1. “It is important that students bring a certain ragamuffin, barefoot, irreverence to their studies; they are not here to worship what is know, but to question it.” Jacob Chanowski HW2 is due tonight. How’s that going? Tonight: Lab 4: making a CMD. This requires all the skills from the first 3 labs.

2. Review from Monday F-ratio: f/ = F/D plate scale (ps)= 1/(f/.D)
There are ''/radian.
ps= /(f/.D) if D is in mm.
Field-of-view: FoV = ps*L where L is the length of the detector (CCD) on that axis. So FoV is given in two dimensions.
Pixel size: FoV*pixel size (in the same units!)
Telescope Angular resolution: q = (l/D) where l and D must be in the same units and the answer is then in radians.

3. 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.

4. Angular resolution
q = (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.

5. Telescope angular resolution
 = 2.5x10-4 (/D) for in nm and D in meters.
What is the angular resolution of the Celestron 8” (200mm) telescopes for light in the middle of the visible range (550nm)?

6. Telescope angular resolution
 = 2.5x10-4 (/D) for in nm and D in meters.
What is the angular resolution of the Celestron 8” (200mm) telescopes for light in the middle of the visible range (550nm)?
0.69”
(Smaller than our pixel size, so no problem!)

7. Telescope angular resolution
 = 2.5x10-4 (/D) for in nm and D in meters.
What is the angular resolution of the Keck 10 meter telescopes for light in the middle of the visible range (550nm)?

8. Telescope angular resolution
 = 2.5x10-4 (/D) for in nm and D in meters.
What is the angular resolution of the Keck 10 meter telescopes for light in the middle of the visible range (550nm)?
0.014”

9. Telescope angular resolution
 = 2.5x10-4 (/D) for in nm and D in meters.
What is the angular resolution of the Lovell 76 meter telescope at Jodrell Bank? It is a radio telescope that mostly observes at 21cm.

10. Telescope angular resolution
 = 2.5x10-4 (/D) for in nm and D in meters.
What is the angular resolution of the Lovell 76 meter telescope at Jodrell Bank? It is a radio telescope that mostly observes at 21cm.
21cm = 21x107nm.
783.6” = 13'
This is why radio telescopes have to be in arrays.

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

12. But the image is blurred out around that ideal 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)

13. Contributors to the PSF: 1) Diffraction
Contributors to the PSF: 1) Diffraction -large telescopes or short wavelengths 2) Aberrations of mirrors or lenses -Minimized by careful design 3) Atmospheric turbulence -Good ground sites, or go to space 4) Pointing errors -Negligible

14. Contributors to the PSF: 1) Diffraction 2) Aberrations of mirrors or lenses 3) Atmospheric turbulence 4) 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.

15. Light Gathering Power (LGP)
Telescopes are essentially light buckets that collect incoming photons and focus them onto a detector.
The larger the telescope, the more area to collect light.

16. Light Gathering Power (LGP)
The ability of a telescope to capture light.
This depends on the diameter of the telescope:
LGP ~ pD2/4

17. 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.
LGP D12 =
LGP D22

18. Light Gathering Power (LGP)
How much more LGP does the 16” have compared to the 8”?
LGP D12 =
LGP D22

19. Light Gathering Power (LGP)
How much more LGP does the 16” have compared to the 8”?
LGP D12 =
LGP D22
4 times more.

20. Light Gathering Power (LGP)
How much more LGP does the Keck 10m have compared to the Baker 0.4m?
LGP D12 =
LGP D22

21. Light Gathering Power (LGP)
How much more LGP does the Keck 10m have compared to the Baker 0.4m?
LGP D12 =
LGP D22
625 times more.

22. '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'.

23. 'Fast' versus 'Slow' telescopes
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.

24. 'Fast' versus 'Slow' telescopes
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?

25. 'Fast' versus 'Slow' telescopes
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?
Resolution.

26. 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).

27. *Decreasing the focal length (larger f/) gives larger FoV.
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.

28. Brief side trip on errors

29. Most of what we know is derived by making measurements.
Errors
Most of what we know is derived by making measurements.
However, it is never possible to measure anything exactly (eventually Heisenberg's uncertainty principle would bite you!).
So when you measure something, you have to say how precisely you have measured it.

30. The idea of error
A measurement may be made of a quantity which has an accepted value (such as c). However, this value itself is just measured and has an associated error. They are just errors measured by other people. You cannot translate your value to theirs.

31. Correcting our magnitudes to 'standard' values is an example.
The idea of error
Correcting our magnitudes to 'standard' values is an example.
In truth, the standard magnitudes have published errors. I have just not included these (though to be fully correct, they should be).

32. The idea of error
Errors are also not 'blunders' or experimental mishaps which can be fixed.
If a telescope is bumped during an exposure resulting in two sets of stars, the image is simply deleted and redone. If it's not caught at the time, then this datum may be discarded.

33. The idea of error
Errors occur for all measurements. It is impossible to know exactly how far off a measurement is. Otherwise, the measurements would just be 'adjusted' to the proper value. But this is not possible.

34. The classification of error
Errors occur in two types: systematic and random.

35. The classification of error
Systematic errors are errors which shift all measurements in the same way. Things like improper equipment calibration, thicker atmosphere than anticipated, etc.
An example would be switching from instrumental magnitudes to a 'standard' system. Our instrument shifts all our measurements one way and so we work out a correction.

36. The classification of error
Random errors displace measurements in an arbitrary direction (they scatter measurements about a value). They cannot be eliminated, but usually can be reduced (by making multiple measurements).
Each measurement of a star includes random fluctuations caused by seeing, CCD noise, random sky noise, etc.

37. The classification of error
Random errors displace measurements in an arbitrary direction (they scatter measurements about a value). They cannot be eliminated, but usually can be reduced (by making multiple measurements).
Example: If a particular isotope has a decay rate of 1,000 decays per minute, then a 5 minute measurement will count, on average, 5,000 decays. However, very few individual measurements would be 5,000.

38. The classification of error
Random errors: One way to help is to make many measurements.
Example: If a particular isotope has a decay rate of 1,000 decays per minute, then a 5 minute measurement will count, on average, 5,000 decays. The first measurement may have been 4,723. If this is the only measurement, then we would produce an incorrect decay rate.

39. The classification of error
Mean (average) value.

40. The classification of error
Probability of obtaining result x:
Where <x> is the most probable value and s is the standard deviation, which is the width of the distribution.
This is a Gaussian distribution and for large numbers, this usually describes the distribution of values.

41. The classification of error
Probability of obtaining result x:
= s
The formula is the standard deviation, which is the error.

42. The classification of error
Standard deviation.
The standard deviation means that if you take a measurement, 68% of the time, it will be within one standard deviation (1s) of the average.
Of course this means that 32% of the measurements are outside of 1s.

44. The classification of error
Standard deviation.
If you make some measurements and determine that s=25. Then 2s=50, 3s=75, and ns=n*25.
However, the meaning is different.
1s contains 68% of the measurements, but
2s contains 95% of the measurements,
3s contains 99.7% of the measurements, and
4s contains % of the measurements.

45. The classification of error
Confidence levels:
If you make some measurements and determine that s=25. Then 2s=50, 3s=75, and ns=n*25.
However, the meaning is different.
1s contains 68% of the measurements, but
2s contains 95% of the measurements,
3s contains 99.7% of the measurements, and
4s contains % of the measurements.
These can sometimes be called confidence levels. So if someone says they have a 95% confidence level, that means 2s.
But it could also be a different type of test (like false-alarm probability) too!