光强传输方程与图像插值融合的相位恢复

光强传输方程作为典型的相位恢复技术，在已知待测面光强分布与光强轴向微分时，可以通过求解该方程直接得到待测面的相位分布。强度微分可以通过采集沿传播方向的不同散焦面的光强信息以计算强度差分来估计，由此，散焦面的适当选择变得尤为重要。将光强传输方程与图像插值法相结合，在几何光学模型下描述采集的散焦面光强分布与聚焦面光强分布之间的关系，再利用图像插值法计算出模糊参数不同的散焦面的光强分布，由新得到的散焦图和采集的聚焦图代入光强传输方程以计算出相位。该方法只需要采集三幅强度图像，即可计算获得其他位置的强度图像，避免了采集设备的多次移动，也为某些特殊情况下无法获取适合位置的强度图像提供了一种解决途径。实验中搭建了一个实际的光强图像获取系统，所得结果验证了所提算法的有效性。

Phase retrieval based on transport of intensity equation and image interpolation

Phase, as an important property of light field, is difficult to be obtained by the existing detection equipment, which can only detect the intensity information of the light field, however, losing the phase information, hence the phase problem can be summarized as the demand of retrieving a sample's complex-field from measurements of intensity. Transport of intensity equation (TIE) based method is one of the typical phase retrieval approaches. When the intensity distribution of the test plane and the axial intensity derivative are known, the phase distribution of the test plane can be calculated directly by solving the equation. Conventionally, intensity derivative is approximated by a finite difference between one in-focus image and one defocused image or two defocused images recorded symmetrically about the focal plane, therefore the proper selection of the distance parameter between defocused image and in-focus image becomes particularly important. A novel approach combining the image interpolation and lens-based TIE was proposed. Firstly, the relationship among two defocused images and one focused image captured was described in geometrical optics model. Secondly, new defocused images with different blur parameters were calculated by image interpolation. Lastly, these new images interpolated and the focused images captured were applied to calculate the phase information. The method could obtain the desired intensity distribution at any positions rapidly with only three captured intensity images, without the mechanical movement of CCD or sample, providing an available way for some special occasions that the intensity acquisitions at appropriate location existed a certain restriction. A practical image acquisition platform was also constructed, the interpolated intensity image was compared with the intensity image obtained by CCD to verify the correctness of the interpolation result, the phase retrieval results under two different computational intensity derivative conditions were given relatively. The experimental results presented verified the feasibility and effectiveness of the method.