The modulus of the gradient of the color planes (MGC) is implemented to transform multichannel information to a grayscale image. This digital technique is used in two applications: (a) focus measurements during autofocusing (AF) process and (b) extending the depth of field (EDoF) by means of multifocus image fusion. In the first case, the MGC procedure is based on an edge detection technique and is implemented in over 15 focus metrics that are typically handled in digital microscopy. The MGC approach is tested on color images of histological sections for the selection of in-focus images. An appealing attribute of all the AF metrics working in the MGC space is their monotonic behavior even up to a magnification of 100×. An advantage of the MGC method is its computational simplicity and inherent parallelism. In the second application, a multifocus image fusion algorithm based on the MGC approach has been implemented on graphics processing units (GPUs). The resulting fused images are evaluated using a nonreference image quality metric. The proposed fusion method reveals a high-quality image independently of faulty illumination during the image acquisition. Finally, the three-dimensional visualization of the in-focus image is shown.
In this work, the concept of quasi-point source (qps) is used for the restoration of defocused images of extended objects detected with incoherent light. The method consists of the characterization of the optical system by a qps illuminated with coherent light, its defocused image is then introduced in the restoration process, which is a deconvolution performed with a Wiener filter. The results of the restored images are shown and compared with those images restored when the qps is illuminated with incoherent light. Finally, a numerical evaluation using the RMSD (root mean square deviation method) about the quality of the restoration was made for both cases.
An optical system formed by four point-diffraction interferometers is used for measuring the refractive index distribution
of a phase object. The phase of the object is assumed enough smooth to be computed in terms of the Radon Transform
and it is processed with a tomographic iterative algorithm. Then, the associated refractive index distribution is calculated.
To recovery the phase from the inteferograms we use the Kreis method, which is useful for interferograms having only
few fringes. As an application of our technique, the temperature distribution of a candle flame is retrieved, this was made
with the aid of the Gladstone-Dale equation. We also describe the process of manufacturing the point-diffraction
interferometer (PDI) plates. These were made by means of the thermocavitation process. The obtained three dimensional
distribution of temperature is presented.
An optical-digital method is proposed for restoring trichromatic images out-of-focus, detected with a monochromatic
CCD. The optical system (OS) is a microscope working in bright field mode and the source of illumination is
polychromatic. To carry out the restoration, an estimated of the intensity point spread function is obtained from the
image of a non-resolved object (quasi-point source) by the OS in three wavelengths. From the image of the quasi-point
source, its spectrum is calculated for obtaining the optical transfer function associated with each wavelength. The
Wiener filter is built with the spectrum, and the restoration is made for each color. By an addition of the three restored
images, an estimated of the trichromatic object is recovered. The obtained results and conclusions are presented.
In this work, experimental results are obtained from the behavior of the Discrete Wigner Distribution Function (DWDF),
when is applied on a detected image of an object of small dimensions, non-resolved by the optical system (OS). The
object is illuminated with a laser source. We verify that for the average of several detected images the DWDF is positive
inside a frequency interval of four times the bandwidth of the OS. However, when the object is not a quasi-point source
the DWDF has positive and negative values inside the same interval. This is an indication that in this case the object is
resolved by the OS. Numerical and experimental results are shown and compared to support this conjecture.
Wendland radial basis functions are applied as an alternative solution to the interpolation problem when the filtered back
projection algorithm is used in computed tomography. Since we have a regular grid of data points and these functions are
compactly supported, the interpolation can be made as a fast filtering process rather than solving a typical linear system
of equations. This allows us to apply the Error Kernel method, which gives details of the approximation quality in the
frequency domain, when we make interpolation with basis functions such as the B-splines. The Error Kernel provides us
a direct comparison between Wendland functions and B-splines. The comparison shows that the Wendland functions can
offer the same interpolation quality of the B-splines when the support is large, but with a small support the performance
is poor. We see this behavior making tomographic reconstructions with different Wendland functions and also with
different supports. A numerical experiment consisting of successive image rotations to an image was performed to verify
the similarities between the Wendland functions and B-splines.
A simple method for phase unwrapping is proposed. When phase is smooth, continuous and slightly noisy,
morphological processing can be used to estimate the unwrapped phase. The application of morphological processing
converts the continuous (real) range [-π, π) into a discrete (integer) range. This domain transformation
may allow an increase of speed performance in the unwrapping phase processing. Since the wrapped phase is
modulo 2π, it is possible to delimit regions with 4-connectivity that allows the proper phase map estimation.
The maximum intensity of the noise that allows a good reconstruction of the original phase map was 2.
KEYWORDS: Particles, Spherical lenses, Nanoparticles, Near field optics, Near field, Dielectrics, Prisms, Microscopes, Refractive index, Radio propagation
In the aim to understand the nature of the propagation of an electromagnetic field in
the near region, we study the interactions between an evanescent field and two
different samples of spherical dielectric nanoparticles, i.e. a set of five particles and
a single one. Each sample was studied in separated experiments. This is made by
using a Photon Scanning Tunneling Microscope (PSTM) in the constant distance
mode. We also analyze the obtained images and determine that the optical images
show mainly interference between the evanescent field and the reflected field on the
surface of the nanoparticles. Finally, we found that the perturbation of the
evanescent field, produced by imperfections on the substrate, is negligible in
comparison with the interactions intensity.
KEYWORDS: Wigner distribution functions, Optical transfer functions, Imaging systems, Diffraction, Image resolution, Point spread functions, Signal to noise ratio, Image processing, Wavefronts, Visualization
The aim of this work is to propose a positiveness constraint on the Wigner Distribution Function (WDF) of the detected image of two incoherent point sources: if WDF lacks of zeroes along the frequency coordinate the object can not be resolved by imaging and detected systems; otherwise, it can. This criterion can be applied without preference for a circular clear diffraction limited aperture and for complex apertures with small aberration values; furthermore, it holds if the intensity of each source is different or even when the sources are not points.
We propose a simple confocal system that uses a laser Gaussian beam as a probe to measure microstructure features of curved or turned surfaces. The probe beam is focused by a lens with a low numerical aperture to maintain the beam unclipped throughout the detection process and to limit the vertical resolution to several microns. This resolution is suitable for examining the microstructure of machined surfaces. The size of the pinhole in the plane of detection is characterized for optimal depth discrimination. The analytic description is based on the propagation of Gaussian beams by using the scalar Fresnel diffraction integral.
The confocal imaging algorithm is applied to retrieve the profile of 1-D rough surfaces with non-gaussian spectra. Different forms of the autocovariance function are tried in the simulation, gaussian included for reference. The capability and the limitations of the algorithm for each function are to be set in terms of the parameters of roughness such as the rms and the correlation length.
We obtain the reflection spectra of p-polarized light from metallic gratings fabricated by means of the interference technique. The gratings have constant period and heights are varied by changing the exposure time of the interference pattern on the sample. The experimental spectra show two minima due to the excitation of surface plasmons, and they are compared with the corresponding numerical results obtained with two models, the Rayleigh theory and the rigorous integral method. In order to demonstrate the validity of the Rayleigh hypothesis the amplitudes of the gratings are chosen close to the Rayleigh limit.
The inverse problem of retrieving the particle size distribution from the intensity of the diffracted field is solved using two numerical methods, the Chin-Shifrin algorithm and Singular Value Decomposition. The theory used in the inversion is based on the Fraunhofer approximation. We used the Lorenz-Mie theory to generate the intensity data produced from a series of normal size distributions. The distributions scan the interval of radius 0.1 micrometers < a < 17 micrometers . From our result we can set limits to the interval of particle size where the Fraunhofer approximation is valid.
Based on the capability of confocal microscopy to profile rough surfaces, Quartel and Sheppard have proposed an algorithm to reconstruct surface profiles from scattering data. We determine the range of applicability of the algorithm by investigating the effects of the roughness and correlation length of a random surface on the reconstruction.
Comparisons of theoretical and experimental images of optically thick objects are presented. Selected objects are phase steps and ridges of rectangular profile, of a conducting material. To obtain the experimental images a Linnik interference microscope is used. To simulate the images a theory based on the integral equation method is employed.
A rigorous numerical technique to calculate images of optically thick one-dimensional objects as formed by an optical scanning microscope is presented. The geometry of the selected system allows us to simulate microscopes in various modes of image formation (coherent, partially coherent, bright-field, dark-field, and confocal). We consider the cases of s- and p- polarized illumination. The samples consist of dielectric film structures deposited on perfectly conducting flat substrates, and are characterized by the surface profile, the film thickness, and the complex refractive index of the dielectric. Examples of bright-field coherent images calculated with this technique are shown.
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