The articles in this special feature in Measurement Science and Technology concern exciting new developments in the field of digital holography—the process of electronically recording and numerically reconstructing an optical field [1]. Making use of the enormous advances in digital imaging and computer technology, digital holography is presented in a range of applications from fluid flow measurement and structural analysis to medical imaging.

The science of digital holography rests on the foundations of optical holography, on the work of Gabor in the late 1940s, and on the development of laser sources in the 1960s, which made his vision a practical reality [2]. Optical holography, however, uses a photosensitive material, both to record a latent image and subsequently to behave as a diffractive optical element with which to reconstruct the incident field. In this way display holograms, using silver halide materials for example, can produce life-size images that are virtually indistinguishable from the object itself [3]. Digital holography, in contrast, separates the steps of recording and reconstruction, and the final image is most often in the form of a 3D computer model.

Of course, television cameras have been used from the beginnings of holography to record interferometric images. However, the huge disparity between the resolution of holographic recording materials (more than 3000 cycles/mm) and television cameras (around 50 cycles/mm) was raised as a major concern by early researchers. TV holography, as it was sometimes called, generally recorded low numerical aperture (NA) holograms producing images with characteristically large speckle and was therefore more often referred to as electronic speckle pattern interferomery (ESPI) [4]. It is possible, however, to record large NA holograms on a sensor with restricted resolution by using an objective lens or a diverging reference wave [5]. This is generally referred to as digital holographic microscopy (DHM) since the resolution now places a limit on the size of the object that can be recorded.

Some 60 years after the pioneering work of Gabor, digital imaging and associated computer technology offers a step change in capability with which to further exploit holography. Modern image sensors are now available with almost 30 million photosensitive elements, which corresponds to a staggering 100-fold increase compared to standard television images. At the same time personal computers have been optimized for imaging and graphics applications and this allows more sophisticated algorithms to be used in the reconstruction process. Although resolution still falls short of the materials used for optical holography, the ability to process data numerically generally outweighs this drawback and presents us with a host of new opportunities.

Faced with the ability to record and process holograms numerically, it is natural to ask the question 'what information is present within recordings of scattered light?'. In fact this question could be posed by anyone using light, or indeed any other wave disturbance, for measurement purposes. For the case of optical holography, Wolf published his answer in 1969 [6], showing that for the case of weak scattering (small perturbations) and plane wave illumination, the amplitude and phase of each plane wave within the scattered field are proportional to those of a periodic variation in the refractive index contrast (i.e. a Bragg grating). This Fourier decomposition of the object was published almost simultaneously by Dandliker and Weiss [7], who also provided a graphical illustration of the technique. These works are the basis of optical tomography and provide us with the link between holographic data and 3D form.

Digital holographic reconstruction and optical tomography was the theme of an international workshop [8] held in Loughborough in 2007, and many of the topics debated at the workshop have become the subject of the papers in this issue. In general terms the papers we present describe closely related holographic techniques that address application areas within the field of engineering.

The application of digital holography to 3D fluid flow measurement is addressed by several authors. Salah et al demonstrate the simplicity of digital holography with an in-line multiple exposure holographic system using a low-cost laser diode. Soria and Atkinson discuss limitations of low NA holography in fluid velocimetry and demonstrate the potential of a multiple camera, in-line technique which they call Tomographic Digital Holographic Particle Image Velocimetry (Tomo-HPIV).

Problems caused by the twin images (real and virtual) of in-line HPIV are described by Ooms et al. It is shown how sign ambiguity can be eliminated and bias errors suppressed by the application of a suitable threshold in piecewise correlation of the reconstructed field. Denis et al explain the problem of twin image removal as a deconvolution process and compare suppression algorithms based on wavelet decomposition. This process can be considered as an inverse problem and the benefits of this approach are discussed with reference to particulate holograms by Gire et al. Of course, the twin image problem can be solved by off-axis holographic geometries which, in effect, add a carrier modulation. Arroyo presents a comparison of carrier modulation strategies that have been presented in the literature and shows circumstances in which the information in each of the real and virtual images can be separated when the sensor resolution is less than that required by the NA of the objective.

State-of-the-art digital holographic microscopy (DHM) is presented by Kühn et al. This paper uses an off-axis geometry that simultaneously records images at two wavelengths. The microscope allows the surface profile to be measured from a single recording and sub-nanometre axial resolution is demonstrated. Another interesting application of DHM is addressed by Grilli et al. They report a transmission set-up to investigate poling in a lithium niobate crystal.

Developments in the field of optical tomography are covered by the majority of the papers in this issue. The paper by Debailleul et al shows the differences between images reconstructed from a single holographic recording and those synthesized from a series of holograms made with different plane wave illumination. This is optical diffraction tomography (ODT), the original method discussed by Wolf that is characterized by large NA and monochromatic illumination. An alternative strategy is to synthesize the image from holograms made at several wavelengths with low NA optics. This can be done either by sweeping the source or detector response or the reference path in a white light interferometer. These methods are called spectral domain and temporal domain optical coherence tomography (SD-ODT and TD-OCT) respectively. SD-OCT is illustrated in the paper by Potcoava and Kim for biomedical applications. SD- and TD-OCT are compared with confocal microscopy in the paper by Stifter et al. The huge potential of OCT as a diagnostic in polymer and composite materials is apparent from this work.

There are clearly many different ways to implement optical tomography, and several established techniques, such as scanning white light interferometry (SWLI) and confocal microscopy, can be considered to be tomographic processes. We present two papers in this issue. The first attempts to bring together the topics of holography, microscopy and tomography within the framework of linear systems theory. It is shown that the images (or interferograms) produced by these instruments can be considered as estimates of refractive index contrast that are obtained using a linear inversion of the scattered field data. It is noted, however, that this is only strictly correct for the case of weak scattering and this is only a crude approximation for many cases of practical interest. The second paper that we present illustrates this for the case of mono-disperse particles in air. Here the number density of the particles is such that multiple scattering is prevalent; however, a priori knowledge of particle size and refractive index allows individual particles to be located accurately.

In general, reconstruction can be thought of as a nonlinear optimization process that is used to discover the object which best explains the measured field and is consistent with a priori information. As Gire et al point out in their article, a priori knowledge can also be used to overcome the Nyquist sampling criteria. Although some caution should be exercised (for example, it is not usually possible to decide whether a given solution is unique), it is interesting to note that despite the disparity in resolution, digital holography and computer technology might yet create 3D images of greater clarity than the best optical holograms.

References

[1] Schnars U and Jueptner W 2005 Digital Holography (Berlin: Springer) ISBN: 978 3 540 21934 7
[2] Gabor D 1948 A new microscopic principle Nature 161 777–8
[3] Bjelkhagen H I 1993 Silver-Halide Recording Materials (Berlin: Springer) ISBN 3 540 58619 9
[4] Leendertz J A 1970 Interferometric displacement measurement on scattering surfaces utilizing speckle effect J. Phys. E: Sci. Instrum. 3 214–8
[5] Marquet P, Rappaz B, Magistretti P J, Cuche E, Emery Y, Colomb T and Depeursinge C 2005 Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy Opt. Lett. 30 468–70
[6] Wolf E 1969 Three-dimensional structure determination of semi-transparent objects from holographic data Opt. Commun. 1 153–6
[7] Dandliker R and Weiss K 1970 Reconstruction of the three-dimensional refractive index from scattered waves Opt. Commun. 1 323–8
[8] Coupland J and Lobera J 2007 International Workshop on Digital Holographic Reconstruction and Optical Tomography for Engineering Applications ISBN 978 0 947974 56 5