Abstract The phase measuring deflectometry is a promising method for the high precision measurement of optical freeform surfaces. However, it fails to measure the double surfaces of transparent lenses, because the fringes reflected from both the upper and the lower surfaces are superimposed in the captured images. An effective method is proposed to solve this problem by displaying a set of fringe patterns with different frequencies and retrieving the fringe phases associated with both surfaces. The form of the lower surface is reconstructed using a hybrid reflection-refraction model. Experimental results demonstrate that the proposed method can reliably reconstruct both surfaces of a lens, making deflectometry capable of measuring transparent optics with high accuracy.

中文翻译：

---

使用相位测量偏转法同时测量透明透镜的双面

摘要 相位测量偏转法是一种很有前途的光学自由曲面高精度测量方法。但是，它无法测量透明镜片的双面，因为从上表面和下表面反射的条纹会叠加在捕获的图像中。通过显示一组不同频率的条纹图案并检索与两个表面相关的条纹相位，提出了一种有效的方法来解决这个问题。使用混合反射-折射模型重建下表面的形状。实验结果表明，所提出的方法可以可靠地重建透镜的两个表面，使偏转法能够以高精度测量透明光学器件。