Please cite this article in press as: N. Akhter, et al., A comparative study of reconstruction algorithms in digital holography, Optik - Int. J. Light Electron Opt. (2012), http://dx.doi.org/10.1016/j.ijleo.2012.09.002 ARTICLE IN PRESS G Model IJLEO-52609; No. of Pages 4 Optik xxx (2012) xxx–xxx Contents lists available at SciVerse ScienceDirect Optik jo ur n al homepage: www.elsevier.de/ijleo A comparative study of reconstruction algorithms in digital holography Naseem Akhter a , Gihyeon Min a , Ju Wan Kim b , Byeong Ha Lee a,b,∗ a School of Information and Communications, Gwangju Institute of Science and Technology, 261 Cheomdan-gwagiro, Buk-gu, Gwangju 500-712, Republic of Korea b Department of Medical System Engineering, Gwangju Institute of Science and Technology, 261 Cheomdan-gwagiro, Buk-gu, Gwangju 500-712, Republic of Korea a r t i c l e i n f o Article history: Received 25 April 2012 Accepted 2 September 2012 Keywords: Reconstruction algorithms Digital holography Fresnel diffraction Fourier transform a b s t r a c t Comparative studies of the different reconstruction algorithms in digital holography are presented. It shows that each method has different properties with respect to available reconstruction distances, res- olution of reconstructed images and computational load. It is very important to choose an appropriate method for the reliable reconstruction in a given situation. Although the method based on Fresnel diffrac- tion formula can still give an accurate reconstruction for smooth and slowly varying objects where the Fresnel approximation is not strictly satisfied, it cannot correctly reconstructed near wave-fields for more diffractive objects, where the higher-order terms in the expansion of the Fresnel approximation are more significant. Angular spectrum method can be a way out of those problems in Fresnel or con- volution method, because of its validity for the closer region that the Fresnel region and is very useful for the measurement of microscopic samples requiring a high-numerical aperture imaging system as a necessity. We present one example of quantitative phase-contrast microscopy of small particles and its 3D prospective. © 2012 Elsevier GmbH. All rights reserved. 1. Introduction Numerical reconstruction of digital holograms offers much more possibilities than conventional processing. Also, in con- nection with the various methods for the three-dimensional measurements, many reconstruction algorithms have been devel- oped to meet the specific conditions and to add some useful capabilities [1–3]. For different recording conditions and dif- ferent properties of objects, different reconstruction algorithms are required. Each method has its limitation in the valid range for correctly calculating the diffraction integral. For last several decades, holographic method has been widely used to measure three-dimensional (3D) aspects of samples qualitatively and quan- titatively including surface profile, refractive index, 3D particle tracking, etc. [4–7]. In 3D imaging, however, information about areas other than the parallel planes would be more interesting, and the capability to inspect them is necessary [8–10]. There are many methods of numerical image reconstruction in digital holography. Fresnel transform method (FTM), convolution method and angular spectrum method (ASM), also known as plane wave expansion method, are the main methods, in the order of long to short reconstruction distance [11–13]. The single Fourier ∗ Corresponding author at: School of Information and Communications, Gwangju Institute of Science and Technology, 261 Cheomdan-gwagiro, Buk-gu, Gwangju 500- 712, Republic of Korea. E-mail address: leebh@gist.ac.kr (B.H. Lee). transform method is valid for far Fresnel zone hologram, whereas the convolution method is appropriate for near Fresnel holograms. The methods mentioned so far can reconstruct images only on planes that are parallel to the hologram. The first of these meth- ods is valid for the paraxial case, and the rest are for ranges closer than the Fresnel region. However, there are increasing demands for the means to measure objects requiring high-numerical-aperture (NA) imaging optics or causing high-order diffraction, especially in biomedical sciences. In these cases, the object may not be located in the paraxial region [14,15]. It is important to choose the appropriate reconstruction method for better image quality and high accuracy. Angular spectrum method can be a way out of those problems and the ASM has been especially widely used because of its appli- cability to the range closer than Fresnel region in addition to the following advantages [15]. First, the ASM is a convolution-based algorithm that uses direct and inverse Fourier transforms succes- sively, as the convolution method does. The convolution-based algorithms make the unnecessary scaling, that is, caused by the fast Fourier transforms (FFTs) cancel out unless the size of the Fourier- transformed space is changed. Second, the spatial frequency of the propagation kernel of the ASM is directly proportional to the reconstruction distance [16,17]. So far as the Nyquist condition is satisfied, therefore, the closer an object is located to the detector; the more accurately it can be reconstructed using a high-NA with a slowly varying propagation kernel [13]. Several articles have been published in the literature that has successfully attempted to explain the reconstruction algorithms of digital holography based on in-line configuration as well as off-axis 0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.09.002