Referenceless phase holography (RELPH) is a lensless holographic method that generates the full (amplitude and phase) optical field if intensity and phase distributions of this field in one plane are given as numerical data. It is based on the interference of two pure phase fields that are produced by reflection of two mutually coherent plane waves at two phase modulating spatial light modulators (SLM). The optical field of any real or artificial three-dimensional (3D) scene can be displayed. This means that referenceless phase holography is a promising method for future 3D television or 3D cinema as well as for interferometric metrology. We introduce the theory of RELPH, possible technical realizations, and discuss the numerics. The possibilities and problems in calculating the diffraction fields of given 3D scenes are worked out, modifications of the algorithms are presented. Experiments are shown, not only proving the practicability of RELPH, but also confirming the various 3D cues, such as depth of field, occlusion, and parallax. Two approaches to multicolor display are presented and experimentally verified. The benefits and advantages of RELPH are outlined, open problems and necessary technological developments as well as possibilities and future prospects are discussed.
KEYWORDS: Digital signal processing, Analytical research, Clouds, Tin, Modulation, Physics, Electrical engineering, Materials processing, Americium, All optical signal processing
The structure function is a tool for characterizing technical surfaces that exhibits a number of advantages over Fourierbased analysis methods. So it is optimally suited for analyzing the height distributions of surfaces measured by full-field non-contacting methods. The structure function is thus a useful method to extract global or local criteria like e. g. periodicities, waviness, lay, or roughness to analyze and evaluate technical surfaces. After the definition of line- and area-structure function and offering effective procedures for their calculation this paper presents examples using simulated and measured data of technical surfaces including aircraft parts.
We propose a new application of broad band lasers for digital holography. The aim is to capture the shape of
objects by a single hologram using multiple wavelengths. Our approach is to separate the reference wave spectrally
by a grating while the object wave remains unaffected. This leads to many lamellar holograms in one hologram.
As consequence different restrictions like aperture and wavelength dependency of the reconstruction algorithm
have to be taken into account. In experiments we have successfully demonstrate that lamellar holograms can be
generated, reconstructed and that all necessary steps for shape measurement are accomplishable.
The paper gives an overview on 3D television which can be realized by a number of methods: stereoscopy, autostereoscopy,
integral imaging, volumetric display, and digital holography where digital holograms - recorded
or computed - are fed to spatial light modulators (SLM). All methods have their specific advantages and disadvantages,
which can be reduced parallax, lacking motion parallax, limited lateral resolution, occlusion problem,
or the severe accomodation conflict, causing eye fatigue and other discomforts. By principle holography exhibits
none of these imperfections, but the problem of the necessary high space-bandwidth-product is the main obstacle
for its introduction for 3D TV up to now. The needed high space-bandwidth-product requires CCDs and SLMs
with higher number of pixels, a shorter pixel pitch, and faster computers than available today. Here we present
first solutions to the space-bandwidth-product problem, e. g. by restricting on horizontal parallax only, by
using eye-trackers resulting in calculation of only the observed small parts of the hologram, by employing image
plane holography instead of Fresnel- or Fraunhofer-holography, or by using a proper combination of electrically
together with optically addressable SLMs.
Wavelet analysis is a processing method for the description of single- or multi-dimensional signals in multiple
scales and therefore well suited for describing technical surfaces with variable resolution. Here optically measured
height data of technical surfaces are wavelet-transformed along two dimensions with two different objectives: One
is the representation with only a few coefficients in the sense of an efficient data compression, the other is the
reliable detection of defects, which can be regarded as a pattern recognition task. A systematic comparison of
various wavelet families results in the choice of the biorthogonal pseudo-coiflets for representing the surfaces,
and differentiating wavelets like Burt-Adelson-wavelet or short-range Daubechies-wavelets for solving the defect
detection problem. It is shown that the representation can be improved by not using the most significant
wavelet-values - which can be interpreted as low-pass filtered coefficients, but to maintain those with the largest
weights. Thus the variance between the original surface and that reconstructed from the representation data
is minimized by a factor up to 4. Defect detection is best performed with separate transformation in two
orthogonal directions with subsequent superposition. The procedures obtained here are applied to surfaces like
a coin-surface, a copper-mirror surface, and a lacquered surface.
KEYWORDS: Holography, Digital holography, Lenses, Holograms, Charge-coupled devices, Digital recording, 3D image reconstruction, 3D displays, Metrology, Holographic interferometry
Digital holography captures holograms by charge-coupled device or complementary metal-oxide semiconductor cameras, which have a spatial resolution still not reaching that of silver-halide holofilms. Thus, due to the sampling theorem, the angle between the reference and object wave is limited. Only fields coming from small objects, objects far away, or optically reduced fields can be recorded. Here we investigate optical reduction by a system of lenses, and show that a system of two concave lenses results in a drastic reduction of the object-target distance, while the effect of using more lenses is insignificant. Experimental results obtained with Fresnel and lensless Fourier-transform geometry are presented, and implications on holographic interferometric metrology as well as on holographic 3-D television are given.
We present a new approach for single shot multi wavelengths contouring using the broad spectrum of a fs-laser. The
spectral distribution of a fs-laser contains a multitude of discrete frequencies which principally can be separated and
simultaneously used for gathering holograms with different wavelengths. In order to investigate the characteristics of this
approach, we have built up a setup using a tuneable dye-laser. Several wavelengths of the dye laser have been spatially
distributed for the reference wave on the hologram target. Holograms at different wavelengths are recorded and
superimposed numerically afterwards to guarantee resemblance to the fs-laser setup. In this paper we describe the
theoretical background, derive an algorithm for noise-reduced reconstruction and show corresponding experimental
results.
The refractive index distribution over a cross-section of an optical fiber can differ between core and cladding, can
vary over the core in graded index fibers, or may even have a more complicated form in polarization preserving
fibers. Besides this intended variations the refractive index may vary due to a loading of the fiber like pressure
or bending or due to a faulty production. Digital holographic interferometry is a suitable means for measuring
the refractive index distribution. In the experiments reported here the fiber is embedded into an index matching
fluid, which is mixed so as to match the index of the cladding. Phase-shifted digital holograms are recorded
and the interference phase distribution is calculated. From a single demodulated interference phase distribution
the refractive index field is determined by an algorithm based on a model which takes into account the known
symmetry of the fiber. It can be shown that the obtained accuracy is better than that of classical two-beam
interferometry. Results of experiments with step-index, with graded index, and with polarization preserving
fibers are demonstrated.
KEYWORDS: Digital holography, Holograms, 3D displays, Liquid crystal on silicon, Cameras, 3D image reconstruction, Holography, Spatial light modulators, Visualization, Optoelectronics
In digital holography, holograms are usually optically captured and then two-dimensional slices of the reconstruction
volume are reconstructed by computer and displayed on a two-dimensional display. When the recording is
of a three-dimensional scene then such two-dimensional display becomes restrictive. We outline our progress on
capturing larger ranges of perspectives of three-dimensional scenes, and our progress on four approaches to better
visualise this three-dimensional information encoded in the digital holograms. The research has been performed
within a European Commission funded research project dedicated the capture, processing, transmission, and
display of real-world 3D and 4D scenes using digital holography.
The resolution of digital holography as an optical imaging system is described by the point spread function of the system. Here the point spread function of double-aperture digital holography is determined. It promises the possibility of a resolution increase by the use of synthetic apertures, where we combine the digital holograms of two CCD arrays in one large hologram and reconstruct, or we superpose coherently the two reconstructed wave fields after a proper shift. An experimental method for the determination of this shift with subpixel accuracy is given. Furthermore, experimental results on numerically reconstructed wave fields from synthetic holograms stemming from two mutually shifted digital holograms of the same scene are presented.
The recording of holograms and the numerical reconstruction of the wave fields became possible with the development of high-resolution CCD-cameras and fast computers. This technique called Digital Holography is used for example in particle measurements and deformation analysis. Using an inline holography setup for particle measurements the particle distribution is calculated numerically from the recorded hologram. By varying the recording distance particles can be found in different depths of the analyzed volume.
Using holographic film, the reconstruction process provides only the intensity of the recorded objects. With Digital Holography also the phase of the reconstructed object wave can be calculated. The question is whether the phase of the reconstructed optical field contains additional information compared to the intensity which can be used for example to find the depth coordinate with a much higher resolution. However the experiments show that the dimension of the recording system, the wavelength of the light used and the distance between object and recording system are still limiting factors for lateral and depth resolution. The presented paper gives an overview over phase reconstruction in particle analysis.
In this paper we present the first steps to an algorithm for effective compression of digital holograms. This algorithm is based on the properties of the electromagnetic field that generates the holograms. The investigation of the underlying physical behavior allows us a better reduction of the number of bits needed to compress the data. We show that the quantization in the frequency domain as contained in the extended JPEG compression is suitable for high quality compression of holograms. We present the application of this approach to holograms with low space-bandwidth products and perform a generalization to typical holograms with high space-bandwidth products. Our tests using simulated and real world holograms from different origins show approximately the same performance on the same levels of compression. This performance is better concerning the quality of the data compared to the one of the standard JPEG implementation and can be improved concerning the file size. While the visual impression of the intensity reconstruction is good even for 2bit compression, the reconstruction of the phase for higher compression ratios shows remarkable errors. In the future we want to better adopt our approach to the extended JPEG standard based in the way that we use 8x8 clusters instead of the whole image for quantization. This gives hope to further increase the reconstruction quality and the compression ratio in the future.
The resolution of digital holography as an optical imaging system is described by the point spread function of the system. The point spread function of double aperture digital holography is determined. It promises the possibility of a resolution increase by the concept of synthetic apertures. First results of numerically reconstructed wave fields from synthetic digital holograms combined of two single holograms are shown. Furthermore an experimental method for the exact determination of the mutual CCD position and orientation is presented.
Resolution and speckle size in the reconstructed wavefields of digital holography depend on the aperture defined by the size of the CCD-array. Here we introduce the concept of synthesizing a larger aperture by recording simultaneously the same scene by at least two CCD-arrays. It is shown that an improvement in resolution can be obtained which corresponds to a virtual aperture of the size defined by the distance between the two CCDs. This is shown by a comparison of the point spread functions of systems with one and with two apertures. Open problems are stated and future prospects are presented.
KEYWORDS: Digital micromirror devices, Holograms, Digital holography, Holographic interferometry, 3D image reconstruction, Micromirrors, Holography, Charge-coupled devices, Mirrors, Binary data
Digital recording of holograms followed by numerical reconstruction of the wave field offers new alternatives in particle diagnostics. A plane wave passes a particle stream and the hologram is recorded directly by a CCD-sensor without any focusing optics. The reconstruction of the particle distribution and velocity from the recorded hologram is done numerically. Multiple holograms of the particle stream are recorded at a single instant of time from different directions. By evaluating these holograms independently it is possible to determine the 3D distribution and velocity of particles with a very high accuracy.
Size, position, and velocity of particles or droplets in 3D- space can be measured contactlessly by in-line holography. In digital in-line holography the holograms are recorded by a CCD-array and stored digitally, the reconstruction of the complex wavefields is performed numerically in the computer. By an arrangement allowing the laser beam to pass several times through the particle field before hitting the CCD, several angular views are recorded simultaneously. In the reconstruction stage the viewed are separated by numerical focusing to the different distances, and by a tomography- related method the 3D-positions of the particles are determined. Double pulse recording enables to determine also the velocity of the particles. The paper gives a short introduction to digital holography, explains several holographic arrangements for multipass in-line holography, presents some experimental results of position and velocity measurements, and discusses some typical errors.
Fresnel or Fraunhofer holograms recorded on CCD arrays can be numerically reconstructed either by the discrete finite Fresnel transform or by solving the diffraction integral using the convolution theorem. Applications in holographic interferometric deformation measurement with effective digital filtering to enhance the interference phase are presented. The detection, location, and size determination in holographic particle analysis can use reconstructed images which are orthogonally oriented with respect to the hologram plane or employ different angular views reconstructed from a single hologram in a tomographic approach.
KEYWORDS: Digital holography, Holograms, Holographic interferometry, Charge-coupled devices, 3D image reconstruction, Convolution, Digital filtering, Digital recording, Fourier transforms, Diffraction
Fresnel or Fraunhofer hologram s can be recorded by CCD arrays as long as the sampling theorem is fulfilled. The numerical reconstruction of the wavefields is performed either by the discrete finite Fresnel transform or by solving the diffraction integral using the convolution theorem. The availability of the digitally evaluated complex wavefield instead of only the intensity field in optical reconstruction allows the subtraction of the phase distributions belonging to two states of the object to yield the sign-correct interference phase distribution with high accuracy. A numerical compensation for excess motion as well as effective filtering of the interference phase modulo 2(pi) are feasible.
Optically generated holograms can be recorded on CCD-arrays if the sampling theorem is obeyed. The digitized and quantized holograms are processed digitally for the reconstruction of intensity and phase of the real or virtual image. This digital reconstruction consists in a numerical realization of the diffraction integral One approach is the Fresnel approximation employing a single Fourier transform, the other is the interpretation of the diffraction formula as a convolution integral and calculation of this convolution by a double or triple Fourier transform. In this convolution approach the impulse response of free space propagation has to be defined which is then Fourier transformed or the free space transfer function is defined immediately. Impulse response as well as transfer function can be defined exactly or in an approximated version. The main difference between the Fresnel and the convolution approach is the different size of the resulting images. Furthermore in the Fresnel case this size depends on the wavelength and the distance of the object from the CCD, in the other case it does not. In this paper consequences on the reconstructed wavefields and on the interference phase distributions of holographic interferometry are indicated and demonstrated by experimental results.
A method for particle size and position measurement based on digital holography is described. A plane wave passes a particle stream and the diffracted wave is recorded directly by a CCD-sensor without any focusing optics. The reconstruction of the particle distribution from the recorded diffraction pattern is done numerically with a computer. Diffraction patterns from different directions are taken at a fixed instant of time, evaluated independently and finally the reconstructed scenes are combined by tomographic methods.
Direct recording of Fresnel holograms on a CCD (charge-coupled device) and their numerical reconstruction is possible, if the maximum spatial frequency of the holographic microstructure is adapted to the spatial resolution of the detector array. The maximum spatial frequency is determined by the angle between the interfering waves. For standard CCDs with spatial resolution of approximately 110 lines/mm the angle between reference and object wave is limited to a few degrees. This limits the size of the objects to be recorded or requires a large distance between object and CCD-target. In this paper a method is described in which the primary object angle is optically reduced, so that objects with larger dimensions can be recorded. The principle is demonstrated at the example of deformation analysis. Two Fresnel holograms, which represent the undeformed and the deformed state of the object, are generated on a CCD-target, stored electronically and the wave fields are reconstructed numerically. It is shown that the interference phase can be calculated directly from the digital holgrams, without generating an interference pattern.
The possibilities of artificial neural networks in computer-aided evaluation of holographic interference patterns are shown at three examples: demodulation of the interference phase modulo 2(pi) in one and two dimensions by a time-discrete recurrent Hopfield network, fringe tracking by a self organizing feature map network of the Kohonen-type, and the automatic detection of partial patterns due to material defects by a multilayer network trained by backpropagation.
Pattern recognition is a part of modern information processing with the objective to automate perceptive abilities. There are three paradigms mainly used for practical solutions: neural networks, statistical procedures, and knowledge based systems. Each of them is based on different assumptions and requirements. In our case the automatic recognition and classification of characteristic fringe patterns being indicative for special kinds of flaws on or under the surface of the investigated object is of interest -- especially with respect to an automatic and non-destructive quality control of industrial products. A serious problem of all optical methods is the fact that the used techniques are sensitive only for changes on the surface. Therefore flaws under the surface can be detected just by their affects on the surface. The conclusion from the characteristics in the observed fringe patterns (ring shaped fringes, displacement or distortion of fringes, varying fringe density, ...) to the kind of fault in the measured object (separation, delamination, debond, crack, inclusion, ...) is based on experimental results and practical experience. To solve the task the implementation of two approaches is preferred: neural networks and knowledge based systems. Both approaches have common qualities such as e.g., the preprocessing of noisy interferograms and the selection of representative features but also important differences such as the used recognition architecture. In this paper these aspects are discussed on examples of simple, so-called basic fringe patterns. For these pattern types spot checks are generated using mathematical simulation and practical preparation of loaded samples. Furthermore, the choice of robust features discriminating different basic patterns (classes) and the proposal for a special system architecture are discussed.
To prove the possibility of detecting internal inhomogeneities in thick walled structures by holographic interferometry we measured the deformations of the outer surface of a thick walled pressure vessel above an internal weld point. The measured deformations were confirmed by calculations of the deformation field by the method of finite elements.
The Fourier-transform method determines the interference phase distribution from an interference pattern. If evaluating only a single pattern, the sign remains unknown. Methods for interactive sign correction and for determination of the sign by two phase shifted interferograms are presented. For demodulation of the wrapped phase, a path independent algorithm is described.
Methods for determination of the interference phase distributions from interference patterns are presented and the most important methods, which are fringe tracking, temporal heterodyning, phase shifting and Fourier transform evaluation are compared with regard to experimental requirements, achievable resolution and precision, as well as inherent noise suppression and image enhancement. The comparison shows: whenever phase shifting is possible, it is the best choice. If only one interference pattern is offered, Fourier transform evaluation is recommendable.
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