Telescopes!. Telescopes Telescopes perform key functions: – Collect light (EM radiation) from...

Telescopes!

Telescopes•Telescopes perform key functions:–Collect light (EM radiation) from astronomical sources.–Record information on that light:•Position•Arrival time•Energy

•Different telescopes and detector combinations measure some or all of this information (and can be optimized for specific wavelengths/energies).

Positional information -structure of galaxies

-motions of stars (distances)

Energy information: A spectrum (or color information using multiple filters).

We get compositions.

If we use time information, we get a lightcurve.- Study transits (exoplanets)- Binary stars (masses & distances)- Asteroseismology (everything!)

Positional information -structure of galaxies-motions of stars (distances)

Energy information: A spectrum (or color information using multiple filters).- Composition

If we use time information, we get a lightcurve.- Study transits (exoplanets)- Binary stars (masses & distances)- Asteroseismology (everything!)

What we wish to know dictates the telescope/instrument used

Lenses– Lens brings parallel rays to focus at point

on the focal plane.– Rays parallel to optical axis converge at

prime focus, P– Ray passing along optical axis is undeviated– Distance CP is Focal Length, F

Refraction – The change in direction of travel of a light ray as it passes from one transparent material into another. Index of refraction = n = Speed of light in a vacuum___ Speed of light in some material Material n Vacuum 1.0 Air 1.0003 Water 1.33 Glass ~1.5 Diamond ~2.4 A light ray is refracted toward the normal (direction perpendicular to the boundary) in passing from low to high n.

Snell’s Law

For air, n1 ~ 1, so that:

(1) sin 1 = n2 sin 2

or sin 1 = n2 sin 2

so sin 2 = sin 1 / n2

and, generally sin 2 1/n

Now, n = n(), with n greater for shorter . Thus, 2 is smaller for violet light and larger for red light,

so violet light is refracted the most and red light the least… i.e., white light is spread or DISPERSED into its component colors. Dispersion – Decomposition of light into its component colors by differential refraction. Note that for a slab of plate glass, this dispersion will be exactly undone when the various colors of light pass back out into air from the glass. In fact, a piece of flat glass can only translate the beam of white light (shift to a parallel path).

Chromatic Aberration

– Focal length depends on refractive index n of lens material:

– Where r1 and r2 are the radii of curvature of lens surfaces.

– Refractive index depends on l: n=n(l)– dn/dl measures how strongly n changes with

l• Dispersion of the lens material



– n is typically higher for blue light over red light.

– F is then shorter for blue light than red light

• Gives colored edges to images.



– n is typically higher for blue light over red light.

– F is then shorter for blue light than red light

• Gives colored edges to images.* Only occurs for lenses, not mirrors.* Can be corrected using a 2nd lens (but lose light).

Mirrors

– For a spherical mirror:• C is center of curvature• CM is radius of curvature, R

– For this mirror, P is prime focus, PM is the focal length, F

Mirrors

– For a spherical mirror, light rays closer to the optical axis focus at a different location than those farther away from the optical axis.

Mirrors

– For a spherical mirror, light rays closer to the optical axis focus at a different location than those farther away from the optical axis.

– The cure is a parabolic mirror.

Image size– Source has angular diameter q– Rays from 'top edge' of object are parallel

to each other when they reach the telescope, at angle q to the optical axis.

– Image diameter y=F tan q– y~Fq for small q

The same for a spherical mirror (parabolic mirror is very close to the same too).

Image size– Source has angular diameter q– Rays from 'top edge' of object are parallel

to each other when they reach the telescope, at angle q to the optical axis.

– Image diameter y=F tan q– y~Fq for small q

If you use an eyepiece,

than the magnification

of this image is F/Feye

Image sizeIf you use an eyepiece,



Our 8” telescopes have F=200mm. If you use an eyepiece with F=25mm, what is the magnification?

Image sizeIf you use an eyepiece,



Our 8” telescopes have F=200mm. If you use an eyepiece with F=25mm, what is the magnification?200/25 = 8. The object will appear 8 times larger.

Plate (image) Scale

•A more useful measure is the plate scale. This tells us the size in mm of an object of angular size q.

•Why would we want to know this?

Plate (image) Scale

•A more useful measure is the plate scale. This tells us the size in mm of an object of angular size q.

•Why would we want to know this?•Because the size of CCDs are measured in millimeters!

Plate (image) Scale•A more useful measure is the plate scale. This tells us the size in mm of an object of angular size q.

•First we have to define the f-ratio: f/ = F/D which is the focal length over the diameter of the mirror.


•F-ratio: f/ = F/D

•Then plate scale = 1/(f/.D) •(one over the f-ratio times the diameter of the telescope mirror) in radians per whatever D is measured in.


•F-ratio: f/ = F/D

•Then plate scale = 1/(f/.D) •(one over the f-ratio times the diameter of the telescope mirror) in radians per whatever D is measured in.

•Most useful is ''/mm (arcseconds per millimeter).•There are 206265''/radian

Plate (image) Scale

•Then plate scale = 1/(f/.D) •Most useful is ''/mm (arcseconds per millimeter).•There are 206265''/radian.

•Plate scale = 206265/(f/.D) if D is in mm.

Plate (image) Scale•Then plate scale = 1/(f/.D) •Most useful is ''/mm (arcseconds per millimeter).•There are 206265''/radian.


•For the Celestron 8” (200mm) telescopes we use, f/10 (that is the f-ratio = 10, I don't know why we write it that way!). What is the plate scale?

Plate (image) Scale•Then plate scale = 1/(f/.D) •Most useful is ''/mm (arcseconds per millimeter).•There are 206265''/radian.


•For the Celestron 8” (200mm) telescopes we use, f/10 (that is the f-ratio = 10, I don't know why we write it that way!). What is the plate scale?

•ps = 206265/(10*200) = 103''/mm (1.72'/mm)

Field-of-View (FoV)

•The field-of-view is how much of the sky appears in each image.

•FoV = ps*L where L is the length of the detector (CCD) on that axis. So FoV is given in two dimensions.

Field-of-View (FoV)

•The field-of-view is how much of the sky appears in each image.•FoV = ps*L where L is the length of the detector (CCD) on that axis. So FoV is given in two dimensions.•For the Celestron 8” telescopes, we have determined•ps = 206265/(10*200) = 103''/mm (1.72'/mm)

•For the SBIG ST-I, the CCD size is 4.8x3.6mm (648x486 7.4 micron square pixels)

• What is the FoV of these CCDs?

What is the size of each pixel in arcseconds? (Angular resolution limit)

•For the Celestron 8” telescopes, we have determined•ps = 206265/(10*200) = 103''/mm (1.72'/mm)


•For the Celestron 8” telescopes, we have determined•ps = 206265/(10*200) = 103''/mm (1.72'/mm)•Since the pixel sizes are the same, in both cases, the scale is (103''/mm)*(7.4/1000) = 0.76''/pixel.


•Since the pixel sizes are the same, in both cases, the scale is (103''/mm)*(7.4/1000) = 0.76''/pixel.

•That means that we will not be able to see any features smaller than 0.76'' based on the detector.

•Of course seeing will make this much worse!

Angular resolution

•The ability to separate two objects. We have seen there is a hard limit based on the CCD. There is also a limit based on the telescope

mirror.

•sin(q) = 1.220 (l/D) for small angles•q = 1.220 (l/D) where l and D must be in the same units and the answer is then in radians.

Angular resolution

•q = 1.220 (l/D) where l and D must be in the same units and the answer is then in radians.

•So the resolution depends on the size of the telescope and the wavelength used.

Angular resolution

•q = 1.220 (l/D) where l and D must be in the same units and the answer is then in radians.

•A more useful formula is•q = 2.5x10-4 (l/D) for l in nm and D in

meters.

Diffraction limited

•What does this phrase mean?

We have to go back and think about light.

•Light can act as a particle or a wave.

But when put through slits, it will

interfere with itself like a set of

waves.

We have to go back and think about light.

•The pattern seen is called a

diffraction pattern.

Light entering a telescope will see the edges of the telescope as a wide slit.

This will cause light to diffract.

Which takes us back to the definition of the angular resolution of a telescope.

Back to diffraction limited.Ideally, a telescope would focus light

to a perfect point.

But the image is blurred out around that ideal point.

The function that describes this spread is called the instrument's Point Spread Function (PSF)

Contributors to the PSF:1) Diffraction

-large telescopes or short wavelengths2) Aberrations of mirrors or lenses

-Minimized by careful design3) Atmospheric turbulence

-Good ground sites, or go to space4) Pointing errors

-Negligible

Contributors to the PSF:1) Diffraction2) Aberrations of mirrors or lenses3) Atmospheric turbulence4) Pointing errors

If diffraction is the major contributor to the PSF, then the telescope is said to be diffraction limited. Which is the best that can be done.

Light Gathering Power (LGP)

•Telescopes are essentially light buckets that collect incoming (falling?) photons and focus

them onto a detector.

•The larger the telescope, the more area to collect light.


•The ability of a telescope to capture light.

•This depends on the diameter of the telescope:•LGP ~ pD2/4

Light Gathering Power (LGP)•This depends on the diameter of the telescope:

• LGP ~ pD2/4

•Phrased as a comparison: Compare to another telescope, or a 1m telescope.

• LGP1 D12

• ------------ = ----------

• LGP2 D22


•How much more LGP does the 16” have compared to the 8”?

•LGP1 D12

•------------ = ----------

•LGP2 D22

Light Gathering Power (LGP)•How much more LGP does the 16” have

compared to the 8”?•LGP1 D1

2

•------------ = ----------

•LGP2 D22

•4 times more.

Light Gathering Power (LGP)•How much more LGP does the Keck 10m

have compared to the Baker 0.4m?•LGP1 D1

2

•------------ = ----------

•LGP2 D22

Light Gathering Power (LGP)•How much more LGP does the Keck 10m

have compared to the Baker 0.4m?•LGP1 D1

2

•------------ = ----------

•LGP2 D22

•625 times more.

'Fast' versus 'Slow' telescopes

•Telescopes focus light to an image size. If the image size is larger, then the light is spread out farther. If the image is smaller, then the

light is concentrated.

•Telescopes that concentrate light on fewer pixels are called 'fast' while those that spread

light out are called 'slow'.


•Telescopes that concentrate light on fewer pixels are called 'fast' while those that spread

light out are called 'slow'.

•This depends on the f-ratio. So f/4 telescopes are considered quite fast, while something

like f/16 would be considered slow.




•“Fast” comes at a price. What's that price?




•“Fast” comes at a price. What's that price?•Resolution.

Put it all together:

*Increasing the focal length (larger f/#) gives larger image scale- can study smaller features.-But decreases speed, so need to expose longer.

-Can compensate with increased mirror diameter, so more LGP.

-Increased mirror diameter increases atmospheric aberration.

-Can compensate using space telescopes or adaptive optics (not yet discussed).

Put it all together:

Decreasing the focal length (larger f/#) gives larger FoV.-But increases speed, so gathers light quickly.

-Good for smaller telescopes.-But, lose detail of small features.

- can become pixelated if pixel size is larger than seeing.

Telescope types

•2 basic types:• -Refractors use lenses.• -Reflectors use mirrors.

Refracting telescopes

Original design (Galileo)

Advantages:1) Direct design- light enters the front and leaves the back.2) Whole diameter is gathering light (no obstructions).

Refracting telescopes

Original design (Galileo)

Disadvantages:1) Large piece of perfect glass required.2) Lens can only be supported at the edges.3) Larger telescope = thicker lens = more diffraction and light loss.4) Chromatic aberration.

Largest refractor is Yerkes 1m, built in 1897.

Reflecting telescopesAdvantages: Uses a mirror1) Do not need thick glass, so large size is not a problem.2) Mirror can be supported everywhere, so weight is not a problem.3) Minimal chromatic aberration

Problem: the light is inside the tube!

Reflecting telescopesProblem: the light is inside the tube!

The solution is put a second mirror inside the telescope to move the light to a convenient location.

Newtonian: Moves light to the side. Developed by Newton in 1688. Uses parabolic primary mirror and flat secondary mirror.

But the image is distorted by the secondary mirror.


The secondary blocks some of the light! What if you have a 10 meter telescope with a 1 meter secondary. What percent of light reaches the detector?


The secondary blocks some of the light! What if you have a 10 meter telescope with a 1 meter secondary. What percent of light reaches the detector?It goes as the area: So the light blocked is 12/102=1/100 or 1 part in 100, which means that 99% of the light reaches the detector. Not a problem!

Back to telescopes:Telescope types

•2 basic types:• -Refractors use lenses. Not commonly used anymore.• -Reflectors use mirrors. Most common type.

Reflecting telescopesNewtonian/Dobsonian: Use secondary mirror to get light out at the top of the telescope.

Reflecting telescopesCassegrain telescope. The light reflects off a central mirror and out the back of the telescope. Requires a hole in the primary mirror. Extra advantage: changing the shape of the secondary mirror changes the focal length, so can get quite long focal length for high spatial resolution. Or short focal length for faster telescopes.

Reflecting telescopesCassegrain telescope variations. Ritchey-Chretien variant: Uses hyperbolic mirrors. Reduces off-axis distortions. Tend to be less expensive.

Reflecting telescopesCassegrain telescope variations. Schmidt-Cassegrain. Uses a corrector to effect the light path. Then the primary mirror can be spherical (cheaper to make). Also uses a closed tube and no need for a secondary support system.

Reflecting telescopesPrime focus: It is also possible to put the detector at prime focus.

Advantages: Fewer lenses.Shorter f/# so faster optics.Wider FoV.

Disadvantages: Still blocking light (not a problem these days).

Here is a picture of a spectrograph at cassegrain focus.Notice the huge size of the instrument!

This is partially responsible for modified mounts.

Telescope mounts with light paths:Nasmyth

With this mount, the light comes out the side axis of the mount.Advantages: 1) 2 sides! Can easily switch between 2 instruments. 2) Weight of the instruments is on the mount brace, not the telescope.3) Instruments do not move.

Disadvantage: Needs a field rotator.

Telescope mounts with light paths:Coude

With this mount, the light comes out the side axis of the mount and is fed down into a room.Advantages: 1) Extremely long focal length.2) Instruments can be in a room where they are stable.

Telescope mounts with light paths:Coude

Fiber-fed instruments.

Today, many instruments are supplied light from

the telescope via optical fiber. This way the

instrument can be in a different, controlled,

room.

Telescope mounts.

Telescope mounts.

Alt-Az mount. Flat stand.

Advantages: Easy to make. Simple design.

Disadvantages: Both axes have to move to follow objects.Fields rotate during the night.

Telescope mounts.

Fork Mount: Simple, but weight is not even, so bottom of fork must be very strong.

German Equatorial Mount: Telescope is nicely balanced, but requires offsetting weights, which means it weighs twice as much. Also will not look at zenith and has to switch sides at some point.

Telescope mounts.

Yoke mount: Nicely balanced, but cannot look at the pole.

Horseshoe mount: Can look at the pole.

Telescope mounts.Cross-axis equatorial mounts are fairly common.

Still requires large counterweights. Telescope may need to switch sides

during observations.

Instrumentation

•What goes on the telescope?

Imagers• These days, these are all CCDs.

CCD Imagers: Many specialty systems. Large arrays (usually called mosaics).

If you move the telescope a tiny amount between images, then you can assemble an image without gaps.This technique is called dithering and is also useful for

imperfections which flats do not fix well.

CCD Imagers: Many specialty systems. Large arrays (usually called mosaics).Here is the one flying on Kepler.

3-CCD imagers

On to spectroscopy!

•Recall that light acts like a particle AND a wave.

Telescopes!. Telescopes Telescopes perform key functions: – Collect light (EM radiation) from...

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