Aberration-free reconstruction algorithm for high numerical aperture digital hologram

Abstract

In digital holographic microscopy, a high numerical aperture object lens of good quality is required in order to achieve high lateral resolution. As well known, such lenses usually have large aberrations and are difficult to fabricate, especially in the ultra-violet and infrared spectral regions. In these circumstances, a system without objective lens is highly preferred. According to imaging theory, this means that the hologram should be recorded with a high numerical aperture (NA). For the reconstruction of high NA holograms, the Rayleigh-Sommerfeld diffraction integral without approximation must be evaluated. However the current mostly used three algorithms, namely, the Fresnel algorithm, the angular spectrum algorithm, and the convolution algorithm are not suitable. In this paper, the properties of these algorithms are presented. Then a modified convolution algorithm is proposed. In this method, a shift parameter is introduced in the discrete representation of diffraction kernel and then reconstructions with different shift values are combined. The modified convolution method is able to give samplings of diffraction-limited resolution for the full field of view. The simulation results of point field with different reconstruction algorithm are presented. Experimental results of a test dot array are also given.