Typically, x-ray imaging is limited to detection of an object’s absorption or attenuation.  Because many materials have similar absorption coefficients, it is challenging to discriminate between different substances.  Moreover, when resolution is limited by large pixels, as is often the case with medical or security scanners, it is also difficult to distinguish between, for example, liquids and powders.  However, current advances have allowed simple grating-based interferometer versions of x-ray imaging systems to be constructed.  These systems, referred to as Talbot-Lau interferometers, not only provide traditional attenuation images, but they also generate differential phase contrast and scattering (or so-called dark-field) images.  These additional imaging modalities allow for better discrimination between different materials based on varying chemical composition as well as microstructure. 

To date, simulation of Talbot-Lau x-ray imaging interferometers has been restricted to physical optics techniques which are quite limited in the size and complexity of the objects that can be modeled.  However, Jeff Wilde and Lambertus Hesselink at Stanford University have recently shown that non-sequential ray tracing can be used to overcome this limitation.  Above are simulated x-ray images of a monolithic PMMA toothpaste tube, a PMMA shaving cream can, and a stainless-steel jack knife.  Image (a) is a standard x-ray attenuation image.  Image (b) shows the differential phase contrast version, while (c) is the dark field image.  Bulk ray scattering was implemented for the toothpaste tube to make it stand out in dark-field mode; this can represent, for example, scattering from a granular paste.

To simulate their x-ray interferometer using raytrace information, the Stanford scientists combined the power of Matlab with the power of OpticStudio’s Application Programming Interface (API).  The API is an object-oriented programming tool that allows virtually any program full control of OpticStudio.  By combining a raytracing tool with an advanced mathematical tool, new classes of problems can be solved.

The Talbot-Lau interferometer uses three gratings. Grating G0 converts the circular source into an array of quasi-line sources at a specific spatial frequency.  Grating G2, which has a period equal to that of the fringe pattern, is used as a signal analyzer because the detector pixels are too large to directly detect the interferometric fringes.  Grating G1 is used to generate the two interfering beams; the +1 and -1 diffraction orders leave the grating at slightly different angles and interfere at the detector plane.

When no objects are present, a reference interferogram forms on the G2 plane.  When one or more objects are introduced into the beam, the interferogram is perturbed.  Two rays, a reference ray and an object ray, can be traced to predict the local change to the interferogram at the spatial location where the object ray intercepts the detector.  First, the average value of the fringe pattern in the vicinity of the object ray can decrease if the object ray intensity is reduced by attenuation compared to the reference ray.  In addition, the amount of ray deflection due to refraction yields the local fringe phase shift.  By tracing many source rays, the change to the entire interferogram can be ascertained.  Ray scattering, which is a random version of ray deflection, can cause a random combination of fringe phase shifts over any given pixel that receives the scattered rays.  This in turn reduces the detected fringe contrast, which gives rise to the dark-field signal.  So, by tracing a sufficiently large number of rays, high-quality images of realistic objects can be constructed for all three imaging modalities.

The optical model used (sketched below) was in nonsequential mode, and OpticStudio tools such as CAD import, surface scattering, and bulk scattering were utilized.  Matlab was used to control the model, turn objects off and on, launch raytraces, save rays, carry out custom ray sorting and analysis, and reconstruct the final images.

This new approach to Talbot-Lau interferometer modeling can help enable the next generation of medical and security scanners with improved performance and extended capabilities.

Details of the x-ray interferometry work including an experimental verification of the simulation technique can be found in Optics Express.

For detailed information about the optical model by Jeff Wilde and Lambertus Hesselink from Stanford University please read the whitepaper.

Writtent by:

Dr. Jeff Wilde
Stanford University

Erin Elliott
Research and Prototyping Engineer
Zemax