Download Stops, Pupils, Field Optics and Cameras

A6525 - Lec. 03
Stops, Pupils, Field Optics
and Cameras
Astronomy 6525
Lecture 03
Outline
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Stops
Étendue
Pupils and Windows
Vignetting
The periscope, and field lenses
A simple camera
Supplemental Material
 Stops and aberrations: Examples
 Field lenses and the PMT
Stops, Pupis, etc.
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Stops
A stop is something in the optical system that limits the
Aperture
diameter of the beam of light.
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Aperture Stop: Like an iris in a camera or your
eye. Limits the size of the primary optic.

Field Stop: Limits the size of the field of view –
the amount of “sky” that reaches the detector,
as in the photomultiplier tube below, or for
CCD arrays, it is the physical size of a pixel or
of the array in the focal plane.
Stop
Field Stop
PMT
Stops, Pupis, etc.
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Etendue: Stops & Throughput
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The étendue, or area – solid angle product, AΩ, (also
called the throughput) of an optical system is
determined by the combination of the aperture and
field stops.
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Pupils
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A is limited by the aperture stop
Ω is limited by the field stop
The entrance pupil is the image of the aperture stop through
the optical system from the front
The exit pupil is the image of the aperture stop from the back
Aberrations
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The position of stops can affect system aberrations.
Stops, Pupis, etc.
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Stop at mirror – causes aberations
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Consider a spherical mirror with an aperture stop at mirror
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There is now an axis defined by the line from the center of the
stop (center of the mirror) to the center of curvature.
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The location of the aperture stop controls aberrations.
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Off-axis  coma
Stops, Pupis, etc.
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Stop at center of curvature: control aberrations
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Consider a spherical mirror with an aperture stop at the center of
curvature
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The “on-axis” and “off-axis” beams pass around the center of
curvature and hit the mirror. There is no “optical axis” for a
sphere so there are no “off-axis” rays.
No off-axis aberrations -- just spherical aberration!
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Stops, Pupis, etc.
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Pupils and Windows in Optical Systems: I
2f
2f
2f
2f
f
f
Exit pupil
Chief Rays
Boyd, page 73
Entrance pupil
and aperture stop
Entrance pupil – the image of the aperture stop in object space
Exit pupil – the image of the aperture stop in image space
All the light transmitted by the optical system must pass through the
entrance and exit pupils
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Chief Ray – any ray that passes through the center of the aperture
stop. It will also pass through the center of the entrance and exit
pupils. Different chief rays will correspond to different object and image
points
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Stops, Pupis, etc.
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Pupils and Windows in Optical Systems: 2
2f
Entrance
window
2f
2f
2f
f
f
Exit pupil
Chief
Rays
Entrance pupil
and aperture stop
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Field stop and
exit window
Boyd, page 73
The maximum cone of light defined by the chief rays
corresponding to different object and image points defines the
field stop
 Entrance window – the image of the field stop in object
space
 Exit window – the image of the field stop in image space
Stops, Pupis, etc.
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Vignetting
Aperture image in
object space A
P
object
plane
exit
Last optical pupil
surface
st
entrance 1 optical
surface
pupil
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As we move off-axis, all the rays from a point
in the object plane may not make it through
the optical system.
For example, due to an undersized mirror,
represented by “A”, not all the rays from
point P make it through the entrance pupil.
This phenomena is called vignetting.
Stops, Pupis, etc.
image
plane
Exit
pupil
Bundle of rays
that are passed
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A Simple Periscope
2f
2f
2f
2f
lens 2
lens 1
object
image 2
C
A
E
B
D
entrance window (image
of lens 2 by lens 1)
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image 1
The optical system above transfers an upright, one-to-one image
Either lens 1, or lens 2 may be thought of as the aperture stop, since both
define the same cone as seen from the image point A
 Lens 2 defines the field stop
One can show that the diameter of the entrance window is 1/3 the
diameter of each lens, d, therefore, AE/AD =(d/6)/CD, so that the field of
view (FOV) of the object is given by:
2AE =AD/CD⋅(d/3) = d/2, since CD =4/3 ⋅f, and AD = 2f.
The maximum image size is ½ the size of the lens that is used!
Stops, Pupis, etc.
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Field Lenses
object
lens 1
lens 3
lens 2
aperture 3'
apertures
1' & 2'
image 1
image 2
Inserting lens 3 (which has the same focal length and aperture
of lenses 1 and 2) into the system doubles the field of view
The entrance pupils are all the same size (imaged to locations
1', 2', and 3' above).
The entrance window is now the image of lens 3 (aperture 3')
which has the same diameter as the image.
Lens 3 is called a field lens. When the entrance window
coincides with the object, there is no vignetting, and the
illumination over the whole field of view is uniform
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Stops, Pupis, etc.
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A Simple Camera: 1
primary
lens or
mirror
Lyot
stop (at
pupil)
telescope
image plane
detector
image
plane
filter
relay lens or
mirror
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Simple optical/infrared imaging systems will contain four major
elements:
1. Relay lens
2. Lyot stop
3. Filters
4. Detector
Stops, Pupis, etc.
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primary
lens or
mirror
A Simple Camera: 2
Lyot
stop (at
pupil)
telescope
image plane
detector
image
plane
filter
relay lens or
mirror
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Relay lens – reimages telescope focal plane onto the
detector focal plane. Reimaging f/# chosen to match
physical size of the pixels
Lyot stop – a stop (baffle) on which the secondary (or
primary for a refractor) is imaged by the relay lens. For
thermal IR systems, this stop is a cold baffle that prevents
unwanted thermal radiation (such as from the ground) from
reaching the detector.
Stops, Pupis, etc.
primary
lens or
mirror
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A Simple Camera: 3
telescope
image plane
Lyot
stop (at
pupil)
detector
image
plane
filter
relay lens or
mirror
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Filters limit the range of wavelengths that can reach the detector
so as to obtain the best sensitivity, and photometry or
spectroscopy. Filters are often put at the Lyot stop for a variety of
reasons, including
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Small imperfections in the filter will have a small effect on all pixels – if
in the image plane, get spots in the image!
Resonant filters (e.g. Fabry-Perot etalons) may require near normal
incidence to function properly
Pupils often have the smallest requirements for filter size – especially
good for wide field cameras
Stops, Pupis, etc.
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Matching to the Focal Plane
primary
lens or
mirror
relay lens or
mirror
telescope
image plane
Dc
Lyot
stop (at
pupil)
Dp
detector
image
plane
filter
i
o
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Dc = diameter of relay (camera)
Dp = diameter of primary
Matching to the focal plane
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Suppose the focal plane has 18 micron pixels (xp) and we wish map these to
0.5′′ (θs) on the sky which covers a distance (xt) in the telescope focal plane.
=
=
but
#
=

#
or
=
#
Stops, Pupis, etc.
#
=
&
#
=
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The Power of Étendue conservation
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Looking at our last equation, we have
=
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#
#
=
or
Squaring both sides of the second equation shows that the
étendue of the system is conserved
 Except for certain circumstances (such as broadening of the
beam in optical fibers) étendue conservation defines the
properties of the beam at any element in the optical system
(in terms of AΩ).
Ω
= AΩ
irrespective of any intervening optical
elements!
 To match detector to sky you only need to look at the (final)
camera f-number.
Stops, Pupis, etc.
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primary
lens or
mirror
Collimating the Beam
Lyot
stop (at
pupil)
telescope
image plane
detector
image
plane
filter
collimator
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camera
Typically one wants a collimated beam to fall upon the filter or
dispersive element
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Otherwise there can be aberrations and/or degradation of
spectral resolution
Since étendue is conserved, an angle, , on the sky
corresponds to an angle
=
/ at the filter.
We have as before the camera
Stops, Pupis, etc.
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#
is set by
#
#
=
/
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Diffraction Limited Observations
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Starting with the equation that defines the focal plane camera fnumber
#
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Under diffraction limited observations: = /
Let assume we want 2 pixels across the diffraction disk, then the
f-number of the camera is given by
#
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=
=
2
And hence, the size of the telescope does not matter
Stops, Pupis, etc.
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Example: FORCAST
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Faint Object Infrared Camera for the Sofia Telescope
5 to 38 μm 2 color facility camera that employs 256 × 256 pixel
Si:As, and Si:Sb BIB arrays
Pixel size: 50 µm, wish to fully sample at shortest diffraction
limited wavelength of 2.5 m SOFIA telescope: 15 µm
 For full sampling, we have f#⋅λ/2 = 50 μm
 f# = 2⋅50/15 = 6.7 at the focal plane
 For a 2.5 m telescope, θdiffraction ~ λ/D = λ/10, so at 15 μm,
θdiffraction = 1.5”
 pixel size on sky is 1.5”/2 = 0.75”
Heavily over sampled at the longest wavelengths:
 5 pixels per beam at 38 µm
For more info see: "First Science
Observations with SOFIA/FORCAST:
Field of view: 3.2’ × 3.2’
The FORCAST Mid-infrared Camera,"
Herter et al. 2012, ApJ, 749, L18
Stops, Pupis, etc.
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Supplemental Material
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References
Stop and aberration examples
Field lens example: Photomultiplier tubes (PMT)
Stops, Pupis, etc.
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Some References
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Telescope Optics: Evaluation and Design
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Astronomical Optics
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R. N. Wilson
Optics
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Daniel Schroeder
Reflecting Telescope Optics
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Harrie Rutten and Martin van Venrooij
Hecht and Zajac
Principles of Optics
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Born and Wolf
Stops, Pupis, etc.
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Stops and
Distortion
The position of
a stop can
affect distortion.
Stops, Pupis, etc.
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Stops and
Distortion
(cont’d)
Placing the stop
symmetrically
eliminates distortion
(and coma).
Stops, Pupis, etc.
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Stops and Vignetting
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If your eye is placed next to the eyepiece (E0), you don’t see the
whole field. This FOV is vignetted.
Put your eye at E (the exit pupil) to see the whole field.
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But eyepiece must be large!
Stops, Pupis, etc.
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Stop and Field Lens
exit pupil
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Field lens
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Place a lens at L3 (common focus) which reimages L1 onto L2.
The field lens does not change the intermediate image
In practice, don’t put exactly at focus (dust, etc.)
Now your eye can be next to the eyepiece.
Stops, Pupis, etc.
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Field Optics and the PMT: 1
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Consider a device such as the photomultiplier tube drawn below, that is
designed to accurately measure the flux from faint stars
The star is imaged directly onto the face of the PMT, which at first
glance appears OK. However, due to atmospheric seeing, the star’s
image will wander about on the surface of the PMT
Since the sensitivity of the PMT is not strictly uniform, the output signal
varies:
Field Stop
PMT
Hot spot
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This is not
photon noise!
Signal
Dead spot
Time
Stops, Pupis, etc.
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Field Lenses and the PMT: 2
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To mitigate this problem, one can use a field lens, that makes an
image of the objective, matched in size to fill the aperture stop.
field lens
aperture stop
PMT
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field stop
objective lens
Any light that leaves the objective and hits the field lens will go
through the aperture stop. The PMT does not have an image of
the star, but rather an image of the objective.
So, if the star wanders around in the field stop, the PMT will
remain uniformly illuminated (but from different angles).
Stops, Pupis, etc.
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Field Lenses and the PMT: 3
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For example:
star in center
PMT
star at the edge
PMT
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Note: It is best not to place the field lens exactly in the
focus of the primary, because small imperfections (e.g.
dust, finger prints, scratches, etc…) can scatter a
significant amount of light.
Stops, Pupis, etc.
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