两相干平面波照射球体的远场干涉及直径测量

Far-field Interference and Diameter Measurement on Two Coherent Plane Waves Irradiating Sphere

提出一种球远场干涉理论模型,即两相干平面波以任意夹角照射表面光滑球体,其反射波在远场发生干涉.推出两反射波在远场的光程差公式,并用远场干涉准确测量球直径,给出了测量球直径的公式.用分光仪、CCD照相机、氦氖激光器、光学平台和电脑等组成测量系统,给出使用原始激光束测量球直径的方法.将远场干涉法测量结果与阿贝比较仪测量结果进行比较,相对差为0.2%;使用高斯光束所产生的测量误差为5×10-5 mm且可略.此测量方法还可对相机镜头畸变实现自校正.结果表明理论和测量方法正确,用高斯激光束测量球直径可行.

A theoretical model of the sphere far-field interference was given. When two coherent plane waves are irradiating the smooth sphere at any included angle, the reflected waves interfere in the far- field. A formula on optical path difference of reflected waves is derived in the far field. The sphere diameter can be accurately measured with far field interference and a formula on measuring the diameter is given. The measurement system contains spectrometer, CCD camera, helium-neon laser, optical platform and computer. The method is given to measure the diameter of the sphere with original laser beam. The measured results of diameter by far-field interference are compared with that by the Abbe comparator, the relative difference of which is 0.2~. The measurement error generated by Gaussian beam is 5 × 10 5mm and can be negligible. This measurement method can achieve self-camera lens distortion correction. It shows that the theory and method of measurement is accurate. Gaussian laser beams is possible to measure the diameter of the sphere.