Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms
TL;DR: A method for controlling the size of amplitude and phase images reconstructed from digital holograms by the Fresnel-transform method is proposed and demonstrated and solves the problem of superimposition in multiwavelength digital holography for color display and holographic interferometry applications.
Abstract: A method for controlling the size of amplitude and phase images reconstructed from digital holograms by the Fresnel-transform method is proposed and demonstrated. The method can provide a constant reconstruction pixel width in the reconstructed image plane, independent of the recording and reconstruction distance. The proposed method makes it possible to maintain the size of an object for a sequence of digital holograms recorded at different distances and, therefore, to subtract phase maps for an object recorded at different distances. Furthermore, the method solves the problem of superimposition in multiwavelength digital holography for color display and holographic interferometry applications.
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TL;DR: Digital holography is an emerging field of new paradigm in general imaging applications as discussed by the authors, and a review of a subset of the research and development activities in digital holographic microscopy techniques and applications is presented.
Abstract: Digital holography is an emerging field of new paradigm in general imaging applications. We present a review of a subset of the research and development activities in digital holography, with emphasis on microscopy techniques and applications. First, the basic results from the general theory of holography, based on the scalar diffraction theory, are summarized, and a general description of the digital holographic microscopy process is given, including quantitative phase microscopy. Several numerical diffraction methods are described and compared, and a number of representative configurations used in digital holography are described, including off-axis Fresnel, Fourier, image plane, in-line, Gabor, and phase-shifting digital holographies. Then we survey numerical techniques that give rise to unique capabilities of digital holography, including suppression of dc and twin image terms, pixel resolution control, optical phase unwrapping, aberration compensation, and others. A survey is also given of representative application areas, including biomedical microscopy, particle field holography, micrometrology, and holographic tomography, as well as some of the special techniques, such as holography of total internal reflection, optical scanning holography, digital interference holography, and heterodyne holography. The review is intended for students and new researchers interested in developing new techniques and exploring new applications of digital holography.
672 citations
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...A better solution is provided by zero padding [142], where the hologram is padded with zero-valued pixels around the boundary, so that the effective hologram size X′ 0 = N ′δx increases linearly with the reconstruction distance z, and the pixel resolution at the image plane δx ′ = λz X′ 0 remains constant....
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TL;DR: It is shown that operations usually performed by optical components and described in ray geometrical optics, such as image shifting, magnification, and especially complete aberration compensation, can be mimicked by numerical computation of a NPL.
Abstract: The concept of numerical parametric lenses (NPL) is introduced to achieve wavefront reconstruction in digital holography. It is shown that operations usually performed by optical components and described in ray geometrical optics, such as image shifting, magnification, and especially complete aberration compensation (phase aberrations and image distortion), can be mimicked by numerical computation of a NPL. Furthermore, we demonstrate that automatic one-dimensional or two-dimensional fitting procedures allow adjustment of the NPL parameters as expressed in terms of standard or Zernike polynomial coefficients. These coefficients can provide a quantitative evaluation of the aberrations generated by the specimen. Demonstration is given of the reconstruction of the topology of a microlens.
329 citations
TL;DR: A focus plane determination method that computes the digital refocus distance of an object investigated by digital holographic microscopy working in transmission and it is shown that when the focus distance is reached, the integrated amplitude is minimum for pure amplitude object and maximum for pure phase object.
Abstract: We propose and test a focus plane determination method that computes the digital refocus distance of an object investigated by digital holographic microscopy working in transmission. For this purpose we analyze the integrated amplitude modulus as a function of the digital holographic reconstruction distance. It is shown that when the focus distance is reached, the integrated amplitude is minimum for pure amplitude object and maximum for pure phase object. After a theoretical analysis, the method is demonstrated on actual digital holograms for the refocusing of pure amplitude and of pure phase microscopic samples.
327 citations
TL;DR: It is demonstrated that an extended focused image of an object can be obtained through digital holography without any mechanical scanning or special optical components.
Abstract: In microscopy, high magnifications are achievable for investigating micro-objects but the paradigm is that higher is the required magnification, lower is the depth of focus. For an object having a three-dimensional (3D) complex shape only a portion of it appears in good focus to the observer who is essentially looking at a single image plane. Actually, two approaches exist to obtain an extended focused image, both having severe limitations since the first requires mechanical scanning while the other one requires specially designed optics. We demonstrate that an extended focused image of an object can be obtained through digital holography without any mechanical scanning or special optical components. The conceptual novelty of the proposed approach lies in the fact that it is possible to completely exploit the unique feature of DH in extracting all the information content stored in hologram, amplitude and phase, to extend the depth of focus.
268 citations
TL;DR: It is demonstrated that spatial resolution in the reconstructed plane can be written as a convolution product of functions that describe these influences of each of the physical effects invoked in digital holography.
Abstract: We present a detailed analysis of image formation in digital Fresnel holography. The mathematical modeling is developed on the basis of Fourier optics, making possible the understanding of the different influences of each of the physical effects invoked in digital holography. Particularly, it is demonstrated that spatial resolution in the reconstructed plane can be written as a convolution product of functions that describe these influences. The analysis leads to a thorough investigation of the effect of the width of the sensor, the surface of pixels, the numerical focusing, and the aberrations of the reference wave, as well as to an explicit formulation of the Shannon theorem for digital holography. Experimental illustrations confirm the proposed theoretical analysis.
193 citations
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TL;DR: The principles and major applications of digital recording and numerical reconstruction of holograms (digital holography) are described, which are applied to measure shape and surface deformation of opaque bodies and refractive index fields within transparent media.
Abstract: This article describes the principles and major applications of digital recording and numerical reconstruction of holograms (digital holography). Digital holography became feasible since charged coupled devices (CCDs) with suitable numbers and sizes of pixels and computers with sufficient speed became available. The Fresnel or Fourier holograms are recorded directly by the CCD and stored digitally. No film material involving wet-chemical or other processing is necessary. The reconstruction of the wavefield, which is done optically by illumination of a hologram, is performed by numerical methods. The numerical reconstruction process is based on the Fresnel–Kirchhoff integral, which describes the diffraction of the reconstructing wave at the micro-structure of the hologram. In the numerical reconstruction process not only the intensity, but also the phase distribution of the stored wavefield can be computed from the digital hologram. This offers new possibilities for a variety of applications. Digital holography is applied to measure shape and surface deformation of opaque bodies and refractive index fields within transparent media. Further applications are imaging and microscopy, where it is advantageous to refocus the area under investigation by numerical methods.
1,171 citations
TL;DR: A phase-imaging method with an axial range that can in principle be arbitrarily large compared to the wavelength and does not involve the usual phase unwrapping by detection of phase discontinuity is presented.
Abstract: We present a phase-imaging method with an axial range that can in principle be arbitrarily large compared to the wavelength and does not involve the usual phase unwrapping by detection of phase discontinuity. The method consists of the generation and combination of two phase maps in a digital holography system by use of two separate wavelengths. For example, we reconstructed the surface of a spherical mirror with approximately 10-nm axial resolution and an axial range of approximately 3 microm.
350 citations
TL;DR: Compared the images reconstructed by two algorithms using a single Fourier transformation and a convolution with each other by both experiments and numerical simulations have proved not to cause serious deterioration of the reconstructed images.
Abstract: Digital holography with a three-wavelength laser and a color CCD has been demonstrated. With the phase shifting of the reference beam, in-line holograms for three wavelengths are recorded simultaneously for derivation of the complex amplitude at each wavelength, and then the three monochromatic images are reconstructed and combined into full-color images in the computer. Laser power variation for wavelengths can be compensated for in the reconstruction process. We have compared the images reconstructed by two algorithms using a single Fourier transformation and a convolution with each other by both experiments and numerical simulations. Phase-shifting errors arising at two of the three wavelengths have proved not to cause serious deterioration of the reconstructed images.
273 citations
TL;DR: A new method for focus tracking during the recording of a sequence of digital holograms while the sample experiences axial displacement is proposed and can be applied as a quasi-real-time procedure.
Abstract: We propose a new method for focus tracking during the recording of a sequence of digital holograms while the sample experiences axial displacement. Corrected reconstruction distances can be automatically calculated, and well-focused amplitude and phase-contrast images can be obtained for each digitized hologram. The method is demonstrated for inspection of microelectromechanical systems subjected to thermal load. The method can be applied as a quasi-real-time procedure.
171 citations
TL;DR: A method for direct holographic comparison of the shape or the deformation of two objects when it is not necessary that both samples be located at the same place is described.
Abstract: We described a method for direct holographic comparison of the shape or the deformation of two objects when it is not necessary that both samples be located at the same place. In contrast to the well-known incoherent techniques based on inverse fringe projection, this new approach uses a coherent mask that is imaged onto a sample object that has a microstructure different from that of the master object. The coherent mask is created by digital holography to permit instant access to complete optical information on the master object at any wanted place. Transmission of the digital master holograms to the relevant places can be made with a broadband digital telecommunication network such as the Internet.
136 citations