How accurately can one reconstruct an index profile from transverse measurement data?

Glantschnig, Werner J.

doi:10.1109/jlt.1985.1074221

Cited by 15 publications

(9 citation statements)

References 21 publications

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“…For practical usage it would be of interest to add some random noise to ΔðpÞ representing uncertainties of measurement and see how this affects the recovered profile for nðrÞ. To some extent, and in a more general context, the numerical stability of Abel inversion has been discussed in [4,5,7,45] (extensions to discontinuous profiles have also been investigated [6,7]). This approach, perhaps coupled with the above-mentioned work could be usefully applied to current studies in fiber optics and nanotechnology.…”

Section: Resultsmentioning

confidence: 99%

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Zero-order bows in radially inhomogeneous spheres: direct and inverse problems

Adam¹

2011

Appl. Opt.

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Zero-order ray paths are examined in radially inhomogeneous spheres with differentiable refractive index profiles. It is demonstrated that zero-order and sometimes twin zero-order bows can exist when the gradient of refractive index is sufficiently negative. Abel inversion is used to "recover" the refractive index profiles; it is therefore possible in principle to specify the nature and type of bows and determine the refractive index profile that induces them. This may be of interest in the field of rainbow refractometry and optical fiber studies. This ray-theoretic analysis has direct similarities with the phenomenon of "orbiting" and other phenomena in scattering theory and also in seismological, surface gravity wave, and gravitational "lensing" studies. For completeness these topics are briefly discussed in the appendixes; they may also be of pedagogic interest.

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Section: Resultsmentioning

confidence: 99%

“…In [43] a parabolic profile of the form nðrÞ ¼ a − br 2 also yields a result also in terms of a purely imaginary elliptic integral of the third kind. Related numerical studies can be found in [44][45][46][47].…”

Section: Ray Path Integralmentioning

confidence: 99%

Zero-order bows in radially inhomogeneous spheres: direct and inverse problems

Adam¹

2011

Appl. Opt.

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“…The index curve is then obtained as an Abel transform. Following the description in [6], the index profile is obtained by the equation:…”

Section: Measurement Principlementioning

confidence: 99%

“…For preforms, non-destructive techniques are particularly useful. One such technique is to measure the deflection of a transversely directed beam scanned along the diameter of the preform [1][2][3][4][5][6][7]. After measuring the deflection, the index profile is calculated.…”

Section: Introductionmentioning

confidence: 99%

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Practical aspects on measuring refractive index profiles of non-circular fibreoptic preforms

Helander¹

2005

Meas. Sci. Technol.

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The influence of a non-circular cross section of a preform on the measurement of the refractive index was investigated. The deviation of the refractive index value from the value for a circular cross section can be both positive and negative depending on the rotational orientation of the preform. Therefore, the measurement is done at many rotational angles and the refractive index is calculated by averaging over the angles. The best solution was to define a number of layers and calculate the thickness and index for each layer in the preform. This was done for each angle and then the average of all index values for all angles was calculated. With this approach, the obtained refractive index is almost independent of the ovality for a variation of the diameter of ±10%.

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