, a Controller for Counting Photons, is presented. This new controller uses a totally new clocking architecture and allows to drive the in a special way. Its design is optimized for the driving of at up to 20MHz of pixel rate and fast vertical transfer. Using this controller, the dominant source of noise of at low flux level and high frame rate, the Clock Induced Charges, were reduced to 0.001 – 0.0018 electron/pixel/frame (depending of the electron multiplying gain), making efficient possible. will be deployed in 2009 on the ESO NTT through the 3D-NTT1 project and on the SOAR through the BTFI project.
Electron Multiplying Charge Coupled Devices () allows one to apply a gain to the pixel’s charge before it reaches the noisy output amplifier where the charge-tension conversion is made.2 A gain G in the charge domain affects the effective readout noise by the relation σeff = σreal / G . Sub-electron effective readout noise levels are thus achievable. However, the electron multiplying process is stochastic. This statistical behaviour adds an excess noise factor that reaches a value of 21/2 at high gains.3 The effect on the signal-to-noise ratio ( ) of the system is the same as if the quantum efficiency ( ) of the would be halved.
Some authors proposed offline data processing to lower the excess noise factor induced by the multiplication register.4, 5 However, the only way to overcome the excess noise factor without any a priori knowledge or stability assumption on the signal is to consider the pixel binary by applying a single threshold to the output signal. This way, only one photon per pixel per frame can be counted and the fullof the silicon can be recovered, making the a theoretically perfect device. The highest flux rate that can be observed in this mode will thus depend of the frame rate at which the is operated. However, charges are generated as the is read out. Clock Induced Charges ( ), a well know source of noise affecting all kinds of , were typically measured in the range of 0.1 to 0.01 electron per pixel per frame6–8 (for a 512 x 512 CCD97 frame transfer from E2V Technologies) and quickly dominate the or even the photon flux as the frame rate in increased. Thus, in order to make efficient at low flux with an , the must be reduced to a minimum. Some techniques were proposed to reduce the 8–13 but so far, no commercially available controller was able to implement all of them and get efficient results.
, a Controller for Counting Photons, has been designed with the aim of reducing the generated when an is read out. It is optimized for the driving of at high speed, both vertically and horizontally, but may be used for driving classical as well. Using this controller, levels as low as 0.001 – 0.0018 event per pixel per frame (as opposed to per transfer) were measured on the 512 x 512 CCD97 from E2V Technologies operating in inverted mode (as opposed to non-inverted mode). The impact of this level of on the efficiency of an will be discussed in this article. Data gathered using the controller will also be presented.
Throughout this article,is referred to as being the process by which the output signal of the is thresholded to a single value. Pixels having an output value higher than the threshold are considered having undergone one and only one event. Pixels having an output value lower than the threshold are considered not having undergone an event. This processing is opposed to the analogic processing, where the output signal of the is divided by the mean gain of its EM register to allow more than one event per pixel per frame to be considered. Operating an in mode allows the excess noise factor to be reduced to a value of 1.
2.1 Effect of gain and readout noise
Sub-electron readout noise is not necessarily synonym of efficient. When one takes a look at the histogram of an operated under low flux (left panel of figure 1), he realizes that a significant amount of events may be hidden in the readout noise, below the threshold. The proportion t of events lost due to a cut level, cut (expressed in electrons), may be calculated by means of the following convolution:
where f(n, λ) is the Poissonian probability of having n photons during an integration period under a mean flux of λ (in photon/pixel/frame) and p(x, n, G) is the probability of having x output electrons when n input electrons are present at the input of the EM stage at a gain of G. This probability is defined by
Intuitively, the higher the cut level, the more events lost. Since the cut level is determined by the real readout noise, the factor to optimize will thus be the ratio of the gain over the readout noise. Right panel of figure 1 shows the relation between the ratio and the proportion of counted events. In order to count ∼ 90% of the events, a ratio of 50 must be achieved. For a readout noise of 60 electrons (typical value at 10MHz of pixel rate), a gain of 3000 is necessary. However, one can not increase the gain without limit. Thewill also increase with the gain, as discussed in section 3.2.
The choice of the threshold is important and is resumed by figure 2. Choosing a threshold that is too low yields the counting of pixels whose values above the threshold are due solely to the readout noise, as shown by the left panel of figure 2. However, choosing a threshold that is too high yields the missing of real events (right panel). Given that thelevel achieved with is about 0.001 event per pixel per frame, which represents the lowest count rate that will be seen in an image, a threshold of 5 σ will cause a maximum of one pixel out of a million to have a noise event, while allowing nearly 90% of the events to be counted (left panel of figure 1), depending of the gain/noise ratio. Figure 3 summarizes the fate of photons in mode.
2.2 Coincidence losses
The drawback of theoperation is that two events occurring during a single integration time will be counted as only one. Thus, events will be lost. Poissonian statistics allows one to count g, the proportion of counted photons as a function of λ, the mean number of photons expected during the integration period:
From that equation, in order to be able to count more than 90% of the events, the expected flux should not be higher than 0.2 event per pixel per frame.
2.3: the dominant noise source
Efficientwith an requires low . generated during the vertical transfer is dependant, among other things, of the operation mode of the , namely inverted or non-inverted. As specified in Ref. 8, the amount of generated during the vertical transfer could be lowered by a factor of ∼30 by switching from inverted to non-inverted mode, at the price of an increased dark noise. However, the surface , which is suppressed by the inverted operation, is expected to dominate the bulk by a factor of ∼200 at cryogenic temperatures. Thus, a reduction of a factor of 30 in comes at the price of an increase of hundreds in dark signal.
Figure 4 shows how badly theaffects the of an observation in mode. The left panel shows the simulation of a device in Inverted Mode Operation ( ), while the right panel show the simulation of a device in Non Inverted Mode Operation ( ). The used for the plot is the one measured on a CCD97 at -85◦C (see temperatures considerations in section 3.4) and the used for the plots is calculated from equation 1 in Ref. 8 for a 16×16µm pixel at -85◦C (which is the size of the pixel of the CCD97). From these figures, is clearly the operation mode to favour if one is able to achieve levels in the range of 0.001 event/pixel/image. Very little gain in could be achieved from driving the in even if that would reduce the further, since the noise would be dominated by the dark noise. It is not expected that the driving of the in with would reduce the since the generated during the vertical transfer is very low (see section 3.1 for more details).
This section presents data obtained withusing a scientific grade CCD97 from E2V Technologies operated at a pixel rate of 10MHz in . Event rates presented in the figures represents not only the counted events (events above the threshold), but all the events generated during the read out process, including those buried in the readout noise. In order to achieve this, event rates are calculated by fitting the output histogram with the output probability function (equation 2) of the EM stage. Least square minimization is then made to find the exact parameters of the output signal. This yields the and the mean event level at the same time and most importantly, this allows the exact event rate to be determined for low gain/readout noise ratios (recall figure 1, right panel).
3.1in the vertical transfer
Even when operated in Inverted mode,manages to keep the low during the parallel transfer, as shown by figure 5. The flatness of the plots is something that is expected: the high voltage phase plays no role in the vertical transfer. The small effect of the temperature (left panel) is due to the dark noise that is generated during the read out of the , as this process takes ∼30 milliseconds. Thus, at higher temperatures, more events are seen, even for a 0 second integration. The dark component has been suppressed from the figure in the right panel and curves in this figure should represent only the generated during the vertical transfer.
3.2in the horizontal transfer
The high voltage phase of theis meant to produce impact ionization and multiply the pixel’s charge. Electrons may however be generated even in the absence of an electron at the input of the EM register. This generated in the horizontal register will produce charges appearing at the output of the EM register that may be above the threshold. Dark events generated in the horizontal register will also undergo the EM amplification and appear as photon events at the output. Thus, the amount of events generated in the serial register will depend mostly on . Figure 6 shows these relations. Temperature does not play a significant role in the amount of events generated during the horizontal transfer.
The totalis considered to be the sum of vertical and horizontal . In fact, the vertical presented in figure 5 is computed from the total minus the horizontal . Thus, the data presented at figure 7 correspond to what is actually seen when the image section of the device is read. Even at EM gains as high as 4000, the total measured is less than 0.002 event/pixel/frame. By comparing this figure with figures 5 and 6, one sees immediately that the horizontal is dominating over the vertical one at all gains (> 800). Given its strong gain dependance, the horizontal is mostly due to the high voltage clock.
3.4 Temperature and
It is very tempting to lower the operating temperature of abelow -100◦C in order to reduce the dark noise to a minimum. However, the Charte Transfer Efficiency ( ) in the horizontal register degrades very quickly as the temperature is lowered. The left panel of figure 8 shows the amount of bad events that are seen in an image as a function of both the gain and the temperature. Bad events are defined as being an event (> 5σ) immediately followed (pixel-wise) by another. This kind of event should not occur more than once every event rate, which is only the rate in this case (0.001 – 0.002 event/pixel/image). However, at temperatures below -100◦C, this can account for more than 10% of the events at high gain. This is due to the events that are ”leaking” into neighboring pixels as they are shifted. This phenomenon is shown by the top right panel of figure 8, where the energy distribution of the events is plotted as a function of temperatures. Each line represents the mean energy contained in a pixel at a given offset from the event (the event is at offset 0). At -105◦C, less than 80% of the energy is contained in the pixel at offset 0. at -85◦C, this reaches 95%.
This phenomenon would be hard to correct, since the dispersion of the energy distribution is considerable, as show by the bottom right panel of figure 8. The standard deviation of the value of the neighboring pixels around an event is at least equal to the pixel value. Thus, it would not be possible to use a post-processing based on the mean profile to compensate for the bad. The shape of the profile of an event will hardly be the same as the shape of the mean profile. Thus, at high gain, temperatures below -90◦C should be avoided. Simulations are needed to find the perfect operating temperature, but -85◦C seems to be a good compromise.
3.5 Gain stability
The stability of theis not very critical for operation. However, for amplified operation, it is mandatory to have a good gain stability to ensure photometric continuity across multiple images. Two factors affects the : the high voltage phase and the temperature. From data shown in figure 9, left panel, one sees that in order to have a ±1% stability on the gain, one must have no more than ±0.14◦C temperature variation and ±5mV variation on the high voltage clock (at -85◦C, 43.48V HV clock, which gives a gain of ∼3900). However, at lower gains, the constraint on the relative gain variation per ◦C and per mV relaxes.
The right panel of figure 9 shows data acquired over time, showing a gain variation of ∼ ±1%. The two dotted lines shows the variation that is expected from the temperature stability of the test dewar, which is about 0.3◦C peak-to-peak. From this data alone, one can not tell if the stability of the high voltage clock is sufficient; gain variation due to the high voltage clock variation could be hidden in the temperature variations. However, this data shows that precise temperature control is mandatory if less than 1% variation on the gain is expected, at high gain. Measurements of the high voltage clock with an oscilloscope showed no more that 5mV variation through an image and over hours of operation. In fact, the oscilloscope was the limiting factor in this measurement.
It is of interest to compare the expected efficiency inmode of an driven by with the systems actually in operation. In order to have zero readout noise, GaAs photocathode-based image amplifiers are often placed in front of a fast read-out .14, 15 Photons hitting the photocathode are amplified several hundreds of thousands times and produce a bright spot of a few pixels wide on the imaging . Centering must then be made on these spots to recover the exact location of the incident photon. Coincidence losses on these Image Photon Counting Systems (IPCS) is thus higher than on an in mode: two incident events that are located near from one another will be counted as only one. However, the IPCS do not suffer from and their dark noise is typically an order of magnitude lower than the one of a . The biggest drawback of these systems is their limited Quantum Efficiency ( ): the photocathode itself has a peak of ∼25%. of are the same as classical and can be higher than 80% on a wide spectral range (450-800nm) and peak at >95%.
Figure 10 compares the efficiency of such a photocathode-based system and the CCD97 driven by. The characteristics of each system is given in the caption of the figure. When taking into account all the sources of noise (dark noise, , readout noise) and losses (coincidence, threshold), the left panel of the figure shows that en will outperform an IPCS for incident fluxes higher than 0.022 photon per pixel per second (1 photon per 45 seconds). Thus, for the same pixel size, the gain in observing efficiency will be as shown in the right panel. The observing efficiency is defined as being the time it takes to reach a given at a given flux. The efficiency of the in at low flux could be raised by lowering the frame rate since the noise is dominated by the in this flux regime. operation of the with would not benefit from the lowering of the frame rate as the image would be quickly dominated by dark noise (figure 4).
Tests made withon a CCD97 shows that the can be greatly reduced without having to resort to Non Inverted Mode Operation. The low level of of 0.001 – 0.0018 event/pixel/frame, depending on the gain, allows one to use an in mode and be more efficient than a GaAs IPCS at fluxes higher than ∼0.02 photon/pixel/second.
Analogic (amplified, no threshold) and conventional (no amplification) operation of thewith is also possible: the controller has the possibility to read the two outputs of the . So far, only the CCD97 was tested, but the controller is technically able to drive other as well as classical . is designed to operate the vertical and horizontal clocks at the maximum speed specified by manufacturers, allowing fast read-out. Lower speed operation is also possible, down to a few kHz of pixel rate.
 M. Marcelin, “3D-NTT: A New Instrument for the NTT Based on Versatile Tunable Filter Technology,” in Science Perspectives for 3D Spectroscopy, M. Kissler-Patig, J. R. Walsh, and M. M. Roth, eds., pp. 15–+, 2007.
 P. Jerram, R. Pool, R. Bell, D. Burt, S. Bowring, M. Spencer, M. Hazelwood, I. Moody, N. Catlett, and P. Heyes, “The l3ccd: Low-light imaging without the need for an intensifier,” tech. rep., E2V Technologies, http://www. e2vtechnologies.com/secure/datasheets/l3vision_ccds/4306a_20.pdf, 2001.
 M. Stanford and B. Hadwen, “The noise performance of electron multiplying charge coupled devices,” IEEE Transactions on Electron Devices 1488R, Dec. 2002.
 E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for with ,” MNRAS 386, pp. 2262–2270, June 2008.
 A. G. Basden, C. A. Haniff, and C. D. Mackay, “ strategies with low-light-level ,” MNRAS 345, pp. 985–991, Nov. 2003.
 S. Tulloch, “Monte Carlo Modeling of L3 Detectors in High Time Resolution Applications,” in High Time Resolution Astrophysics: The Universe at Sub-Second Timescales, American Institute of Physics Conference Series 984, pp. 148– 161, Feb. 2008.
 Y. Wen, B. J. Rauscher, R. G. Baker, M. C. Clampin, P. Fochie, S. R. Heap, G. Hilton, P. Jorden, D. Linder, B. Mott, P. Pool, A. Waczynski, and B. Woodgate, “Individual using e2v L3 for low background astronomical spectroscopy,” in High Energy, Optical, and Infrared Detectors for Astronomy II. Edited by Dorn, David A.; Holland, Andrew D.. Proceedings of the SPIE, Volume 6276, pp. 62761H (2006)., Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference 6276, July 2006.
 “Low-light technical note 4 dark signal and clock-induced charge in l3vision ccd sensors,” tech. rep., E2V Technologies, http://www.e2vtechnologies.com/secure/datasheets/l3vision_ccds/ low_light_tn4.pdf, June 2004.
 J. R. Janesick, Scientific charge-coupled devices, Scientific charge-coupled devices, Bellingham, WA: SPIE Optical Engineering Press, 2001, xvi, 906 p. SPIE Press monograph, PM 83. ISBN 0819436984, 2001.
 J.-L. Gach, C. Guillaume, O. Boissin, and C. Cavadore, “First Results of an L3CCD in Photon Counting Mode,” in Scientific Detectors for Astronomy, The Beginning of a New Era, P. Amico, J. W. Beletic, and J. E. Belectic, eds., Astrophysics and Space Science Library 300, pp. 611–614, 2004.
 O. Daigle, J.-L. Gach, C. Guillaume, C. Carignan, P. Balard, and O. Boisin, “L3CCD results in pure photoncounting mode,” in Optical and Infrared Detectors for Astronomy., J. D. Garnett and J. W. Beletic, eds., pp. 219–227, Sept. 2004.
 C. Mackay, A. Basden, and M. Bridgeland, “Astronomical imaging with L3CCDs: detector performance and highspeed controller design,” in Optical and Infrared Detectors for Astronomy. Edited by James D. Garnett and James W. Beletic. Proceedings of the SPIE, Volume 5499, pp. 203-209 (2004)., J. D. Garnett and J. W. Beletic, eds., Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference 5499, pp. 203–209, Sept. 2004.
 S. Tulloch, “L3 Wavefront Sensor Developments at the ING,” in Scientific Detectors for Astronomy 2005, J. E. Beletic, J. W. Beletic, and P. Amico, eds., pp. 303–+, Mar. 2006.
 J.-L. Gach, O. Hernandez, J. Boulesteix, P. Amram, O. Boissin, C. Carignan, O. Garrido, M. Marcelin, G. Ostlin, ¨ H. Plana, and R. Rampazzo, “Fabry-P´erot Observations Using a New GaAs Photon-counting System,” PASP 114, pp. 1043–1050, Sept. 2002.
 O. Hernandez, K. Fathi, C. Carignan, J. Beckman, J. . Gach, P. Balard, P. Amram, J. Boulesteix, R. L. M. Corradi, M. de Denus-Baillargeon, B. Epinat, M. Rela˜no, S. Thibault, and P. Vall´ee, “GHαFaS : Galaxy H-alpha Fabry-Perot System for the WHT,” ArXiv e-prints 805, May 2008. Accepted for publication in PASP.