PupilPupil

Defines the bundle of rays at the image

Q’’ T

O’ α’

O

T’

P’’ FieldField StopStop

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

FS

A θ

d

A = field of view at distance d θ = angular field of view FieldField StopStop

The aperture that controls the field of view by limiting the solid angle formed by chief rays

As seen from the centre of the entrance pupil

(EnP), the field stop (or its image) subtends the smallest angle.

In previous example, the lens L1 is the field stop Entrance Window (E W) Entrance Window (EnnW)

The image of the field stop in all elements preceding it

Defines the lateral dimension of the object that will be viewed

Example: Camera

Where is the entrance window?

AS FS Exit Window (E W) Exit Window (ExxW)

The image of the field stop in all elements following it

Defines the lateral dimension of the image that will be viewed

Example: Camera

Where is the exit window?

AS FS Entrance window and Angular field of view Angular field of view in object plane

angle subtended by entrance window (EnW) at centre of entrance pupil (EnP)

Exit window and Angular field of view Angular field of view in image plane

angle subtended by exit window (ExW) at centre of exit pupil (ExP) Field Stop

That component whose entrance window (EnW) subtends the smallest angle at the centre of the

entrance pupil (EnP) FieldField ofof aa positivepositive thinthin lenslens

FS=EnW ld Im ie ag Eye pupil P Q’ t f e f Eye pupil ec ield bje O α α’

F Q P’

Object point must be within cone Entrance pupil (to left of lens) to be seen AS=ExP (small) α = field of view in object space α’ = field of view in image space FieldField ofof aa positivepositive thinthin lenslens

FS=EnW

P Q’ P

F Q P’

Full cone of rays received Entrance pupil AS=E P Entrance pupil from all points on object x (small) Stops,Stops, pupilspupils andand windowswindows inin anan opticaloptical systemsystem

α α’

EnP EnW AS FS ExP ExW