[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

The probability of absorption in the detection module

Info icon This preview shows pages 230–233. Sign up to view the full content.

View Full Document Right Arrow Icon
The probability of absorption in the detection module entrance window can be expressed as exp(- µρ s) where µ , ρ , and s are, respectively, the mass attenuation coefficient, the density, and the thickness of the window mater- ial. Beryllium is a very common material used for windows. In Fig. 4.5, the transmission probability versus the energy for different Be window thickness is plotted, while in Fig. 4.6 the high transmission capability of an ultra-thin polymer window (from MOXTEK) is reported [15]. For “window-less” detection modules, the detection efficiency in the low energy range is limited by the unavoidable presence of a dead layer in the radi- ation entrance region of the detector itself. This limitation involves especially semiconductor detectors where the presence of an electrode deposited or implanted on the detector surface determines a thin region which could absorb the photon with a partial or incomplete release of signal charge. A model for the entrance window for silicon X-ray detectors is presented in [16]. An example of quantum efficiency measured in the low energy range for a silicon detector is shown in Fig. 4.20. on p. 227. Energy Resolution In most X-ray fluorescence applications an accurate energy distribution of the incident photons has to be measured. The energy resolution ∆E of a spec- troscopy system (detector + readout electronics) represents the capability of
Image of page 230

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
210 A. Longoni and C. Fiorini Transmission of light elements Ka 0 20 40 60 80 100 0 500 1000 1500 2000 Energy (eV) Transmission (%) 8 m m Be AP3.3 Film Na C N O F B Fig. 4.6. X-ray transmission of an ultrathin polymer window (graph courtesy of MOXTEK, Inc.). For comparison, the transmission of an 8 µ m Be window is also reported the system to distinguish photons closely separated in energy. As shown in Fig. 4.7, the pulse height distribution in a typical measurement of photons of energy E 0 is broadened with respect to an ideal Dirac- δ -like distribution due to several sources of statistical fluctuation affecting the measurement. The energy resolution is commonly expressed as full-width-at-half-maximum (FWHM) of the measured distribution. The larger the FWHM, the more dif- ficult will be the identification of peaks corresponding to photons of close energies. Alternatively, the energy resolution can be expressed also as per- centage R , defined as the ratio between the FWHM and the centroid value of the distribution: R = ∆ E FWHM /E 0 . (4.4) Very often, the measured distribution can be described by means of a Gaussian function, whose expression is given by: G ( E ) = N 0 σ 2 π exp ( E E 0 ) 2 2 σ 2 , (4.5) where σ is the standard deviation, N 0 is peak area, and E 0 is the peak centroid. For the Gaussian distribution the FWHM results related to the σ as FWHM = 2 . 35 σ . Different sources of statistical fluctuation limit the energy resolution E meas of a detection system, as indicated in the following expression: E 2 meas = ∆ E 2 statistical + ∆ E 2 el . noise + ∆ E 2 multiplication + ∆ E 2 collection . (4.6)
Image of page 231
X-Ray Detectors and XRF Detection Channels 211 E 0 0.0 0.5 1.0 FWHM d n d E E Fig. 4.7.
Image of page 232

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 233
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern