Method for Refractive Index Uniformity Measurement Based on Two-flat and Three-flat Test

Traditionally, the interferometric method has been employed to test the refractive index uniformity of flat optical materials. The method mainly involves two approaches:the overturning method and the transmission method. Both methods require a minimum of three flat samples, including the reference flat, the transmission flat, and the sample flat to be tested. This requirement for multiple flats increases the overall cost of testing. We have proposed a novel method for evaluating the refractive index uniformity of transmission flats, which only requires two flats, offering a significant improvement over existing method. The method is realized by using two surfaces of the transmission flat and one surface of the reference flat, and the sample flat is used as the transmission flat. Based on the even-and-odd functions, we can get the even-odd, odd-even and odd-odd parts of the refractive index uniformity directly. To the even-even part, we resolve it as the even-even-even (eee) and even-even-odd(eeo) part and we can calculate the eeo part by rotate 90 degrees measurement result. Then we resolve the eee part into even-even-even-even(eeee)and even-even-even-odd(eeeo)part and get eeeo part through the rotate 45 degrees measurement result. Finally, by neglecting high-order rotational symmetry terms, we can calculate the refractive index uniformity from the obtained components. This method with its step-by-step decomposition providing an effective and efficient approach to characterize the optical properties of the flat under test. Four random wavefronts are generated as the initial three surface error and the refractive index uniformity errors. The uniformity errors are recovered according to the proposed method. Compared the difference between the recovered results and the initial values, that only 0.6 ppm(10(-6)) in differ. Additionally, the residual error exhibits rotation invariance, which aligns with theoretical expectations. It is important to note that in the low and middle frequency ranges, the residual error is not affected by the surface error of the flat, but solely determined by the refractive index uniformity itself. The theory is verified the experiment on a 100 mm Zygo interferometer and the refractive index uniformity of the same flat is measured by the three flat transmission method. The test flat is made by quartz. The surface error of the two surfaces are better than lambda/10. The flat has a certain wedge angle. The front and the back surface will not generate interference fringes. The reference flat is a microcrystalline flat, better than lambda/10 as well. The result of the two flat method have the same shape with the three flat transmission method. The refractive index uniformity obtained by the two flats methods is only 0.2 ppm different from that obtained by the transmission method, and the peak-valley value is 3 nm different. To ensure accuracy in the evaluation process, error influence is analyzed considering factors such as rotation angle errors and pix offset errors. By evaluating the influence of error, the experimentally verified results illustrate the effectiveness of this method in accurately evaluating the refractive index uniformity of flat optical materials. The proposed method demonstrates promising potential in the evaluation of refractive index uniformity, reducing resource requirements, and improving cost-effectiveness.