1. HgCdTe Noise from µHz to kHz Roger Smith, Gustavo Rahmer, David Hale, Elliott Koch Caltech Detectors for Astronomy Garching, 2009-10-14

2. HgCdTe Noise from µHz to kHz 2 Outline Motivation: WFS (ms), Imaging (minutes), Spectroscopy (Hours) Optimal pixel timing for multiple sampling. Spatial variation in noise. Why it matters. How it changes! Noise vs frame rate examples from WFS and Spectroscopy. Potential sources of noise floor. Noise spectra: 1E-4 Hz < Nyquist < 1E+4 Hz Aliasing effects. Effect of processing on noise spectrum …bandpass shaping

3. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 3 Conclusion In theory, there is no difference between theory and practice, but, in practice, there is. Jan L. A. van de Snepscheut or Yogi Berra ? Measure it the way you will use it.

4. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 4 Noise studies in progress We are particularly interested in the noise floor where many samples are combined. At the extremes of exposure time, are the causes for the noise floor the same ? ApplicationsExp. tWindowProcessing Wavefront Sensingmillisec4x4Extreme Fowler ImagingminutesFull frameModerate Fowler Spectroscopyhours300x500Extreme, least squares fit

5. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 5 First, optimize pixel timing 10 µs/pixel is standard. We had 3µs dwell. We reduced overheads to 2.16µs, and overlapped this with signal settling. For 3µs dwell, pixel time is halved: sample twice as often with same noise bandwidth. For Astronomical Research Cameras Inc. 8ch IR video card

6. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 6 Settle and Dwell Time Optimization 6 Will Signal-to-Noise ratio be improved more by: – increasing settling time above 2µs, or – adding more dwell time (noise BW limiting), or – coadding more frames ? More coadds are better than more settling. More dwell is better at high frequency, with most gain by 4us; slightly worse at low frequency. 6µs/pixel is good compromise. Small window for fast readout

7. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 7 Conversion gains used in previous slide 7 For constant flux slopes scale accurately with dwell time, And to first order conversion gain from photon transfer scales correctly, and is does not decrease with settling time. Deviations from perfect scaling are believed to be due to uncorrected non- linearity. This is TBC but we note that slower SUR at same flux = more signal and the sign of the non-linearity effect is correct.

8. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 8 Possible causes of noise floor ? Dark current I dark < 0.002 e-/s for 1.7µm @120K, < 0.004 e-/s for 2.5µm @80K. Mux glow ? I glow < 0.0034 e-/read for 5µs/pixel. Keep sample rate << 1.7s/read, so I glow << I dark 1/f noise in detector material. RTS noise in mux (on small number of pixels) Bias variations Stabilize biases; remove common mode with ref pixels. Thermal variations Good temperature control (~0.8e-/mK) Constant cadence clocking for uniform self heating. Could use metal trace on mux to track its temperature better then apply correction based on per pixel temperature coefficient.

9. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 9 Dark signal … Is this mux glow? 9 For SUR at 2s/sample, I dark = 0.008 e-/s For small fast windows, 0.0034e-/read at 6µs/pixel Frame number Time (s)

10. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 10 Self-heating masquerades as mux glow As window size is reduced same power is concentrated in smaller area so temperature rises: dark current increases with number of reads rather like mux glow. 8x8 window After160,000 frame SUR in 75s 32x32 window After 10,000 frame SUR in 75s 8x8 Hot spot in next readout

11. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 11 Dark current -- still subdominant Shot noise only a a marginal contributor even in 3 hour exposure for best devices Shot noise <3 e- in 1hr, <5e- in 3hr. Dark current image (fm SUR fits after skipping any transients at frame start) Dark current histogram

12. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 12 Spatial variation in noise Noise histogram has high tail. Why worry?.. Wavefront sensing: don’t want small guide window to land on a bad pixel. Spectrocopy: don’t want key spectral feature on a bad pixel. RTS noise in mux ?

13. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 13 Raw pixel values vs Time (no coadding) Noisiest pixels exhibit “Random Telegraph Signal” a bimodal noise distribution due to single traps in or channel near buffer FET. Number of such traps and distance from channel produce a spectrum of amplitudes. Characteristic time constants vary widely. All silicon transistors suffer from this to some extent. In big transistors many traps are in play and it accounts for 1/f noise. In small transistors one or a few traps produce RTS noise. Cooling increases the time constant. Slow traps become so slow they become invisible, but fast traps which would average to zero now move into signal passband. Quiet pixel Excess noise is due to RTS in mux Raw value minus 1st frame (ADU) Frame number Noisy pixel

14. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 14 Histogram of RTS noise for the nasty case of two traps about the same size Time series

15. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 15 Same after coadd and subtract (100 coadds) For time series on previous slide Differencing turns steps into spikes. Coadding helps but noise is still Better to reject outliers than try to average them away

16. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 16 Spatial distribution of Noise different processing of same data in each case Fowler 1Fowler 16Fowler 256

17. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 17 Noise vs exposure time Same SUR data in both cases: For CDS use samples n sec apart. For CDS sum or n sec, then subtract from sum of next n sec. Maximum number of fowler samples at 0.5Hz fitting into each exposure time, for this data point fowler 50. Fowler 5

18. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 18 Power Spectral Distribution From SUR data used in previous slide

19. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 19 Noise Spectra for 10,000s time series 2nd plot: Show several pixels. Do they differ in shape as well as amplitude? Show spectrum for noisy pixels, Average spectrum for core of noise histogram.

20. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 20 Raw, CDS with alternate samples SUR at 0.5Hz: CDS frames synthesized from alternate samples

21. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 21 Raw, CDS with alternate samples SUR at 0.5Hz: CDS frames synthesized every 2nd sample.

22. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 22 Raw, CDS with alternate samples

23. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 23 Raw, CDS with alternate samples

24. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 24 PSD for CDS and Fowler 100

25. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 25 Noise vs frame rate for small windows, deep sampling Turn up due to dark current + mux glow Latest low noise 2.5µm recipe Frame rate after fowler sampling Noise floor due to 1/f noise. Kink Fixed by excluding hot pixels not present in smaller windows

26. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 26 Power spectra vs Sample rate 26 1/f noise causes floor at low frequencies If noise power spectrum is a property of the detector, why does the 1/f corner and white noise floor change with SUR sample rate (window size) ? Nyquist ~ 2.1kHz 1/f corner ~ 3.5Hz

27. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 27 PSD, sampling at 0.5Hz Frequency range for previous slide Nyquist =0.25 Hz 1/f corner = 0.0035Hz Isn’t the power spectrum a property of the detector? How can it change with sample rate ?

28. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 28 Aliasing “101” Power Density Sample rate/2 Sample rate Sample rate*3/2 BW ~ 1/pixel time ~ 1/ frame time

29. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 29 Aliasing “101” Power Density Sample rate/2 Sample rate Sample rate*3/2

30. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 30 Simulated Aliasing of 1/f + white noise White noise above nyquist shows up in baseband due to aliasing. Nyquist frequency No aliasing Elevated noise floor due to aliases With alias Without alias

31. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 31 Aliasing of pure 1/f noise Even pure 1/f looks like it has a white noise floor after aliasing. Nyquist frequency No aliasing Flattening due to aliases With aliasing Without

32. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 32 Why does 1/f corner move ? Noise BW ~ 2/pixel_T –For CCD, sample rate = 1/pixel_T –For mulitplexed detector, sample rate = 1/frame_T ……most of the noise BW is above Nyquist. White noise floor is raised by aliasing …illustrated in next slides … This lowers the 1/f corner. This explains how fowler sampling can still work even when one expects 1/f noise to dominate.

33. Garching, 2009-10-14HgCdTe Noise from µHz to kHz 33 Conclusion In theory, there is no difference between theory and practice, but, in practice, there is. Jan L. A. van de Snepscheut or Yogi Berra ? Measure it the way you will use it. PS: Data comparing noise spectra for 1.7µm and 2.5µm materials will be submitted on the web site.