Ultra-high Dynamic Range Method

The dynamic range which can be achieved by a photon counting system is in principle only limited by the statistical shot noise, which is equal to the square root of the number of counts in the bins of interest. In order to increase the dynamic range, either the integration time or the count rate should be increased. However, the integration time is limited to the period over which beam conditions can be considered constant, while the deadtime of the detector limits the count rate at which the detector can be run without losing counts from the end of the

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bunch and the trailing satellites. In practice, furthermore, other factors such as the imperfect subtraction of afterpulses reduce the dynamic range.

The dynamic range could be increased considerably by the use of two detectors, one operating in gated mode. This detector would be blind to the main bunches, and would thus be able to accept many more photons from the ghost and satellite bunches. The Monte Carlo simulation of such a system was shown in 4.4.5. However, as has been shown in chapter 4.5.4, the APD cannot be gated at sufficient speed.

An alternative method is to gate the light before it is incident on the detector. A number of methods exist by which light can be switched at very high speeds [180]. For example, optical switches based on a miniaturised Mach-Zehnder interferometer [181] are routinely used in the telecommunications industry and achieve switching times as low as 8 ps. However, the switching is only effective for a single wavelength, making this solution unsuitable for broadband light sources such as those available in the BSRT. Ultrafast non-linear interferometers such as that illustrated in [182] suffer the same limitation. Movable mirrors based on microelectromechanical systems (MEMS) clearly do not have any wavelength dependence, but cannot achieve the switching speed required, and their reliance on moving parts makes them insufficiently robust.

A Pockels cell [183] can be used as a light shutter if it is placed between crossed polarisers. When a voltage is applied to the cell, the polarisation of light passing through it is rotated, allowing some light to pass the second polariser. This method has been demonstrated for synchrotron light diagnostics at the Spring-8 synchrotron [184]. However, the shutter has a limited repetition frequency due to heating of the Pockels cell. Opening the shutter with a low duty cycle would increase the required integration time and thus negate the benefits of the two-detector system. In principle, a series of shutters could be used to overcome the repetition frequency limit, but such a system would be expensive and would require very careful optical alignment.

The solution proposed is to use an electro-optic (EO) deflector [185] as an optical switch. The deflector would be located several metres upstream of the APD, such that the deflection is translated into a horizontal displacement. EO deflectors can give an angular deflection of several mrad with a relatively low voltage and high frequency [186]. A displacement of up to 1

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cm might then be expected close to the APD. Since this is much larger than the horizontal spot size, a large extinction ratio should be possible.

A lab test of the deflector-based optical gate has been carried out. A custom-made EO deflector was manufactured by Leysop [187]. Two deflecting crystals are combined in series to obtain a large angular deflection. A resonant circuit tuned to 20 MHz is used to modulate the deflector, allowing a relatively small input voltage to be used. A modulation of 20 V should produce a deflection of 6 mrad [188]. However, for this lab test a suitable driver was not available, and only 5 V could be produced at the required frequency, leading to a maximum deflection of 1.5 mrad. Nonetheless, this allowed the principle to be shown.

A low-power laser beam was shone through the deflector and onto the APD, which was located at a distance of 2 m from the deflector. The signal generator produced a 5 V, 20 MHz sine wave which was used to drive the deflector. It also produced a synchronisation signal which was used to trigger the TDC. The output of the APD was connected to the TDC STOP channel and the photon-counting histogram was built up. An example is given in Figure 100. An extinction ratio of 20:1 was achieved. This was mostly limited by diffraction. Since the aperture of the deflector is small, it causes significant diffraction of the laser beam as it passes through. Diffraction rings were visible at the APD. When the main spot is deflected off the APD, the diffraction ring might still hit it, meaning that the transmission does not drop to zero. This problem could be overcome by using a deflector with a larger clear aperture. In addition, using a specially-built generator to produce a 20 V, 20 MHz wave would allow a greater deflection to be achieved and thus a better extinction ratio.

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Figure 100. APD counts against time. Optical gating using the electro-optic deflector. An extinction ratio of 20:1 is achieved.

Installing a mask across which the light beam is scanned would allow the transmission to be varied with any waveform required [189]. In the LDM case, it would be desirable to have high transmission for most of the time, with zero transmission for a period of 2.5 ns coinciding with each nominal LHC bunch. In this case, a lens with a diameter greater than the maximum deflection would be placed in front of the APD, such that all of the light is gathered onto the active area of the APD regardless of the deflection given. A mask consisting of a single opaque line would then be placed in front of the lens (Figure 101). As the beam is swept across the mask, the light is blocked for a short period. If the deflector is modulated with a sinusoidal voltage, then the sweep speed will be greatest at the centre of the pattern, i.e. the position with zero deflection. A faster switching speed can be achieved by placing the blocking mask at this position, since the switching time is the size of the beam spot divided by the speed at which the spot is swept across the mask plane. Since the spot is swept across the centre twice in each cycle, it is sufficient to operate the deflector at half the LHC bunch frequency.

An example of the high duty cycle that can be achieved using this method is shown in Figure 102. Once again, diffraction rings around the beam spot limit the extinction ratio and cause additional structure in the waveform.

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Figure 101. Layout of the proposed deflector-based optical gate. The beam spot is swept across a mask which blocks the light coming from the nominal LHC bunches. A lens then gathers all the remaining light onto the active area of the APD.

Figure 102. APD counts against time. Adjusting the position of the mask allows different transmission waveforms to be created. In this example, the transmission peak is broadened and the system is strongly attenuating for only a short period, as would be required for the LHC 50 ns filling scheme.

Such a system could dramatically increase the dynamic range. Equivalently, the desired dynamic range could be achieved in a much shorter time, allowing for example to check the quality of a fill before proceeding to the energy ramp. In principle, if the gate operated with a 100% extinction ratio, the dynamic range could be doubled. In practice it would be preferable for the ranges of the gated and free-running detectors to overlap, in order to allow cross-

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calibration, and the improvement in dynamic range would then be slightly less than a factor of two.

Provided that sufficient light is available, any number of detectors could be employed, each with different gating schemes and attenuation rates, to achieve an arbitrarily large dynamic range. For example, one detector would be free-running, the second sensitive to everything but the main bunches, the third could be gated off during all filled slots, and a fourth gated on only during the Abort Gap. The splitting ratio and/or attenuations would be adjusted so that each detector operates at the optimum average count rate of 1 photon per deadtime period. Only when there is insufficient light available to achieve this optimum count rate is it futile to add further detectors.

Chapter Summary

Further potential improvements of the LDM system, which could not be completed within the time-frame of the project, are outlined. In particular, a novel scheme for increasing the dynamic range with the use of an optically gated detector is presented, and a suitable ultra-fast optical gating scheme is suggested. A prototype of this scheme has been tested in the laboratory and showed promising results.

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