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Dipl.-Inf. Wilhelm Haas

Alumnus of the Pattern Recognition Lab of the Friedrich-Alexander-Universität Erlangen-Nürnberg

Technology is for humanity and not vice versa

PHACT - Phase-Contrast Imaging

Motivation

X-rays contain not only information about the absorption properties of a sample but also about the influences of the object material on the phases of the X-ray beams. In the last decades many different approaches have been invented to measure this information. They can be classified in three groups: interferometry, diffractometry and in-line holography. Subject of our research is an approach of the group interferometry, the so called Talbot-grating interferometry [1]. It's one of the first phase-contrast imaging systems which has the potential to be applied in a medical environment.

PHACT Logo

Grating-based Interferometer

Phase-contrast imaging is an approach to gain information about a sample by measuring the local phase of X-rays passing through it. Nowadays experimental techniques have become applicable not only for optical wavelengths but also for wavelengths in the X-ray range [2]. One of them is the grating based interferometry [3], [1], which resolves both the phase and the absorption of the investigated sample.

Setup

Talbot-grating interferometer [1] ( Figure 1) consists of three gratings the source grating G0, phase grating G1 and analyzer grating G3. Each grating has a specific period p and distances l and d. As the name implies this approach is based on the Talbot effect.

Basic setup of a Talbot-grating interferometer
Figure 1: Basic setup of a Talbot-grating interferometer

Talbot effect

Talbot effect was first reported by Talbot in 1836 [4]. It states that a coherent illumination of a periodic structure leads to repetitive intensity patterns in certain distances downstream the wave propagation, frequently called self images. For a phase-grating (with a period p1) impressing a phase shift of π onto an impinging plane wave-front leads to an intensity distribution with a periodicity of p1 / 2 in the following distances

Talbot-distance formula

where λ is the wavelength and n a positive integer. In case of a spherical wave these Talbot-distances rescale to

Rescaled Talbot-distance formula

Differential Phase-Contrast Imaging

Objects placed right in front of the phase-grating G1 distort the interference pattern in the detection plane, which is chosen to be in one of the Talbot- distances. The distortion of a phase-object is given by a local angular deviation of the pattern. For X-rays, with λ ≤ 10-10m, the angle is typically in the order of a few microradians. The principle of differential phase contrast imaging is to detect these deviations by placing an absorption grating G2 with the periodicity of the interference fringes p2 right in front of the detection plane [1]. In case of a X-ray tube with a large focal spot p0 >> p2 · l / d an absorption grating G0 has to be placed directly in front of the latter to achieve a sufficient degree of spatial coherence [1]. To gain the differential phase of an object one now acquires a sequence of images with an appropriate pixelated detector behind the analyzer grating [5]. After each image the grating is moved a fraction of its own periodicity until at least one period of p2 is stepped. Doing this for each single pixel an intensity-modulation with respect to the grating position can be seen. In an ideal setup this modulation is described by a triangle-function as both the interfering intensity pattern and the absorption grating G2 are equal rectangle functions. If an object in the way of the wave-field shifts the intensity pattern laterally the detected modulation in each pixel will as well be shifted.

The triangle function as the ideal intensity modulation
Figure 2: The triangle function as the ideal intensity modulation.

Figure 2 depicts the ideal case of the described procedure for one pixel. The shifted phase between the images without and with an object in the wave- field is the desired measure of the angular deviation. Knowing this local deviation it is straight forward to calculate the gradient of the total phase shift Φ throughout the object by [6]

Phase Integration Formula

Herein x denotes the axis perpendicular to the grating bars. The phase shift can be subsequently obtained after one dimensional integration.

Examples

Following images were taken in our Lab at the ECAP Institute. Figure 3 shows a small fish and Figure 4 a rasin. Both data were acquired with a 80 keV tungsten spectrum and the Medipix 2 detector. The images show from left to right the differential phase-contrast image, absorption image and a so called dark-field image.

Differential Phase-Contrast Image of a small fish
Figure 3: From left to right: differential phase-contrast image, absorption image and dark-field image of a small fish

Differential Phase-Contrast Image of a raisin
Figure 4: From left to right: differential phase-contrast image, absorption image and dark-field image of a raisin

Publications

Journal Articles
Weber, Thomas; Bayer, Florian; Haas, Wilhelm; Pelzer, Georg; Rieger, Jens; Ritter, André; Wucherer, Lukas; Durst, Jürgen; Michel, Thilo; Anton, Gisela
Energy-dependent visibility measurements, their simulation and optimisation of an X-ray Talbot-Lau Interferometer
Journal of Instrumentation, vol. 7.02, pp. P02003, 2012 (BiBTeX, Who cited this?)
Weber, Thomas; Bayer, Florian; Haas, Wilhelm; Gödel, Karl; Pelzer, Georg; Rieger, Jens; Ritter, André; Lukas Wucherer; Durst, Jürgen; Michel, Thilo; Anton, Gisela
Spectrum optimization of a Talbot-Lau interferometer towards clinical application
Proceedings of SPIE, vol. 8313, pp. 83135F-83135F-6, 2012 (BiBTeX, Who cited this?)
Bayer, Florian; Gödel, Karl; Haas, Wilhelm; Rieger, Jens; Ritter, André; Weber, Thomas; Wucherer, Lukas; Durst, Jürgen; Michel, Thilo; Anton, Gisela
Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer
Proceedings of SPIE, vol. 8313, pp. 83135I, 2012 (BiBTeX, Who cited this?)
Articles in Conference Proceedings
Haas, Wilhelm; Polyanskaya, Maria; Bayer, Florian; Gödel, Karl; Hofmann, Hannes; Rieger, Jens; Ritter, André; Weber, Thomas; Wucherer, Lukas; Durst, Jürgen; Michel, Thilo; Anton, Gisela; Hornegger, Joachim
SPIE Medical Imaging 2012 (Conference) (SPIE Medical Imaging 2012), San Diego, CA, USA, 04.02.2012 - 09.02.2012, pp. n/a, 2012 (BiBTeX, Who cited this?)
Bayer, Florian; Anton, Gisela; Durst, Jürgen; Haas, Wilhelm; Michel, Thilo; Pelzer, Georg; Rieger, Jens; Ritter, André; Weber, Thomas
Defect Site Detection in CFRP Composite Materials Using Interferometric X-Ray Phasecontrast Imaging
DGZfP-Proceedings BB 138 (4th International Symposium on NDT in Aerospace), Augsburg, November 13-15, pp. -, 2012, ISBN 978-3-940283-46-7 (BiBTeX, Who cited this?)
Journal Articles
Weber, Thomas; Bayer, Florian; Haas, Wilhelm; Pelzer, Georg; Rieger, Jens; Ritter, André; Wucherer, Lukas; Durst, Jürgen; Michel, Thilo; Anton, Gisela
Energy-dependent visibility measurement and its simulation in X-ray Talbot interferometry
2011 IEEE Nuclear Science Symposium Conference Record, pp. 2488-2490, 2011 (BiBTeX, Who cited this?)
Weber, Thomas; Bartl, Peter; Durst, Jürgen; Haas, Wilhelm; Michel, Thilo; Ritter, André; Anton, Gisela
Measurements and simulations analysing the noise behaviour of grating-based X-ray phase-contrast imaging
Nuclear Instruments and Methods in Physics Research Section A, vol. 648, pp. 273-275, 2011 (BiBTeX, Who cited this?)
Weber, Thomas; Bartl, Peter; Bayer, Florian; Durst, Jürgen; Haas, Wilhelm; Michel, Thilo; Ritter, André; Anton, Gisela
Noise in x-ray grating-based phase-contrast imaging
Medical Physics, vol. 38.7, pp. 4133-4140, 2011 (BiBTeX, Who cited this?)
Ritter, André; Bartl, Peter; Bayer, Florian; Durst, Jürgen; Haas, Wilhelm; Michel, Thilo; Pelzer, Georg; Weber, Thomas; Anton, Gisela
Optimization of differential phase-contrast imaging setups using simulative approaches
Proceedings of SPIE, vol. 7961, pp. 79614V, 2011 (BiBTeX, Who cited this?)
Bartl, Peter; Bayer, Florian; Durst, Jürgen; Haas, Wilhelm; Michel, Thilo; Ritter, André; Weber, Thomas; Anton, Gisela
Simulations and Measurements of Grating Based X-ray Phase-Contrast Imaging
Nuclear Instruments and Methods in Physics Research Section A, vol. 648, pp. 269-272, 2011 (BiBTeX, Who cited this?)
Weber, Thomas; Bartl, Peter; Bayer, Florian; Durst, Jürgen; Haas, Wilhelm; Michel, Thilo; Pelzer, Georg; Ritter, André; Anton, Gisela
Spectroscopic measurements concerning grating-based x-ray phase-contrast imaging
Proceedings of SPIE, vol. 7961, 2011 (BiBTeX, Who cited this?)
Bartl, Peter; Bayer, Florian; Durst, Jürgen; Haas, Wilhelm; Michel, Thilo; Ritter, André; Weber, Thomas; Anton, Gisela
Grating-based High Energy X-ray Interferometry with the Medipix-Detector in Simulation and Measurement
Journal of Instrumentation, vol. 5.10, pp. P10008, 2010 (BiBTeX, Who cited this?)
Bartl, Peter; Durst, Jürgen; Haas, Wilhelm; Hempel, Eckard; Michel, Thilo; Ritter, André; Weber, Thomas; Anton, Gisela
Simulation of X-ray Phase-Contrast Computed Tomography of a Medical Phantom Comprising Particle and Wave Contributions
Proceedings of SPIE, vol. 7622, pp. 76220Q, 2010 (BiBTeX, Who cited this?)
Bartl, Peter; Durst, Jürgen; Haas, Wilhelm; Michel, Thilo; Ritter, André; Weber, Thomas; Anton, Gisela
Simulation of X-ray phase-contrast imaging using grating-interferometry
2009 IEEE Nuclear Science Symposium Conference Record, pp. 3577-3580, 2010 (BiBTeX, Who cited this?)
Articles in Conference Proceedings
Haas, Wilhelm; Bartl, Peter; Bayer, Florian; Durst, Jürgen; Grund, Thomas; Kenntner, Johannes; Michel, Thilo; Ritter, André; Weber, Thomas; Anton, Gisela; Hornegger, Joachim
Nuclear Science Symposium and Medical Imaging Conference Records (2010 Nuclear Science Symposium and Medical Imaging Conference), Knoxville, TN, USA, 30.10.2010-6.10.2010, pp. -, 2010 (BiBTeX, Who cited this?)

References

  1. F. Pfeiffer, T.Weitkamp, O. Bunk, C. David, "Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources," Nature Phys. 2, 258-261, 2006
  2. S.W. Wilkins, T.E. Gureyev, D. Gao, A. Pogany, A.W. Stevenson, "Phase-contrast imaging using polychromatic hard x-rays," Nature 384, 335-337, 1996
  3. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, T. Hattori, "Phase tomography by X-ray Talbot interferometry for biological imaging," Jpn. J. Appl. Phys., 45 (6A), 5254-5262, 2006
  4. Talbot, H.F., Philos. Mag., 9, 403, 1836
  5. Weitkamp, T., et al., "X-ray phase imaging with a grating interferometer," Optics Express Vol. 13, No. 16, 6296-6304, 2005
  6. Born, M., Wolf E., "Principles of Optics," Cambridge University Press, 1997