REVIEW OF SCIENTIFIC INSTRUMENTS 85, 075103 (2014)
A new clocking method for a charge coupled device Rika Umezu,1 Shunji Kitamoto,1,a),b) and Hiroshi Murakami2,a) 1 Department of Physics, College of Science, Rikkyo University, 3-34-1, Nishi-Ikebukuro, Toshima–ku, Tokyo 171–8501, Japan 2 Department of Information Science, Faculty of Liberal Arts, Tohoku Gakuin University, 2-1-1 Tenjinzawa, Izumi-ku, Sendai, Miyagi 981-3193, Japan
(Received 11 January 2014; accepted 16 June 2014; published online 9 July 2014) We propose and demonstrate a new clocking method for a charge-coupled device (CCD). When a CCD is used for a photon counting detector of X-rays, its weak point is a limitation of its counting rate, because high counting rate makes non-negligible pile-up of photons. In astronomical usage, this pile-up is especially severe for an observation of a bright point-like object. One typical idea to reduce the pile-up is a parallel sum (P-sum) mode. This mode completely loses one-dimensional information. Our new clocking method, panning mode, provides complementary properties between the normal mode and the P-sum mode. We performed a simple simulation in order to investigate a pile-up probability and compared the simulated result and actual obtained event rates. Using this simulation and the experimental results, we compared the pile-up tolerance of various clocking modes including our new method and also compared their other characteristics. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4885468] I. INTRODUCTION
A charge-coupled device (CCD) can be used as a photon counting detector. Especially, in X-ray astronomy, it is now a standard focal plane imager of X-ray telescopes.1–3 Its energy resolution has been achieved almost theoretical limit as a Si detector.3–5 The image resolution is ultimately limited by its pixel size, which is an order of ∼ 10 μm, although, in most cases of X-ray observatories, the point-spread functions (PSFs) of their telescopes are larger than the pixel size. In a usual observation, a big merit of the CCD is that it can obtain both the energy and position of each photon together. But its one weak-point is that it takes substantial time to read-out one full image. Relating this long read-out time, the pile-up problem is a severe drawback of the CCD. Suppose an observation of a point-like object with a telescope. The telescope focuses all photons into a certain small area on its focal plane. High quality telescopes make it small and we can have a high Signal to Noise ratio of the image. If we use a CCD as a focal plane detector, we have a problem for the observation of a bright source. Since a CCD is an integration type device,6 if more than one photon enter into one pixel during an exposure time, we cannot know the original photon’s energy, and even the number of photons. To make matters worse, the electrons produced by a photon sometimes spread out over two or more neighboring pixels. Thus if more than one photon enter even into neighboring pixels, we cannot know the original photons energies. We call them “pile-up”.7 So far, some methods, in order to avoid the pile-up, have been proposed and actually applied for the bright source observations. Any methods have a merit and a demerit. Here
a) Also at Research Center for Measurement in Advanced Science, Rikkyo
University, 3-34-1, Nishi-Ikebukuro, Toshima-ku, Tokyo 171–8501, Japan.
b) Electronic mail: [email protected]
0034-6748/2014/85(7)/075103/5/$30.00
we propose a new method, which complements previous methods. II. PREVIOUS METHODS
Although there are various types of CCDs, in the X-ray astronomy, a frame transfer type is widely used. Here we mainly discuss on the frame transfer CCD. The frame transfer CCD has an image array and a storage array. The storage array is covered to avoid the entrance of photons and the image array is exposed to photons. After certain time (an exposure time), the integrated signals in the image array are moved to the storage array by vertical clockings. The signals in the storage array are read out in turn from a read-out node. During read-out of the signals in the storage array, the image array is exposed to photons. Since this frame transfer CCD does not require a shutter mechanism and there are no loss of the exposure time, it is preferred in the astronomical usage. In the “Normal mode,” all the pixels in the storage array are read out, in turns. Read-out of one full image needs substantial time. In the case of a frame transfer CCD, an exposure time is assigned to be longer than the read-out time of all the pixels, in order to avoid a loss of the observation time. The clocking speed of the charge transfer is limited by a noise tolerance, and it is roughly 100 kHz. Consequently, the exposure time becomes typically more than several seconds.3–5 If the observing object is faint enough to neglect a probability of the pile-up and the observer does not require a fast timing information, this normal mode has no problem. When we need a full image but the probability of the pileup is not negligible, then the “Burst mode” is used. For the names of various modes, we follow that used for the Suzaku, XIS, see “The Suzaku Technical Description”.15 Note that different names are also used for the other instruments, see “The Chandra Proposers’ Observatory Guide”,16 “XMMNewton: A Technical Description”,17 and “Swift Technical
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Description”.18 In the burst mode, the readout cycle begins by rapidly transferring all charge in the image array to a single CCD row, leaving the image array in an unexposed state. Photons are accumulated in the image array for a specified time, which may be very short compared the time required for readout, and then transferred rapidly to the storage array. The image in the storage array is then readout. Since the exposure time can be short, this mode reduces the probability of pile-up, but the fraction of time that photons are being collected, and thus the total number of photons detected, are also reduced. Another option is the “Window mode.” In this mode, by giving up an observation of a full image, the read-out region is limited to be a fraction of the full image. If we set the limited region as one fourth of the full image, every one fourth of the exposure time of the normal mode, the limited region in the image array is transferred to the end of the storage array. The pixels of the limited array (one fourth of the image) are read out taking one fourth of the exposure time of the normal mode. This mode makes the actual time of the imaging and read-out cycle short, and consequently the probability of the pile-up becomes small, although the observable image area becomes small. For an observation of a point-like object, this mode is useful, by setting the limited region to cover the image of the source. The limitation of the window area is restricted by the PSF of the X-ray telescope. If the limited region is smaller than the PSF, we lose a part of the photons from the object. If the PSF of the telescope is not well, such as Suzaku XRT,8 the actual useful window area is restricted to be one fourth or one eighth of the full image. Also for the observation of an extended- or a multiple-source object, the available window area is restricted. For an observation of a very bright point-like object, both the burst and window mode can be used, in order to avoid the pile-up. More drastic idea is the parallel sum mode (“P-sum mode”), where we lose one-dimensional information. In this mode, the image array is continuously vertically transferred and a given number of rows are summed-up in one row at the end of the image array. The summed-up row is finally transferred to the serial register. The serial register is readout normally. Thus the number of the rows, obtained during one exposure time of the normal mode, is roughly same to the actual number of the rows, because the one exposure time of the normal mode is usually adjusted to be roughly same to the read-out time of a full image. If the number of the summedup raw is determined to be the size of the PSF, the photons, from the point-like object detected during the vertical transfer of the number of the summed-up rows, are accumulated in one row. Thus the effective exposure time for a row is this transfer time, which can be much shorter than the normal exposure and the pile-up probability becomes much small. Also in the above situation, the sequence of the rows corresponds to the time, when the photons are detected on the CCD. Therefore, effectively short-term resolution can be achieved. This P-sum mode has good pile-up tolerance but completely lose one-dimensional information of the image. Binning of the pixels does not help to avoid the pile-up. A vertical binning can shorten the read-out time of the image. Two-line binning makes the number of the read-out half and
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thus the exposure time can be half, but the photons coming into final binned pixel is doubled. Consequently, the pile-up tolerance does not change. Of course, the resolution of the image becomes worse.
III. NEW CLOCKING METHOD: PANNING MODE
We propose a new clocking method, “Panning mode.” In the case of the normal mode of a frame transfer CCD, the signals in the storage array are normally clocked and are read out during an exposure. In the panning mode, besides the normal read out of the storage array, a certain number of the vertical transfer, which is fixed in advance, is performed in the image array during one exposure. Consequently, the image is panned and the time interval, during which a focused image of a point-like object is exposing a certain pixel, is shortened. Some rows must be transferred out from the image array during panning. The signal in the rows is accumulated at the bottom of the image array, or at the bottom of the storage array. Therefore, some part of the image was lost. This mode does not require any special gate. In this mode, the obtained image is two dimensional, but the angular resolution of one dimension along the vertical transfer becomes worse. Demonstration of the clockings, including the Panning mode, is performed in our laboratory, using our handmade CCD driver, which can change the clocking mode flexibly. The CCD is a full frame transfer type with 512×512 array. In Figure 1, sample images obtained by the Normal mode, the Binning mode, the P-sum mode, and the Panning mode are shown. The images are simulating an observation of multiple point sources, by using a mask with nine pinholes mimicking
FIG. 1. Demonstrations of images obtained by various modes using our handmade CCD driver. (a) Normal, (b)vertical two-line- binning, (c) P-sum, and (d) panning mode with 128 lines. Since the direction of the charge transfer is downward, the 128 lines of the bottom of the image were lost.
Before discussing pile-up, we have to define “event.” We assume that a size of electron-cloud produced by one Xray is smaller than the size of one pixel. Except for a special case, for example, an escape photon makes a signal in a non-neighboring pixel, the signals of one soft X-ray should produce one of the following patterns; a single pixel, two neighboring pixels, three pixels which make “L” shape, or 2 × 2 pixels.9 We call these patterns as “possible-patterns.” In the case of the X-ray astronomy, the pixel size is typically 24 μm4, 10 and this is much larger than the size of the electroncloud produced by a soft X-ray.11, 12 If an event pattern is not categorized into any of the above possible-patterns, we can consider that the event is not produced by one soft X-ray. It may be produced by a gamma ray or a charged particle or by multiple X-rays (i.e., pile-up event). This categorization of events pattern can be used for the background rejection by extracting only the possible-patterns.13, 14 Thus we call here the event showing one of the possible patterns, as an “apparent good event.” Some pile-up events, however, may still show one of the possible-patterns and may be recognized to be an “apparent good event.” In a real experiment, we cannot recognize such pile-up events with one of the possible-patterns, but in a computer simulation we can distinguish them. Thus we define a “true good event,” which shows one of the possible-pattern and is not really a pile-up event. By defining these events, we performed a Monte Carlo simulation for an estimation of pile-up probability, which is defined as, 1-(the number of the “true good events”)/(the number of detected photons). In the case of an experiment, we have to use the number of the “apparent good events,” instead of the “true good events.” The probability strongly depends on the appearance probability of the possible-patterns. For just an example of the pile-up estimation, we assume the probabilities of the various shapes of the possible-patterns in advance, as 77.49%, 22.11%, 0.30%, and 0.10% , for single, double, L-shape and 2×2 pixels, respectively. These values were determined from the data obtained by our laboratory experiments, where we used 5.9 keV X-rays from a 55 Fe isotope. Also we do not consider any background, such as the gamma ray and charged particles. For the simulation, we first give a mean number of detected photons, λ, by one pixel during one exposure. Each pixel detects the number of photons, which is determined by a Poisson statistics with the mean number of λ. The signals make one of the possible-patterns, according to the given probability. We fix the original amount of the charge produced by one photon. The fraction of the charge in each pixel, in the case of split-events, is determined by a random number. By examining all pixels, we can have one image. Then we extract “events” by analyzing the image. We check all the events whether they are “apparent good events” or not,
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IV. SIMULATION OF PILE-UP
Apparent Good Events True Good Events 0
a star cluster. The number of vertical transfer in the Panning mode, shown in Figure 1, is 128 lines. We can recognize that the panning model makes the image worse, but it still shows a two dimensional image.
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(Number of Detected Events)/ (Number of Detected Photons)
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0.01 0.1 Mean Number of Detected Photons, λ (Counts/exposure/pixel)
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FIG. 2. The ratios of the “apparent good events” and of the “true good events” to the number of detected photons, as a function of the mean number of photons in one pixel, λ, counts/pixel/exposure. Simulations for the “apparent good events” rates and the “true good events” rates are plotted by the black and red lines. The circles show data obtained by the experiment. The vertical axis shows ratio of the measured “apparent good events” divided by an estimated number of the detected photons. The horizontal axis shows the estimated mean number of photons in one pixel, λ, counts/pixel/exposure (see text).
and also whether they are the “true good event” or not. In the simulation, the only parameter is just the mean number of detected photons, λ photons exposure−1 pixel−1 . Figure 2 shows the results of the simulation. The horizontal axis is just the mean number of detected photons, λ photons exposure−1 pixel−1 . The black and red lines show fractions of the number of the “apparent good events” and of the “true good events,” to the number of the detected photons, respectively. In this case, if the mean number of detected photons, λ, is less than 0.01 counts exposure−1 pixel−1 , the pile-up events are less than 10%. As the λ becomes large, the ratio of the “apparent good events” becomes small. Furthermore, the fraction of the “true good event” in the “apparent good events” becomes small. The apparent good event is the event, which shows one of the possible patterns. As the λ increases, the patterns of some events are overlapped. Some become other of the possible patterns. Thus the rate of the apparent good event decreases. Some pile-up events may still show one of the possible patterns. Since the true good events does not include such pile-up events, the number of the true good events decreases more rapidly. The justification of the simulation is confirmed by experimental data. The CCD, which is clocking by the “Normal mode,” is exposed to X-rays from a 55 Fe isotope. By changing an exposure time, we can take data with various mean number of detected photons, λ. We assume that obtained data with the shortest exposure time has no pile-up, and assume that extracted event number is the number of detected photons. Then we estimate the mean number of detected photons, λ, of the shortest exposure time. The λ of other exposure is assumed to scale with the exposure time. The “apparent good events” are extracted from the obtained images and the ratio of the number of “apparent good events” to the expected number of detected photons are plotted in Figure 2. We obtained reasonable agreement between the simulation and the experiments.
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In this simulation and the experiment described here, we assumed the uniform distribution of the X-rays on the CCD. When we consider a pile-up probability using a particular PSF, we first estimate a local mean number of the detected photons in certain part of the PSF. Then we can estimate a local pile-up probability. V. COMPARISON BETWEEN PANNING MODE AND OTHER MODES
The tolerance of the pile-up of the various modes can be estimated by considering only the mean number of detected photons, λ, which changes depending on the modes. In the observation of a point source with the window mode, the actual exposure time of the window mode is reduced by the number −1 . Thus the λ becomes of the window (Nwindow ) to be Nwindow −1 Nwindow and Nwindow times bright source can be observed with no loss of the photons. In the Burst mode, the exposure time is −1 actually reduced. If the exposure time is reduced to be Nburst −1 of the normal mode, then the λ becomes Nburst , and bright sources can be observed. But the total number of photons also −1 . becomes Nburst In the P-sum mode, the pile-up tolerance depends on the size of the PSF, i.e., the performance of the telescope. For example, if the size of the PSF (for example, half power diameter) is Npsf -pixels, and the number of line of the image array is Nline , the image size detected by P-sum mode during one exposure time of the Normal mode becomes Nline × Npsf . Therefore, the λ becomes ∼ up tolerance becomes
Nline , Npsf
Nline ×Npsf Npsf ×Npsf
. Consequently, the pile-
where we assume that the read-out
time of the Nlines in the P-sum mode is the same to the exposure time of the Normal mode. In the case of Suzaku XIS, Nline is 1024, and Npsf is ∼100 pixel. Thus roughly 10 times bright-point-like sources can be observed. But we lose onedimensional information of the image. If the telescope has better imaging capability, the improvement of the pile-up tolerance is much higher. In the case of the panning mode, the image size of the point source can be arbitrary changed between the size of the PSF and that of the P-sum mode. Therefore, the pile-up tolerance is between those of the normal and of the P-sum mode. Hence the information loss of the one dimension is also between those of the normal and of the P-sum mode.
Properties of the various modes are summarized in Table I. The time resolution of the Normal mode is just the exposure time, which is usually assigned to be longer than the read-out time of all the pixels. In the Burst mode, although the exposure time is limited to be much shorter than the readout time, the one sequence of this mode is usually adjusted to be the same to the exposure time of the Normal mode, because one sequence of the bust mode should be longer than the read-out time of all the pixels. Therefore, the time resolution, determined by the image sampling rate, is the same to that of the Normal mode. The time resolution of the window mode is Nwindow times shortened. In the P-sum mode, the time resolution may depend on Npsf . However, by adding some rows, the width of which is broader than the size of PSF (Npsf ), into one row, the time resolution can be shortened to be −1 Nlines of the Normal mode for a point source. In the Panning mode, the time resolution for a point-like object also depends on Npsf . Since we do not intend to add any rows, Npsf works as a window function on the time sequence of the panning. If the number of the vertical transfer in one exposure, Npan , is smaller than Npsf , the time resolution is not improved from the normal mode. But if Npan is larger than Npsf , the image can be divided into Npan /Npsf , which is qualitatively a sequence of the time. Thus the time resolution becomes Npsf /Npan , of the normal mode. Since Npan can be selected from 1 to Nlines , the time resolution of the Panning mode is 1∼ Npsf /Nline of the Normal mode. The extraction of the “possible-patterns” can help the background rejection, in all the modes other than the P-sum mode. The signal patterns obtained by the P-sum mode are not same to the “possible-patterns,” since some lines are summed-up and the information of the vertical pattern is lost, although similar pattern selection with one dimensional information can be possible. The image size becomes large in the Panning mode, but it is between the P-sum mode and Normal mode. Other modes do not change the image size. The degradation of the energy resolution by the panning may be worried. However, this mode does not require any special clocking, and clocking of the image area during an exposure is performed in the P-sum mode. Since no degradation of the energy resolution of the P-sum mode is reported, we can also expect no degradation in the Panning mode.
TABLE I. Characteristics of various modes, for the observation of point-like objects.
Pile-up tolerance Field of view The number of photons Time resolution Pattern selection Image size
Normal
Window
Burst
P-sum
Panning
1 1 1 1 d Npsf × Npsf
Nwindow 1/Nwindow 1 1/Nwindow Npsf × Npsf
Nburst 1 1/Nburst 1a Npsf × Npsf
Nline /Npsf 1 1 1/Nline b e Nline × Npsf
1∼ Nline /Npsf (Nline − Npan )/Nline 1 1∼ Npsf /Nline c Npsf × Npsf ∼ Nline × Npsf
a
We assume that one image is obtained every exposure time of the Normal mode. We assume that the number of the summed-up rows is larger than the size of PSF (Npsf ). c Depending on the Npan , the time resolution changes from 1 to Npsf /Nline of the normal mode (see text). b
d
The pattern selection of the event, using the possible patterns, can be applied as a background rejection. The pattern selection cannot be simply applied, but a different pattern selection might be possible, by defining another possible patterns. e
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VI. CONCLUSION
New clocking method, panning mode, is presented and demonstrated with our handmade CCD driver. This mode has the moderate pile-up tolerance by victimizing onedimensional resolution. The properties of the various clocking modes are discussed. The panning mode provides complementary properties between the normal mode and the P-sum mode. ACKNOWLEDGMENTS
This work was supported by JSPS KAKENHI Grant No. 21740191. This work was also partially supported by a research fund from the Research Center for Measurement in Advanced Science of Rikkyo University. 1 K.
Mitsuda et al., Publ. Astron. Soc. Jpn. 59, S1 (2007). C. Weisskopf, B. Brinkman, C. Canizares et al., Publ. Astron. Soc. Pac. 114, 1 (2002). 3 L. Struder et al., Astron. Astrophys. 365, L18 (2001). 4 K. Koyama et al., Publ. Astron. Soc. Jpn. 59, S23 (2007). 2 M.
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P. Garmire, M. W. Bautz, P. G. Ford, J. A. Nousek, G. R. Ricker, Jr., Proc. SPIE 4851, 28–44 (2003). 6 K. Hashimotodani, T. Toneri, S. Kitamoto, H. Tsunemi, K. Hayashida, E. Miyata, K. Katayama, T. Kohmura, R. Asakura, K. Koyama, K. Yamamoto, K. Miyaguchi, and H. Suzuki, Rev. Sci. Instrum. 69, 392–395 (1998). 7 S. Yamada, H. Uchiyama, T. Dotani et al., Publ. Astron. Soc. Jpn. 64, 53 (2012). 8 P. J. Serlemitsos, Y. Soong, K.-W. Chan et al., Publ. Astron. Soc. Jpn. 59, S9 (2007). 9 B. E. Burke, R. W. Mountain, D. C. Harrison, M. W. Bautz, J. P. Doty, G. R. Ticker, and P. J. Daniels, IEEE Trans. 38, 1069 (1991). 10 M. W. Bautz, G. Y. Prigozhin, M. J. Pivovaroff et al., Nucl. Instrum. Methods Phys. Res., Sect. A 436, 40 (1999). 11 G. R. Hopkinson, Opt. Eng. 26, 766 (1987). 12 H. Tsunemi, J. Hiraga, K. Mori, K. Yoshita, and E. Miyata, Nucl. Instrum. Methods Phys. Res., Sect. A 436, 32 (1999). 13 H. Yamaguchi, H. Nakajima, K. Koyama et al., Proc. SPIE 6266, 626642 (2006). 14 H. Murakami, M. Kitsunezuka, M. Ozaki, T. Dotani, and T. Anada, Proc. SPIE 6266, 62662Y (2006). 15 See http://www.astro.isas.jaxa.jp/suzaku/doc/suzaku_td/. 16 See http://cxc.harvard.edu/proposer/POG/html/index.html. 17 See http://xmm.esac.esa.int/external/xmm_user_support/documentation/ technical/. 18 See https://www.swift.psu.edu/xrt/techDescription.html.
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A new clocking method for a charge coupled device Rika Umezu,1 Shunji Kitamoto,1,a),b) and Hiroshi Murakami2,a) 1 Department of Physics, College of Science, Rikkyo University, 3-34-1, Nishi-Ikebukuro, Toshima–ku, Tokyo 171–8501, Japan 2 Department of Information Science, Faculty of Liberal Arts, Tohoku Gakuin University, 2-1-1 Tenjinzawa, Izumi-ku, Sendai, Miyagi 981-3193, Japan
(Received 11 January 2014; accepted 16 June 2014; published online 9 July 2014) We propose and demonstrate a new clocking method for a charge-coupled device (CCD). When a CCD is used for a photon counting detector of X-rays, its weak point is a limitation of its counting rate, because high counting rate makes non-negligible pile-up of photons. In astronomical usage, this pile-up is especially severe for an observation of a bright point-like object. One typical idea to reduce the pile-up is a parallel sum (P-sum) mode. This mode completely loses one-dimensional information. Our new clocking method, panning mode, provides complementary properties between the normal mode and the P-sum mode. We performed a simple simulation in order to investigate a pile-up probability and compared the simulated result and actual obtained event rates. Using this simulation and the experimental results, we compared the pile-up tolerance of various clocking modes including our new method and also compared their other characteristics. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4885468] I. INTRODUCTION
A charge-coupled device (CCD) can be used as a photon counting detector. Especially, in X-ray astronomy, it is now a standard focal plane imager of X-ray telescopes.1–3 Its energy resolution has been achieved almost theoretical limit as a Si detector.3–5 The image resolution is ultimately limited by its pixel size, which is an order of ∼ 10 μm, although, in most cases of X-ray observatories, the point-spread functions (PSFs) of their telescopes are larger than the pixel size. In a usual observation, a big merit of the CCD is that it can obtain both the energy and position of each photon together. But its one weak-point is that it takes substantial time to read-out one full image. Relating this long read-out time, the pile-up problem is a severe drawback of the CCD. Suppose an observation of a point-like object with a telescope. The telescope focuses all photons into a certain small area on its focal plane. High quality telescopes make it small and we can have a high Signal to Noise ratio of the image. If we use a CCD as a focal plane detector, we have a problem for the observation of a bright source. Since a CCD is an integration type device,6 if more than one photon enter into one pixel during an exposure time, we cannot know the original photon’s energy, and even the number of photons. To make matters worse, the electrons produced by a photon sometimes spread out over two or more neighboring pixels. Thus if more than one photon enter even into neighboring pixels, we cannot know the original photons energies. We call them “pile-up”.7 So far, some methods, in order to avoid the pile-up, have been proposed and actually applied for the bright source observations. Any methods have a merit and a demerit. Here
a) Also at Research Center for Measurement in Advanced Science, Rikkyo
University, 3-34-1, Nishi-Ikebukuro, Toshima-ku, Tokyo 171–8501, Japan.
b) Electronic mail: [email protected]
0034-6748/2014/85(7)/075103/5/$30.00
we propose a new method, which complements previous methods. II. PREVIOUS METHODS
Although there are various types of CCDs, in the X-ray astronomy, a frame transfer type is widely used. Here we mainly discuss on the frame transfer CCD. The frame transfer CCD has an image array and a storage array. The storage array is covered to avoid the entrance of photons and the image array is exposed to photons. After certain time (an exposure time), the integrated signals in the image array are moved to the storage array by vertical clockings. The signals in the storage array are read out in turn from a read-out node. During read-out of the signals in the storage array, the image array is exposed to photons. Since this frame transfer CCD does not require a shutter mechanism and there are no loss of the exposure time, it is preferred in the astronomical usage. In the “Normal mode,” all the pixels in the storage array are read out, in turns. Read-out of one full image needs substantial time. In the case of a frame transfer CCD, an exposure time is assigned to be longer than the read-out time of all the pixels, in order to avoid a loss of the observation time. The clocking speed of the charge transfer is limited by a noise tolerance, and it is roughly 100 kHz. Consequently, the exposure time becomes typically more than several seconds.3–5 If the observing object is faint enough to neglect a probability of the pile-up and the observer does not require a fast timing information, this normal mode has no problem. When we need a full image but the probability of the pileup is not negligible, then the “Burst mode” is used. For the names of various modes, we follow that used for the Suzaku, XIS, see “The Suzaku Technical Description”.15 Note that different names are also used for the other instruments, see “The Chandra Proposers’ Observatory Guide”,16 “XMMNewton: A Technical Description”,17 and “Swift Technical
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Description”.18 In the burst mode, the readout cycle begins by rapidly transferring all charge in the image array to a single CCD row, leaving the image array in an unexposed state. Photons are accumulated in the image array for a specified time, which may be very short compared the time required for readout, and then transferred rapidly to the storage array. The image in the storage array is then readout. Since the exposure time can be short, this mode reduces the probability of pile-up, but the fraction of time that photons are being collected, and thus the total number of photons detected, are also reduced. Another option is the “Window mode.” In this mode, by giving up an observation of a full image, the read-out region is limited to be a fraction of the full image. If we set the limited region as one fourth of the full image, every one fourth of the exposure time of the normal mode, the limited region in the image array is transferred to the end of the storage array. The pixels of the limited array (one fourth of the image) are read out taking one fourth of the exposure time of the normal mode. This mode makes the actual time of the imaging and read-out cycle short, and consequently the probability of the pile-up becomes small, although the observable image area becomes small. For an observation of a point-like object, this mode is useful, by setting the limited region to cover the image of the source. The limitation of the window area is restricted by the PSF of the X-ray telescope. If the limited region is smaller than the PSF, we lose a part of the photons from the object. If the PSF of the telescope is not well, such as Suzaku XRT,8 the actual useful window area is restricted to be one fourth or one eighth of the full image. Also for the observation of an extended- or a multiple-source object, the available window area is restricted. For an observation of a very bright point-like object, both the burst and window mode can be used, in order to avoid the pile-up. More drastic idea is the parallel sum mode (“P-sum mode”), where we lose one-dimensional information. In this mode, the image array is continuously vertically transferred and a given number of rows are summed-up in one row at the end of the image array. The summed-up row is finally transferred to the serial register. The serial register is readout normally. Thus the number of the rows, obtained during one exposure time of the normal mode, is roughly same to the actual number of the rows, because the one exposure time of the normal mode is usually adjusted to be roughly same to the read-out time of a full image. If the number of the summedup raw is determined to be the size of the PSF, the photons, from the point-like object detected during the vertical transfer of the number of the summed-up rows, are accumulated in one row. Thus the effective exposure time for a row is this transfer time, which can be much shorter than the normal exposure and the pile-up probability becomes much small. Also in the above situation, the sequence of the rows corresponds to the time, when the photons are detected on the CCD. Therefore, effectively short-term resolution can be achieved. This P-sum mode has good pile-up tolerance but completely lose one-dimensional information of the image. Binning of the pixels does not help to avoid the pile-up. A vertical binning can shorten the read-out time of the image. Two-line binning makes the number of the read-out half and
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thus the exposure time can be half, but the photons coming into final binned pixel is doubled. Consequently, the pile-up tolerance does not change. Of course, the resolution of the image becomes worse.
III. NEW CLOCKING METHOD: PANNING MODE
We propose a new clocking method, “Panning mode.” In the case of the normal mode of a frame transfer CCD, the signals in the storage array are normally clocked and are read out during an exposure. In the panning mode, besides the normal read out of the storage array, a certain number of the vertical transfer, which is fixed in advance, is performed in the image array during one exposure. Consequently, the image is panned and the time interval, during which a focused image of a point-like object is exposing a certain pixel, is shortened. Some rows must be transferred out from the image array during panning. The signal in the rows is accumulated at the bottom of the image array, or at the bottom of the storage array. Therefore, some part of the image was lost. This mode does not require any special gate. In this mode, the obtained image is two dimensional, but the angular resolution of one dimension along the vertical transfer becomes worse. Demonstration of the clockings, including the Panning mode, is performed in our laboratory, using our handmade CCD driver, which can change the clocking mode flexibly. The CCD is a full frame transfer type with 512×512 array. In Figure 1, sample images obtained by the Normal mode, the Binning mode, the P-sum mode, and the Panning mode are shown. The images are simulating an observation of multiple point sources, by using a mask with nine pinholes mimicking
FIG. 1. Demonstrations of images obtained by various modes using our handmade CCD driver. (a) Normal, (b)vertical two-line- binning, (c) P-sum, and (d) panning mode with 128 lines. Since the direction of the charge transfer is downward, the 128 lines of the bottom of the image were lost.
Before discussing pile-up, we have to define “event.” We assume that a size of electron-cloud produced by one Xray is smaller than the size of one pixel. Except for a special case, for example, an escape photon makes a signal in a non-neighboring pixel, the signals of one soft X-ray should produce one of the following patterns; a single pixel, two neighboring pixels, three pixels which make “L” shape, or 2 × 2 pixels.9 We call these patterns as “possible-patterns.” In the case of the X-ray astronomy, the pixel size is typically 24 μm4, 10 and this is much larger than the size of the electroncloud produced by a soft X-ray.11, 12 If an event pattern is not categorized into any of the above possible-patterns, we can consider that the event is not produced by one soft X-ray. It may be produced by a gamma ray or a charged particle or by multiple X-rays (i.e., pile-up event). This categorization of events pattern can be used for the background rejection by extracting only the possible-patterns.13, 14 Thus we call here the event showing one of the possible patterns, as an “apparent good event.” Some pile-up events, however, may still show one of the possible-patterns and may be recognized to be an “apparent good event.” In a real experiment, we cannot recognize such pile-up events with one of the possible-patterns, but in a computer simulation we can distinguish them. Thus we define a “true good event,” which shows one of the possible-pattern and is not really a pile-up event. By defining these events, we performed a Monte Carlo simulation for an estimation of pile-up probability, which is defined as, 1-(the number of the “true good events”)/(the number of detected photons). In the case of an experiment, we have to use the number of the “apparent good events,” instead of the “true good events.” The probability strongly depends on the appearance probability of the possible-patterns. For just an example of the pile-up estimation, we assume the probabilities of the various shapes of the possible-patterns in advance, as 77.49%, 22.11%, 0.30%, and 0.10% , for single, double, L-shape and 2×2 pixels, respectively. These values were determined from the data obtained by our laboratory experiments, where we used 5.9 keV X-rays from a 55 Fe isotope. Also we do not consider any background, such as the gamma ray and charged particles. For the simulation, we first give a mean number of detected photons, λ, by one pixel during one exposure. Each pixel detects the number of photons, which is determined by a Poisson statistics with the mean number of λ. The signals make one of the possible-patterns, according to the given probability. We fix the original amount of the charge produced by one photon. The fraction of the charge in each pixel, in the case of split-events, is determined by a random number. By examining all pixels, we can have one image. Then we extract “events” by analyzing the image. We check all the events whether they are “apparent good events” or not,
0.5
IV. SIMULATION OF PILE-UP
Apparent Good Events True Good Events 0
a star cluster. The number of vertical transfer in the Panning mode, shown in Figure 1, is 128 lines. We can recognize that the panning model makes the image worse, but it still shows a two dimensional image.
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(Number of Detected Events)/ (Number of Detected Photons)
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0.01 0.1 Mean Number of Detected Photons, λ (Counts/exposure/pixel)
1
FIG. 2. The ratios of the “apparent good events” and of the “true good events” to the number of detected photons, as a function of the mean number of photons in one pixel, λ, counts/pixel/exposure. Simulations for the “apparent good events” rates and the “true good events” rates are plotted by the black and red lines. The circles show data obtained by the experiment. The vertical axis shows ratio of the measured “apparent good events” divided by an estimated number of the detected photons. The horizontal axis shows the estimated mean number of photons in one pixel, λ, counts/pixel/exposure (see text).
and also whether they are the “true good event” or not. In the simulation, the only parameter is just the mean number of detected photons, λ photons exposure−1 pixel−1 . Figure 2 shows the results of the simulation. The horizontal axis is just the mean number of detected photons, λ photons exposure−1 pixel−1 . The black and red lines show fractions of the number of the “apparent good events” and of the “true good events,” to the number of the detected photons, respectively. In this case, if the mean number of detected photons, λ, is less than 0.01 counts exposure−1 pixel−1 , the pile-up events are less than 10%. As the λ becomes large, the ratio of the “apparent good events” becomes small. Furthermore, the fraction of the “true good event” in the “apparent good events” becomes small. The apparent good event is the event, which shows one of the possible patterns. As the λ increases, the patterns of some events are overlapped. Some become other of the possible patterns. Thus the rate of the apparent good event decreases. Some pile-up events may still show one of the possible patterns. Since the true good events does not include such pile-up events, the number of the true good events decreases more rapidly. The justification of the simulation is confirmed by experimental data. The CCD, which is clocking by the “Normal mode,” is exposed to X-rays from a 55 Fe isotope. By changing an exposure time, we can take data with various mean number of detected photons, λ. We assume that obtained data with the shortest exposure time has no pile-up, and assume that extracted event number is the number of detected photons. Then we estimate the mean number of detected photons, λ, of the shortest exposure time. The λ of other exposure is assumed to scale with the exposure time. The “apparent good events” are extracted from the obtained images and the ratio of the number of “apparent good events” to the expected number of detected photons are plotted in Figure 2. We obtained reasonable agreement between the simulation and the experiments.
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In this simulation and the experiment described here, we assumed the uniform distribution of the X-rays on the CCD. When we consider a pile-up probability using a particular PSF, we first estimate a local mean number of the detected photons in certain part of the PSF. Then we can estimate a local pile-up probability. V. COMPARISON BETWEEN PANNING MODE AND OTHER MODES
The tolerance of the pile-up of the various modes can be estimated by considering only the mean number of detected photons, λ, which changes depending on the modes. In the observation of a point source with the window mode, the actual exposure time of the window mode is reduced by the number −1 . Thus the λ becomes of the window (Nwindow ) to be Nwindow −1 Nwindow and Nwindow times bright source can be observed with no loss of the photons. In the Burst mode, the exposure time is −1 actually reduced. If the exposure time is reduced to be Nburst −1 of the normal mode, then the λ becomes Nburst , and bright sources can be observed. But the total number of photons also −1 . becomes Nburst In the P-sum mode, the pile-up tolerance depends on the size of the PSF, i.e., the performance of the telescope. For example, if the size of the PSF (for example, half power diameter) is Npsf -pixels, and the number of line of the image array is Nline , the image size detected by P-sum mode during one exposure time of the Normal mode becomes Nline × Npsf . Therefore, the λ becomes ∼ up tolerance becomes
Nline , Npsf
Nline ×Npsf Npsf ×Npsf
. Consequently, the pile-
where we assume that the read-out
time of the Nlines in the P-sum mode is the same to the exposure time of the Normal mode. In the case of Suzaku XIS, Nline is 1024, and Npsf is ∼100 pixel. Thus roughly 10 times bright-point-like sources can be observed. But we lose onedimensional information of the image. If the telescope has better imaging capability, the improvement of the pile-up tolerance is much higher. In the case of the panning mode, the image size of the point source can be arbitrary changed between the size of the PSF and that of the P-sum mode. Therefore, the pile-up tolerance is between those of the normal and of the P-sum mode. Hence the information loss of the one dimension is also between those of the normal and of the P-sum mode.
Properties of the various modes are summarized in Table I. The time resolution of the Normal mode is just the exposure time, which is usually assigned to be longer than the read-out time of all the pixels. In the Burst mode, although the exposure time is limited to be much shorter than the readout time, the one sequence of this mode is usually adjusted to be the same to the exposure time of the Normal mode, because one sequence of the bust mode should be longer than the read-out time of all the pixels. Therefore, the time resolution, determined by the image sampling rate, is the same to that of the Normal mode. The time resolution of the window mode is Nwindow times shortened. In the P-sum mode, the time resolution may depend on Npsf . However, by adding some rows, the width of which is broader than the size of PSF (Npsf ), into one row, the time resolution can be shortened to be −1 Nlines of the Normal mode for a point source. In the Panning mode, the time resolution for a point-like object also depends on Npsf . Since we do not intend to add any rows, Npsf works as a window function on the time sequence of the panning. If the number of the vertical transfer in one exposure, Npan , is smaller than Npsf , the time resolution is not improved from the normal mode. But if Npan is larger than Npsf , the image can be divided into Npan /Npsf , which is qualitatively a sequence of the time. Thus the time resolution becomes Npsf /Npan , of the normal mode. Since Npan can be selected from 1 to Nlines , the time resolution of the Panning mode is 1∼ Npsf /Nline of the Normal mode. The extraction of the “possible-patterns” can help the background rejection, in all the modes other than the P-sum mode. The signal patterns obtained by the P-sum mode are not same to the “possible-patterns,” since some lines are summed-up and the information of the vertical pattern is lost, although similar pattern selection with one dimensional information can be possible. The image size becomes large in the Panning mode, but it is between the P-sum mode and Normal mode. Other modes do not change the image size. The degradation of the energy resolution by the panning may be worried. However, this mode does not require any special clocking, and clocking of the image area during an exposure is performed in the P-sum mode. Since no degradation of the energy resolution of the P-sum mode is reported, we can also expect no degradation in the Panning mode.
TABLE I. Characteristics of various modes, for the observation of point-like objects.
Pile-up tolerance Field of view The number of photons Time resolution Pattern selection Image size
Normal
Window
Burst
P-sum
Panning
1 1 1 1 d Npsf × Npsf
Nwindow 1/Nwindow 1 1/Nwindow Npsf × Npsf
Nburst 1 1/Nburst 1a Npsf × Npsf
Nline /Npsf 1 1 1/Nline b e Nline × Npsf
1∼ Nline /Npsf (Nline − Npan )/Nline 1 1∼ Npsf /Nline c Npsf × Npsf ∼ Nline × Npsf
a
We assume that one image is obtained every exposure time of the Normal mode. We assume that the number of the summed-up rows is larger than the size of PSF (Npsf ). c Depending on the Npan , the time resolution changes from 1 to Npsf /Nline of the normal mode (see text). b
d
The pattern selection of the event, using the possible patterns, can be applied as a background rejection. The pattern selection cannot be simply applied, but a different pattern selection might be possible, by defining another possible patterns. e
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VI. CONCLUSION
New clocking method, panning mode, is presented and demonstrated with our handmade CCD driver. This mode has the moderate pile-up tolerance by victimizing onedimensional resolution. The properties of the various clocking modes are discussed. The panning mode provides complementary properties between the normal mode and the P-sum mode. ACKNOWLEDGMENTS
This work was supported by JSPS KAKENHI Grant No. 21740191. This work was also partially supported by a research fund from the Research Center for Measurement in Advanced Science of Rikkyo University. 1 K.
Mitsuda et al., Publ. Astron. Soc. Jpn. 59, S1 (2007). C. Weisskopf, B. Brinkman, C. Canizares et al., Publ. Astron. Soc. Pac. 114, 1 (2002). 3 L. Struder et al., Astron. Astrophys. 365, L18 (2001). 4 K. Koyama et al., Publ. Astron. Soc. Jpn. 59, S23 (2007). 2 M.
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P. Garmire, M. W. Bautz, P. G. Ford, J. A. Nousek, G. R. Ricker, Jr., Proc. SPIE 4851, 28–44 (2003). 6 K. Hashimotodani, T. Toneri, S. Kitamoto, H. Tsunemi, K. Hayashida, E. Miyata, K. Katayama, T. Kohmura, R. Asakura, K. Koyama, K. Yamamoto, K. Miyaguchi, and H. Suzuki, Rev. Sci. Instrum. 69, 392–395 (1998). 7 S. Yamada, H. Uchiyama, T. Dotani et al., Publ. Astron. Soc. Jpn. 64, 53 (2012). 8 P. J. Serlemitsos, Y. Soong, K.-W. Chan et al., Publ. Astron. Soc. Jpn. 59, S9 (2007). 9 B. E. Burke, R. W. Mountain, D. C. Harrison, M. W. Bautz, J. P. Doty, G. R. Ticker, and P. J. Daniels, IEEE Trans. 38, 1069 (1991). 10 M. W. Bautz, G. Y. Prigozhin, M. J. Pivovaroff et al., Nucl. Instrum. Methods Phys. Res., Sect. A 436, 40 (1999). 11 G. R. Hopkinson, Opt. Eng. 26, 766 (1987). 12 H. Tsunemi, J. Hiraga, K. Mori, K. Yoshita, and E. Miyata, Nucl. Instrum. Methods Phys. Res., Sect. A 436, 32 (1999). 13 H. Yamaguchi, H. Nakajima, K. Koyama et al., Proc. SPIE 6266, 626642 (2006). 14 H. Murakami, M. Kitsunezuka, M. Ozaki, T. Dotani, and T. Anada, Proc. SPIE 6266, 62662Y (2006). 15 See http://www.astro.isas.jaxa.jp/suzaku/doc/suzaku_td/. 16 See http://cxc.harvard.edu/proposer/POG/html/index.html. 17 See http://xmm.esac.esa.int/external/xmm_user_support/documentation/ technical/. 18 See https://www.swift.psu.edu/xrt/techDescription.html.
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