Refractive-index profile is measured nondestructively

July 1, 2005
The industry standard for the determination of refractive-index profiles for axially symmetric optical fibers is the refracted-near-field (RNF) technique.

The industry standard for the determination of refractive-index profiles for axially symmetric optical fibers is the refracted-near-field (RNF) technique. This destructive and calibration-intensive method involves measuring the refraction of a laser beam through the endface of a specially prepared (very flat, very clean) optical-fiber sample.

Researchers at the University of Melbourne (Victoria, Australia) have developed a new technique that determines fiber refractive-index profiles based on imaging phase gradients within an optical fiber viewed from the side using bright-field microscopy. This nondestructive method has high spatial resolution, requires no calibration, and yields results comparable to those obtainable using RNF techniques. One of the key advantages of this technique is that it can easily image a fiber in which the index profile varies along its length.

By taking in-focus and defocused bright-field images of the side or transverse view of an optical fiber (with acrylic coating removed), a series of mathematical algorithms can be applied to obtain the refractive-index variation of the optical fiber as a function of the distance from the fiber axis (see figure). By determining the rate at which the intensity of a bright-field image changes with defocus, an algorithm based on fast Fourier transforms can be used to determine the phase gradients introduced into the optical field by the specimen. Once the transverse component of the phase gradient has been computed, knowing that the object is cylindrically symmetric is sufficient to reconstruct the index profile of the optical fiber using the inverse Abel transform.

A transverse phase gradient from the side of a photosensitive optical fiber can be computed from in-focus and defocused bright-field microscope images of the fiber (left). By decomposing the transverse phase gradient as a Fourier series, the inverse Abel transform can be used to reconstruct the refractive-index profile, assuming the fiber is axially symmetric (red line at right; blue line is the result from a commercial refracted-near-field measurement).
Click here to enlarge image

The researchers obtained bright-field images of two different optical fibers-a single-mode photosensitive fiber produced by the Optical Fibre Technology Centre (Sydney, Australia) and a multimode fiber with 62.5-μm core diameter from Corning (Corning, NY)-to demonstrate their technique. Bright-field images were obtained with a microscope using a 40×, 0.85-NA (numerical-aperture) objective lens for the single-mode fiber and a 20×, 0.7-NA objective for the multimode fiber. The condenser NA was set to 0.2 to increase the phase sensitivity by maximizing the spatial coherence of the incident light. An in-focus image and images at ±2-μm defocus were obtained with a 12-bit, 1317 × 1035-pixel CCD camera and incident light was filtered through a bandpass filter with a central wavelength of 521 nm and a passband of 10 nm. The quantitative phase-gradient image of the optical fiber and the refractive-index profiles as a function of radius were determined.

Comparison of the calculated profile to that obtained with a commercially available RNF system (S14 from Photon Kinetics in Beaverton, OR) yielded some differences: mainly, that the calculated profile using the phase-­gradient technique was able to see fabrication arti­facts near the peak of the index profile and was better able to resolve deposition layers in the depressed inner cladding of the single-mode fiber.

Although this technique seems in some respects to represent an improvement over the RNF standard, the researchers note that the recovered refractive-index profile is influenced by the choice of defocus distance; that is, increasing defocus distance also increases refractive-index sensitivity, but at the expense of poorer spatial resolution. For small defocus distances, it was shown that the spatial resolution was diffraction limited, as is the case with the RNF method. “We are currently ­investigating extensions of the technique to 3-D imaging of nonaxially symmetric fibers and to its use with polarized light for studies of stress within fibers,” says Ann Roberts, associate professor of physics.


1. E. Ampem-Lassen et al., Optics Express13(9) 3277 (May 2, 2005).

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