Research Highlights

Electron Radiography

An electron-radiography system, employing the charged-particle radiography technique, was built and commissioned in 2003 to demonstrate the capabilities of low-energy electrons to radiograph thin, static systems. The charged-particle radiography technique was developed with the 800-MeV protons at LANSCE¹ and 24-GeV protons at the Alternating Gradient Synchrotron (AGS) at BNL.² At these facilities, protons have been used to radiograph over 150 dynamic events and countless static objects.

At the front end of the electron radiography system, a “matched” electron beam is injected into the object to be radiographed. As the electrons pass through the object, they interact with the nuclei and electrons of the object, scattering the electrons away from their initial trajectory. After leaving the object, the electrons enter a magnetic lens quadrupole system that focuses the electrons back to an image, removing blur introduced by scattering within the object. A collimator, located at the center of the magnetic lens, is used to remove electrons that have been scattered to large angles within the object. The collimator removes fewer electrons passing through thin sections of the object than it does electrons passing through thick sections of the object. Therefore, the electron transmission at each position in the image provides a measure of the integrated density, or areal density, through the object. A schematic of the electron trajectories through the imaging system is shown in Figure 1. Electrons enter from the left, interact with a thin aluminum foil called a diffuser and are prepared for injection to the object as they pass through two matching quadrupoles. With no object in place, as shown in Figure 1(a), the electrons pass through the center of the collimator, and all electrons will arrive at the image location. In Figure 1(b), a scatterer has been placed at the object location. As the electrons pass through the object, they are scattered away from the injected trajectory. The collimator intercepts electrons that are scattered to large angles. Those electrons that pass through the collimator are refocused to an image at the image location. The measured electron transmission at each point at the image location can then be used to calculate an area density map of the object.

Theory

The magnetic imaging lens is setup in a symmetric Russian quadruplet configuration with alternating quadrupole gradients and is designed to provide a one-to-one map of the electron positions at the object location to positions at the image location. This mapping is described in Equation 1 in TRANSPORT notation:
(1)
where χ₀ and χ'₀ are position and angle at the object location, χ_i is the electron position at the image location, and R is the first order TRANSPORT matrix. By choosing the quadrupole spacings and gradients so that R₁₁ = -1 and R₁₂ = 0, we achieve the one-to-one mapping of electron position while also removing blur from scattering within the object.

As the electrons pass through the object, they also lose energy through interactions with electrons in the object materials. The resulting energy spread of electrons exiting the object makes second-order corrections important in the design of the radiography system. In addition to the first-order mapping (described above), Equation 2 shows the second-order mapping of electron position from the object location to image location: (2)

In Equation 2, T₁₁₆ = ∂χ_i/∂χ₀∂δ and T₁₂₆ = ∂χ_i/∂χ'₀∂δ are elements of the second-order TRANSPORT tensor, and δ = Δ p/p is the fractional momentum deviation away from the central momentum. When optimizing the resolution in the design of the electron-radiography system, delta is determined by the thickness and composition of the object, and T₁₁₆ and T₁₂₆ are parameters of the lens system and cannot be adjusted without disturbing the first-order focus. Therefore, we must choose the position-angle correlation of the electrons entering the object, also called the matching condition, to be χ'_o/χ_o = -T₁₁₆/T₁₂₆ to minimize the effect of second-order chromatic aberations. With this matching condition, the remaining second-order contribution results from scattering in the object, which moves the electrons away from this ideal position-angle correlation. As the electrons pass through the object, they are scattered away from the matched trajectories by an angle, θ. The resulting position mapping from object to image is shown in Equation 3. As shown by this equation, T₁₂₆ becomes the parameter that determines the ultimate position resolution of the electron-radiography system:
(3)

An additional requirement of the electron-radiography system is that the scattering angle within the object, θ, is mapped to the radial position at the collimator location. This angle-to-position mapping will allow the precise removal of electrons that are scattered by the object to angles larger than the collimator cut angle, θ_c. Equation 4 shows the mapping of position and angle at the object location to position at the collimator location, χ_c. Here M is the TRANSPORT matrix from the object location to the center of the imaging lens at the collimator location:
(4)

If we prepare the position angle correlation at the object location χ'₀/χ₀ = -M₁₁/M₁₂, Equation 4 becomes χ'_c = M₁₂θ, which is a simple mapping of scattering suffered in the object to position at the collimator location independent of position at the object location. Mottershead and Zumbro³ have shown that this correlation requirement is equivalent to the correlation needed to cancel the second-order chromatic effects as discussed above. The fortunate coincidence that the same position-angle correlation of the beam both corrects the chromatic effects and maps scattering angle to position at the collimator location has become known as the “Mottershead miracle” and is a characteristic of the symmetric Russian quadruplet lens system.

Because the requirements of a charged-particle radiography system are simple and the Russian quadruplet configuration meets these requirements in an elegant and compact way, a radiography system can be quickly and efficiently designed and constructed. To demonstrate the capabilities of electron radiography, a prototype system was designed, constructed, and tested using off-the-shelf components.

Prototype System

Because of the development of low-energy electron accelerators by the medical industry for cancer-treatment therapy, the technology required to generate high currents of 20-MeV electrons is commercially available. The IAC in Pocatello, Idaho, has salvaged two of these accelerators from medical facilities and operates them for scientific use. The prototype of the electron-radiography system was therefore designed to use 20-MeV electrons from a Varian Clinac S-band accelerator, which operates at 2.9 GHz and provides a 3.25-mA average current for a pulse length ranging from 200 ns to 2 µs. In this configuration, the Varian Clinac S-band accelerator can deliver up to 4 x 10¹⁰ electrons per pulse through the electron-radiography system.

The magnetic lens for the prototype electron-radiography system was designed to use an existing set of quadrupole magnets that were salvaged by the IAC from Boeing’s Free-Electron Laser program. The lens system consisted of six quadrupole magnets. The first two magnets in combination with a diffuser foil setup the injection match to the object location. The remaining four magnets form the imaging lens with a collimator at the center of the radiography system and the image location at the exit of the vacuum system after the last quadrupole. A picture of the radiography system installed at the IAC is shown in Figure 2.

Results from the Prototype System

The first radiographs that were collected with the prototype system were of a 1/16-in.-thick piece of aluminum with “LANL” machined through the plate. Figure 3 shows the results from the first series of radiographs with the prototype system along with a measure of the resolution from this radiograph. The “step” transition along an edge in the radiograph was used to determine the Gaussian line spread function, which was best fit with a Gaussian distribution having a root-mean-square width of 350 µm as expected from the analysis of chromatic blur for this lens system as discussed above.

Because of their small mass, low-energy electrons are easily scattered. To demonstrate this sensitivity, a gold-marker pen manufactured by the Pilot pen company was used to write “eRad” on a piece of paper. The resulting radiograph of this paper is shown in Figure 4. The ink from this pen is 17% copper and the handwriting resulted in a layer of copper on the paper less than 0.001 in. thick. The ink was clearly imaged with ~ 20% contrast. The radiograph also shows the ~ 5% fluctuations caused by areal-density variations within the paper. Also shown in Figure 4 is a radiograph of the magnetic field from a flat dipole magnet similar to those commonly used to make refrigerator magnets. The electrons are scattered as they pass through the magnetic field of the dipole magnet, similar to multiple scattering within an object. These scattered electrons were then removed by the collimator and re-formed into an image mapping out the integrated magnetic-field strength of the dipole magnet.

An aluminum step wedge was also radiographed with a 10-mrad collimator (Figure 5) to demonstrate the capability of electron radiography to measure areal-density variations of thin systems. The three-step aluminum step wedge was constructed out of 0.0015-in.-thick aluminum foil, resulting in area densities of 10 mg/cm², 20 mg/cm², and 30 mg/cm². A plot of the measured transmission across the step wedge (datapoints, blue) is also shown in Figure 5 along with a theoretical calculation of the expected transmission (solid line, red) based on the known areal density and collimator cut angle.

Further Development

Encouraged by the success of the prototype electron-radiography system, a new effort, recently initiated, will improve spatial resolution and increase the penetration capabilities to extend this radiographic technique to thicker systems. The prototype electron-radiography system was designed to use existing quadrupole electro-magnets available at the IAC. To significantly improve the resolution of the radiography system, the quadrupole gradient strength must be increased and the magnets shortened, as demonstrated by Mottershead et al.⁴ with 800-MeV protons. Higher gradient and shorter quadrupoles are easily achieved through the use of permanent magnet quadrupoles. These magnets can be configured in a x5 magnifier geometry to improve the resolution of a 20MeV electron-radiography system by a factor of five over the prototype system. The principles behind the magnifying electron-radiography system are identical to the identity lens system, but they introduce a magnification factor into the beam optics. Using these concepts, an electron-radiography system with commercially available permanent magnet quadrupoles has been designed and is being constructed.

Higher-energy electrons must be used to increase the penetration capabilities of electron radiography. The prototype system was designed for 20-MeV electrons because this energy is easily achieved with readily available electron sources. A program is under way to build a 40-MeV electron-radiography system that will also be constructed from readily available and existing accelerator structures and technology. In the future, a pulsed photocathode injector could be coupled to this 40-MeV accelerator to collect multiple radiographs of dynamic events within thin systems.

Conclusion

A prototype electron-radiography system has been constructed and commissioned at the IAC. This prototype system successfully demonstrated the capabilities of low-energy electrons to image thin, static objects. The experimental measurements of spatial resolution and density reconstruction agree well with models and theoretical predictions. With the proof-of-principle work complete, the concepts of charged-particle radiography are now being used to extend the capabilities of electron radiography to radiograph thicker systems with improved resolution.

References

1. N.S.P King et al., “An 800-MeV proton radiography facility for dynamic experiments,” Nuclear Instruments and Methods in Physics Research A 424, 84-91 (1999).
2. G.E. Hogan et al., “Proton radiography,” in Proceedings of the 1999 Particle Accelerator Conference, A. Luccio and W. MacKay, Eds. (IEEE, Piscataway, NJ, 1999), Vol. 1, pp. 579–584.
3. C.T. Mottershead and J.D. Zumbro, “Magnetic optics for proton radiography,” in Proceedings of the 1997 Particle Accelerator Conference, M. Comyn, M.K. Craddock, M. Reiser, and J. Thomson, Eds. (IEEE, Piscataway, NJ, 1997), Vol. 2, pp. 1397–1400.
4. C.T. Mottershead, D. Barlow, B. Blind et al., “Design and operation of a proton microscope for radiography at 800 MeV,” in Proceedings of the 2003 Particle Accelerator Conference (to be published by IEEE).

Acknowledgment

We would like to thank Tom Mottershead for his valuable insight and guidance in designing the prototype and magnifier lens systems. We would also like to thank Frank Harmon, the IAC director, for his support of these efforts and the support we received from the IAC staff: Brett King for his attention to detail while constructing the prototype system and Kevin Folkman for his untiring operation of the electron accelerator during our experimental campaigns. This work was funded by the LANL LDRD program.

F.E. Merrill, C. Morris, A. Saunders (P-25), K.B. Morley (P-23)

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For more information, contact Frank Merrill at fmerrill@lanl.gov.

Figure 1. Electron trajectories through the electron radiography imaging system. In Figure 1(a), electrons travel along their "ideal" trajectories because there is no scattering within an object. In Figure 1(b), electrons are scattered away from their ideal trajectory as they pass through the object. The electrons that are scattered to large angles are removed at the collimator location. Those electrons that pass through the collimator are reformed to an i mage at the image location.

Figure 2. The prototype electron-radiography system. The electrons from the accelerator enter from the left and are prepared for injection into the object by the diffuser foil and the first two matching quadrupoles. They then pass through the first half of the imaging lenses, a collimator, and the second half of the imaging lenses where they exit the vacuum jacket and form an image at the image location.

Figure 3. Results of the first radiographs collected with the prototype electron-radiography system. This is a radiograph of a 1/16-in. -thick piece of aluminum with "LANL" machined through the plate. The data points in Figure 3(b) show the measured transition in electron transmission across a sharp edge in the radiograph. The line is a fit to the data points assuming a Gaussian line spread function with a root-mean-square width of 350 µm.

Figure 4. Figure 4(a) is a radiograph of "eRad" written on a piece of paper with a golden marker Pilot pen. This ink is 17% copper, and the writing resulted in a layer of copper less than 0.001 in. thick. The radiograph shows ~ 20% contrast in the writing and 5% variations in the areal density of the paper itself. Figure 4(b) is a radiograph of a dipole magnet similar to those used to make refrigerator magnets. The radiograph shows contours of integrated field strength across the surface of the magnet.

Figure 5. A 20-MeV electron radiograph of an aluminum step wedge with 0.002-, 0.004- and 0.006-in. -thick aluminum steps.