Optik - International Journal for Light and Electron Optics
A comparative study of reconstruction algorithms in digital holography
Introduction
Numerical reconstruction of digital holograms offers much more possibilities than conventional processing. Also, in connection with the various methods for the three-dimensional measurements, many reconstruction algorithms have been developed to meet the specific conditions and to add some useful capabilities [1], [2], [3]. For different recording conditions and different 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 quantitatively including surface profile, refractive index, 3D particle tracking, etc. [4], [5], [6], [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], [9], [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], [12], [13]. The single Fourier 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 methods 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 applicability 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 successively, 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 configuration [11], [16], [17], [18], [19], [20], although, our main interest lies in the comparative study of the reconstruction algorithms and its application to the three-dimensional prospective of the reconstructed images. In this paper, the digital holography experiments are performed to demonstrate the theoretical analysis; we report the results of recent experiments to improve the techniques of digital holography in order to obtain high-resolution, high-fidelity images of quantitative phase-contrast microscopy. The improvement is achieved in main part by the use of the angular spectrum method, which has several advantages over more commonly used Fresnel transformation or Huygens convolution method. The reconstruction distance can be any small distance because the minimum distance requirement does not apply and the off-axis angle between the object and reference can be lower than the Fresnel requirement. Spurious noise and interference components can be tightly controlled through the analysis and filtering of the angular spectrum. We present one example of quantitative phase-contrast microscopy of small particles and its 3D prospective.
Section snippets
Fresnel transform method (FTM)
Digital holograms, which are recorded on CCDs using off-axis or in line digital holography set-ups, are reconstructed by numerical procedures based on scalar diffraction theories. There are three main reconstructed algorithms most widely used. Fresnel transform method (FTM) is the most widely used and the most popular one in digital holographic image reconstruction, because of its computational efficiency. This method is based upon Fresnel diffraction formula expressed as follows [11]:
Experiment and results
The digital holography experiments are performed to demonstrate the theoretical analysis and experimental set-up shown in Fig. 2. A 1951 USAF resolution target was used and illuminated with a collimated He–Ne laser beam (wavelength 632.8 nm), spatial-filtered, is split into two (reference and object) beams in an interferometer based on the Mach–Zender configuration. The object (specimen) mounted on a xyz-translation stage and located on the optical z-axis at a distance ‘z’ in front of the CCD
Conclusion
To conclude, we have studied the different reconstruction methods (algorithms) and its application to the small particle field imaging microscopy to obtain the 2D and 3D images. It shows that each method has different properties with respect to available reconstruction distances, resolution of reconstructed images and computational load. Angular spectrum method can be a way out of the significant problems in digital holography, because of its validity for the closer region that the Fresnel
Acknowledgment
This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology (R15-2008-006-02002-0).
References (21)
- et al.
Sectional image reconstruction and three-dimensional microscopy of small particles using angular spectrum method
Optik
(2011) - et al.
Reconstruction of digital holograms of small particles on arbitrarily tilted plane using digital holography
Opt. Commun.
(2010) - et al.
Wave front reconstruction by means of phase-shifting digital in-line holography
Opt. Commun.
(2000) - et al.
Phase-shifting digital holography
Opt. Lett.
(1997) - et al.
Fourier phase microscopy for investigation of biological structures and dynamics
Opt. Lett.
(2004) - et al.
Studies of digital microscopic holography with applications to microstructure testing
Appl. Opt.
(2001) - et al.
Three-dimensional microscopy with phase-shifting digital holography
Opt. Lett.
(1998) - et al.
Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy
Opt. Express
(2005) Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography
Opt. Express
(2000)- et al.
Angular spectrum method with correction of anamorphism for numerical reconstruction of digital holograms on tilted planes
Opt. Express
(2005)
Cited by (11)
Single-shot digital holography of multiple-beam Fizeau holograms for optical phase reconstruction through the focal depth of optical fibers
2024, Optics and Lasers in EngineeringStudy of the padding effects in numerical reconstruction of digitally recorded holograms
2018, OptikCitation Excerpt :Digital holography (DH), understood as the numerical reconstruction of digitally recorded holograms, replaces the holographic film used in the first step of optical holography by a digital camera. The second step, the optical reconstruction process that is accomplished by illuminating the developed holographic film with the reference wave in optical holography, in DH is done by a numerical process that is carried out in the memory of a computer [1–3]; different numerical algorithms recreate the diffraction process of the reference wave on the digitally recorded hologram. Based on sharing the same foundations of the optical holography [4], DH has been applied on similar applications as the former [5,6] and many more [7,8].
The feasibility of automatic focusing in digital holography by using Fresnel transform as numerical holographic reconstruction algorithm
2017, OptikCitation Excerpt :In contrast to the Fresnel transform method, the use of convolution or angular spectrum reconstruction method provides significant advantages in holographic reconstruction and focusing. They maintains the pixel resolution of the reconstructed image, preserve a constant image scale [26,27]. Therefore, most of literatures on the issue of automatic focusing in DH are utilizing the angular spectrum method to reconstruct the digital hologram.
The suppression of phase error by applying window functions to digital holography
2016, Optics and Lasers in EngineeringCitation Excerpt :The CCD size, pixel size and the distance from the object to the CCD are 4.762 mm, 4.65 μm and 100 mm, respectively. In both simulation and experiment, the angular spectrum algorithm is used for the numerical reconstruction due to its advantages over the Fresnel and convolution methods [34,35]. The second phenomenon which is more important in Fig. 2e is the cluster distribution of different window functions in axis of axial error.
Autofocusing in off-axis digital Fresnel holography using S-th power weighted neighborhood correlation coefficient
2023, Japanese Journal of Applied Physics