Study on extending the depth of field in reconstructed image for a micro digital hologram

Abstract

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 microscopes 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 m 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.