Seelamantula Chandra Sekhar, Pavillon Nicolas, Depeursinge Christian, Unser Michael
Department of Electrical Engineering, Indian Institute of Science, Bangalore, India.
J Opt Soc Am A Opt Image Sci Vis. 2012 Oct 1;29(10):2118-29. doi: 10.1364/JOSAA.29.002118.
We propose a Riesz transform approach to the demodulation of digital holograms. The Riesz transform is a higher-dimensional extension of the Hilbert transform and is steerable to a desired orientation. Accurate demodulation of the hologram requires a reliable methodology by which quadrature-phase functions (or simply, quadratures) can be constructed. The Riesz transform, by itself, does not yield quadratures. However, one can start with the Riesz transform and construct the so-called vortex operator by employing the notion of quasi-eigenfunctions, and this approach results in accurate quadratures. The key advantage of using the vortex operator is that it effectively handles nonplanar fringes (interference patterns) and has the ability to compensate for the local orientation. Therefore, this method results in aberration-free holographic imaging even in the case when the wavefronts are not planar. We calibrate the method by estimating the orientation from a reference hologram, measured with an empty field of view. Demodulation results on synthesized planar as well as nonplanar fringe patterns show that the accuracy of demodulation is high. We also perform validation on real experimental measurements of Caenorhabditis elegans acquired with a digital holographic microscope.
我们提出一种用于数字全息图解调的里兹变换方法。里兹变换是希尔伯特变换的高维扩展，并且可以指向期望的方向。全息图的精确解调需要一种可靠的方法来构建正交相位函数（或简称为正交分量）。里兹变换本身并不能产生正交分量。然而，可以从里兹变换出发，通过使用准本征函数的概念构建所谓的涡旋算子，这种方法能得到精确的正交分量。使用涡旋算子的关键优势在于它能有效处理非平面条纹（干涉图样）并具有补偿局部方向的能力。因此，即使在波前不是平面的情况下，该方法也能实现无像差全息成像。我们通过从用空视场测量的参考全息图估计方向来校准该方法。对合成的平面和非平面条纹图样的解调结果表明解调精度很高。我们还对用数字全息显微镜获取的秀丽隐杆线虫的实际实验测量进行了验证。
