Chapter V
Field stop and aperture stop
视场光阑与孔径光阑
5.1
Field stop and aperture stop 视场光阑与孔径光阑
5.2
Filed of view 视场
5.3
Vignetting and field lens 渐晕与场镜
5.4
Telecentric system 远心系统
5.5
Depth of focus and depth of field 焦深与景深
5.6
Stray light in lenses 透镜中的杂散光
5.1 Field stop and aperture stop
一、Field stop and aperture stop
Aperture stop:
The stop close to lens limits the size of the bundles of rays of axis point. It determines the amount of
light reaching any given point in the image, therefore controls the brightness of image (image plane).
Field stop:
Just front of the focal plane limits the angle at which the incident bundles can get through to this plane
(image plane). It determines the extent of the object or the field. (Field stop is usually made to coincide
with image.)
二、Entrance pupil and exit pupil
EP : The image of aperture stop formed by preceding it.
E ' P : The image of aperture stop formed by following it.
The image of this stop, as formed by the lens is found to lie at the position
PL .
*Since P ' L' is inside the focal plane, its image PL lies in the object space and is virtual and erect,
PL called entrance pupil.
' '
* P L lies in the image space, called exit pupil.
'
'
'
`* P P , LL , E E are pairs of conjugated points. Any ray in the object space directed through one of
these points will after refraction pass through its conjugate point in the image space.
三、Chief
ray
Any ray in the object space that passes through the center of entrance pupil is called chief ray. After
refracting also pass through the center of the exit pupil.*Chief ray is a central ray of oblique rays.
l
n
preliminary design of an optical instrument, must determine which one actually does the limiting?
The entrance pupil of the centric system is the image of the aperture stop formed by all lenses preceding
it.
The exit pupil is the image formed by all lenses following it.
四、Stop between two lenses
Chief ray pass through the entrance pupil, the stop and the exit pupil.
How to determine aperture stop?
五、 Two lenses with no stop
The periphery of any lens in system is a potential stop.
Object at infinity,
Object at A,
M 1 N1 : entrance pupil.
P2' L'2 : entrance pupil
Determination of the aperture stop
The system consists of tow lenses and a stop.
P12'
is the virtual image of the first
lens1 ( L1 )and a stop formed by lens 2 ( L2 )
P0' : Virtual image of the stop P formed by lens 2 .
P0 : Virtual image of the stop formed by lens1 .
P21 : Virtual image of the second lens formed by lens1 .
For all axial object points lying to the left of X,
P0
limits the entrance bundle of rays to the smallest
angle.
P0
constitutes the entrance pupil.
P0'
constitutes the exit pupil.
For all axial object point lying to the right of Z,
P21
is the entrance pupil and
P2'
is the exit pupil.
Nominal aperture stop: The aperture stop of any system may change with a change in the object position.
General rule: the aperture stop of the system is determined by that stop or image of stop which subtends
the smallest angle as seen from the object point.
Telescope and microscope (low power): usually aperture stop is selected at the large-sized objective lens.
5.2 Field of view
一、Field of view
2W: object field and image field
Look out at landscape through a window.
Fig 1: The field of view is limited by the size of window and by the position of the eye. Window is field
stop.
General speaking, field stop is at image plane. ( such as telescope, microscope) The margin of reticle or
film is field stop or frame.
二、Field of a plane mirror
The field of view offered by a plane mirror is very similar to that of a simple window.
'
M ' N : observer’s eye, which constitutes the exit pupil.
MN : The entrance pupil, virtual image of the eye pupil formed by mirror.
Chief rays define the field of view.
The object B and entrance pupil MN are in the object space.
三、How can you define the field of view of a convex mirror?
四、Field of a positive lens
The pupil of eye is an exit pupil and aperture stop.
MN : the image of eye is an entrance pupil.
The field stop in this case is the lens itself.
Object
AB
is in a position inside the primary focal point
L , rays are drawn from B '
F . Through each of three points P 、 E 、
to lens.
Refracted rays are directed through
P ' 、 E ' 、 L , virtual image is located at B ' .
*When converging lens is used as a magnifier, the eye should be placed close to the lens, since this
widens the image-fieldangle.
For visual visional optical instruments, the eye should be placed the exit pupil of optical system, such as
telescopes and microscopes.
五、Entrance window and exit window
Entrance window is the image of field stoop formed by all lenses preceding it.
Exit window is the image of field stoop formed by all lenses following it.
Both entrance and exit window are at infinity.
六、Aperture angle and field angle
Aperture angle
: Aperture angle in the object space. On-axis point subtend to the margin of entrance pupil.
u
u ' : Aperture angle in the image space. On-axis image point subtend to the margin of exit pupil.
Field angle
w: The center of entrance pupil subtended to the margin of entrance window.
w' : The center of exit pupil subtended to the margin of exit window.
5.3 Vignetting and Field lens
一、Vignetting
At small filed of view, the highest and lowest rays passing through the lens, strike the top and bottom
'
of AS , EP , E P .
At greater field of view, entrance upper and lower rays are often limited by the front and rear lens
openings. The failure of an oblique beam is known as vignetting.
The brightness of an image will be gradually decreased darken, when the field of view increased.
Coefficient of vignetting
k
Dw
D
Chief ray (principal ray): passes through the middle of aperture stop from off-axis object point or the
ray that enters the lens midway between the highest and lowest rays of oblique beam.
二、Field lens
(1) In order to reduce the size of following optical system, field lens is usually at the image plane.
l  l'  0    1
Free from
(See chapter I)
S I S II S III C I CII
There are only field curvature
S IV
and distortion
SV
caused by
S IV .
(2)Field lens can be used to change the position of exit pupil to satisfy pupil connection.
Exit pupil of preceding system should be coincide with entrance pupil of following system.
I Galilean telescope
Aperture stop: rim of objective so is entrance pupil
Field stop: eye piece so is exit window
II Kepler telescope
reticle is field stop.
Entrance window and exit window are at infinity. Field angle:
D1

tgw


2 f1'


tgw'  D2

2 f 2'
Exit pupil is close to
F2' .
if eye iris is less than exit pupil, iris is aperture stop.
III Microscope with low magnification
Aperture stop is the rim of objective so is entrance pupil.
Field stop is the rim of reticle.
Entrance window coincides with object plane.
Exit window coincide with image plane (infinity).
5.4 Telecentric system
I object space telecentric system
II image space telecentric system
III double telecentric system
*In most cases, the aperture stop is located somewhere inside the lens, such as photographic cameras.
*eyepieces condenser are exceptions.
一、Telecentric system
1) Telecentric system in the object space:
The aperture stop is at the rear focal plane
F' .
The entering principal ray is parallel to axis.
2) Telecentric system in the image space:
The aperture stop is at the front focus F .
The entering beam come from infinity, and exiting principal ray is parallel to axis.
3)Telecentric system at the both ends:
The aperture stop is at
F1' F2 . F1'
and
F2
are coincided.
The system usually used as inverting system and relay lens.
二、 Contour projector
Contour or profile projector is a instrument for projecting a magnified image of a small mechanical parts
to check its dimensions.
5 10 20 50
The optical system is invariable telecentric, the virtual of a telecentric system is that the size of the
projected image does not alter, if the image is slightly out of focus.
The diameter of the lens aperture must be greater than the diameter of the object.
Condenser lens near the lamp, providing collimated light, must also be larger than the largest object to be
projected.
Final image is generally projected on a ground glass screen, sometimes equipped with Fresnel lens to
brighten up the outer parts of screen.
5.5 Depth of focus and depth of field
一、concept
Assuming the lens is free from all aberrations.
1) There will be a ceitain plane in the object space that is precisely conjugate to the film plane in the
image space. This is known as the focused plane in the object.
2) The observer’s eyes have a limited acuity.
There will be a small amount of tolerable blur in a photograph that observer will be unable to distinguish
it from sharp image.
 a point object may be imaged as a small circle of confusion on the film.
The depth of focus of lens is the distance along the of sharp definition to the plane where the image of a
point source just reaches this circle of confusion.
The depth of field of lens is the corresponding distance of an object point from the focused plane in
object space to the plane where its image reaches the permissible circle of confusion in the film plane.
二、calculation
1. Depth of focus is obviously equal to the product of the diameter
C'
of the permissible circle of
confusion on the film and the F-Number F of the lens.
'  C ' * N  C ' *
f'
D
The distance is the same whether the image is just within or just beyond the
film plane.
C'  ?
how large?
When a picture is viewed by an observer, most people are incapable of distinguishing between a perfect
point and a small circle of confusion that subtends about 2 arc-min.
2. The depth of field
The diagram is based on the fact that everything lying in the focused plane will be imaged sharply on the
film.
C
is the object of
C'
(circle of confusion in image space) or
C
the diameter of the acceptable
circle of confusion in the focused plane.
A1
and
A2
are the far and near object point which is imaged and forms a circle of confusion
1 is far depth of field.
 2 is near depth of field.
1
2
C


2  p  1  p   2

1

Cp
 Cp
; 2 
,
C  2a
C  2a
1 is larger than  2 .( 1 >  2 )
If
2a  c , entrance pupil equal to circle of confusion in object space.
1 becomes infinity.( 1   ， p 2   2 
2ap
)
C  2a
if 2a is reduced, the depth of field 1  2 increased.
2ap
C  2a
2ap
Near object point p 2  p  2a 
C  2a
Far object point p1  p   1 
The diameter of aperture stop controls five separate performance of system.
1) System field of view determined by vignetting.
2) Photometric speed of system or light collecting ability.
3) Depth of focus and depth of field.
4) Amount of aberration degrading image quality.
5) Diffraction based performance of system.
C' .
5.6 stray light in lenses
Stray light does not form any recognizable ghost or flare spots, it is generally referred to as veiling glare.
This has the effect of lowering the overall contrast of the image.
How come (arise)?
1) Arise from mechanical scattering on the inside of the lens barrel and ground rims of the lenses.
2) Arise from interreflection between pairs of lens surfaces.
Since the surface is spherical and polished a series of image of a bright source is formed, even if the
source is outside the picture.
These so called ghost image are often seen in motion picture, mast of the ghost image will be out of
focus, and appears as irregular.
3) Stop of limiting stray light
4) Lens coating untireflection film