6. Optical instrumentation 6. Optical instrumentation
Last chapter
¾
Chromatic Aberration¾ Third-order (Seidel) Optical Aberrations
Spherical aberrations, Coma, Astigmatism, Curvature of Field, DistortionThis chapter
¾
Aperture stop, Entrance pupil, Exit pupil¾ Field stop, Entrance window, Exit window
¾ Depth of field, Depth of focus
¾ prism and dispersion
¾ Camera
¾ Magnifier and eyepiece
¾ Microscope
¾ Telescope
Aperture effects on image
Optical instruments
Stops in Optical Systems Stops in Optical Systems
Larger lens improves the brightness of the image
S S’
Two lenses of the same Two lenses of the same focal length (
focal length (f), but f), but diameter (D) differs diameter (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 lens larger lens Image of S Image of S formed at formed at the same the same place by place by both lenses both lenses
Stops in Optical Systems 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
Stops in Optical Systems Stops in Optical Systems
How much of the object we see is determined by:
How much of the object we see is determined by:
Field of View Field of View
QQ’’
(not seen) (not seen)
Rays from Q do not pass through system Rays from Q do not pass through system
We can only see object points closer to the axis of the system We can only see object points closer to the axis of the system
Thus, the Field of view is limited by the system Thus, the Field of view is limited by the system
Aperture Stop 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
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
Entrance Pupil (E
nP) Entrance Pupil (E
nP)
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
EEnnPP –– defines defines the cone of rays the cone of rays accepted by the accepted by the system
system FF11’’
E’E’E’E’ = E= EnnPP
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”” = = EExxPP
Location of Aperture Stop (AS) 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, Telescope Example, Telescope
eyepiece eyepiece Objective = AS =
Objective = AS = EEnnPP O
Example: Find the AS of the Eyepiece Example: Find the AS of the Eyepiece
EE
EE
9 cm 9 cm
ФФ11 = 1 cm= 1 cm
ФФ22 = 2 cm= 2 cm ff11’’ = 6 cm= 6 cm ff22’’ = 2 cm= 2 cm
ФФASAS= 1 cm= 1 cm
1 cm
1 cm 3 cm3 cm
OO
Diaphragm
Example: Eyepiece Example: Eyepiece
Find 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
find EEnnPP for each (Lens 1, diaphragm, Lens 2)for each (Lens 1, diaphragm, Lens 2)
(a) E(a) EnnPP ofof Lens 1Lens 1 –– no elements to the leftno elements to the left tan tan µµ11 = 1/9= 1/9
defines cone of rays accepted defines cone of rays accepted
9 cm9 cm
1 cm1 cm OO µµ11
Example: Eyepiece Example: Eyepiece
cm s
s
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.
(b) E(b) EnnPP of Diaphragmof Diaphragm –– lens 1 to the leftlens 1 to the left EE
EE
9 cm9 cm 1 cm1 cm
2 . ' =1
−
= s M s
ФФDD’’ = 1.2 cm= 1.2 cm EE’’
EE’’
1.2 cm 1.2 cm
Look at the system Look at the system from behind the slide from behind the slide OO
ff11’’ = 6 cm= 6 cm
Example: Eyepiece Example: Eyepiece
Calculate maximum angle of cone of rays accepted by entrance Calculate maximum angle of cone of rays accepted by entrance pupil of diaphragm
pupil of diaphragm
EE’’
EE’’
OO 0.6 cm0.6 cm
9 + 1.2 cm 9 + 1.2 cm
µµ22
tan tan µµ22 = 0.6/10.2 ≈= 0.6/10.2 ≈ 1/171/17
Example: Eyepiece Example: Eyepiece
(c) E(c) EnnPP of Lens 2of Lens 2 –– 4 cm to the left of lens 14 cm to the left of lens 1
cm s
s 12 '
6 1 '
1 4
1
−
=
= +
4 3 12 ' = =
−
= s M s
ФФ22’’ = 6 cm= 6 cm Look at the system Look at the system from behind the slide from behind the slide
9 cm
9 cm 4 cm4 cm
OO
ФФ22 = 2 cm= 2 cm
Example: Eyepiece Example: Eyepiece
Calculate 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 cm 9 + 12 cm µµ33
tan tan µµ33 = 3/21 = 1/7= 3/21 = 1/7
Example: Eyepiece Example: Eyepiece
8.1 tan µ3 = 1/7
Lens 2
3.4 tan µ2 = 1/17
Diaphragm
6.3 tan µ1 = 1/9
Lens 1
Acceptance cone angle (degrees)
Entrance pupil Component
Thus
Thus µµ22 is the smallest angle is the smallest angle
The diaphragm is the element that limits the cone of rays from O The diaphragm is the element that limits the cone of rays from O Therefore,
Therefore, Diaphragm = Aperture Stop Diaphragm = Aperture Stop in this eyepiecein this eyepiece
Example: Eyepiece Example: Eyepiece
Entrance pupil is the image of the diaphragm in L Entrance pupil is the image of the diaphragm in L11..
9 cm 9 cm
EE’’
EE’’
1.2 cm 1.2 cm
OO
µµ22 = tan= tan-1-1 (1/17)(1/17)
ФФDD’’ = 1.2 cm= 1.2 cm EEnnPP
Example: Eyepiece Example: Eyepiece
Exit pupil is the image of the aperture stop (diaphragm) in L Exit pupil is the image of the aperture stop (diaphragm) in L22..
EE
EE
9 cm 9 cm
ff22’’ = 2 cm= 2 cm
ФФDD = 1 cm= 1 cm
1 cm
1 cm 3 cm3 cm
OO
cm s
s 6 '
2 1 '
1 3
1
=
= +
3 2 6 ' = − = −
−
= s M s
ФФ22’’ = 2 cm= 2 cm
Example: Eyepiece Example: Eyepiece
EE
EE
ff22’’ = 2 cm= 2 cm
ФФDD = 1 cm= 1 cm
3 cm 3 cm
OO
ФФEExxPP’’ = 2 cm= 2 cm E’E’
EE’’
6 cm 6 cm
E E
xxP P
Chief Ray Chief Ray
• 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
• E
nP and E
xP are also conjugate planes
of the complete system
Marginal Ray Marginal Ray
• Those rays (for a given object
point) that pass through the edge of the entrance and exit pupils
(and aperture stop).
Ray tracing with pupils and stops Ray tracing with pupils and stops
PP’’
QQ’’ OO
EEnnPP
Q’’Q’’
P’’P’’
EExxPP PP
QQ ASAS TT
Marginal Rays from T,O Marginal Rays from T,O
•Must proceed towards edges of •Must proceed towards edges of EEnnPP
•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 ExxP.P.
LL11 LL22
Chief Ray from T Chief Ray from T
•Proceed toward centre of •Proceed toward centre of EEnnPP
•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 EExxPP
TT’’ OO’’
Exit Pupil Exit Pupil
Defines the bundle of rays at the image Defines the bundle of rays at the image
OO
Q’’Q’’
P’’P’’
TT
TT’’
OO’’ α’α’
Field Stop Field Stop
That component of the optical system that 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 The aperture that controls the field of view by limiting the solid angle formed by
limiting the solid angle formed by chief rays chief rays As seen from the centre of the entrance pupil As seen from the centre of the entrance pupil ( ( E E
nnP P ), the field stop (or its image) subtends the ), the field stop (or its image) subtends the smallest angle.
smallest angle.
In previous example, the lens L
In previous example, the lens L
11is the field stop is the field stop
Entrance Window (E
nW) Entrance Window (E
nW)
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
xW) Exit Window (E
xW)
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?
Angular field of view in
Angular field of view in object object plane plane angle subtended by entrance window (
angle subtended by entrance window (E E
nnW) W ) at centre of entrance pupil (
at centre of entrance pupil ( E E
nnP P ) )
Angular field of view in
Angular field of view in image image plane plane angle subtended by exit window (
angle subtended by exit window ( E E
xxW W ) at ) at centre of exit pupil (
centre of exit pupil ( E E
xxP P ) )
Exit window and Angular field of view
That component whose
That component whose entrance window entrance window (E ( E
nnW) W ) subtends the smallest angle at the centre of the subtends the smallest angle at the centre of the entrance pupil (
entrance pupil (E E
nnP P ) )
Field Stop
Entrance window and Angular field of view
Field of a positive thin lens Field of a positive thin lens
Eye pupil Eye pupil
AS= AS= E E
xxP 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