Precision flatness measurement based on orbital angular momentum

Abstract We propose a method to measure the flatness of an object with a petal-like pattern generated by the interference of the measured orbital angular momentum (OAM) beam and the reference OAM beam which carries the opposite OAM state. By calculating the difference between the petal rotation angle without/with the object, the thickness information of the object, and then the flatness information, can be evaluated. Furthermore, the direction of the object’s flatness can be determined by the petal’s clockwise/counterclockwise rotation. We theoretically analyze the relationship between the object’s thickness and petal rotation angle, and verify the proposed method by experiment. The experimental results show that the proposed method is a high precision flatness measurement and can obtain the convex/concave property of the flatness. For the 1.02 mm glass sample, the mean deviation of the flatness is 1.357 × 10 −8 and the variance is 0.242 × 10 −16 . For the 0.50 mm glass sample, the mean deviation of the flatness is 1.931 × 10 −8 and the variance is 2.405 × 10 −16 . Two different topological charges are adopted for the 2.00 mm glass sample, and their flatness deviations are 0.239 × 10 −8 ( ℓ = 1) and 0.246 × 10 −8 ( ℓ = 2), where their variances are 0.799 × 10 −18 ( ℓ = 1) and 0.775 × 10 −18 ( ℓ = 2), respectively. It is shown that the flatness measured by the proposed method is the same for the same sample when different topological charges are used. All results indicate that the proposed method may provide a high flatness measurement, and will be a promising way to measure the flatness.