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.

开发了一种衍射菲涅耳法，可精确测量圆形金属圆柱体的直径，范围从几单位到几百毫米，并具有从圆柱体表面反射的任意光反射系数。该方法基于确定在自由空间中形成的物体的菲涅耳图案中的第一最大值的位置。圆柱函数的平面模型的衍射菲涅耳图案的表达式是在特殊函数（菲涅耳积分）类中得出的。基于该表达式，找到用于考虑作为光反射系数的函数的场的第一最大值的位置的位移的公式。通过使用适当的校正添加剂，由该因素引起的测量误差分量可以减少一个数量级以上。本研究的结果可用于开发圆柱形物品的精密尺寸检查的光电系统。