The Optical Vortex Metrology is based on the possibility of characterizing, through topological and morphological parameters, each one of the vortices existing in the phase of the optical field, or in a pseudo-phase obtained by means of the Hibert, Reisz or Laguerre-Gauss transforms. On this basis, it is possible tracking and pairing the homologous vortices. Then, the locations and relative displacements between the homologous vortices are determined with sub-pixel precision. Because of the statistical nature of the measurements, their quality is determined, among other factors, by the amount of available vortices per unit area. In this work, it is proposed to use the internal modulation of the speckles to generate a significant increase in the vortex density, which can be achieved by employing a double aperture pupil optical system. Simulations of the speckle distributions are presented to analyze the increase of the vortex density as a function of the distance between the apertures, and to evaluate the influence of the increment of this density in the quality of uniform in-plane displacements measurements. The results corresponding to modulated speckles are compared with those obtained with a single aperture.
The fourth-order spatial coherence state of wave-fields is described in the framework of the classical wave picture, by
means on the four-order spatial coherence wavelets. This strategy suggests that the fourth-order spatial coherence state of
light can be modelled in terms of three layers of point sources in order to increase the performance of numerical
algorithms. The model is illustrated by applying it to the Hanbury-Brown & Twiss effect.
Due to analytical and numerical difficulties, the propagation of optical fields in any state of spatial coherence is
conventionally computed through severe approximations; Fresnel-Fraunhofer approach is one of the most widely used.
These approximations provide in many cases a rough knowledge of the actual light behavior as it propagates. However,
the complexity of the actual developments requires non-approximated procedures capable of modeling the propagation
of optical fields in any state of spatial coherence. The proposed model bases on expressing the classical cross-spectral
density in center-difference coordinates, which allows for its exact calculation in very practical cases. The results reveal
unaware behavior of light as it propagates, and equal those obtained with the conventional computation approaches as
approached to the Fresnel-Fraunhofer regime. Light behavior close to the diffraction transmittances can also be learned
with the aid of the proposed modeling tool.
The spatial coherence wavelets theory provides more insight into the understanding of interference and diffraction
because they are the primary carriers of power and correlation of light. In this context, novel keys for analyzing the
physical properties of light are revealed by these wavelets, as discussed in the present work. Particularly, the bright and
the dark rays and related features as the energy flux vectors - parallel and anti-parallel to the Poynting vector, and the
transverse energy transference, provide insight into the mechanism of energy distribution of a wavefield after diffraction
and its dependence on spatial coherence properties of the field. These properties could be experimentally controlled by
modulating the spatial coherence of the light, offering new possibilities of technological applications in subjects
involving beam shaping.
Previous researches have shown that spatial coherence wavelets provide the phase-space representation for optical fields
in any state of coherence and polarization and can represent the radiometric properties of optical sources. In this paper,
we have developed a research about their holographic features and particularly we have found the cross-spectral density
at the observation plane should be regarded as the second-order wave reconstructed from the Fourier hologram of the
marginal power spectrum, where the power spectrum corresponds to the zeroth-order of the reconstruction and the
characteristic hermiticity of the cross-spectral density determines the twin images. In a similar way, the holographic
reconstruction of the cross-spectral density at the aperture plane has been stated, taking the marginal power spectrum as
its Fourier hologram, the power spectrum at the aperture plane related to its zeroth-order, and its twin images determined
by the hermiticity of the cross-spectral density at aperture plane. After realizing that spatial coherence wavelets can be
regarded as Wigner distribution functions with similar morphology to the hologram diagrams recently proposed for
formulating holography in the phase-space by Lohmann and Testorf, we recognized their power for providing a precise
and wide physical interpretation of optical signals in phase space which enables us to apply these holographic features in
many fields like optical coherence modulation and beam shaping.
The concept of spatial coherence wavelet has been introduced some years ago with very productive results. It has given
new insight on the fundamental optical phenomena, and has predicted novel light characteristics like polarizations
domain and transverse energy transference. The concept of marginal power spectrum emerges as the amplitude of the
wavelet and provides a phase-space representation of the optical field in any state of spatial coherence. Its values have
energy units and are carried by the spatial coherence wavelets along specific paths or rays. Some of them, called carrier
rays, are corresponding to the radiant energy of the field, but the rest, called dark (or tamasic) rays, do not contribute to
the radiant energy, i.e. they take on positive and negative values, symmetrically distributed, which are responsible for the
constructive and destructive interference after redistributing the radiant energy of the field. This description of
interference is illustrated by analyzing the Young experiment, gratings and one-dimensional apertures. Furthermore, the
principle of spatial coherence modulation is introduced, showing its feasibility for practical applications in beam
A strategy for to compress color images in digital holograms of gray tones was developed. The procedure codifies the
information of each channel of the RGB model in a system of fringes, it is a gray image denominated "hologram". The
fringes in their intensity of gray tone carry the signal of the channel, in this manner the amplitude information for each
channel of color image is stored. The angles of fringes define how the information of each channel will be
The sum of the different gray fringes images is the hologram, it is the "object" for a digital holographic system. The
RGB channels are high intensity peaks of information in the hologram's Fourier space, and when the peaks are filtered
each channel can be extracted.
Parameters such as: space frequency, visibility, direction and quality of the fringes affect the quality of the reconstructed
image. However, the propose methodology allow a radius 3:1 for the compression of color image, too with this
process is possible the compression of different spectrum in a one color image.
For the first time, transmission digital holography microscopy is applied to observe coal palynofacies, which are organic
fossil microcomponents contained in the coal grains. The recorded holograms were produced by using microscope lenses
with 20x and 40x of lateral magnification respectively, and He-Ne laser of wavelength 594.5 nm. The results show that
reflection digital holography microscopy is required for observing relative opaque particles, because the phase recovery
is strong diminished by light transmission in those cases. On the other hand, the phase distribution is related to the relief
of the particles and the variations of their refraction index. Therefore, a priori information should be necessary to
properly relate the phase information to physical features of the particles. Numerical unwrapping procedures are also
crucial. Procedures with special requirements can be needed for analysing fast varying phase distributions. However,
digital holography microscopy becomes a high performance tool for 3D modelling of fossil particles if the above
requirements are enough fulfilled.
Defocused imaging can be analyzed as Fresnel diffraction. The defocus parameter, that characterizes this imaging, is related to an effective Fresnel number, which is induced by the geometry of the imaging set-up. From this point of view, perfectly focused images result from Fraunhofer diffraction. Therefore, the same criteria for distinguishing between Fraunhofer and Fresnel diffraction can be applied to determine if the image is or not focused. As a consequence, new definitions of the focus depth can be deduced. In addition, resolution of two point-objects under different states of spatial coherence and focus conditions is discussed and some resolution criteria are deduced. Then, they are compared to the classical resolution criteria, which are considered as applicable to the extreme cases of fully spatial coherence and fully spatial incoherence. Some classical examples, such as, imaging of one point object and two near point objects, are discussed to illustrate the analysis.
The single cell gel electrophoresis assay is a sensitive, rapid, and visual technique for deoxyribonucleic acid (DNA) strand-break detection in individual mammalian cells, whose application has significantly increased in the past few years. The cells are embedded in agarose on glass slides followed by lyses of the cell membrane. Thereafter, damaged DNA strands are electrophoresed away from the nucleus towards the anode giving the appearance of a comet tail. Nowadays, charge coupled device cameras are attached at optical microscopes for recording the images of the cells, and digital image processing is applied for obtaining quantitative descriptors. However, the conventional software is usually expensive, inflexible and, in many cases, can only provide low-order descriptors based in image segmentation, determination of centers of mass, and Euclidean distances. Associated density functions and centered reduced moments offer an effective and flexible alternative for quantitative analysis of the comet cells. We will show how the position of the center of mass, the lengths and orientation of the main semiaxes, and the eccentricity of such images can be accurately determined by this method.
Generalized radiance was introduced for analyzing the behavior of radiant surfaces in any state of spatial coherence. Some of its properties make difficult to interpret it physically. In particular, generalized radiance is a Wigner distribution function that can take positive and negative values, so that it does not have the meaning of an energy flux at all. Supported on the concept of radiator pairs we will express the generalized radiance, the generalized radiant emittance and the generalized radiant intensity first proposed by Marchand and Wolf. Then, we will analyze the extreme cases of spatially coherent and incoherent sources and propose a new physical interpretation for the negative values of the generalized radiance.
A fundamental problem in holography, as well optical as digital, is the presence of speckle noise in the reconstruction process. Many approaches have been carried out in order overcome such a problem, ranging from altering the spatial coherence (optical techniques) of the illumination to imaging processing techniques (digital techniques). This work shows the merged use of digital imaging techniques in order to reduce the speckle noise in digital reconstruction of optically recorded Fresnel's holograms. The proposed filtering techniques are illustrated with experimental results.
In this work a method for retrieving the magnitude and phase of the complex degree of spatial coherence is shown. To apply it only the recording of the spot intensity is required. Afterwards, centered reduced moments of the spot are calculated, in order to use them as coefficients of a series to expand the complex degree of spatial coherence. Experimental results for Schell-model spots are shown. The Fourier spectra corresponding to the experimentally recorded sots, are calculated in order to show the equivalency between the proposed method and the Fourier one.
The dyadic shift-based image processing uses the address permutation of the individual pixels or the permutation of their gray levels or both by means of the XOR operation. It is properly described within the framework of the two-dimensional Walsh functions and Walsh transforms. The dyadic shift procedures allow the transformation of the original image and its posterior recovery without information loss by simply performing further permutations. In addition, comparison of particular features of different images can be achieved by applying dyadic correlations, which in turn can also take advantage of the Walsh transforms. Therefore, the dyadic shift-based image processing has potential applications on image encryption, image enhancement and filtering and pattern recognition among others.
Taking advantage of the relationship of the M2 factor for Gaussian Schell model sources on terms of the global coherence parameter, derive for Santansiero et al. in Reference 1, we have shown on this paper the invariance of the M2 factor through its connection with geometrical Etendue of the pencil. This invariance have been shown for each independent coordinate.
Spatial coherence of optical fields can be considered as beam structured if the size of the coherence patch varies slowly through the propagation of the optical field. As a consequence, the correlation of the optical field will be concentrated in a finite region around the direction of propagation. For properly describing it in the Fraunhofer-Fresnel domain, the marginal cross-spectral density is introduced. The superposition of spatial coherence beams in this domain is also analyzed. It produces an interference field and a spatial coherence Moire.
The power spectrum of a diffracted optical field is expanded as the superposition of Young interference patterns produced by all source pairs in the diffracting aperture. It shows clearly that the power spectrum can take negative values for some types of spatially partially coherent optical fields. A renormalization of the definition of the power spectrum based on the etendue is introduced to properly overcome this fact.
The optical field diffracted through a simple circular aperture can produce optical tubular structures single-closed of twice-closed by choosing the suitable experimental conditions. An important characteristic of such structures on this way generated is that they have strong intensity gradients at their edges, making them appropriate structures for optical trapping of particles.
Young's interferograms with high visibility reveals a high degree of spatial coherence. However, effects due spatially partial coherence can be observed when a Young's interference pattern interferes itself through a compensated Michelson's interferometer, which is attached at the exit of the Young's slit pair, as we show in this paper.
In this paper we study the propagation of coherence beams from a non-regular 1D grating to an observation plane in the Fraunhofer domain. The cross-spectral densities at both the grating and the observation plane are analyzed. The concept of spatial coherence Moire was introduced to analyze the cross-spectral density at the observation plane of the corresponding interference field.
The marginal cross-spectral density, a Wigner distribution function allows us to determine the structure of spatial coherence beams. The Fourier spectrum of spatially partial coherent interferograms is described by a triple correlation, which involves the cross-spectral density of the illuminating optical field and the transmittance of the aperture.
Spatial coherence beams, which propagate from a non-regular grating to a Fraunhofer observation plane, yield spatial coherence Moire patterns. Furthermore, as a result of the analysis of the corresponding interferogram, an effective Moire grating is proposed. In both critical and Kohler's microscope illuminations, Besselian coherence beams propagate between the exit pupil and the exit window of the illumination system. The size of their coherence patches is determined by the field stop of this system.
In this report we discuss the method of the analysis of pseudo-identical optical signals. Two similar images, composed by identical apertures, were taken as an example for examination. The difference in their structures can be connected with the value of the apertures' function of transmittance, with the inter-apertures' separation along one direction, or with both these factors simultaneously. The overall functions of the transmittance for this type of pseudo- identical structure can be measured up through comparison of the secondary Fourier spectrums of corresponding transmittance functions.
It is widely known that both the speckle pattern generated by the axial movement of a rigid diffuser surface, as well as the speckle pattern registered with low resolution, present blur-up. In the first case a blur-up criterion was proposed and applied to the study of vibrations. The statistical and optical properties of dynamic diffusers are also well modeled and well known. This paper proposes a numerical criterion to determine the blur-up of the speckle pattern resulting from superposition patterns generated by dynamic diffusers. Its application is illustrated in the analysis of the Brownian motion of colloidal particles.
Incoherent imaging quality of optical systems will depend on the properties of the OTF. In the current paper we show an OTF-based image quality analysis, in which the properties of the OTF are represented by means of matrices, whose components depend only on the centered reduced moments of measured PSFs. Quantitative descriptors of both the geometrical characteristics and the energy distribution of the PSF (i.e. position of centers of mass, length and orientation of semi-axis, eccentricities) are determined as functions of those components. So, different aberration types can be characterized by means of the OTF properties.