HgCdTe Noise from µHz to kHz

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

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

3. Noise studies in progress HgCdTe Noise from µHz to kHz • 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 ?

4. First, optimize pixel timing For Astronomical Research Cameras Inc. 8ch IR video card HgCdTe Noise from µHz to kHz • 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.

5. Settle and Dwell Time Optimization 6 HgCdTe Noise from µHz to kHz • 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 ? Small window for fast readout 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.

6. Possible causes of noise floor ? HgCdTe Noise from µHz to kHz • Dark current Idark < 0.002 e-/s for 1.7µm @120K, < 0.004 e-/s for 2.5µm @80K. • Mux glow ? Iglow < 0.0034 e-/read for 5µs/pixel. Keep sample rate << 1.7s/read, so Iglow << Idark • 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.

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

8. Self-heating masquerades as mux glow HgCdTe Noise from µHz to kHz 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 8x8 Hot spot in next readout 32x32 window After 10,000 frame SUR in 75s

9. Spatial variation in noise HgCdTe Noise from µHz to kHz 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 ?

10. Raw pixel values vs Time (no coadding) HgCdTe Noise from µHz to kHz • 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 Raw value minus 1st frame (ADU) Noisy pixel Frame number Excess noise is due to RTS in mux

11. Histogram of RTS noisefor the nasty case of two traps about the same size HgCdTe Noise from µHz to kHz Time series

12. Same after coadd and subtract (100 coadds) HgCdTe Noise from µHz to kHz • 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

13. Spatial distribution of Noisedifferent processing of same data in each case HgCdTe Noise from µHz to kHz Fowler 1 Fowler 16 Fowler 256

14. Noise vs exposure time HgCdTe Noise from µHz to kHz 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. Fowler 5 Maximum number of fowler samples at 0.5Hz fitting into each exposure time, for this data point fowler 50.

15. Power Spectral Distribution HgCdTe Noise from µHz to kHz From SUR data used in previous slide

16. Raw, CDS with alternate samples HgCdTe Noise from µHz to kHz SUR at 0.5Hz: CDS frames synthesized from alternate samples

17. Raw, CDS with alternate samples HgCdTe Noise from µHz to kHz SUR at 0.5Hz: CDS frames synthesized every 2nd sample.

18. Raw, CDS with alternate samples HgCdTe Noise from µHz to kHz

19. Raw, CDS with alternate samples HgCdTe Noise from µHz to kHz

20. PSD for CDS and Fowler 100 HgCdTe Noise from µHz to kHz

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

22. Power spectra vs Sample rate 26 HgCdTe Noise from µHz to kHz 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) ? 1/f noise causes floor at low frequencies Nyquist ~ 2.1kHz 1/f corner ~ 3.5Hz

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

24. Aliasing “101” HgCdTe Noise from µHz to kHz Power Density ~ 1/ frame time Sample rate/2 Sample rate Sample rate*3/2 BW ~ 1/pixel time

25. Aliasing “101” HgCdTe Noise from µHz to kHz Power Density Sample rate/2 Sample rate Sample rate*3/2

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

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

28. Why does 1/f corner move ? HgCdTe Noise from µHz to kHz • 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.

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