Improvement of the Accuracy of the Fresnel Method of Measuring the Diameters of Circular Metallic Cylinders with an Arbitrary Coefficient of Light Reflection

A diffraction Fresnel method of precision measurement of diameters of circular metallic cylinders in the range from several units to hundreds of millimeters with an arbitrary coefficient of light reflection from the cylinder surface is developed. The method is based on determining the position of the first maximum in the Fresnel pattern of the object formed in the free space. An expression for the diffraction Fresnel pattern of a plane model of a cylinder fragment is derived in the class of special functions (Fresnel integrals). Based on this expression, a formula is found for taking into account the displacement of the position of the first maximum of the field as a function of the light reflection coefficient. By using an appropriate correcting additive, the measurement error component induced by this factor can be reduced by more than an order of magnitude. The results of the present study can be used for the development of optical-electronic systems of precision dimensional inspection of cylindrical articles.