International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.5, pp. 125-128

Section 2.5.3.2. 2D detector

B. B. Hea*

aBruker AXS Inc., 5465 E. Cheryl Parkway, Madison, WI 53711, USA
Correspondence e-mail: bob.he@bruker.com

2.5.3.2. 2D detector

| top | pdf |

Two-dimensional (2D) detectors, also referred to as area detectors, are the core of 2D-XRD. The advances in area-detector technologies have inspired applications both in X-ray imaging and X-ray diffraction. A 2D detector contains a two-dimensional array of detection elements which typically have identical shape, size and characteristics. A 2D detector can simultaneously measure both dimensions of the two-dimensional distribution of the diffracted X-rays. Therefore, a 2D detector may also be referred to as an X-ray camera or imager. There are many technologies for area detectors (Arndt, 1986[link]; Krause & Phillips, 1992[link]; Eatough et al., 1997[link]; Giomatartis, 1998[link]; Westbrook, 1999[link]; Durst et al., 2002[link]; Blanton, 2003[link]; Khazins et al., 2004[link]). X-ray photographic plates and films were the first generation of two-dimensional X-ray detectors. Now, multiwire proportional counters (MWPCs), image plates (IPs), charge-coupled devices (CCDs) and microgap detectors are the most commonly used large area detectors. Recent developments in area detectors include X-ray pixel array detectors (PADs), silicon drift diodes (SDDs) and complementary metal-oxide semiconductor (CMOS) detectors (Ercan et al., 2006[link]; Lutz, 2006[link]; Yagi & Inoue, 2007[link]; He et al., 2011[link]). Each detector type has its advantages over the other types. In order to make the right choice of area detector for a 2D-XRD system and applications, it is necessary to characterize area detectors with consistent and comparable parameters. Chapter 2.1[link] has more comprehensive coverage on X-ray detectors, including area detectors. This section will cover the characteristics specifically relevant to area detectors.

2.5.3.2.1. Active area and pixel size

| top | pdf |

A 2D detector has a limited detection surface and the detection surface can be spherical, cylindrical or flat. The detection-surface shape is also determined by the detector technology. For example, a CCD detector is made from a large semiconductor wafer, so that only a flat CCD is available, while an image plate is flexible so that it is easily bent to a cylindrical shape. The area of the detection surface, also referred to as the active area, is one of the most important parameters of a 2D detector. The larger the active area of a detector, the larger the solid angle that can be covered at the same sample-to-detector distance. This is especially important when the instrumentation or sample size forbid a short sample-to-detector distance. The active area is also limited by the detector technology. For instance, the active area of a CCD detector is limited by the semiconductor wafer size and fabrication facility. A large active area can be achieved by using a large demagnification optical lens or fibre-optical lens. Stacking several CCD chips side-by-side to build a so-called mosaic CCD detector is another way to achieve a large active area.

In addition to the active area, the overall weight and dimensions are also very important factors in the performance of a 2D detector. The weight of the detector has to be supported by the goniometer, so a heavy detector means high demands on the size and power of the goniometer. In a vertical configuration, a heavy detector also requires a heavy counterweight to balance the driving gear. The overall dimensions of a 2D detector include the height, width and depth. These dimensions determine the manoeuvrability of the detector within a diffractometer, especially when a diffractometer is loaded with many accessories, such as a video microscope and sample-loading mechanism. Another important parameter of a 2D detector that tends to be ignored by most users is the blank margin surrounding the active area of the detector. Fig. 2.5.10[link] shows the relationship between the maximum measurable 2θ angle and the detector blank margin. For high 2θ angle measurements, the detector swing angle is set so that the incident X-ray optics are set as closely as possible to the detector. The unmeasurable blank angle is the sum of the detector margin m and the dimension from the incident X-ray beam to the outer surface of the optic device h. The maximum measurable angle is given by[2{\theta _{\max }} = \pi - {{m + h} \over D}.\eqno(2.5.16)]It can be seen that either reducing the detector blank margin or optics blank margin can increase the maximum measurable angle.

[Figure 2.5.10]

Figure 2.5.10 | top | pdf |

Detector dimensions and maximum measurable 2θ.

The solid angle covered by a pixel in a flat detector is dependent on the sample-to-detector distance and the location of the pixel in the detector. Fig. 2.5.11[link] illustrates the relationship between the solid angle covered by a pixel and its location in a flat area detector. The symbol S may represent a sample or a calibration source at the instrument centre. The distance between the sample S and the detector is D. The distance between any arbitrary pixel P(x, y) and the detector centre pixel P(0, 0) is r. The pixel size is Δx and Δy (assuming Δx = Δy). The distance between the sample S and the pixel is R. The angular ranges covered by this pixel are Δα and Δβ in the x and y directions, respectively. The solid angle covered by this pixel, ΔΩ, is then given as[\Delta \Omega = \Delta \alpha \Delta \beta = {D \over {{R^3}}}\Delta y \Delta x = {D \over {{R^3}}}\Delta A,\eqno(2.5.17)]where ΔA = ΔxΔy is the area of the pixel and R is given by[R = ({D^2} + {x^2} + {y^2})^{1/2} = ({D^2} + {r^2})^{1/2}. \eqno(2.5.18)]When a homogeneous calibration source is used, the flux to a pixel at P(x, y) is given as[F(x,y) = \Delta \Omega B = {{\Delta ADB} \over {{R^3}}} = {{\Delta ADB} \over {{{({D^2} + {x^2} + {y^2})}^{3/2}}}},\eqno(2.5.19)]where F(x, y) is the flux (in photons s−1) intercepted by the pixel and B is the brightness of the source (in photons s−1 mrad−2) or scattering from the sample. The ratio of the flux in pixel P(x, y) to that in the centre pixel P(0, 0) is then given as[{{F(x,y)} \over {F(0,0)}} = {{{D^3}} \over {{R^3}}} = {{{D^3}} \over {{{({D^2} + {x^2} + {y^2})}^{3/2}}}} = {\cos ^3}\phi, \eqno(2.5.20)]where [\phi] is the angle between the X-rays to the pixel P(x, y) and the line from S to the detector in perpendicular direction. It can be seen that the greater the sample-to-detector distance, the smaller the difference between the centre pixel and the edge pixel in terms of the flux from the homogeneous source. This is the main reason why a data frame collected at a short sample-to-detector distance has a higher contrast between the edge and centre than one collected at a long sample-to-detector distance.

[Figure 2.5.11]

Figure 2.5.11 | top | pdf |

Solid angle covered by each pixel and its location on the detector.

2.5.3.2.2. Spatial resolution of area detectors

| top | pdf |

In a 2D diffraction frame, each pixel contains the X-ray intensity collected by the detector corresponding to the pixel element. The pixel size of a 2D detector can be determined by or related to the actual feature sizes of the detector structure, or artificially determined by the readout electronics or data-acquisition software. Many detector techniques allow multiple settings for variable pixel size, for instance a frame of 2048 × 2048 pixels or 512 × 512 pixels. Then the pixel size in 512 mode is 16 (4 × 4) times that of a pixel in 2048 mode. The pixel size of a 2D detector determines the space between two adjacent pixels and also the minimum angular steps in the diffraction data, therefore the pixel size is also referred to as pixel resolution.

The pixel size does not necessarily represent the true spatial resolution or the angular resolution of the detector. The resolving power of a 2D detector is also limited by its point-spread function (PSF) (Bourgeois et al., 1994[link]). The PSF is the two-dimensional response of a 2D detector to a parallel point beam smaller than one pixel. When the sharp parallel point beam strikes the detector, not only does the pixel directly hit by the beam record counts, but the surrounding pixels may also record some counts. The phenomenon is observed as if the point beam has spread over a certain region adjacent to the pixel. In other words, the PSF gives a mapping of the probability density that an X-ray photon is recorded by a pixel in the vicinity of the point where the X-ray beam hits the detector. Therefore, the PSF is also referred to as the spatial redistribution function. Fig. 2.5.12[link](a) shows the PSF produced from a parallel point beam. A plane at half the maximum intensity defines a cross-sectional region within the PSF. The FWHM can be measured at any direction crossing the centroid of the cross section. Generally, the PSF is isotropic, so the FWHMs measured in any direction should be the same.

[Figure 2.5.12]

Figure 2.5.12 | top | pdf |

(a) Point-spread function (PSF) from a parallel point beam; (b) line-spread function (LSF) from a sharp line beam.

Measuring the PSF directly by using a small parallel point beam is difficult because the small PSF spot covers a few pixels and it is hard to establish the distribution profile. Instead, the line-spread function (LSF) can be measured with a sharp line beam from a narrow slit (Ponchut, 2006[link]). Fig. 2.5.12[link](b) is the intensity profile of the image from a sharp line beam. The LSF can be obtained by integrating the image from the line beam along the direction of the line. The FWHM of the integrated profile can be used to describe the LSF. Theoretically, LSF and PSF profiles are not equivalent, but in practice they are not distinguished and may be referenced by the detector specification interchangeably. For accurate LSF measurement, the line beam is intentionally positioned with a tilt angle from the orthogonal direction of the pixel array so that the LSF can have smaller steps in the integrated profile (Fujita et al., 1992[link]).

The RMS (root-mean-square) of the distribution of counts is another parameter often used to describe the PSF. The normal distribution, also called the Gaussian distribution, is the most common shape of a PSF. The RMS of a Gaussian distribution is its standard deviation, σ. Therefore, the FWHM and RMS have the following relation, assuming that the PSF has a Gaussian distribution:[{\rm{FWHM}} = 2[- 2\ln (1/2)]^{1/2} {\rm{RMS}} = 2.3548\times {\rm{RMS}}.\eqno(2.5.21)]The values of the FWHM and RMS are significantly different, so it is important to be precise about which parameter is used when the value is given for a PSF.

For most area detectors, the pixel size is smaller than the FWHM of the PSF. The pixel size should be small enough that at least a 50% drop in counts from the centre of the PSF can be observed by the pixel adjacent to the centre pixel. In practice, an FWHM of 3 to 6 times the pixel size is a reasonable choice if use of a smaller pixel does not have other detrimental effects. A further reduction in pixel size does not necessarily improve the resolution. Some 2D detectors, such as pixel-array detectors, can achieve a single-pixel PSF. In this case, the spatial resolution is determined by the pixel size.

2.5.3.2.3. Detective quantum efficiency and energy range

| top | pdf |

The detective quantum efficiency (DQE), also referred to as the detector quantum efficiency or quantum counting efficiency, is measured by the percentage of incident photons that are converted by the detector into electrons that constitute a measurable signal. For an ideal detector, in which every X-ray photon is converted to a detectable signal without additional noise added, the DQE is 100%. The DQE of a real detector is less than 100% because not every incident X-ray photon is detected, and because there is always some detector noise. The DQE is a parameter defined as the square of the ratio of the output and input signal-to-noise ratios (SNRs) (Stanton et al., 1992[link]):[{\rm DQE} = {\left({{{{{(S/N)}_{\rm out}}} \over {{{(S/N)}_{\rm in}}}}} \right)^2}.\eqno(2.5.22)]

The DQE of a detector is affected by many variables, for example the X-ray photon energy and the counting rate. The dependence of the DQE on the X-ray photon energy defines the energy range of a detector. The DQE drops significantly if a detector is used out of its energy range. For instance, the energy range of MWPC and microgap detectors is about 3 to 15 keV. The DQE with Cu Kα radiation (8.06 keV) is about 80%, but drops gradually when approaching the lower or higher energy limits. The energy range of imaging plates is much wider (4–48 keV). The energy range of a CCD, depending on the phosphor, covers from 5 keV up to the hard X-ray region.

2.5.3.2.4. Detection limit and dynamic range

| top | pdf |

The detection limit is the lowest number of counts that can be distinguished from the absence of true counts within a specified confidence level. The detection limit is estimated from the mean of the noise, the standard deviation of the noise and some confidence factor. In order to have the incoming X-ray photons counted with a reasonable statistical certainty, the counts produced by the X-ray photons should be above the detector background-noise counts.

The dynamic range is defined as the range extending from the detection limit to the maximum count measured in the same length of counting time. The linear dynamic range is the dynamic range within which the maximum counts are collected within the specified linearity. For X-ray detectors, the dynamic range most often refers to linear dynamic range, since only a diffraction pattern collected within the linear dynamic range can be correctly interpreted and analysed. When the detection limit in count rate approaches the noise rate at extended counting time, the dynamic range can be approximated by the ratio of the maximum count rate to the noise rate.

Dynamic range is very often confused with the maximum count rate, but must be distinguished. With a low noise rate, a detector can achieve a dynamic range much higher than its count rate. For example, if a detector has a maximum linear count rate of 105 s−1 with a noise rate of 10−3 s−1, the dynamic range can approach 108 for an extended measurement time. The dynamic range for a 2D detector has the same definition as for a point detector, except that with a 2D detector the whole dynamic range extending from the detection limit to the maximum count can be observed from different pixels simultaneously. In order to record the entire two-dimensional diffraction pattern, it is necessary for the dynamic range of the detector to be at least the dynamic range of the diffraction pattern, which is typically in the range 102 to 106 for most applications. If the range of reflection intensities exceeds the dynamic range of the detector, then the detector will either saturate or have low-intensity patterns truncated. Therefore, it is desirable that the detector has as large a dynamic range as possible.

2.5.3.2.5. Types of 2D detectors

| top | pdf |

2D detectors can be classified into two broad categories: photon-counting detectors and integrating detectors (Lewis, 1994[link]). Photon-counting area detectors can detect a single X-ray photon entering the active area. In a photon-counting detector, each X-ray photon is absorbed and converted to an electrical pulse. The number of pulses counted per unit time is proportional to the incident X-ray flux. Photon-counting detectors typically have high counting efficiency, approaching 100% at low count rate. The most commonly used photon-counting 2D detectors include MWPCs, Si-pixel arrays and microgap detectors. Integrating area detectors, also referred to as analogue X-ray imagers, record the X-ray intensity by measuring the analogue electrical signals converted from the incoming X-ray flux. The signal size of each pixel is proportional to the fluence of incident X-rays. The most commonly used integrating 2D detectors include image plates (IPs) and charge-coupled devices (CCDs).

The selection of an appropriate 2D detector depends on the X-ray diffraction application, the sample condition and the X-ray beam intensity. In addition to geometry features, such as the active area and pixel format, the most important performance characteristics of a detector are its sensitivity, dynamic range, spatial resolution and background noise. The detector type, either photon-counting or integrating, also leads to important differences in performance. Photon-counting 2D detectors typically have high counting efficiency at low count rate, while integrating 2D detectors are not so efficient at low count rate because of the relatively high noise background. An MWPC has a high DQE of about 0.8 when exposed to incoming local fluence from single photons up to about 103 photons s−1 mm−2. The diffracted X-ray intensities from a polycrystalline or powder sample with a typical laboratory X-ray source fall into this fluence range. This is especially true with microdiffraction, where high sensitivity and low noise are crucial to reveal the weak diffraction pattern. Owing to the counting losses at a high count rate, the DQE of an MWPC decreases with increasing count rate and quickly saturates above 103 photons s−1 mm−2. Therefore, an MWPC is not suitable for collecting strong diffraction patterns or for use with high intensity sources, such as synchrotron X-ray sources. An IP can be used in a large fluence range from 10 photons s−1 mm−2 and up with a DQE of 0.2 or lower. An IP is suitable for strong diffraction from single crystals with high-intensity X-ray sources, such as a rotating-anode generator or synchrotron X-ray source. With weak diffraction signals, the image plate cannot resolve the diffraction data near the noise floor. A CCD detector can also be used over a large X-ray fluence range from 10 photons s−1 mm−2 to very high fluence with a much higher DQE of 0.7 or higher. It is suitable for collecting diffraction of medium to strong intensity from single-crystal or polycrystalline samples. Owing to the relatively high sensitivity and high local count rate, CCDs can be used in systems with either sealed-tube X-ray sources, rotating-anode generators or synchrotron X-ray sources. With a low DQE at low fluence and the presence of dark-current noise, a CCD is not a good choice for applications with weak diffraction signals. A microgap detector has the best combination of high DQE, low noise and high count rate. It has a DQE of about 0.8 at an X-ray fluence from single photons up to about 105 photons s−1 mm2. It is suitable for microdiffraction when high sensitivity and low noise are crucial to reveal weak diffraction patterns. It can also handle high X-ray fluence from strong diffraction patterns or be used with high-intensity sources, such as rotating-anode generators or synchrotron X-ray sources.

References

Arndt, U. W. (1986). X-ray position-sensitive detectors. J. Appl. Cryst. 19, 145–163.Google Scholar
Blanton, T. N. (2003). X-ray film as a two-dimensional detector for X-ray diffraction analysis. Powder Diffr. 18, 91–98.Google Scholar
Bourgeois, D., Moy, J. P., Svensson, S. O. & Kvick, Å. (1994). The point-spread function of X-ray image-intensifiers/CCD-camera and imaging-plate systems in crystallography: assessment and consequences for the dynamic range. J. Appl. Cryst. 27, 868–877.Google Scholar
Durst, R. D., Carney, S. N., Diawara, Y. & Shuvalov, R. (2002). Readout structure and technique for electron cloud avalanche detectors. US Patent No. 6, 340, 819. Google Scholar
Eatough, M. O., Rodriguez, M. A., Blanton, T. N. & Tissot, R. G. (1997). A comparison of detectors used for microdiffraction applications. Adv. X-ray Anal. 41, 319–326.Google Scholar
Ercan, A., Tate, M. W. & Gruner, S. M. (2006). Analog pixel array detectors. J. Synchrotron Rad. 13, 110–119.Google Scholar
Fujita, H., Tsai, D.-Y., Itoh, T., Doi, K., Morishita, J., Ueda, K. & Ohtsuka, A. (1992). A simple method for determining the modulation transfer function in digital radiography. IEEE Trans. Med. Imag. 11, 34–39.Google Scholar
Giomatartis, Y. (1998). Development and prospects of the new gaseous detector `Micromegas'. Nucl. Instrum. Methods A, 419, 239.Google Scholar
He, T., Durst, R. D., Becker, B. L., Kaercher, J. & Wachter, G. (2011). A large area X-ray imager with online linearization and noise suppression. Proc. SPIE, 8142, 81421Q.Google Scholar
Khazins, D. M., Becker, B. L., Diawara, Y., Durst, R. D., He, B. B., Medved, S. A., Sedov, V. & Thorson, T. A. (2004). A parallel-plate resistive-anode gaseous detector for X-ray imaging. IEEE Trans. Nucl. Sci. 51, 943–947.Google Scholar
Krause, K. L. & Phillips, G. N. (1992). Experience with commercial area detectors: a `buyer's' perspective. J. Appl. Cryst. 25, 146–154.Google Scholar
Lewis, R. (1994). Multiwire gas proportional counters: decrepit antiques or classic performers? J. Synchrotron Rad. 1, 43–53.Google Scholar
Lutz, G. (2006). Silicon drift and pixel devices for X-ray imaging and spectroscopy. J. Synchrotron Rad. 13, 99–109.Google Scholar
Ponchut, C. (2006). Characterization of X-ray area detectors for synchrotron beamlines. J. Synchrotron Rad. 13, 195–203.Google Scholar
Stanton, M., Phillips, W. C., Li, Y. & Kalata, K. (1992). Correcting spatial distortions and nonuniform response in area detectors. J. Appl. Cryst. 25, 549–558.Google Scholar
Westbrook, E. M. (1999). Performance characteristics needed for protein crystal diffraction X-ray detectors. Proc. SPIE, 3774, 2–16.Google Scholar
Yagi, N. & Inoue, K. (2007). CMOS flatpanel detectors for SAXS/WAXS experiments. J. Appl. Cryst. 40, s439–s441.Google Scholar








































to end of page
to top of page