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.

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Principles and techniques of digital holographic microscopy

We call “natural” image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of Gaetano Kanizsa according to which visual perception tends to remain stable with respect to these basic operations. We define a contrast invariant presentation of the digital image, the topographic map, where the subjacent occlusion-transparency structure is put into evidence by the interplay of level lines. We prove that each topographic map represents a class of images invariant with respect to local contrast changes. Several visualization strategies of the topographic map are proposed and implemented and mathematical arguments are developed to establish stability properties of the topographic map under digitization.

Topographic Maps and Local Contrast Changes in Natural Images

Wolff's law of trajectorial orientation proposes that trabecular struts align with the orientation of dominant compressive loads within a joint. Although widely considered in skeletal biology, Wolff's law has never been experimentally tested while controlling for ontogenetic stage, activity level, and species differences, all factors that may affect trabecular bone growth. Here we report an experimental test of Wolff's law using a within-species design in age-matched subjects experiencing physiologically normal levels of bone strain. Two age-matched groups of juvenile guinea fowl Numida meleagris ran on a treadmill set at either 0° (Level group) or 20° (Incline group), for 10 min per day over a 45-day treatment period. Birds running on the 20° inclined treadmill used more-flexed knees than those in the Level group at midstance (the point of peak ground reaction force). This difference in joint posture enabled us to test the sensitivity of trabecular alignment to altered load orientation in the knee. Using a new radon transform-based method for measuring trabecular orientation, our analysis shows that the fine trabecular bone in the distal femur has a high degree of correspondence between changes in joint angle and trabecular orientation. The sensitivity of this response supports the prediction that trabecular bone adapts dynamically to the orientation of peak compressive forces.

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Trabecular bone in the bird knee responds with high sensitivity to changes in load orientation.

The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the area of optical signal processing) to calculate the discrete FT, FRT, and FST. All of these algorithms are based on the use of the fast Fourier transform (FFT). In this paper we develop theory for the discrete linear canonical transform (DLCT), which is to the LCT what the discrete Fourier transform (DFT) is to the FT. We then derive the fast linear canonical transform (FLCT), an NlogN algorithm for its numerical implementation by an approach similar to that used in deriving the FFT from the DFT. Our algorithm is significantly different from the FFT, is based purely on the properties of the LCT, and can be used for FFT, FRT, and FST calculations and, in the most general case, for the rapid calculation of the effect of any QPS.

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Fast numerical algorithm for the linear canonical transform.

In a double random-phase encoding system operating in the Fresnel domain, the recovered image would become meaningless noise when the random phase masks shifted sufficiently far from their original positions. Hence multiple images can be encrypted and decrypted with different sets of spatial position parameters. This technique is referred to as position multiplexing. We first describe the basic principle of multiple-image encryption by use of position multiplexing, and then numerically analyse the factors that affect the minimum position separation and the multiplexing capacity. We also present methods to enlarge the multiplexing capacity.

Position multiplexing for multiple-image encryption

Fast numerical calculation of Fresnel patterns in convergent systems

Conselleria de Empresa, Universitat i Ciencia of the Generalitat Valenciana, through the project nr. GV04A/578, and by the Ministerio de Educacion y Ciencia through the project nr. FIS2005-05053. Spanish Ministry of Health, Instituto Carlos III, Red Tematica de Investigacion en Oftalmologia, Subproyecto de Cirugia Refractiva y Calidad Visual (C03/13) and by a grant from the Spanish Generalitat Valenciana, ref: Grupos05/036 Grants and Support for scientific research and technological development in the Comunidad Valenciana for the year 2005

Optical analysis of presbyLASIK treatment by a light propagation algorithm.

http://rua.ua.es/dspace/bitstream/10045/17502/2/proofsa.pdf

Pupil detection and tracking for analysis of fixational eye micromovements

Analysis of vibrations and displacements is a hot topic in structural engineering. Although there is a wide variety of methods for vibration analysis, direct measurement of displacements in the mid and high frequency range is not well solved and accurate devices tend to be very expensive. Low-cost systems can be achieved by applying adequate image processing algorithms. In this paper, we propose the use of a commercial pocket digital camera, which is able to register more than 420 frames per second (fps) at low resolution, for accurate measuring of small vibrations and displacements. The method is based on tracking elliptical targets with sub-pixel accuracy. Our proposal is demonstrated at a 10 m distance with a spatial resolution of 0.15 mm. A practical application over a simple structure is given, and the main parameters of an attenuated movement of a steel column after an impulsive impact are determined with a spatial accuracy of 4 µm.

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Measurement of wide frequency range structural microvibrations with a pocket digital camera and sub-pixel techniques

This study was supported in part by a grant of the Spanish Ministry of Health, Instituto Carlos III, Red Tematica de Investigacion en Oftalmologia, Subproyecto de Cirugia Refractiva y Calidad Visual (C03/13) and by the Ministerio de Educacion y Ciencia through the project nr FIS2005-05053.

Carlos Illueca

Papers

Fast numerical calculation of Fresnel patterns in convergent systems

Optical analysis of presbyLASIK treatment by a light propagation algorithm.

Pupil detection and tracking for analysis of fixational eye micromovements

Measurement of wide frequency range structural microvibrations with a pocket digital camera and sub-pixel techniques

Pseudoaccommodation and visual acuity with Technovision presbyLASIK and a theoretical simulated Array multifocal intraocular lens.