Nonlinear metasurfaces that dynamically manipulate the phase of a passing light beam are of interest for a wide range of applications. The controlled operation of such devices requires accurate measurements of the optical transmission phase in both the linear and nonlinear regime, an experimentally challenging task. In this paper we show that this phase information can be extracted directly from simple transmission measurements, using a Hilbert transform approach, removing the need for complicated, interferometric experimental set-ups, and enabling direct measurements of the phase in conditions not suitable for other traditional approaches, such as Z-scan measurements.

动态操纵通过光束的相位的非线性超表面对于广泛的应用是令人关注的。这种设备的受控操作需要在线性和非线性两种状态下对光传输相位进行准确的测量，这是一项具有实验挑战性的任务。在本文中，我们证明了可以使用希尔伯特变换方法直接从简单的传输测量中提取该相位信息，从而消除了对复杂的干涉实验设置的需要，并且可以在不适合其他传统方法的条件下直接测量相位方法，例如Z扫描测量。