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NERS/BIOE 580
Lab08 - Detector Module B

Purpose:

In the previous module, we computed the signal and noise that would result if an ideal detector was employed in a radiation imaging system. The results were used to establish the noise equivalent fluence, i.e. NEF or (signal/noise)2, for a system using an ideal detector.

In this module we consider actual detectors which integrate all of the energy or charge produced within the detection device. The response of the detector with respect to the detection of signal and formation of noise have been precomputed and stored in tables of efficiency. These efficiencies are used to determine the noise equivalent fluence (NEF) observed when recording a spectrum of radiation. The results are then evaluated in relation to the ideal NEF to estimate the detective quantum efficiency, DQE, of the system.

Discussion:

For every x-ray impinging on the surface of an imaging device, only a limited number may deposit signal in the detector. For those that do deposit signal, the quantity of energy or charge produced may vary. For x-rays of a particular energy, a distribution function describes the probability that one incident x-ray will deposit energy e or charge n: p(e,E)de or p(n,E)dn These distributions are normalized such that the integral over all possible e or n will be 1.0. The probability value associated with p(0,E)de or p(0,E)dn accounts for x-rays of energy E which do not interact in the detector in a manner which would produce signal.

X-rays may interact by Compton scattering or photoelectric absorption and the energetic electrons produced in these interactions will produce numerous ion pairs. Following photoelectric absorption, the atom involved will produce additional fluorescent radiation as the vacated electron shell is filled by electrons from higher shells. Thus a significant number of secondary radiations from the active detector material or adjacent material will influence p(n,E)dn. The p(n,E)de distributions for the detecters considered in this module were determined by a Monte Carlo radiation transport analysis which described K, L, and M shell secondary radiations. Additional dispersion in the conversion of energy to collected charge was then accounted for to estimate p(n,E)dn.

For monoenergetic radiation, the signal and noise is determined by the first and second moment integral of p(n,E)dn. The signal absorption efficiency and noise transfer efficiency are defined by expressing the result of these integrals relative to E and E2. The signal and noise for a broad spectrum of radiation are then computed by the first and second energy moments of the spectrum with the signal absorption and noise transfer efficiency included within the integral. As described in the documentation, the program detect reads the efficiencies for a specified detector and evaluates these integrals.

Task Det-B1: Detection efficiencies for two actual detectors.

In the _detectors directory are two detector efficiency files called CsI-ccd.det and Sel-tft.det (i.e. in $XSPECT_DIR/_detectors). Examine both of these files.

The CsI-ccd detector data is for a relatively thin layer of CsI (60 microns) coupled to a CCD photodetector array. The optical coupling is through a 4mm thick fiber optic plate which helps shield the CCD from the incident x-ray beam. Without this fiber optic unit, the direct interaction events in the CCD cause excessive noise in the total signal. This detector is designed for imaging with low energy radiation and has been used for speciman imaging with a molybdenum x-ray source. It is typical of detectors that have been considered for digital mammography systems.

The Sel-tft detector data is for a 500 micron thick photoconductive layer of selenium. The charge produced in this layer is assumed to be directly read by a thin film transister array made from amorphous silicon circuits on a glass plate. Radiation transport associated with interactions in the glass and noise associated with the collection of the charge are accounted for with this data. This detector is similar to a commercial system originally developed by Dupont and a similar detector made by Shimadzu for general radiography.

The detective quantum efficiency is the (signal/noise)2 recorded by a detector relative to what would be recorded by an ideal detector. For monoenergetic radiation, the ideal (signal/noise)2 is just equal to the number of monoenergetic quanta. The DQE for monoenergetic radiation of energy E, DQE_E, is then just equal to the signal absorbtion efficiency squared divided by the noise transfer efficiency. DQE_E is tabulated in the fourth column of these detector files.

Use a gnuplot file, L08-Det-B1.gpl, to plot the monoenergetic DQE(E) for the CsI-ccd and Sel-tft detectors over the energy range from 0 to 150 keV;

  • cd '.......\_Rad-Img\_detectors'
  • set title "DQE(E) for monoenergetic x-rays"
  • set xlabel "Energy, keV"
  • set ylabel "DQE(E)"
  • set yrange [0:1.0]
  • set xrange [0:150.0]
  • plot 'CsI-ccd.det' using 1:4 w l t 'CsI ccd', \
  •       'Sel-tft.det' using 1:4 w l t 'Sel tft'
In the first line, use the full path to the _detectors directory. The w l arguments in the plot commands stand for with lines. The t 'text' arguments in the plot commands set the title (t) value for the key legend on the plot. Note the K absorbtion edges for the CsI detector and how the thicker selenium can be used for recording higher energy radiation. Place appropriate legend and titles on this plot and save as L08-Det-B1.png

Task Det-B2: Detection efficiency for a low energy spectrum.

The CsI-ccd detector is typical of detectors used for digital mammography. In this task we will set up a model representative of a clinical mammography system. and compute the NEF and DQE of the system.

As before, make a copy of the labHeader.tcl file and rename for use on this lab (i.e. something like L08-Det.tcl). Set up a model by adding a sequence of procedure calls:

  • spectGen
    • (Molybdenum target x-ray source)
  • atten
    • (intrinsic & added filtration)
  • sr2cm
    • (distance to the object)
  • mR
    • (object entrance exposure)
  • atten
    • (object attenuation)
  • cm2cm
    • (distance to the detector)
  • detect
    • (NEQ for ideal detector)
  • detect
    • (NEQ for CsI-ccd detector)

For the x-ray source, use a molybdenum target with a constant potential and a target angle of 16 degrees. Input the kVp as a variable (kVp) and set the variable to 28.0 for the initial computations. For added filtration use .08cm of Berylium which is the actual exit port material for a Eureka Rad-71 molybdenum x-ray tube. Additionally, use an added filter of .006cm of Molybdenum.

Set the distance to the object with the sr2cm routine at 60 cm and the distance to the detector with the subsequent cm2cm routine at 70 cm. For the object use a total thickness of 6 cm comprised of 2 cm of muscle and 4 cm of fat. This is typical of the composition and thickness of the human breast compressed in clinical mammography systems.

As was done for the previous lab module (Detector-A), set the results of the entrance exposure computation to a variable, (i.e. set mR [lindex [mR] 2] ). To obtain realistic value of NEQ, the detector pixel area (Ap) and the mas for the exposure (mas) must be properly specified. It will be convenient to define these as variables, $Ap and $mAs, early in the script so that they may be conveniently changed. For typical mammography detectors you should set Ap = .000025 cm2 (ie 50 micron pixels). Realistic entrance exposures may be obtained with mas = 50.

For the detectors, define separate NEQ variables for the ideal detector (iNEQ) and the actual detector (aNEQ).

  • set iNEQ [lindex [detect ideal.det $mas $Ap 0] 3]
  • set aNEQ [lindex [detect CsI-ccd.det $mas $Ap 0] 3]
Note: We refer in this section to Noise Equivalent Quanta (NEQ) rather than Noise Equivalent Fluence (NEF) since we are accounting for the detector pixel area, the tube current, and the exposure time.
The DQE is then simply the ratio of aNEQ/iNEQ.
  • set DQE [expr $aNEQ/$iNEQ]
At the end of this model, print out the NEQ, DQE, and mR. Recall that the mR result is returned with mR per mas units. You will need to multiplying by the mas ( i.e. set mR [expr $mR*$mas] ) to get the actual mR.

A statement similar to that used previously can be used to format the results,

  • puts [format "kVp= %3.0f DQE= %4.3f aNEF= %5.0f \
  •         mR= %6.1f" $kVp $DQE $NEF $mR]
In this expression, the format command specifies the value format and provides text strings to identify each value. Further information on the format specifiers is available in any of the Tcl references.

When you run this script, you should get a DQE of 0.529, an actual NEF of 62 #/pixel, and an entrance exposure of 276 mR for the 28 kVp technique which is typical for mammography. In the detector file used, CsI-ccd.det, you can see that the monoenergetic DQE with similar value occurs at about 16 keV which is near the characteristic x-ray peaks for Molybdenum targets.

Task Det-B3: Detection efficiency for a high energy spectrum.

The Sel-tft detector is typical of devices used for general medical radiography and medical chest radiography.

Make a copy of the model just built and modify it to represent conditions relevant to chest radiography. Specifically,

  • X-ray tube changes:
    • tungsten target
    • kVp = 120.0
    • target angle = 10.0
  • filtration changes;
    • .24cm glass-pyrex
    • .31cm oil
    • .27cm lexan (GE Maxiray 125)
    • added .15cm al_1100
  • distance changes;
    • 150 cm to the object
    • 180 cm to the detector (chest imaging)
    object (total thickness of 20 cm);
    • 17cm muscle
    • 3cm fat
  • Sel-tft detector;
    • pixel area of .0004 cm2 (200 microns)
    • mas of 3

When you run this script, you should get a DQE of 0.377, an actual NEF of 424 #/pixel, and an entrance exposure of 19.1 mR for the 120 kVp technique which is typical for chest radiography. In the detector file used, Sel-tft.det, you can see that the monoenergetic DQE with similar value occurs at about 65 keV which is near the characteristic x-ray peaks for Tungsten targets.

Task Det-B4:

Using the scripts for the two system models above, add an appropriate shell loop to compute DQE as a function of kVp. As with the previous module, an appropriate construction would surround the model statements with;

  •     ...
  • set minKV 50
  • set maxKV 150
  • set Incr 10
  • set kVp $minKV
  • while {$kVp <= $maxKV} {
  •     ...
  •     script(Task Det-B3)
  •     ...
  •     incr kVp $Incr
  • }
Where the result is written to the console file, add an additional statement to write the results to a file
  • puts $fileID [format "%3.0f %4.3f %5.0f %6.1f" \
  •       $kVp $DQE $aNEQ $MR]
You will also need to open the file at the beginning of the script
  • set fileID [open L08-Det-tungDQE.txt w+]
  • puts $fileID "# DQE for a tungsten source"
  • puts $fileID "# kVp DQE NEF mR "
and close the file at the end. For the Sel-tft detector and tungsten source use a kVp range from 50 to 150 in increments of 10 as shown in the example above. For the CsI-ccd detector and Molybdenum source use a kVp range from 22 to 50 in increments of 2 and write the results to L08-Det-B4_molyDQE.txt.

For both the CsI-ccd results and the Sel-tft results, use gnuplot to plot DQE vs kVp with appropriate labels using commands similar to those used in the previous lab. As we have done before, you may want to open a file to write the gnuplot commands and execute gnuplot from the script.

Comment:

You will see little variation in DQE at low kVp for the model with the Molybdenum x-ray tube. This is due to the predominant role of the characteristic spectrum which maintains the same energy as kVp is increased. The Molybdenum filter used passes characteristic radiation which is just below the K absorption edge but attenuates the higher energy radiation. The decrease that occurs at somewhat higher values of kVp is caused by bremstrahlung radiation of higher energy which begins to penetrate the Molybdenum filter. This can be seen by examining the shape of the spectrum stored in the spectra.tmp file created when executing the model. The point at which the bremstrahlung "breakthrough" occurs can be changed by changing the molybdenum filter thickness.

For the tungsten target model, the majority of the energy in the x-ray beam is in the bremstrahlung radiation. A more significant and continuous decrease in DQE is observed as the kVp is increased which is associated with the continuous decrease in the detector efficiencies with energy.

The monoenergetic DQE_E has been labeled in this lab with a subscript notation. It is important to recognize that this is only valid for monoenergetic xray spectra. As such, it is rarely measured. Typically, results for DQE_E in the literature have been computed. It is particularly important to realize that the DQE for a polyenergetic spectra can NOT be obtained by integration of DQE_E times the normalized xray energy probability. Rather, one must independently determine the polyenergetic signal and polyenergetic noise by separate integrations using the signal absorption probability and the noise transfer probability. DQE is then deduced for the defined spectrum by computing the SNR2 in relation to that for an ideal detector. This has been done in this module using 'detect'.

Lab08 Results:

For this module, please turn in the plots for the DQE_E versus monenergetic energy and plots and data files for DQE versus kVp for both the tungsten and molybdenum targets. Additionally turn in the final scripts producing the DQE versus kVp results for tungsten and molybdenum targets.

  • L08-Det-B1.png : Monoenergetic DQE plots for two detectors.
  • L08-Det-B4_moly.tcl : Tcl script for Molybdenum target and CsI detector.
  • L08-Det-B4_tung.tcl : Tcl script for Tungsten target and Sel detector.
  • L08-Det-B4_moly.txt : Four column result data file for Molybdenum target.
  • L08-Det-B4_tung.txt : Four column result data file for Tungsten target.
  • L08-Det-B4_moly.png : DQE vs kVp plot for Molybdenum target.
  • L08-Det-B4_tung.png : DQE vs kVp plot for Tungsten target.

L08-Det-B1 Reference script: Lab08_Det-B1.gpl
L08-Det-B4 Reference script: Lab08_Det-B4_moly.tcl
L08-Det-B4 Reference script: Lab08_Det-B4_tung.tcl

Next:

The next module is 09-Image-A.