Stops, Pupils, Field Optics and Camerashosting.astro.cornell.edu/academics/courses...A6525 - Lec. 03...
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Stops, Pupils, Field Optics and Cameras
Astronomy 6525
Lecture 03
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Outline 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
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Stops
A stop is something in the optical system that limits the diameter of the beam of light.
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.
Aperture Stop
PMT
Field Stop
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Etendue: Stops & Throughput
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. A is limited by the aperture stop
Ω is limited by the field stop
Pupils 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 The position of stops can affect system aberrations.
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Stop at mirror – causes aberations
There is now an axis defined by the line from the center of the stop (center of the mirror) to the center of curvature. Off-axis coma
The location of the aperture stop controls aberrations.
Consider a spherical mirror with an aperture stop at mirror
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Stop at center of curvature: control aberrations
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!
Consider a spherical mirror with an aperture stop at the center of curvature
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Pupils and Windows in Optical Systems: I
Entrance pupil – the image of the aperture stop in object space Exit pupil – the image of the aperture stop in image spaceAll the light transmitted by the optical system must pass through the
entrance and exit pupils 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
f
Boyd, page 73
2f 2f 2f 2f
Entrance pupil and aperture stop
Exit pupil
Chief Rays
f
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Pupils and Windows in Optical Systems: 2
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
Boyd, page 73
f
2f 2f 2f 2f
Entrance pupil and aperture stop
Field stop and exit window
Exit pupilEntrance window
f
Chief Rays
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Vignetting
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.
object plane
image plane
entrance pupil
exit pupil1st optical
surfaceLast optical surface
Aperture image in object space A
P
Exit pupil
Bundle of rays that are passed
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A Simple Periscope
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!
2f 2f 2f 2f
entrance window (image of lens 2 by lens 1)
A
lens 1 lens 2object
image 1
image 2
E
C
D
B
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Field Lenses
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
aperture 3' apertures 1' & 2'
lens 1 lens 2lens 3object
image 1
image 2
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relay lens or mirror
primary lens or mirror
Lyot stop (at pupil)
telescope image plane
detector image plane
filter
A Simple Camera: 1
Simple optical/infrared imaging systems will contain four major elements:
1. Relay lens
2. Lyot stop
3. Filters
4. Detector
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A Simple Camera: 2
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.
relay lens or mirror
primary lens or mirror
Lyot stop (at pupil)
telescope image plane
detector image plane
filter
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A Simple Camera: 3
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 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
relay lens or mirror
primary lens or mirror
Lyot stop (at pupil)
telescope image plane
detector image plane
filter
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Matching to the Focal Plane
Matching to the focal plane 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.
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relay lens or mirror
primary lens or mirror
Lyot stop (at pupil)telescope
image plane
detector image plane
filter
io
Dp
Dc
Dc = diameter of relay (camera)Dp = diameter of primary
= but = = # & = # = ## # =or
The Power of Étendue conservation
Looking at our last equation, we have= ## 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.
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Collimating the Beam
Typically one wants a collimated beam to fall upon the filter or dispersive element
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 # is set by # = #/
collimator
primary lens or mirror
Lyot stop (at pupil)
telescope image plane
detector image plane
filter
camera
Diffraction Limited Observations
Starting with the equation that defines the focal plane camera f-number # =
Under diffraction limited observations: = / Let assume we want 2 pixels across the diffraction disk, then the
f-number of the camera is given by
# = 2 And hence, the size of the telescope does not matter
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Example: FORCAST Faint Object Infrared Camera for the Sofia Telescope
5 to 38 μm 2 color facility camera that employs 256 × 256 pixelSi: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
Field of view: 3.2’ × 3.2’For more info see: "First Science
Observations with SOFIA/FORCAST: The FORCAST Mid-infrared Camera,"
Herter et al. 2012, ApJ, 749, L18
Supplemental Material
References
Stop and aberration examples
Field lens example: Photomultiplier tubes (PMT)
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Some References
Telescope Optics: Evaluation and Design Harrie Rutten and Martin van Venrooij
Astronomical Optics Daniel Schroeder
Reflecting Telescope Optics R. N. Wilson
Optics Hecht and Zajac
Principles of Optics Born and Wolf
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Stops and Distortion
The position of a stop can affect distortion.
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Stops and Distortion (cont’d)
Placing the stop symmetrically eliminates distortion (and coma).
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Stops and Vignetting
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. But eyepiece must be large!
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Stop and Field Lens
Field lens 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.
exit pupil
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PMT
Field Stop
Field Optics and the PMT: 1 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:
This is not
photon noise!
Hot spot
Dead spot
Signal
Time
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Field Lenses and the PMT: 2 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.
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).
aperture stop
PMT
field lens
field stopobjective lens
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star at the edge
PMT
star in center
PMT
Field Lenses and the PMT: 3 For example:
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.