OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 13 — Jun. 21, 2010
  • pp: 13478–13491
« Show journal navigation

Assessment of the use of a diffuser in propagation-based x-ray phase contrast imaging

S. C. Irvine, K. S. Morgan, Y. Suzuki, K. Uesugi, A. Takeuchi, D. M. Paganin, and K. K. W. Siu  »View Author Affiliations


Optics Express, Vol. 18, Issue 13, pp. 13478-13491 (2010)
http://dx.doi.org/10.1364/OE.18.013478


View Full Text Article

Acrobat PDF (14875 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A rotating random-phase-screen diffuser is sometimes employed on synchrotron x-ray imaging beamlines to ameliorate field-of-view inhomogeneities due to electron-beam instabilities and beamline optics phase artifacts. The ideal result is a broader, more uniformly illuminated beam intensity for cleaner coherent x-ray images. The spinning diffuser may be modeled as an ensemble of transversely random thin phase screens, with the resulting set of intensity maps over the detector plane being incoherently averaged over the ensemble. Whilst the coherence width associated with the source is unaffected by the diffuser, the magnitude of the complex degree of second-order coherence may be significantly reduced [K. S. Morgan, S. C. Irvine, Y. Suzuki, K. Uesugi, A. Takeuchi, D. M. Paganin, and K. K. W. Siu, Opt. Commun. 283, 216 (2010)]. Through use of a computational model and experimental data obtained on x-ray beamline BL20XU at SPring-8, Japan, we investigate the effects of such a diffuser on the quality of Fresnel diffraction fringes in propagation-based x-ray phase contrast imaging. We show that careful choice of diffuser characteristics such as thickness and fiber size, together with appropriate placement of the diffuser, can result in the ideal scenario of negligible reduction in fringe contrast whilst the desired diffusing properties are retained.

© 2010 OSA

1. Introduction

As mentioned previously, the need for a diffuser stems from the difficulty in achieving a perfectly uniform x-ray beam for the full field of view using a synchrotron source. This is particularly evident when the area to be illuminated is relatively large (e.g. several millimeters to centimeters in extent), as required in biomedical small animal in vivo imaging [5

5. T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen's rays: Propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005–102012 (2009). [CrossRef]

], where the frame-to-frame movement of the beam is particularly problematic. Further to this, short exposure times (e.g. on the order of 100ms) are helpful in avoiding image blur due to animal movement, and those experiments which attempt to observe rapid biomedical dynamics such as blood flow [6

6. S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008). [CrossRef]

,7

7. S. C. Irvine, D. M. Paganin, A. Jamison, S. Dubsky, and A. Fouras, “Vector tomographic X-ray phase contrast velocimetry utilizing dynamic blood speckle,” Opt. Express 18, 2368-2379 (2010). [CrossRef] [PubMed]

], require even shorter exposures. With such short exposures it becomes more apparent that fluctuations in the electron-beam stability are causing a time-varying beam, which imposes undesirable inhomogeneities in propagation-based x-ray phase contrast images.

Further image inhomogeneities may be imposed by imperfections in various beamline components [8

8. J. M. Cowley, Diffraction physics (third edition) (Amsterdam: North-Holland Publication, and New York: Elsevier Publication Co., 1995).

,3

3. P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29(1), 133–146 (1996). [CrossRef]

]. Indeed, it is precisely because propagation-based x-ray phase contrast is so sensitive to transverse phase variations, that even minute variations (due e.g. to beryllium windows, insufficiently flat reflecting optics, inhomogeneities in beam curvature etc.) may lead to artifacts in the image of a sample. The introduction of a diffuser will both minimize the presence of these phase artifacts in the final image of the sample, as well as creating a more stable area of uniform intensity [2

2. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995). [CrossRef]

,3

3. P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29(1), 133–146 (1996). [CrossRef]

,9

9. D. L. White, O. R. Wood, J. E. Bjorkholm, S. Spector, A. A. MacDowell, and B. LaFontaine, “Modification of the coherence of undulator radiation,” Rev. Sci. Instrum. 66(2), 1930 (1995). [CrossRef]

]. One thereby remains sensitive to transverse phase gradients imposed by the sample, whilst simultaneously being insensitive to transverse phase gradients which are not due to the sample.

As an example of the non-uniform illumination which will be present in even the best of third-generation synchrotrons, a 25keV (as used in biomedical imaging [10

10. R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49(16), 3573–3583 (2004). [CrossRef] [PubMed]

]) flat field image observed at the bio-medical imaging hutch of beamline 20XU at SPring-8, Japan, is shown in Fig. 1
Fig. 1 Flat field at BL20XU as seen (a) without a diffuser, (b) with a stationary diffuser and (c) with a spinning diffuser. Power spectra (|FFT{I}|2) are shown inset. (Media 1).
. Without a diffuser present (Fig. 1a), the beam shows a high intensity peak (visible as a red stripe in the false-color map), which represents the temporally-varying incident intensity averaged over a single exposure. As shown in the movie supplementary to Fig. 1 (Media 1), consecutive image frames show significant frame-to-frame variation. There is also propagation-based phase contrast introduced by the non-ideal optics, as indicated by the arrows. As shown in Fig. 1b, when a stationary diffuser (see Sec. 2 for details) is introduced, the illuminating area becomes significantly more uniform, but still shows some movement with time (supplementary Fig. 1 (Media 1)). The flat field has phase images and intensity variations characteristic of the part of the diffuser positioned in the beam. Rotating the diffuser, so that the illuminated area changes over time, will mean that these variations are averaged out over the exposure time. This will produce a field that is even in space and over time, provided that the image exposure time is long compared to the characteristic timescale of the rotating diffuser (Fig. 1c and supplementary Fig. 1 (Media 1)). The placement of this random phase screen directly after the optics means that the phase artifacts in the flat-field image are blurred out.

As seen in the inset to Fig. 1c, the impulse-like power spectrum of the spinning diffuser flat-field map clearly indicates a uniform intensity. However with either the stationary diffuser or no diffuser, further components are introduced in the low frequency (beam shape), medium frequency (diffuser pattern) and high frequency (beam-line optics phase artifacts) spatial regions of the power spectra. Note that the dark rings, present in the insets to Figs. 1a and 1b, are zeros in the phase contrast transfer function for the coherent x-ray imaging system [8

8. J. M. Cowley, Diffraction physics (third edition) (Amsterdam: North-Holland Publication, and New York: Elsevier Publication Co., 1995).

].

In some bio-medical imaging applications, a single bright/dark phase contrast fringe is all that is desired, to reveal the position of an interface [4

4. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996). [CrossRef]

]. Other applications require multiple fringes, either to permit use of a phase retrieval algorithm [16

16. T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004). [CrossRef]

], or so that the fringe pattern may be easily identified amid surrounding intensity variations [17

17. K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008). [CrossRef] [PubMed]

]. It is for this reason that we study the optimal diffuser set-up in this paper.

This analysis looks at both simulated and experimental propagation-based phase contrast images with 25keV energy and an object-to-detector propagation distance of between 0.5 and 1.45 meters. The computer simulation is based on a diffuser model described in [1

1. K. S. Morgan, S. C. Irvine, Y. Suzuki, K. Uesugi, A. Takeuchi, D. M. Paganin, and K. K. W. Siu, “Measurement of hard x-ray coherence in the presence of a rotating random-phase-screen diffuser,” Opt. Commun. 283(2), 216–225 (2010). [CrossRef]

], evaluating the incoherent sum of a number of simulated phase contrast images, each produced with an incident field that has incurred random transverse phase variations of a specified characteristic depth and width at the diffuser position. The incoherent ensemble average, due to these many diffuser positions over a complete exposure, forms the phase contrast image.

We close the introduction with a summary of the remainder of the paper. In section 2, we outline our phase contrast x-ray imaging experiment and describe the key observations relating to the effect of a phase diffuser on our phase contrast images. The numerical simulation, based on our model for the phase diffuser, is detailed and implemented in section 3. The final section compares theory and experiment, quantifying the effect of a diffuser on the visibility and number of observable fringes in a phase-contrast x-ray image of an edge. We conclude with some practical recommendations for future experiments. The most important recommendation is to place the diffuser as close as possible to the x-ray source, in order to retain desired fringe information while simultaneously suppressing phase-contrast artifacts due to imperfections in the illuminating beam.

2. Experiment on propagation-based phase contrast imaging with a diffuser

X-ray images were acquired on BL20XU, an undulator-source beamline at the SPring-8 synchrotron in Japan. We worked at the downstream hutch, which gives a source-sample distance of 240m. A double crystal Si-111 monochromator was used to select x-rays at an energy of 25keV. The high resolution detector system used comprised a 4008 × 2672 pixel CCD camera coupled to a Hamamatsu AA50 x-ray converter with a 50× objective lens, yielding an effective pixel size of 0.18μm.

The diffuser utilized at this beamline consists of a ≈12cm diameter circular disk of conventional office-grade white copy paper (80 g/m2) which was made to rotate within a plane perpendicular to the x-ray optical axis. A set of slits created a 300 μm × 300 μm aperture which acted as a secondary source. The diffuser used on this beamline was located approximately 78m from the source and 29m from the aperture (see Fig. 2
Fig. 2 Experimental set-up at SPring-8 x-ray synchrotron beamline BL20XU, using 25keV x-rays to produce propagation based phase contrast images (object-to-detector propagation distance between 0.5 and 1.45m). Images recorded on a CCD camera coupled to a phosphor screen and optical lens, producing 0.18μm effective pixel size.
).

Samples for this experiment were a cylindrical perspex rod (diameter 3.0mm), and two perspex spheres of 1.5mm diameter which in projection overlapped very slightly (region of overlap was approximately 30μm at its widest point, see inset to Fig. 3a
Fig. 3 The observed effects of a diffuser on the visibility of fringes in the propagation-based phase contrast image of two 1.5mm diameter Perspex spheres at 1.45m object-to-detector propagation distance. In projection, the spheres share an overlap region of up to 30μm, which results in a complex interference pattern. (a) Image in the absence of a diffuser. The field-of-view here is illustrated by the black box in the inset, which shows the projected thickness image of the two spheres. (b) Magnified region of lattice-like interference pattern in Fig. 3a (region denoted by red box), still in the absence of a diffuser. (c) The same region, this time taken with diffuser present. Note the absence of central intersecting fringes in (c), when compared to (b).
). On this beamline, at sample-to-detector propagation distances ranging from 0.5 to 1.45m, these objects produce tens of Fresnel-regime phase contrast fringes. In the case of the overlapping spheres, these fringes intersect, forming lattice-like sets of intensity peaks whose visibility is highly sensitive to the effect of a diffuser. Such a region is shown in Figs. 3b and 3c, clearly demonstrating the reduction in area and visibility of fringes when a diffuser is introduced in the experiment.

3. Model for x-ray diffuser in propagation-based phase contrast imaging

The effect of the spinning diffuser is computationally modeled as a series of random transverse phase perturbations, each added to the phase of the simulated x-ray wavefield at the position of the diffuser, propagated and the resulting intensity map summed incoherently at the detector plane. The random transverse phase distribution is characteristic of the thickness and fiber size of the paper. An optical microscopic image of the paper surface (at 12.5× magnification) is shown in Fig. 4
Fig. 4 (a) Optical microscope image of the diffuser paper used. (b) Line profile through one two-dimensional realization of the transversely random phase map used to simulate the diffuser as a thin phase screen, before propagation.
, demonstrating a range of features ranging from coarse (e.g. α) to fine (e.g. β). The azimuthally-averaged power spectrum of this image is well approximated by a two-dimensional Lorentzian whose full width at half maximum (FWHM) corresponds in real space to 7µm. For each term in the time-sum, a particular random phase screen realization is generated beginning with a normally-distributed white-noise random two-dimensional array which is then spatially smoothed by Fourier-space multiplication with the normalized Lorentzian. The smoothed transversely random array is multiplied by the mean paper thickness Tpaper, the vacuum x-ray wavenumber (2π/λ) and the refractive index phase decrement δ according to the projection approximation (see [18

18. D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, New York, 2006).

]) (Eq. (1)). This phase shift is then added to the diffuser-incident phase φbefore diffuser(x,y), to give the diffuser-exit phase φafter diffuser(x,y) as a function of coordinates (x,y) perpendicular to the optic axis:

φafter diffuser(x,y)=φbefore diffuser(x,y)2πλδpaperTpaper×Random Screen(x,y).
(1)

We used δ = 2.75 x 10−7 for paper, producing phase depths with a standard deviation of approximately 1.25 radian at 25keV, illustrated by the example profile in Fig. 4b.

In the diffuser plane, the phase shift of the modeled paper is added to the wavefield phase, which is then propagated to the sample position. The projection approximation is again utilized to calculate the relative phase change and attenuation due to the sample of material components j:

Ψ(x,y,z=z0)=exp{ikj[δjiβj]dz}Ψ(x,y,z=0).
(3)

Parameters δj and βj=λμj/4π respectively quantify the refractive and absorptive properties of material j, where μj is the linear absorption coefficient.

The angular-spectrum formalism (Eq. (2)) is then used once more to simulate the propagation over the object-to-detector distance. A single intensity image over the detector plane then simulates a single position of the diffuser. The incoherent ensemble average over many such diffuser positions produces a smooth background in the final image, simulating the observed image for a complete exposure.

Note that the very long propagation distances from diffuser to object (over 150m), and an object resolution of micrometers, necessitated use of the 32GB RAM VPAC computer cluster [21

21. VPAC, “Victorian Partnership for Advanced Computing,” (2010), http://www.vpac.org/.

] to sustain very large array calculations (up to 8000 × 8000 pixels) for accurate resolution of the free-space propagator (for small wavelengths, the limiting propagation distance is proportional to the array dimensions and the square of the pixel size) [22

22. A. Barty, “Quantitative Phase-Amplitude Microscopy, PhD Thesis,” (University of Melbourne, Melbourne, 1999).

].

Figures 5a-5c, shown below, illustrate the effect of this process. In Fig. 5a, simulated phase contrast fringes present due to Fresnel diffraction from the edges of a 3mm diameter perspex cylinder are seen. Figure 5b shows a single realization of the diffuser model, with distorted fringes and overlying ‘image’ of the diffuser. Interestingly, the speckle from the given realization of the diffuser’s thin random phase screen, has a visibility comparable to the fringes produced by the object. (The intensity variations of Fig. 5b are greater than that seen in the observed stationary diffuser flat field of Fig. 1b due to the finite length of the exposure time and beam movement within this time.) These random undulations in the phase incident on the sample locally distort the image for each diffuser realization. Figure 5c is the incoherent sum of 1000 realizations of the diffuser model, wherein the phase contrast fringes of Fig. 5a are once again apparent but at a reduced visibility. Several of the narrowest fringes are no longer visible. The speckles due to the diffuser itself are no longer seen, as the ensemble average of many random realizations over the full exposure time becomes a smooth background of unresolved x-ray speckle.

To complete the simulations, the modelled phase contrast images were convolved with the detector point spread function (PSF). The 1D PSF was measured from experiment as the derivative of a knife-edge image [23

23. W. Leitenberger, H. Wendrock, L. Bischoff, and T. Weitkamp, “Pinhole interferometry with coherent hard X-rays,” J. Synchrotron Radiat. 11(2), 190–197 (2004). [CrossRef] [PubMed]

], yielding a PSF of 1.2μm FWHM.

The results of this simulation modeling the same two spheres as in Fig. 3, are shown below in Fig. 6
Fig. 5 Simulated phase contrast images of a 3mm diameter cylinder with 1.45m propagation, using (a) no diffuser, (b) a single diffuser position and (c) the incoherent sum over 1000 diffuser realizations.
Fig. 6 Simulated phase contrast images of 1.5mm diameter spheres seen experimentally in Fig. 3, modelled without, then with a diffuser. (a) Image in the absence of a diffuser. (b) Magnified region of the lattice-like interference pattern (region denoted by red box) in (a). (c) The same region of a similar image, this time modelled with diffuser present.
, matching very well in terms of the fringe patterns and visibility. Again, both the contrast and number of visible fringes are greatly reduced when the diffuser is present (Fig. 6c) compared to when the diffuser is not used (Fig. 6b). The effect is exacerbated when a small degree of noise (approx 2%, consistent with experimental noise levels), is added to the simulated images (not shown).

4. Comparison between modeling and experiment, for x-ray phase contrast diffuser

In order to quantitatively determine the effect of the diffuser on propagation-based x-ray phase contrast images, in both simulation and experiment, we applied Michelson’s measure for interference fringe visibility V over the entire fringe set [24

24. A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, 1927).

,25

25. M. Born, and E. Wolf, Principles of optics (Cambridge University Press, Cambridge, 1999).

]:

V=ImaxIminImax+Imin.
(4)

To obtain a single phase-contrast intensity profile for this analysis, cylinder images were row-averaged, showing reasonable agreement between experimental results and our model, as shown in Fig. 7
Fig. 7 Observed decrease in visibility of phase contrast fringes seen at the edge of a 3mm cylinder, taken with 1.45m propagation, (a) in simulation and (b) observed.
. The diffuser is seen to decrease both the visibility and number of phase contrast fringes, in both experiment and in simulation. This detailed fringe information may be valuable in quantitative image analysis, e.g. in the context of phase-retrieval algorithms which utilize such information [16

16. T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004). [CrossRef]

], however the narrowest fringes are suppressed by the diffuser.

The relative effect of the diffuser on fringe visibility is dependent on the propagation-distance between sample and detector. In the Fresnel regime, increasing propagation causes an increase in fringe contrast and spacing. The visibility of the wider fringes seen at large propagation distances is also less affected by the point spread function of the detector, when compared to the narrower fringes obtained at smaller propagation distances. The rate of increase of fringe visibility as a function of propagation distance is reduced when the diffuser is introduced. This means that the diffuser makes more of a difference at the greater sample-to-detector propagation distances, as shown in Fig. 8a
Fig. 8 (a) Visibility and (b) Width across which fringes from the edge of a 3mm decreases when a diffuser is introduced, with most effect at long propagation distance, both observed and in simulation.
. The percentage decrease in visibility incurred by a diffuser increases by a factor of around 9% when moving from 0.5 to 1.5m propagation.

The phase variations which determine the efficacy of the diffuser may be described by both the phase depth Δφ and characteristic transverse length scale l of the resulting wave-field phase. Speaking only of the un-propagated wavefield (i.e., the wavefield at the exit-surface of the diffuser), the phase depth of the wavefield is determined according to the projection approximation, which incorporates x-ray energy, the phase decrement δ of the diffuser material and the variations in the projected thickness of the material. The characteristic transverse length scale l is determined by the size distribution of the diffuser constituent materials which give rise to those projected thickness variations, together with the thickness of the diffuser.

A simple descriptor which combines the properties Δφ and l is that of a ‘root-mean-square (RMS) transverse phase gradient’; roughly speaking it is given by Δφ/ l. In Figs. 9a
Fig. 9 Visibility of phase contrast fringes decreasing with (a) increasing phase depth Δφ, (b) decreasing characteristic length l. Propagation distance is 1.0 m.
and 9b are shown the simulated effects of changing these properties, on the Fresnel-regime fringes of the Perspex cylinder image. For simplicity the phase of each cylinder-entrance wavefield was generated directly, i.e. without prior propagation, using Gaussian length-scale distributions. Figure 9a keeps l constant at 20μm FWHM and varies the phase-depth Δφfrom a standard deviation of 0.2 rad to 2.0, whilst Fig. 9b keeps Δφ constant at a standard deviation of 1.0 rad and varies l from 2um to 20um.

In Fig. 9a the profile with a Δφ = 0.2 rad is almost indistinguishable from the profile simulated without any diffuser. As the phase depth is increased the profile is increasingly strongly smoothed until the Δφ = 2.0 rad profile is so strongly smoothed as to have lost all fringe information altogether. These profiles are visually comparable to convolution of the no-diffuser profile with a Gaussian whose FWHM varies with the square of the phase depth.

In Fig. 9b, where the characteristic length scale l of the diffuser material is varied, the effect at large length scales (or small phase gradient) is consistent with a slight smoothing effect. As the length scale is decreased, the fringe contrast is further reduced however the smallest fringes are still apparent. The 2μm FWHM length-scale profile has a much smaller absolute visibility than the largest phase depth profile in Fig. 9a and yet has retained significant fringe information. As such, it appears that the larger length scale variations in phase must also be present to smooth out the narrow fringes, as was observed in experiment.

Propagation of the wavefield from diffuser to sample was shown in simulations to result in negligible changes in phase depth. However, due to the relatively large propagation distances involved (see Fig. 2) and the corresponding scaling associated with Fraunhofer diffraction, the characteristic transverse length scale is increased as the whole wavefield is magnified with distance by the factor:
M=R'1+R2R'1,
(5)
where R’1 is the effective source-to-diffuser distance (corresponding to a point source), and R2 is the diffuser-to-sample distance. R’1 in our case was determined by the size of the aperture, and found to be approximately 37m upstream of the aperture.

Figure 11
Fig. 11 The characteristics and position of the diffuser will determine the phase gradient in the field incident at the sample, hence the effect of the diffuser on the visibility of observed phase contrast fringes.
is a plot showing the simulated effects of changing RMS phase gradient on fringe visibility. The decrease in visibility when changing characteristic transverse length scale is shown on the same axis as when changing phase depth. As always the visibility was calculated from the global maxima and minima of the fringes. There is general overlap between the two series of points, which is consistent with the idea of the RMS phase gradient as the determining factor. The series differ most at higher phase gradients, where the length scale was smallest (and less physically likely).

The simulated visibility at the two diffuser positions are also indicated in Fig. 11. It was seen that by moving the diffuser close to the source, the magnification increase led to a relative phase length which was effectively doubled, i.e. halving the phase gradient. This change is consistent with the effect observed in Fig. 10. The additional propagation from the diffuser to the sample increases the observed coherence, in accord with the van Cittert-Zernike theorem [26

26. P. H. van Cittert, “Die Wahrscheinliche Schwingungsverteilung in Einer von Einer Lichtquelle Direkt Oder Mittels Einer Linse Beleuchteten Ebene,” Physica 1(1-6), 201–210 (1934). [CrossRef]

28

28. F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5(8), 785–795 (1938). [CrossRef]

].

Figure 11 may thus be viewed as a plot which summarizes the deleterious effect of the diffuser on the phase contrast fringe information for a given sample-detector distance. The RMS phase gradient of the x-ray wavefield at the sample entrance plane is characterized by the diffuser position and material, and indicates the strength of the diffuser. The visibility of the resulting detected fringes from a typical sample, relative to their visibility in the absence of the diffuser, is proportional to the factor decrease in the observed degree of coherence which the diffuser causes. Use of too strong a diffuser yields a part of the curve where the decrease in observed fringe visibility and hence degree of coherence may be unacceptable to the user. On the other hand, this loss of coherence may be advantageous if the user wishes to remove phase contrast.

If the user wishes to conserve the observed degree of coherence as much as possible, and yet maintain the desired effects of the diffuser on the intensity homogeneity of the detected beam, it is perhaps easiest to move the position of the diffuser, away from the sample and closer to the source.

5. Summary and Conclusion

A spinning piece of paper represents an extremely simple and low-cost method for the diffusion of hard x-ray beams in the context of propagation-based phase contrast imaging. Use of such a diffuser is of particular benefit to imaging experiments which require close to homogeneous intensity over a broad area and increasingly shorter exposure times, for example in many in vivo biomedical imaging applications. As many of these applications depend on a sufficiently high degree of partial transverse coherence for phase contrast, it is important to minimize the potential associated deleterious effects of the diffuser on fringe visibility. In this work which combines experimental propagation-based phase contrast x-ray imaging data using a diffuser with simulations, we have modeled the effect of the diffuser as the time-averaged incoherent sum of random phase perturbations to the x-ray wavefield. Simulated Fresnel-regime fringes with and without a diffuser were consistent with experimental observations, displaying a significant decrease in both the number and visibility of fringes when the diffuser was introduced into its standard position. The effect was greatest at larger sample-detector distances. The role of the phase distribution of the random screen representing the diffuser, in terms of a characteristic phase depth and length scale, was investigated and discussed in terms of an average absolute ‘phase gradient’. This leads to several practical suggestions for the optimization of a diffuser in terms of minimizing the effect on the degree of coherence at the object and detector. Primarily, it is desirable to place the diffuser as close to the source, or secondary source (e.g. aperture), as possible. The resulting increase in far-field propagation and consequent scaling serves to magnify the length scale of the phase distribution, decreasing the phase gradient and hence the effect on fringe contrast. The combination of thickness/roughness and fiber characteristics of the diffuser-material should also be considered given specific requirements for the detail and visibility of a phase contrast fringe set.

Conversely, it is also possible to apply these principles for opposite effect, in situations where a high degree of coherence is temporarily undesirable. One example of this would be on a synchrotron beamline where pure absorption-based CT is required but a contact (zero distance between sample and detector) image is unachievable.

The position of the diffuser along the beamline may therefore be chosen to produce the required degree of coherence for the imaging required. More importantly, the diffuser will spatially even out the beam and reduce phase effects in the final image.

Acknowledgments

The authors thank the Japan Synchrotron Radiation Research Institute (Proposal number 2008B1985) for the privilege of using the SPring-8 facility to conduct these experiments. We acknowledge funding for the trips to SPring-8 for the Australian co-authors from the Access to Major Research Facilities Program, which is supported by the Commonwealth of Australia under the International Science Linkages program. The computational component of our project was supported by the Victorian Partnership for Advanced Computing HPC Facility and Support Services. Kaye Morgan and Sally Irvine acknowledge the support of an Australian Postgraduate Awards. Kaye Morgan also acknowledges a J. L. William Scholarship from Monash University. David Paganin acknowledges the Australian Research Council. We thank Andreas Fouras for the use of his PCO camera during the experiment, as well as Stephen Dubsky and Simon Higgins for their assistance and the use of their optical microscope for Fig. 4.

References and links

1.

K. S. Morgan, S. C. Irvine, Y. Suzuki, K. Uesugi, A. Takeuchi, D. M. Paganin, and K. K. W. Siu, “Measurement of hard x-ray coherence in the presence of a rotating random-phase-screen diffuser,” Opt. Commun. 283(2), 216–225 (2010). [CrossRef]

2.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995). [CrossRef]

3.

P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29(1), 133–146 (1996). [CrossRef]

4.

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996). [CrossRef]

5.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen's rays: Propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005–102012 (2009). [CrossRef]

6.

S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008). [CrossRef]

7.

S. C. Irvine, D. M. Paganin, A. Jamison, S. Dubsky, and A. Fouras, “Vector tomographic X-ray phase contrast velocimetry utilizing dynamic blood speckle,” Opt. Express 18, 2368-2379 (2010). [CrossRef] [PubMed]

8.

J. M. Cowley, Diffraction physics (third edition) (Amsterdam: North-Holland Publication, and New York: Elsevier Publication Co., 1995).

9.

D. L. White, O. R. Wood, J. E. Bjorkholm, S. Spector, A. A. MacDowell, and B. LaFontaine, “Modification of the coherence of undulator radiation,” Rev. Sci. Instrum. 66(2), 1930 (1995). [CrossRef]

10.

R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49(16), 3573–3583 (2004). [CrossRef] [PubMed]

11.

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, New York, 2007).

12.

L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ Pr, Cambridge, 1995).

13.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997). [CrossRef]

14.

Ya. I. Nesterets, “On the origins of decoherence and extinction contrast in phase-contrast imaging,” Opt. Commun. 281(4), 533–542 (2008). [CrossRef]

15.

K. A. Nugent, C. Q. Tran, and A. Roberts, “Coherence transport through imperfect x-ray optical systems,” Opt. Express 11(19), 2323–2328 (2003). [CrossRef] [PubMed]

16.

T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004). [CrossRef]

17.

K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008). [CrossRef] [PubMed]

18.

D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, New York, 2006).

19.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005).

20.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge Greenwood Village, 2007).

21.

VPAC, “Victorian Partnership for Advanced Computing,” (2010), http://www.vpac.org/.

22.

A. Barty, “Quantitative Phase-Amplitude Microscopy, PhD Thesis,” (University of Melbourne, Melbourne, 1999).

23.

W. Leitenberger, H. Wendrock, L. Bischoff, and T. Weitkamp, “Pinhole interferometry with coherent hard X-rays,” J. Synchrotron Radiat. 11(2), 190–197 (2004). [CrossRef] [PubMed]

24.

A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, 1927).

25.

M. Born, and E. Wolf, Principles of optics (Cambridge University Press, Cambridge, 1999).

26.

P. H. van Cittert, “Die Wahrscheinliche Schwingungsverteilung in Einer von Einer Lichtquelle Direkt Oder Mittels Einer Linse Beleuchteten Ebene,” Physica 1(1-6), 201–210 (1934). [CrossRef]

27.

P. H. van Cittert, “Kohaerenz-probleme,” Physica 6(7-12), 1129–1138 (1939). [CrossRef]

28.

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5(8), 785–795 (1938). [CrossRef]

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(030.6140) Coherence and statistical optics : Speckle
(110.4980) Imaging systems : Partial coherence in imaging
(110.7440) Imaging systems : X-ray imaging
(230.1980) Optical devices : Diffusers
(340.7440) X-ray optics : X-ray imaging

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: January 19, 2010
Manuscript Accepted: April 30, 2010
Published: June 8, 2010

Citation
S. C. Irvine, K. S. Morgan, Y. Suzuki, K. Uesugi, A. Takeuchi, D. M. Paganin, and K. K. W. Siu, "Assessment of the use of a diffuser in propagation-based x-ray phase contrast imaging," Opt. Express 18, 13478-13491 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-13-13478


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. S. Morgan, S. C. Irvine, Y. Suzuki, K. Uesugi, A. Takeuchi, D. M. Paganin, and K. K. W. Siu, “Measurement of hard x-ray coherence in the presence of a rotating random-phase-screen diffuser,” Opt. Commun. 283(2), 216–225 (2010). [CrossRef]
  2. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995). [CrossRef]
  3. P. Cloetens, R. Barrett, J. Baruchel, J. P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29(1), 133–146 (1996). [CrossRef]
  4. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996). [CrossRef]
  5. T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen's rays: Propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105(10), 102005–102012 (2009). [CrossRef]
  6. S. C. Irvine, D. M. Paganin, S. Dubsky, R. A. Lewis, and A. Fouras, “Phase retrieval for improved three-dimensional velocimetry of dynamic x-ray blood speckle,” Appl. Phys. Lett. 93(15), 153901 (2008). [CrossRef]
  7. S. C. Irvine, D. M. Paganin, A. Jamison, S. Dubsky, and A. Fouras, “Vector tomographic X-ray phase contrast velocimetry utilizing dynamic blood speckle,” Opt. Express 18, 2368-2379 (2010). [CrossRef] [PubMed]
  8. J. M. Cowley, Diffraction physics (third edition) (Amsterdam: North-Holland Publication, and New York: Elsevier Publication Co., 1995).
  9. D. L. White, O. R. Wood, J. E. Bjorkholm, S. Spector, A. A. MacDowell, and B. LaFontaine, “Modification of the coherence of undulator radiation,” Rev. Sci. Instrum. 66(2), 1930 (1995). [CrossRef]
  10. R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys. Med. Biol. 49(16), 3573–3583 (2004). [CrossRef] [PubMed]
  11. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, New York, 2007).
  12. L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ Pr, Cambridge, 1995).
  13. A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997). [CrossRef]
  14. Ya. I. Nesterets, “On the origins of decoherence and extinction contrast in phase-contrast imaging,” Opt. Commun. 281(4), 533–542 (2008). [CrossRef]
  15. K. A. Nugent, C. Q. Tran, and A. Roberts, “Coherence transport through imperfect x-ray optical systems,” Opt. Express 11(19), 2323–2328 (2003). [CrossRef] [PubMed]
  16. T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231(1-6), 53–70 (2004). [CrossRef]
  17. K. K. W. Siu, K. S. Morgan, D. M. Paganin, R. Boucher, K. Uesugi, N. Yagi, and D. W. Parsons, “Phase contrast X-ray imaging for the non-invasive detection of airway surfaces and lumen characteristics in mouse models of airway disease,” Eur. J. Radiol. 68(3Suppl), S22–S26 (2008). [CrossRef] [PubMed]
  18. D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, New York, 2006).
  19. J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005).
  20. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge Greenwood Village, 2007).
  21. VPAC, “Victorian Partnership for Advanced Computing,” (2010), http://www.vpac.org/ .
  22. A. Barty, “Quantitative Phase-Amplitude Microscopy, PhD Thesis,” (University of Melbourne, Melbourne, 1999).
  23. W. Leitenberger, H. Wendrock, L. Bischoff, and T. Weitkamp, “Pinhole interferometry with coherent hard X-rays,” J. Synchrotron Radiat. 11(2), 190–197 (2004). [CrossRef] [PubMed]
  24. A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, 1927).
  25. M. Born and E. Wolf, Principles of optics (Cambridge University Press, Cambridge, 1999).
  26. P. H. van Cittert, “Die Wahrscheinliche Schwingungsverteilung in Einer von Einer Lichtquelle Direkt Oder Mittels Einer Linse Beleuchteten Ebene,” Physica 1(1-6), 201–210 (1934). [CrossRef]
  27. P. H. van Cittert, “Kohaerenz-probleme,” Physica 6(7-12), 1129–1138 (1939). [CrossRef]
  28. F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica 5(8), 785–795 (1938). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material


» Media 1: MOV (7898 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited