数字显微全息重建图像的景深扩展研究∗

摘要

Digital micro holography offers an in-situ, non-contact and three-dimensional way to explore the microscopic world. However, as it is difficult to focalize the whole object in one single reconstructed image, the application of digital micro holography to cases with a large longitudinal object volume is limited by the microscope’s depth of field. By extending the depth of field in reconstructed micro holograms in the wavelet domain, this paper fully takes advantage of numerical reconstruction algorithms to solve this problem. First, a recorded hologram is rebuilt using the wavelet transform approach by setting up an appropriate longitudinal interval to obtain a series of reconstructed hologram planes. Then each plane is decomposed with wavelet into its sub-images of both high and low frequencies. Furthermore, the local variance of the maximum intensity gradients of the high-and low-frequency coefficients is calculated and utilized as the focus criterion. Finally, the image planes are fused into a single one with the depth of field extended to a large extent. The feasibility and robustness of this reconstruction procedure for both continuum and particle fields are investigated. One of the demonstrations is made in an experiment of a tilted continuum: carbon fiber. It is different from most of the previous applications where the interrogated is the particles and where the area involved is parallel to the CCD. The carbon fiber gets successfully reconstructed in three dimensions, and the measurement errors of its diameter are presented together with the reconstruction distances. Another is an experiment of a dispersed particle field: micro transparent particles are generated by an ultrasonic atomizer, for which the reconstruction procedure achieves an extended depth of field. In addition, a numerical model based on generalized Lorenz-Mie theory is used to simulate the holograms of both opaque and transparent particles of 1—15 µm in diameter. Variations of the longitudinal location errors with the Fraunhofer number are analyzed, and comparisons are made between the results of opaque and transparent particles. Both the experimental and simulation outcomes show that this reconstruction procedure is a reliable one to acquire an extended-depth-of-field hologram for both the continuum and the dispersed particle fields, and then to accurately measure the objects.%显微物镜的景深问题限制数字显微全息在大纵深视场中的应用。本文充分利用数值重建的特点，采取低频和高频系数子图上的最大亮度梯度的局部方差作为聚焦判据，在小波分解域内对显微全息重建图像的景深扩展问题进行了研究。对倾斜的连续物体碳纤维进行三维重建，分析了重建距离与直径测量误差的关系。以超声波雾化器生成的微液滴颗粒场为例，对离散颗粒场的重建图像进行了景深扩展。利用基于广义洛伦兹-米散射理论的模型分别模拟1—15µm的非透明与透明离散颗粒的显微全息图，分析了该方法重建的颗粒场的纵深定位误差与夫琅禾费系数的关系，对比了非透明与透明颗粒纵深定位误差的异同点。实验和模拟结果显示出该方法对于连续物体和离散颗粒场的显微全息重建图像的景深扩展能力，且能由此准确重建物体信息。