1. “Whether they ever find life there or not, I think Jupiter should be considered an enemy planet.” Jack Handy HW2 is due on Wednesday. How’s that going? Weather for Wednesday does not look promising. If cloudy, we will be moving on to Lab 4: making a CMD. This requires all the skills from the first 3 labs.

2. Atmospheric Extinction
The more atmosphere that is between us and our target, the more extinction occurs. This is called atmospheric extinction. Our goal is to approximate observations as if they were above the atmosphere.

3. Through a small telescope, the stars will all dance together.
The atmosphere really consists of many cells, which all move around. This is typically called 'seeing'- the star appears to dance around.
Through a small telescope, the stars will all dance together.

4. Seeing is mostly what the radial profiles in IRAF are measuring
Seeing is mostly what the radial profiles in IRAF are measuring. Therefore, the FWHM is mostly seeing.

5. Through the atmosphere Not through the atmosphere

6. Telescopes!

7. 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

8. 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

9. Chromatic Aberration
Focal length depends on refractive index n of 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.

10. Chromatic Aberration * Only occurs for lenses, not mirrors.
Focal length depends on refractive index n of 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.
* Only occurs for lenses, not mirrors.
* Can be corrected using a 2nd lens (but lose light).

12. 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

13. 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.

14. 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.

15. A compromise for small telescopes

16. 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).

17. Image size If you use an eyepiece, than the magnification
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

18. Image size If you use an eyepiece, than the magnification
of this image is F/Feye
Our 8” telescopes have F=200mm. If you use an eyepiece with F=25mm, what is the magnification?

19. Image size If you use an eyepiece, than the magnification
of this image is F/Feye
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.

20. 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?

21. 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 sizes of CCDs are measured in millimeters!

22. 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.

23. 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.
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.

24. 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.
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 ''/radian

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

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

27. Plate (image) Scale Then plate scale = 1/(f/.D)
Most useful is ''/mm (arcseconds per millimeter).
There are ''/radian.
Plate scale = /(f/.D) if D is in mm.
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 = /(10*200) = 103''/mm (1.72'/mm)

28. 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.

29. What is the FoV of these CCDs?
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 = /(10*200) = 103''/mm (1.72'/mm)
For the SBIG ST-7, the CCD size is 6.9x4.6mm (765x510 (9 micron square) pixels)
For the SBIG ST-9, the CCD size is 13.8x9.2mm (1530x1020 (9 micron square) pixels)
What is the FoV of these CCDs?

30. Field-of-View (FoV) FoV = ps*L
For the Celestron 8” telescopes, we have determined
ps = /(10*200) = 103''/mm (1.72'/mm)
For the SBIG ST-7, the CCD size is 6.9x4.6mm
FoV = 11.9'x7.9'
For the SBIG ST-9, the CCD size is 13.8x9.2mm
FoV = 23.7'x15.8'

31. What is the size of each pixel in arcseconds
What is the size of each pixel in arcseconds? (Angular resolution limit)
For the Celestron 8” telescopes, we have determined
ps = /(10*200) = 103''/mm (1.72'/mm)
For the SBIG ST-7, the CCD size is 6.9x4.6mm (765x510 (9 micron square) pixels)
For the SBIG ST-9, the CCD size is 13.8x9.2mm (1530x1020 (9 micron square) pixels)

32. What is the size of each pixel in arcseconds
What is the size of each pixel in arcseconds? (Angular resolution limit)
For the Celestron 8” telescopes, we have determined
ps = /(10*200) = 103''/mm (1.72'/mm)
For the SBIG ST-7, the CCD size is 6.9x4.6mm (765x510 (9 micron square) pixels)
For the SBIG ST-9, the CCD size is 13.8x9.2mm (1530x1020 (9 micron square) pixels)
Since the pixel sizes are the same, in both cases, the scale is (103''/mm)*(9/1000) = 0.93''/pixel.

33. Of course seeing will make this much worse!
What is the size of each pixel in arcseconds? (Angular resolution limit)
Since the pixel sizes are the same, in both cases, the scale is (103''/mm)*(9/1000) = 0.93''/pixel.
That means that we will not be able to see any features smaller than 0.93'' based on the detector.
Of course seeing will make this much worse!

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

35. What does this phrase mean?
Diffraction limited
What does this phrase mean?

36. 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.

37. We have to go back and think about light.
The pattern seen is called a diffraction pattern.

38. Light entering a telescope will see the edges of the telescope as a wide slit. This will cause light to diffract.

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

41. Back to Angular resolution
q = (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.