白光干涉仪传递函数的成因分析及其非线性研究

为提高光学表面的功率谱密度检测精度，研究了白光干涉仪仪器传递函数（ITF）的产生机理和标定方法。将白光干涉仪作为非相干成像系统，对正弦表面干涉光强进行Bessel函数展开，通过干涉光强的频谱强度变化研究白光干涉仪对正弦表面高度的作用机理，利用数值仿真计算了白光干涉仪对正弦表面的衰减程度。采用30、80、120 nm高度的台阶标准板对商品白光干涉仪的传递函数进行标定，并提出了一种可靠的ITF计算方法。理论分析、数值仿真和实验结果表明:ITF随表面高度的增加而增大，此时白光干涉仪对表面高度的响应表现出明显的非线性；表面高度小于/10得到的ITF曲线与白光干涉仪光学系统调制传递函数非常接近，白光干涉仪对表面高度的响应接近线性。文中对于白光干涉仪频域传递特性研究和光学表面功率谱密度检测具有重要意义。

Determination and nonlinearity study of instrument transfer function of white light interferometer

Instrument transfer function(ITF) of white light interferometer(WLI) influences the measurement accuracy of power spectral density(PSD) for optical surfaces. To understand the nature of ITF, WLI was treated as an incoherent optical system and a sinusoidal surface was the input signal. Studying the Bessel function expansion of interference intensity spectrum of sinusoidal surface, the theoretical analysis indicated that the low pass of optical system led to the surface height attenuation. The nonlinearity of Bessel function resulted in the nonlinear response of WLI to height, and the response approached linear when the height was much less than wavelength. Numerical simulations and experiments validated the theoretical conclusions. Step-artefacts of 30 nm, 80 nm and 120 nm height were employed to calibrate the ITF of a commercial WLI. The experimental result and the simulation result match each other well. ITF rises when the surface height increases, which manifests obvious nonlinearity. If the surface height is less than /10, ITF nearly equals the modulation transfer function of WLI optical system, in which case WLI is approximately linear to surface height. This paper has promotion for understanding WLI transfer characteristic and enhancing PSD measurement accuracy.