Stops, Pupils, Field Optics and Camerashosting.astro.cornell.edu/academics/courses...A6525 - Lec. 03 1 Stops, Pupils, Field Optics and Cameras Astronomy 6525 Lecture 03 A6525 - Lecture

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Stops, Pupils, Field Optics and Cameras

Astronomy 6525

Lecture 03

A6525 - Lecture 03Stops, Pupis, etc. 2

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


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


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


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


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


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.






filter


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






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.




Lyot stop (at pupil)telescope

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





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


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).


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


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


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.

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Stops, Pupils, Field Optics and Camerashosting.astro.cornell.edu/academics/courses...A6525 - Lec. 03 1 Stops, Pupils, Field Optics and Cameras Astronomy 6525 Lecture 03 A6525 - Lecture