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Micro-thin wires are of significant importance to academia, research laboratories as well as industries engaged in
micro-fabrication of products related to diverse fields like micromechanics, bio-instrumentation, optoelectronics etc.
Critical dimension metrology of such wires often demands diameter estimation with tight tolerances. Amongst other
measurement techniques, Optical Diffractometry under Fraunhofer approximation has emerged over years as a nondestructive,
robust and precise technique for on-line diameter estimation of thin wires. However, it is observed that
existing Fraunhofer models invariably result in experimental overestimation of wire diameter, leading to
unacceptable error performances particularly for diameters below 50 μm. In this paper, a novel diffraction model
based on Geometric theory is proposed and demonstrated to theoretically quantify this diameter overestimation. The
proposed model utilizes hitherto unused paths-ways for the two lateral rays that contribute to the first diffraction
minimum. Based the 3-D geometry of the suggested model, a new 'diffraction formulation' is proposed. The
theoretical analysis reveals the following. For diffraction experiment, the Actual diameter of the diffracting wire is a
function of four parameters: source wavelength 'λ', axial distance 'z', diffraction angle corresponding to first
diffraction minimum 'θd' and a newly defined characteristic parameter 'm'. The analysis reveals further that the
proposed characteristic parameter 'm' varies non-linearly with diameter and presents a dependence only on the
experimentally measured diffraction angle 'θd'. Based on the proposed model, the communication reports for the
first time, a novel diameter-inversion procedure which, not only corrects for the overestimated but also facilitates
wire diameter-inversion with high resolution. Micro-thin metallic wires having diameters spanning the range 1-50
μm are examined. Experimental results are obtained that corroborate the theoretical approach.
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