天文觀測 I

1. 天文觀測 I Optical Telescope

2. Telescope • The main purposes of astronomical telescope: • To collect the weak light (photons) from sky. • To map the sky to image • To enhance the angular separations among the astrophysical objects. • The developments of telescopes do not only depend on the telescope developments themselves but also on the improvements of techniques of the analyzers, detectors or even space and computer science.

3. Telescope • Basic equipments of a telescope: • Telescope • Mirrors (reflector), lenses (refractor). • Analyzer • Filter, spectrograph, polarimeter • Detector • Photographic plate, photoelectric device (CCD, PMT, photodiode)

4. Light Collection and Limiting Magnitude • One of the major purposes is to collect the light from astrophysical objects. • The light collection ability is proportional to the area of primary mirror (lens). • Limiting magnitude – the faintest star can be seen • The limiting magnitude for the wide-open, dark-adopted human eyes is +6. • However, if the eyes are well collimated (FOV ~5 arcmin), the limit magnitude can be improved to +8.5 • mlim (human eyes) = +8.5(V) ~200 photons/s

5. Limiting Magnitude • The telescope with eyepiece

6. Limiting Magnitude • For the professional telescope (with detector)

7. Imaging • Basically, the profession astronomers prefer reflecting telescope telescopes rather than refracting ones mainly owing to the chromatic aberration and also the mechanical consideration. • However, for easily drawing, I will use lens instead of mirror to describe the optical properties of telescope.

9. chromatic aberration spherical aberration parabolic mirror spherical mirror

10. Imaging – Geometric Optics • Ray tracing/ matrix method: α x Reference line (Optical axis) + about the reference line:+ x: α: below the reference line: - -

11. Imaging – Geometric Optics M

12. Ray Tracing – Translation α’ x’ α x D

13. Ray Tracing – Lens • For a lens with focal length f and thickness t  0 • (1) Parallel light  concentrated on focus f • (2) Light from focus parallel light f

14. Ray Tracing – Refraction (1)

15. Ray Tracing – Refraction (2)

16. Ray Tracing – Single Lens Focal plane Star light f

17. Telescope • The most important matrix elements in the combined matrix are • m21= f (focal length) • m22=0 • So the x’=fαand independent of x (where the light incident on th elens) • No matter how complex the optical system is, the combined matrix m21=f (effective focal length) and m22=0.

18. Telescope with Eye Piece

19. Telescope with Eye Piece Lens 1 Lens 2 Eye piece • Two lenses with focal lengths of f1 (primary lens) and f2 (eye piece). • The distance between two lenses is D=f1+f2. Star light f1 f2 D

20. Telescope with Eye Piece

21. Off-axis Aberration • The derivations above are only valid for the small incident angle (angle between star light and optical axis) • For the large field of view, higher order terms make off- axis aberration. • Off-axis aberrations: • Coma • Astigmatism • distortion

22. PSR B0540-69 LMC X-1 Extended source?

23. Off-axis aberration

24. Coma

25. Astigmatism

26. Coma

27. Focal Ratio (F-number) • All the images of astrophysical source on the focal plane have finite size even for the point source because • Diffraction • Seeing • Off-axis aberration Diameter: D Focal plane f

28. Focal Ratio (F-number)

29. Focal Ratio (F-number) • f/D = focal ratio, written as f/#, called f-number. • f/3.5  f/D=3.5 • Smaller f/# gives larger image flux • For a faint extended source (e.g. distant galaxy) • Large f/# (small Fd)  D small or f large or both • Small D  small number incident photons • Large f  image spreads out over large area • Need a small f/# • For bright source (e.g. planet) • The flux is not a problem. To resolve the fine structure of the source, large f/# is better.

30. Point-Spread Function (PSF) • Even for a point source, the image on the focal plane would spread out to finite area due to diffraction and seeing. • The extended source would be “smeared”.

31. Point-Spread Function (PSF) Airy disk • Diffraction: size of Airy disk: δθ=1.22λ/D. For D=1m, λ=500nm, δθ=0.1 arcsec • Seeing: due to the disturbance of the atmosphere • Size less than 1 arc second to several arc second, highly dependent on weather and site. Long exposure Short exposure Seeing disk

32. Point-Spread Function (PSF) • IRAF gives 6 functions to model PSF

33. Point-Spread Function (PSF) Lorentz α=2β=1 Lorentz α=1β=2 Lorentz α=1β=1 Gaussian

34. Detector – CCD • CCD -- Charge Coupling Device. • Use photoelectric effect • Unlike the X-ray to measure the energy of photoelectron, the CCD for optical is just “count” the number of photons. In principle 1 photon  1 photoelectron. • Most of photons hit the CCD can be converted into photoelectrons but only a part of them can be collected. However, for the CCD equipped with astronomical telescope, the efficiency (called quantum efficiency (QE)) is very high (>90%), and thus, high sensitivity. • The pixel size can be made very small (~20 μm) so the spatial resolution can be very high.

35. Detector – CCD • The CCDs have been used in LOT

36. CCD Semi conductor: band structure Conducing band (empty) Band gap Eg< 1 eV Valence band (full) Visible light photon energy : 1.7 eV to 3 eV Photoelectron Photon hole Voltage applied

37. Detector – CCD Incident Photon Exposure Photoelectrons Potential well

38. Detector – CCD Reading

39. CCD – Dark Current Thermal electrons

40. CCD – Dark Current

41. CCD – Flat Filed & Bias • The quantum efficiencies (QEs) may different from pixel to pixel and also depend on the wavelength.

42. CCD – Digital Output ADC Analog signal Digitized signal Audio-to-Digital Converter Flat field

43. Data Size of Image

44. Photo Flux Estimation

45. Photo Flux Estimation

46. Optical Spectrograph • For point source: • Photometry : collecting photons and try to concentrate them to focal plane as much as possible • Spectrography: the collected photons have to be reassigned according to the photon wavelength (i.e. spread them out) • Thus to make the optical spectrum of star: • Large telescope is required • Small telescope only for bright sources

47. Optical Spectrograph – Prism • Prism : use the index of refraction as a function of wavelength to separate the light

49. Optical Spectrograph– Prism

50. Optical Spectrograph—Prism