1. 1 Astronomical Observational Techniques and Instrumentation RIT Course Number 1060-771 Professor Don Figer Noise

2. 2 Aims for this lecture review how to calculate signal-to-noise ratio describe processes that add noise to a detector signal give examples of how to combat noise

3. 3 Lecture Outline signal-to-noise ratio noise sources –shot noise signal dark current background –thermal noise (Johnson) –kTC –1/f –read noise in the electronics (summation of many contributors) –electronic crosstalk –popcorn noise –pickup/interference how to combat noise, improving SNR

4. 4 Introduction The ability to detect an object in an image is related to the amplitude of the signal and noise (and by contrast in some cases). The signal can be increased by collecting more photons, e.g. –building a bigger lens, –using more efficient optics, –having a more efficient detector. The noise can be reduced by making better electronics.

5. 5 Signal-to-Noise Ratio

6. 6 What is Signal? What is Noise?

7. 7 SNR and Sensitivity Definitions SNR is the ratio of detected signal to uncertainty of the signal measurement. Higher is better. Sensitivity is the flux level that corresponds to a given SNR for a particular system and integration time. Lower is better.

8. 8 SNR and Sensitivity Both SNR and sensitivity depend on –signal brightness of source absorption of intervening material –gas, dust –particles in the atmosphere –optics size of telescope efficiency of detector integration time –noise detector read noise detector dark current background (zodiacal light, sky, telescope, instrument) shot noise from source imperfect calibrations

9. 9 Signal is that part of the measurement which is contributed by the source. Signal: definition

10. 10 Noise - definition Noise is that part of the measurement which is due to sources other than the object of interest. In sensitivity calculations, the “noise” is usually equal to the standard deviation. Random noise adds in quadrature.

11. 11 Sensitivity is the flux level that corresponds to a given SNR. Sensitivity: definition

12. 12 SNR Example These images show synthetic noise added to a real image of a star cluster obtained using Keck/LGSAO. The maximum signal has been normalized to 100 and shot noise has been added. SNR values are for brightest pixel. SNR=10 read noise=0 e  SNR=9 read noise=5 e  SNR=7 read noise=10 e  SNR=4 read noise=20 e  SNR=2 read noise=50 e 

13. 13 Imaging at Night Signal is diminished as light level is reduced. Read noise is very important for object identification in this case.

14. 14 Read Noise vs. Telescope Size

15. 15 Noise and Performance These plots show system performance for NGST (now called JWST). Note that lower noise gives better performance.

16. 16 Tradeoff Example An improvement in SNR due to one detector property can allow one to relax the performance in another property. One last step in making such a trade is to convert improvements into dollars. Joint Dark Energy Mission, Brown 2007, PhD Thesis

17. 17 Noise Sources: Shot Noise in Signal

18. 18 Shot Noise Described Photons arrive discretely, independently, and randomly. Their arrival times are described by Poisson statistics. Poisson statistics tell us that the Root Mean square uncertainty (RMS noise) in the number of photons per time interval is equal to the square root of the mean photon fluence (average number of photons detected per time interval). Said another way, the signal equals the variance. For example, a star is imaged onto a pixel and it produces on average 10 photo-electrons per second and we observe the star for 1 second, then the uncertainty of our measurement of its brightness will be the square root of 10 i.e. 3.2 electrons. This value is the ‘Photon Noise’. Increasing exposure time to 10 seconds will increase the photon noise to 10 electrons (the square root of 100) but at the same time will increase the ‘Signal to Noise ratio’ (SNR). This noise is often called “Shot Noise” because it is analogous to similar noise in electronics. The concept of shot noise was first introduced in 1918 by Walter Schottky who studied fluctuations of current in vacuum tubes. In the absence of other noise sources, the SNR will increase as the square root of the exposure time due to shot noise of the signal.

19. 19 The uncertainty in the source charge count is simply the square root of the collected charge. Note that if this were the only noise source, then S/N would scale as t 1/2. (Also true whenever noise dominated by a steady photon source.) Photon Shot Noise

20. Photon Transfer 20

21. 21 Noise Sources: Shot Noise from Background

22. 22 Background photons come from everything but signal from the object of interest! Note that the noise contribution is simply the uncertainty in the background level due to shot noise. Noise - sources: Noise from Background

23. 23 Total power onto a detector: P =  A  sky  B (T sky )  : transmission of all optics x Q.E.  sky : emissivity of sky A: telescope area  : solid angle subtended by focal plane aperture  : bandwidth B (T sky ): Planck function At 10  m, typically:  ~ 0.2,  ~ 0.1, A  ~ 3x10 -10 m 2 Sr  ~ 1.5 x 10 13 Hz (10  m filter), T ~ 270 K P ~ 10 -9 W or ~ 4 x 10 10  s -1 Atmospheric emission: Blackbody

24. 24 Atmospheric emission: A Note on Solid Angle Background from the sky can be calculated by multiplying the blackbody equation by the area of the sky seen by the detector and the solid angle subtended by the telescope aperture. The A  product is invariant in a system. A telescope A sky detector D x d F  

25. 25 Noise Sources: Shot Noise from Dark Current

26. 26 Shot Noise of Dark Current Charge can also be generated in a pixel either by thermal motion or by the absorption of photons. The two cases are indistinguishable. Dark current can be reduced by cooling. Dark Current vs. Temperature in Silicon

27. 27 Dark Current Mechanism

28. 28 Dark Current in Infrared Materials Dark current is a function of temperature and cutoff wavelength.

29. 29 Noise Sources: Thermal Noise

30. 30 Properties of Johnson Noise due to random thermal motion of electric charge in conductors independent of current flow noise is random at all frequencies (up to ~1/170 fs), i.e. it is “white” For example, a 1 kΩ resistor at a temperature of 300 K has Johnson noise of

31. 31 Bandwidth The equivalent bandwidth of a circuit is described by the illustration below. In the case of an RC circuit, the bandwidth is given by:

32. 32 Noise Sources: kTC Noise

33. 33 kTC Noise due to random thermal motion of electric charge in conductors, just like Johnson noise in resistors act of “resetting” capacitor freezes in random fluctuation of charge can be removed noiselessly through subtraction

34. 34 kTC Noise as Reset Noise

35. 35 Removing Reset Noise with CDS The reset noise adds an upredictable offset voltage to the signal. This offset can be removed by using correlated double sampling.

36. kTC noise in ROIC kTC noise seen in readout due to reset of AC coupling capacitor. 36

37. 37 Noise Sources: 1/f Noise

38. 38 1/f noise spectral density increases for lower frequencies sometimes called “flicker noise” caused by traps, often near surface interfaces occurs in most devices especially pronounced in FETs with small channels

39. 39 Noise in Time Domain white noise 1/f noise

40. 40 Noise in a MOSFET Noise is a combination of thermal and 1/f noise, with the latter dominating at low frequencies.

41. 41 Noise Sources: Popcorn Noise

42. 42 Popcorn Noise This is the minimum noise you can hear in a movie theatre during a tense scene. This is noise produced by traps in FET channels that temporarily change the properties of the channel. The summation of traps is thought to be a potential source of 1/f noise.

43. 43 Popcorn Noise vs Temperature

44. 44 Popcorn Noise vs Gate Voltage

45. 45 Read Noise

46. 46 Read Noise Read noise is produced by all the electronics in a detector system, e.g. –Johnson noise, –1/f noise, –electronic current shot noise, –unstable power supplies It is usually measured as the standard deviation in a sample of multiple reads taken with minimum exposure time and under dark conditions.

47. 47 Read Noise and SNR Example Fig. 13 - Text superposed on a tonal gradient, with superposed read noise. The contrast difference between text and background rises linearly across the image, while the noise stays constant; thus the S/N ratio rises linearly from zero to eight going from left to right.

48. 48 Noise Sources: Electronic Crosstalk

49. 49 signal Φ1Φ1 Φ2Φ2 Φ3Φ3 Φ R1 Φ R2 Φ R3 Electronic Crosstalk

50. 50 Clocking Feedthrough (Crosstalk) read time, 10.18 us wait time for convert, 8.7 us bandwidth ~ 160 kHz

51. Signal Crosstalk 51

52. 52 Noise Sources: Pickup or Interference

53. 53 Pickup or Interference This noise is produced by ambient electromagnetic fields from nearby radiators. Interference doesn’t have to be periodic, but it often is. As an example, consider the image below which shows ~20kHz interference pattern in a small section of a full 2Kx2K detector readout.

54. 54 Improving SNR

55. 55 SNR SNR can be improved by maximizing the numerator and/or minimizing the denominator of the full SNR equation. The choice of what to optimize often comes down to money. That is, some things are expensive to improve and some are not. For instance, the background flux can be reduced in astrophysics applications by launching the system into space (for the cost of billions of dollars….).

56. 56 Improving SNR Optical effects –Throughput: bigger aperture, anti-reflection coatings –Background: low scatter materials, cooling Detector effects –Dark current: high purity material, low surface leakage –Read Noise: multiple sampling, in-pixel digitization, photon-counting –QE: thickness optimization, anti-reflection coatings, depleted Atmospheric effects –Atmospheric absorption: higher altitude –OH emission: OH suppression instruments –Turbulence: adaptive optics –Ultimate “fix” is to go to space!

57. 57 Increasing Integration Time/Coadds Signal increases with exposure time. Noise can also increase, but not by as much. “Coadding” is summing individual exposures – similar to increasing exposure time.

58. 58 slope=1 (read noise limited) slope=1/2 (flux dominated) Read noise vs. Shot Noise Limited Case

59. 59 Fowler Sampling Fowler sampling uses the averages of groups of non- destructive reads at the beginning and end of exposure. This sampling mode generally reduces random noise by the square root of the number of reads. http://www.stsci.edu/hst/wfc3/documents/ISRs/WFC3-2007-12.pdf

60. 60 Improving SNR: multiple sampling

61. 61 Up-the-ramp Sampling In up-the-ramp sampling, the signal is non-destructively read out many times during an exposure. This read mode generally reduces random noise by the square root of the number of reads. The math can be more difficult than for Fowler sampling. This mode is potentially good for removing cosmic rays.

62. 62 Read Noise Limited Case In the read noise limited case, SNR can be improved through multiple non-desctructive reads. However, some amount of exposure time is lost by performing many reads, so there is a tradeoff that depends on how long it takes to do a read.

63. 63 Background Limited Case In the background limited case, it does not help to obtain multiple samples. It just wastes time and reduces exposure time.

64. 64 Sampling Mode Summary: CDS

65. 65 Sampling Mode Summary: Up-the-ramp

66. 66 Sampling Mode Summary: Fowler

67. 67 Other Electronic Techniques bandwidth limiting filters increasing gain (before noise is injected) reducing the unit cell capacitance (thereby increasing in-pixel gain).