IMAGING: Tomographic imaging reveals PC fiber refractive-index distribution

Tomography—the process of imaging an object by sectioning it and applying a tomographic algorithm for data analysis—can be combined with the multidirectional phase data obtained through interferometry to create three-dimensional (3-D) refractive-index distributions of objects such as gas flows, plasmas, or even optical microelements. Unfortunately, interferometric tomography suffers if diffraction and refraction effects are present within the object to be imaged, such as in the case of photonic-crystal (PC) fibers. However, by using a diffraction-tomography algorithm, rather than the conventional filtered-backprojection algorithm, researchers at the Institut für Technische Optik (Stuttgart, Germany) can successfully reconstruct the refractive-index distribution of a complex PC fiber.¹

Reconstruction methods such as filtered backprojection are based on Fourier-slice theorem. They assume straight lines for the light propagation through an object. However, the Fourier-diffraction theorem allows refraction and small diffraction effects in reconstructing the refractive-index profile for PC fibers. In addition to diffraction effects, radial run-out is also an issue. Radial run-out occurs when the position of the rotation axis of the tested element is unstable and changes in the radial dimension, causing an unwanted radial movement of the object under test. Although an improved setup is being developed to reduce radial run-out, the correction of the position of the fiber is performed manually by the researchers to offset this run-out value, which can result in an error as large as 10 µm for a 1 µm run-out value.

Taking measurements

Within the framework of a project financed by the German Research Foundation (DFG), the compact tomographic microinterferometer for PC fiber measurement was constructed. An 8 mW helium-neon laser was split into two beam paths; one was collimated and sent to the immersion vessel that contained the PC fiber immersed in oil, while the second beam was collimated, modulated, and made to interfere with the output from the first beam at the surface of a beamsplitter. The interference signal was sent to a 1392 × 1040-pixel camera. The measurement was fully automated such that the PC fiber could be rotated (as well as manually translated). The measurement was made by acquiring five interferograms—each with a phase shift of π/2-at 30 angular positions (6° rotation for each measurement to cover 180°), determining the phase map for each angular position, correcting radial run-out, and then performing tomographic reconstruction.

The researchers compared the results of using filtered-backprojection and diffraction-tomographic algorithms to obtain the reconstructed image (see figure). The diffraction-tomography method (based on Fourier diffraction theorem) produced a more accurate result than the filtered-backprojection method derived from the Fourier-slice theorem. When the diffraction-tomography method was used, the shape of the fiber holes was correctly imaged as circles, while filtered backprojection introduced triangular artifacts.

In addition, the authors applied a synthetic-aperture technique to the tomographic microinterferometer, which resulted in a high-resolution tomogram (even with the relatively low numerical aperture of the imaging system) and allowed a longer working distance and fewer aberrations.

“Photonic-crystal fibers have already gained a significant place in the market,” says researcher Witold Gorski. “Technological progress requires a reliable measurement tool, and tomographic microinterferometry has a good chance to become one. Using tomography we obtain direct information about the inner structure of the fiber, while the majority of methods are based on indirect measurements (such as diffraction efficiency). Now, we can detect physical reasons for fiber malfunctions and formulate precise corrections.”

REFERENCES

1. W. Gorski and W, Osten, Optics Letters32(14), 1977 (July 15, 2007).