Geometrical Optics Research Papers

A review of the optical properties of biological tissues

by Scott Prahl

1990, Quantum Electronics, IEEE …

Expressions for light flux solutions of the diffusion equation (11) are The accuracy of this relation decreases with decreasing tatios of scattering to absorption and increasing aniso- tropy (see Table 23 in van de Hulst [4]) and fails com- pletely when absorption dominates scattering (since both the limiting form of (16) changes and the diffusion ap- proximation itself is inaccurate).

The total transmission is T, = T + T,, where T, is given by (5). _ The reflection and transmission of a slab of thickness t with index matched boundaries in the diffusion approxi- mation are given by [2], [4], [15], [16] Measurements of diffuse reflection (R), total transmis- sion (7;,), and unscattered transmission (T.) provide suf- ficient information for uniquely determining three optical parameters ( pg, 4s, 8). However, if only diffuse reflec- tion and total transmission measurements are available, only absorption ( #,) and reduced scattering [pi = p,(1 — g)] coefficients can be calculated. The anisotropy ( ¢) has been incorporated into p; by the similarity relations Ba = Ma and ps(1 — g') = p,(1 — g). Anisotropic scat- tering is reduced to isotropic scattering by setting 2’ = 0 and so wy = (1 — g) pw, [3], [17].

where Axy and Sxy4 are the Kubelka-Munk absorption and scattering coefficients and have units of inverse length (m7'). The parameters x and y are found using (23c). The advantage of the Kubelka-Munk model is that the scat- tering and absorption coefficients may be directly ex- pressed in terms of the measured reflection and transmis- sion The simplicity of the Kubelka-Munk model has made it a popular method for measuring the optical properties of tissue. Unfortunately, the assumptions of isotropic scat- tering, matched boundaries, and diffuse irradiance are atypical of the interaction of laser light with tissue. De- spite attempts to extend the Kubelka~Munk model to col- limated irradiance [16], [22], [23] and anisotropic scat- tering [15], [22], [25], this method remains a poor approximation for laser light propagation in tissue [24].

Fig. 1. Measured values from the unscattered transmission 7,, through a sample of thickness r are analyzed using Beer’s law to provide estimates of the total attenuation coefficient ( ,). (b) Interstitial measurements of fluence rate (or flux) inside a sample with or without an added absorber yield an estimate of the effective attenuation coefficient ( ze) or the ef- fective penetration depth (O.¢ = 1/peq). (c) Measurements of diffuse reflection R,, and diffuse transmission T,, and sample thickness r, for diffuse irradiance are used in (22) to compute Kubelka-Munk absorption Axm and scattering Sxy, coefficients. (d} Measurements of diffuse reflec- tion and transmission for diffuse irradiance lead to Kubelka-Munk coef- ficients; these are then converted to transport parameters. When colli- mated transmission is available, yw, #,, and g can be calculated. (e) If only total reflection and transmission are available, the absorption coef- ficient #, and reduced scattering coefficient »,(1 — g) can be determined with an iterative light transport model. An additional measurement (col- limated transmission or the phase function) permits separate estimation Of fa, Bs, and g.

CONVERSION FORMULAS RELATING KUBELKA—MUNK TO TRANSPORT COEFFICIENTS TABLE I iransport coeticients Can be derived Irom tne collision of a plane wave with a particle [4]. Some of the wave is scattered, some is absorbed, and some is undisturbed. The absorption (o,) and scattering (o,) cross sections (m’) for tissue are ill-defined, because the particles are not sepa- rated from one another. Consequently, with the notable exception of blood [4], these cross sections are not well defined and measured. However, the volumetric absorp- tion and scattering coefficients (m7!) can be defined by using ( p) the average density of particles per unit volume of tissue (m~*). The scattering coefficient is u, = po, and the absorption coefficient is p, = po,. Note that the phase function is not involved in the description of the absorp- tion and scattering coefficients.

FLUENCE MODELS WITH ASSOCIATED OPTICAL PARAMETERS TABLE II

KUBELKA~MUNK COEFFICIENTS IN VITRO Keg Values were obtained directly from interstitial fluence measurements [12], [13], [33]-[35] than those calculated from yz, and y,(1 — g) parameters for bovine (Kara- giannes), human | (Marchesini), ; and murine > (Parsa) livers. ae we ed - a scattering effects in the absorbance measurements. Scat- tering redistributes the light over a broader tissue volume, effectively increasing the pathlength for optical absorp- tion, and hence a larger absorption coefficient would be measured. In fact, examination of Table III reveals that absorption parameters measured by photoacoustic means are generally higher than those made with other tech- niques.

descriptionView Paper arrow_downwardDownload

Vision for mobile robot navigation: A survey

by Dariush Khoorani

2002, Pattern Analysis and Machine …

This paper surveys the developments of the last 20 years in the area of vision for mobile robot navigation. Two major components of the paper deal with indoor navigation and outdoor navigation. For each component, we have further... more

Fig. 1. Indoor robots can now localize themselves using computer vision in scenes of the complexity depicted here. Reprinted with permissior from [75].

Fig. 2. NAVLAB 1 can analyze intensity images such as this and determine the boundaries of a roadway. Reprinted with permission from [143].

Fig. 4. A map of the environment with landmarks indicated by circles. Reprinted with permission from [5]. Again, the intersection of sets x; and y; computed for all regions yields x* and y*. As mentioned at the beginning of

Fig. 3. (a) Largest (full line) and smallest (dotted line) sides. (b) Largest (full line) and smallest (dotted line) angles.

Fig. 5. The evolution of the width of the x and y parameters intervals. Reprinted with permission from [5] commanded motion has been completed. It is known that if this relationship,

Fig. 6. Processing steps in FINALE’s self-locomotion algorithm. where 2 is the Jacobian of the transformation function h. These two equations tell us how to transform the mean and the covariance associated with the position of the robot from just before a commanded motion to just after it, provided we know the functional relationship given by h(p). To discover the form of the h(p) function for the case when the robot executes a translational command, the motion executed in response to such a command is parameterized by d, a, and @, as shown in Fig. 7. In that figure, the robot was commanded to execute a translational motion through a distance dy along its y, axis. But, because of differential slippage in the wheels, the robot ends up at a location given by the distance parameter d and the angle parameters a and (3. By using simple trigonometry, one

Fig. 7. Initial and final position after a translation command. Reprinted with permission from [75]. arrives at the following functional relationship between p and p’:

Fig. 8. Initial and final position after a rotation command. Reprinted with permission from [75]. sure that the command motions are small in size so as not to invalidate the approximations. Note that, as is clear from (2), in the linear regime of operation, we only need to know the Jacobian of the transformation from p to p’. This Jacobian may be found by taking differentials of both sides of (3) for the case of translational commands and of both sides of (4) for the case of rotational commands to give us

where Jr, Jn, Jr,, and Jp, are the Jacobians for the translational and rotational cases as indicated by the indices used. The detailed expressions for the Jacobians are provided in [75]. We can now write down the following equations for propagating the mean and the covariance of the position vector p through translational commands:

Fig. 9. Uncertainties around point landmarks. The Mahalanobis distance d = 1 was used to construct the uncertainty ellipses. Reprinted with permission from [75].

Fig. 9i lustrates the utility of the covariance matrix 4; as a measure of the uncertainty associated with the location of a pixel for panel of t an isolated point in the environment. In the left his figure, a wire-frame rendering of the hallway is shown. This is an expectation map made based on the current value of p, in the sense that this is what the robot would see if its actual position was at the center of the uncertainty region associated with its position. For each end point of a vertical edge in the expectation map, we have in the right panel an uncertainty ellipse which should contain the pixel corre- sponding to the end point with a probability of 86 percent. The ellipse corresponds to one unit of Mahalanobis distance as calculated from the covariance matrix 4; using (8) and the following statistical parameters of the robot's position: An isolated point in the environment is obviously not a perceptually interesting landmark. But, all of the above discussion on projecting robot’s positional uncertainties into the camera image can be extended easily to midlevel features such as straight edges formed by the junctions of walls, borders of doors, windows, bulletin boards, etc. As shown in [75], this is best done in Hough space where each straight line feature can be represented by a single point. So, given a straight line feature in the environment, FINALE would know where in the Hough space it should seek the image of that straight line.

Fig. 10. Some of the intermediate results in FINALE’s localization algorithm. (a) The camera image and the superimposed expectation map (b) Output of the model-guided edge detector. (c) Uncertainty regions associated with the ends of the model line features. (d) Matching after Kalmar filtering. Reprinted with permission from [75].

Fig. 12. Hierarchy of neural networks to perform corridor-following Reprinted with permission from [103].

Fig. 11. (a) Physical structure of a hallway segment showing the doors and alcoves. (b) The topological representation of the hallway in (a). Reprinted with permission from [103].

Fig. 13. Image processing steps in NEURO-NAV. Reprinted with permission from [103].

Fig. 14. Results after each step in Fig. 13. Reprinted with permission from [103]

Fig. 15. Software architecture of FUZZY-NAV. Reprinted with permis- sion from [121].

Fig. 16. Linguistic variables and their associated fuzzy terms used ir FUZZY-NAV. Reprinted with permission from [121].

Fig. 18. Reflecting tape guidance system. Reprinted with permission from [149]. The Fuzzy Supervisory Controller of FUZZY-NAV is a real-time fuzzy expert system that takes in the outputs of all the neural networks and decides what commands to issue to the Robot Control Module (see Fig. 15). To accomplish this, the Fuzzy Supervisory Controller uses three linguistic variables, distance-to-junction, turn-angle, and distance-to- travel. Associated with these linguistic variables are a total of sixteen fuzzy terms, as shown in Fig. 16. The semantics of the linguistic variables distance-to-junction and turn-angle were covered before, when we explained NEURO-NAV, and should be obvious to the reader. The linguistic variable distance-to-travel stands for the current best estimate of how far the robot should plan on traveling straight barring any One can do localization by landmark tracking when both the approximate location of the robot and the identity of the landmarks seen in the camera image are known and can be tracked. The landmarks used may either be artificial ones, such as those shown in Fig. 17, or natural ones, such as doors, windows, etc. The artificial landmarks vary from circles with a unique bar-code for each landmark [66] (same figure) to reflecting tapes stretched along the robot path, as reported by Tsumura in [149] (Fig. 18). In most cases, landmark

where J; and I, are the time and x-spatial derivatives of the image, respectively. The images are smoothed, with respect The above equations are somewhat oversimplified in the sense that they apply only when the two cameras are pointing in symmetrically divergent directions with respect to the direction of motion. Besides that, strictly speaking, the equations, do not permit the direction of motion to be changed, a condition that cannot be satisfied during rotational motions. However, the authors have shown

Fig. 19. Sample of the computed optical flows. Reprinted with permissio! from [133].

Fig. 21. Examples with (center and right) and without (left) the sustained behavior. Reprinted with permission from [133].

Fig. 22. Panoramic view of a place and the corresponding vector of maximum intensities. Reprinted with permission from [43]

Fig. 24. Outline of navigation using the view-sequenced route representation. Reprinted with permission from [98]. table to provide real-world displacements and angles to be used in the steering commands. In 1996, Ohno et al. ([115]) proposed a similar but faster implementation also using sequences of images. But since their system (Fig. 25) uses only vertical hallway lines, it needs less memory and can operate faster. The work of Ohno et al. also includes extensive experimentation that shows how to construct association lists of the changes in the position and the orientation of the robot, on the one hand, and the changes in what the robot sees. For another appearance-based approach that uses elastic template matching—a template is a set of features, each extracted from a 7x7 window in the image and their relative positions Another system built around Matsumoto’s VSRR concept is reported by Jones et al. [64]. There, the robot is given a sequence of images and associated actions (motion com- mands). Using zero-energy normalized cross-correlation, the robot retrieves the image from the database that best matches the view image. If the match is above a certain threshold, the robot performs the commands associated with that image, otherwise it halts.

Fig. 25. (a) Recording the image sequence (top) and comparing the current image with the recorded sequence (bottom). (b) The image processing steps for trajectroy correction. Reprinted with permission from [115].

Fig. 26. Pixel classification: “road” and “nonroad” classes. (a) Original image. (b) Color classification. (c) Texture classification. (d) Final classificatior Reprinted with permission from [143]. As mentioned before, the final classification of a pixel is carried out by combining the results obtained from color and texture. This combination is simply a weighted sum of the two probabilities: assigned a class depending on the color distributions. The road pixels are represented by four separate Gaussian clusters to account for changes in illumination, road surface properties, etc. Similarly, the nonroad pixels are also represented by four separate Gaussian clusters. Each Gaussian distribution is represented by a three-dimensional mean vector (mean R, G, and B), by a three-by-three covariance matrix, and by the fraction of pixels expected a priori to be represented by that distribution. The probability that a pixel with color vector X belongs to the distribution 7, P°, is computed using the Mahalanobis distance: (X — mj) SX —m,). The classification is carried out using the standard maximum-likelihood ratio test. The result is shown in Fig. 26b. As mentioned before, the final classification of a pixel is

Fig. 27. Road Transform. (a) Road description using P and 0. (b) Possible orientations of the road passing thru one point. (c) Best road orientation and intercept (dark square) in the (P,@) space. (d) Detected road using dark point in (c). Reprinted with permission from [143].

Fig. 28. Architecture of the neural network in ALVINN. Reprinted with permission from [125].

Fig. 29. The original and the 14 “distored” images used to train the NN. Reprinted with permission from [125]

Fig. 31. Virtual camera for detecting roads. Reprinted with permissior from [63].

Fig. 30. Virtual images obtained from the actual camera field of view. Reprinted with permission from [61].

Fig. 32. Virtual camera for detecting intersections. Reprinted wit permission from [63]. tO 0 © To fully grasp the functionality of VITS, it has to be seen as a part of the larger reasoning and control framework for Alvin (Fig. 33). The vision system produces a description of

Fig. 34. Example of a road scene and its corresponding model. Reprinted with permission from [151]. So far, we have discussed the architectural context for the vision module. Evidently, the most significant duty assigned to the Vision module is the construction of a scene model from the sensor data. We will now describe briefly the algorithmic steps that extract a description of the road from a camera image. Basic to road-description construction is the segmentation of a camera image into road pixels and nonroad pixels. Because environmental conditions, such as the presence or the absence of shadows caused by trees and

Fig. 33. Alvin system configuration. Reprinted with permission from [151].

Fig. 36. (a) Original road image. (b) Red/Blue clusters. Reprinted with permission from [151].

Unstructured environments arise in cross-country navi- gation as, for example, in planetary (lunar/martian-like) terrain navigation (Fig. 39) [157], [158], [12], [81], [99]. Sometimes in these sorts of applications, the robot is supposed to just wander around, exploring the vicinity of the robot without a clearcut goal [91], [136]. However, in other applications, the task to be performed requires that the robot follow a specific path to a goal position. In those cases, a map of the traversed areas has to be created and a

Fig. 37. (a) Original road image with shadows. (b) Red/Blue clusters. Reprinted with permission from [151].

Fig. 39. Martian terrain. This can be found at the Jet Propulsion Laboratory (JPL) Web site http://mpfwww.jpl.nasa.gov/MPF/index0.html. A highly noted accomplishment in vision-based naviga- tion in unstructured environments is the Mars Pathfinder

Fig. 40. (a) Pathfinder lander and (b) rover. This can be found at the JPL Web site http://mpfwww.jpl.nasa.gov/MPF/index0.html. project [158], [99], [101]. The Mars Pathfinder mission launched in December 1996 and landed in July 1997. was The mission was performed by two devices: the lander and the rover (Fig. 40). The lander is a 1.5 m wide and 1.0 m high tetrahedron with a mass of 264 kg. It is composed of a VME- based, RAD 6000 computer with 128Mb of memor multispectral stereo camera pair with a pan/tilt yr, a base mounted on a mast 1.5 m above the ground. The cameras have a baseline of 15 cm and resolution of 256x256 pi with an angular resolution of 0.001 radians per pixel. xels The rover, Fig. 40b, is 65 cm long, 48 cm wide, and 30 cm high. It is equipped with an Intel 8085 processor and 500K memory. The navigation by the rover, carried ou b of t in cooperation with the lander, consists of four different functions: rover could be commanded to move towards those coordinates using a simple path selection algorithm:

Fig. 42. Rover’s hazard sensors: camera fields of view in solid lines and light stripes in dotted lines. Reprinted with permission from [99]. A common problem in all outdoor navigation systems is that caused by variations in illumination. The differences in contrast and texture in an image as a function of the time of the day, time of the year, weather conditions, etc., can impose serious limitations on the performance of a navigation system. The use of color to com differences in illumination conditions has pensate for these been explored in many outdoor navigation systems. Some of the earliest systems to use color to distinguish shadows from obstacles are by Thorpe et al. [143] and Turk et a . [151]. Another more recent example of this is in [91], w here the authors

-ig. 41. Tracked positions of the rover. This can be found at the JPL Web site http://mpfwww.jpl.nasa.gov/MPF/index0.html.

Fig. 43. Vision-guided obstacle avoidance in [91]. (a) The camera image and the superimposed vertical slice with the safe window at the bottom. (b) Highlights a horizontal slice and the safe window. (c) and (d) Shows the histogram of the areas highlighted in (b).

descriptionView Paper arrow_downwardDownload

An Experimental Comparison of Range Image Segmentation Algorithms

by Hery Afroza

1996, IEEE Transactions on Pattern Analysis and Machine Intelligence

A methodology for evaluating range image segmentation algorithms is proposed. This methodology involves (1) a common set of 40 laser range finder images and 40 structured light scanner images that have manually specified ground truth and... more

descriptionView Paper arrow_downwardDownload

Intensity enhancement in textured optical sheets for solar cells

by Eli Yablonovitch

2000, IEEE Transactions on Electron Devices

We adopt a statistical mechanical approach toward the optics of textured and inhomogeneous optical sheets. As a general rule, the local light intensity in such a medium will tend to be 2 n2(x) times greater than the externally incident... more

descriptionView Paper arrow_downwardDownload

Computing rectifying homographies for stereo vision

by Zhengyou Zhang

1999, … Vision and Pattern Recognition, 1999. IEEE …

descriptionView Paper arrow_downwardDownload

Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet

by Yury Bliokh

2006, Physical Review Letters

We present a solution to the problem of reflection/refraction of a polarized Gaussian beam on the interface between two transparent media. The transverse shifts of the beams' centers of gravity are calculated. They always satisfy the... more

descriptionView Paper arrow_downwardDownload

A Classified and Comparative Study of Edge Detection Algorithms

by Mohsen Sharifi

2002

Since edge detection is in the forefront of image processing for object detection, it is crucial to have a good understanding of edge detection algorithms. This paper introduces a new classification of most important and commonly used... more

descriptionView Paper arrow_downwardDownload

Three-dimensional forest light interaction model using a Monte Carlo method

by Peter North

1996, IEEE Transactions on Geoscience and Remote Sensing

Fig. 1. Variation of probability P of photon escape from canopy with angle relative to the incident direction, after an interaction at an optical depth of 1.0 below canopy surface. The curves show model estimates of P for two values of the foliage size parameter d; and three leaf angle distributions.

Fig. 2. Angular variation of bidirectional reflectance factors predicted by the model, for a solar zenith angle of 45°, at (a) 670 and (b) 850 nm. View zenith angle increases from 0 to 85° from the center to the outside of the graph, while view azimuth increases clockwise.

Fig. 3. Comparison of bidirectional reflectance factors measured using ASAS with those predicted by the three-dimensional model (solid line), and a one-dimensional model (dashed line), at (a) 559, (b) 670, and (c) 850 nm. Results show variation in the principal plane, where a positive view angle indicates back-scattering. The solar zenith angle is 44°. Error bars show standard deviation of the ASAS data.

Fig. 4. Comparison of directional spectra from (a) helicopter mounted SE-590 with (b) spectra predicted by the model. Results show spectral variation in the principal plane, for a solar zenith angle of 43.5°. principal plane between —45 and +45°, shown in Fig. 4(a).

Fig. 5. Prediction of canopy hemispherical albedo. The predicted variation of spectral albedo with illumination angle is shown in (a), for a range of incident zenith angles from 30-85°. Reflectance increases monotonically with incidence angle. The corresponding total solar irradiance is shown in (b) for a range of solar zeniths from 30-85° where incident radiation decreases monotonically with increasing solar zenith angle. Predictions of spectrally integrated canopy albedo are shown in (c), using high spectral resolution (solid line) and a narrow band approximation (dashed line). Pyranometer measurements are shown as asterisks («).

descriptionView Paper arrow_downwardDownload

A survey of shadow algorithms

by Pierre Poulin

2000, IEEE Computer Graphics and Applications

Essential to realistic and visually appealing images, shadows are difficult ta compute in most display environments. This survey characterizes the various types of shadows. It also describes most existing shadow algorithms and discusses... more

Andrew Woo, Pierre Poulin, and Alain Fournier University of Toronto A Survey of Shadow Algorithms

shadow if there exists an occluding surface between light and the region ofinterest, whether transparent or not. A shadow does not necessarily look like a darker region; colored shadows can appear in different ways in a scene. For example, let's say you used two differ- ent colored light sources. A region occluded from only one light source by an opaque object will lie in the shadow of this light source, but the color of the second light source can influence the region. An ob- ject can also act asa filter, with the color of the shadow region depending on the wavelength spectrum fil- tered through the object. Moreover, diffraction of light through a transparent object might provide color within a shadow.

Figure 1. Hard shadows in ray tracing. Ray tracing offers a simple technique to produce sharp shadows. In this image, we used a single directional light source. Notice how the shadow of the table looks sharp and well defined over the objects in shadow.

Figure 4. Soft shadows in cone tracing. Cone tracing can produce soft shadows. (Courtesy of J. Amanatides.)

Figure 6. Area subdivision shadow tracing.

Figure 8. Shadows from transparent objects. Corre shadows produced by transparent objects are hard t calculate. This image illustrates the shadow and th concentration of light produced when the light goe through a glass of water. Pencil tracing was used t simulate this effect. (Courtesy of M. Shinya of NTT.

Figure 9. Incorrect shadowing of transparent objects.

Figure 10. Concentration from parallel rays.

Figure 11. Paraxial approximation theory.

Figure 12. Polygonization. Polygonization offers one answer to the problem of rendering some primitives. However, it has some drawbacks, some of them illus- trated in this image. Notice the silhouette of the sphere and the shadows of the lamp shade on the walls.

Figure 13. Terminator problem. To keep smooth self-shadowing while interpolating normals (the terminator problem) in ray tracing, Sny- der and Barr®® proposed starting the shadow ray fur- ther from the intersection point. However, this can cause further artifacts if poorly approximated.

Figure 14. Shadows on bump-mapped surfaces. The normals of the surface plane have been modified by a bump map function. Notice the shadows of the alge- braic surfaces onto the plane; the shadows are sharp and regular, as if the normals have not been modified on the plane.

Figure 15. Self-shadowing of facets. The bumps over a surface can be so small that you cannot see them. Depending on the orientation of these facets, reflec- tion of the light and shadowing differs. This image shows a simulated Christmas ball. The facets are defined as threads going from one pole of the sphere to the other. Notice the darker area near one pole.

Figure 16. Andre’s forest. This scene of a forest was generated by a particle system. Notice the self-shad- owing of branches of a same tree and the shadows of the trees projected onto the grass. (Courtesy of W. Reeves of Pixar.)

descriptionView Paper arrow_downwardDownload

Occlusions as a guide for planning the next view

by Ruzena Bajcsy

1993, IEEE Transactions on Pattern Analysis and Machine Intelligence

The task of constructing a volumetric description of a scene from a single image is an underdetermined problem, whether it is a range or an intensity image. To resolve the ambiguities that are caused by occlusions in images, we need to... more

Figure 28: Left: second view - occluded region and active edges; right: third view - occluded regions

curve is mapped onto a single point in the camera image plane. The distance of the point on the The depth of the scene is measured by the active range scanner system [14], consisting of a laser, a CCD camera, and a turntable which supports the scanned scene. The laser and the camera are coupled. The laser produces a beam which is spread into an illuminating plane. The illuminating plane intersects with the object surface, forming a planar curve (laser-stripe). Each point on the curve 1s mapped onto a single point in the camera image plane. Lhe distance ol the point on tne curve to the camera center is determined by the intersection of the illuminating plane and the line which goes through the camera center and the point on the image plane. The range imag is obtained by scanning the scene in a series of parallel illuminating planes. This is achieved by} moving the scene support with constant velocity perpendicular to the illuminating plane. The y-axis on the image corresponds to the laser-stripe and the z-axis corresponds to the shift of the support. During the scanning, the laser sweeps out a plane, called the scanning plane (see fig. 1) The distance measurements are transformed into the perpendicular distance between the scanning plane and the surface of the objects and are stored as intensity values in the final range image plane intersects with the object surface, forming a planar curve (laser-stripe). Each point on t! curve to the camera center is determined by the intersection of the illuminating plane and the

A(z, y) = max(hon surfoce@s9)): Figure 2: Height at the point (z,y) is defined by the distance of the closest point on the surface to the scanning plane.

is how to determine the next scanning directions to acquire the missing information. Problem 1: For a given point p;(z,y) in the scanning plane, we want to find all the directions |.1 Problem definition

H is the largest depth which can be detected by the sensor. where L represents the fixed distance between the camera center and the illuminating plane and

Figure 5: The sketch of the inequality (6). 4 GETTING THE COMPLETE 23-D DATA OF THE SCENE

the median of all height values on the contour between the two vertices. Figure 6: Searching directions for the pixel height. The height of the border between two vertices is approximated by a constant. It is defined as

Figure 7: Angle @ of the edge e; with respect to the IP and ISP. 4.3 Analysis of occluded regions

Figure 10: Occluding angle computation. 4 GETTING THE COMPLETE 23-D DATA OF THE SCENE

images of the computed scanning directions in the ISP there still exist occluded regions, then they should be explored from new directions. Since we use only the height information of the borders

complete 24-D data of the scene. In each scan the illuminating plane illuminates the same part

top view, we are now looking from the sides.

Figure 16: Left: image of the first view, taken from the scanning direction 0°; right: occluded regions (grey areas) and active edges of their polygonal approximation.

Figure 18: Left: Further histograms of areas A; right: the final histogram

Figure 19: Left: the second view; right: the third view

Figure 22: Left: histogram of illuminating angles; right; histogram decomposition.

Figure 23: Left: histogram decomposition; right: light simulation from direction 58°.

Figure 24: Left: light simulation from direction 155°; right: light simulation from direction 289°.

Figure 27: Left: image of the third view taken from direction 228°; right: images of first, second,

descriptionView Paper arrow_downwardDownload

Gyrodometry: A new method for combining data from gyros and odometry in mobile robots

by Johann Borenstein

1996

This paper presents a very simple, yet very effective method for combining measurements from a gyro with measurements from wheel encoders (odometry). Sensor-fusion of this kind has been done before, usually by means of a statistical model... more

descriptionView Paper arrow_downwardDownload

A canonical problem in electromagnetic backscattering from buildings

by A. Iodice

2002, IEEE Transactions on Geoscience and Remote Sensing

In this paper, a geometric and electromagnetic model of a typical element of urban structure is presented, in order to analytically evaluate in closed form its electromagnetic return to an active microwave sensor. This model can be used... more

Fig. 1. Geometry of the wall—ground structure.

Fig. 2. (a) Single, (b) double, and (c) triple scattering. ever, closed-form analytically derived solutions are not found in the literature. In addition, dihedrals are generally employed to model actual corner reflectors used in radar techniques as cali- brators; in our model, the dihedral structure models a completely different actual structure so that different approximations can be required to obtain affordable analytical solutions.

SINGLE SCATTERING FROM THE GROUND: GO (UPPER PART) AND PO (LOWER PART) backscattered at the receiver turns out to be a random variable. We evaluate its mean and variance, which are calculated in terms of statistical characteristics of the surface and hence of the sur- face integral. 1) GO Method: In order to apply (3.15), we have to individ- uate the unit vector normal to ground that satisfies (3.16). Then, the stationary phase points are all of the points in which the local normal vector is

the GO-—GO-GO case. The only difference is that the evaluation of the field backscattered by the rough terrain toward the wall is perfomed by using PO formulae. Corresponding final results are collected in Table VI. scattering from terrain and double and triple scattering can be seen as scattering from the same rough surface with different in- cidence and/or observation directions [see Fig. 2(a)—(c)]. Now, it is well known (from optics [8] and from theory of SAR inter- ferometry [9]) that an extremely small variation in incidence or observation direction is sufficient to completely decorrelate the corresponding different scattered fields, so that they can be in- coherently summed up, i.e., the variance of their sum is the sum of their variances.

Fig. 4. RCS versus # for wall—ground double scattering. Wall height h and length J are both 20 m. Terrain roughness, frequency, and wall and ground relative dielectric constant are equal to those of Fig. 3. Wall orientation ¢ is 0° (solid line), 15° (short dashes), 30° (long spaced dashes), and 45° (long dashes). Fig.3. RCS versus ? for single scattering from a very rough terrain. The height standard deviation @ is 0.08 m (i.e., ka = 8.4), and the correlation length /, is 0.3 m. The illuminated effective area is 400 m?. The frequency is 5 GHz (A = 0.06 m), and both the wall and ground have a relative dielectric constant equal to 4 + j0.1.

Fig. 5. RCS versus ¢ for wall—ground double scattering. Wall height h and length J are both 20 m. Terrain roughness, frequency, and wall and ground relative dielectric constant are equal to those of Fig. 3. Look angle 9 is 23° (solid line), 45° (short dashes), and 60° (long spaced dashes).

Fig. 6. RCS versus 3 for wall—ground—wall triple scattering. Wall height h and length / are both 20 m. Terrain roughness, frequency, and wall and ground relative dielectric constant are equal to those of Fig. 3. Wall orientation y¢ is 0° (solid line), 15° (short dashes), 30° (long spaced dashes), and 45° (long dashes).

Fig.7. RCS versus # for single scattering from a moderately rough terrain. The height standard deviation o is 0.003 m (i.e., ka = 0.314), and the correlation length J. is 0.05 m. Illuminated effective area is 400 m*, frequency is 5 GHz (A = 0.06 m), and both wall and ground have a relative dielectric constant equal to 4 + 70.1.

Fig. 8. RCS versus @ for wall—ground double scattering. Wall height and length / are both 20 m. Terrain roughness, frequency, and wall and ground relative dielectric constant are equal to those of Fig. 7. Wall orientation ¢ is 0° (solid line), 15° (short dashes), 30° (long spaced dashes), and 45° (long dashes).

Fig. 9. RCS versus y for wall—-ground double scattering. Wall height h and length / are both 20 m. Terrain roughness, frequency, and wall and ground relative dielectric constant are equal to those of Fig. 7. Look angle # is 23° (solid line), 45° (short dashes), and 60° (long spaced dashes).

Fig. 10. RCS versus ¥ for wall—-ground—wall triple scattering. Wall height h and length / are both 20 m. Terrain roughness, frequency, and wall and ground relative dielectric constant are equal to those of Fig. 7. Wall orientation ¢ is 0° (solid line), 15° (short dashes), 30° (long spaced dashes), and 45° (long dashes).

descriptionView Paper arrow_downwardDownload

Coriolis Effect in Optics: Unified Geometric Phase and Spin-Hall Effect

by vladimir kleiner

2008, Physical Review Letters

We examine the spin-orbit coupling effects that appear when a wave carrying intrinsic angular momentum interacts with a medium. The Berry phase is shown to be a manifestation of the Coriolis effect in a noninertial reference frame... more

descriptionView Paper arrow_downwardDownload

Modeling lidar waveforms in heterogeneous and discrete canopies

by Wenge Ni-Meister

2001, IEEE Transactions on Geoscience and Remote Sensing

This study explores the relationship between laser waveforms and canopy structure parameters and the effects of the spatial arrangement of canopy structure on this relationship through a geometric optical model. Studying laser waveforms... more

This study explores the relationship between laser waveforms and canopy structure parameters and the effects of the spatial arrangement of canopy structure on this relationship through a geometric optical model. Studying laser waveforms for such plant canopies is needed for the advanced retrieval of three-dimensional (3-D) canopy structure parameters from the vegetation canopy lidar (VCL) mission. For discontinuous plant canopies, a hybrid geometric optical and radiative transfer (GORT) model describing the effects of 3-D canopy structure parameters of discrete canopies on the radiation environment has been modified for use with lidar. The GORT model is first used to describe the canopy lidar waveforms as a function of canopy structure parameters and then validated using scanning lidar imager of canopies by echo recovery (SLICER) data collected in conifer forests in central Canada during the boreal ecosystem-atmosphere study (BOREAS). Model simulations show that the clumping in natural vegetation, such as leaves clustering into tree crowns causes larger gap probability and smaller waveforms for discontinuous plant canopies than for horizontally homogeneous plant canopies. Ignoring the clumping effect can result in significantly lower values for the estimated foliage amount in the profile and in turn lower estimated biomass. Because of clumping, only the gap probability and apparent vertical projected foliage profile can be directly retrieved from the canopy lidar data. The retrieval is sensitive to the ratio of the volume backscattering coefficients of the vegetation and background, and this ratio depends on canopy architecture as well as foliage spectral characteristics. Extensions of the GORT model from single-layered canopies to include multilayered ones are also explored. Index Terms-Geometric optical and radiative transfer (GORT) model, heterogeneous plant canopies, lidar waveforms. NOMENCLATURE Roman Alphabet Vertical crown radius (m). Foliage area volume density of a single crown (m). Apparent foliage profile as a function height (m). Actual foliage profile as a function height (m).

descriptionView Paper arrow_downwardDownload

Statistics of Range Images

by Ann Lee

2000

The statistics of range images from natural environments is a largely unexplored e l d o f r esearch. It closely relates to the statistical modeling of the scene geometry in natural environments, and the modeling of optical natural... more

Figure 2: A laser range finder centered at O and two homothetic triangles, AABC' and AA‘B’C". Figure 3: Semi-log (left) and log-log (right) plots of the single pixel statistics (i.e. range statistics). Solid: distribution for the whole image. Dotted: distribution for the bottom half of a range image. Dashed: distri- bution for the top half of a range image.

Figure 4: Top view of a randomly generated forest scene. See text.

Figure 6: Derivative statistics at different scales.

Figure 8: The values for A and the 1D functions gz, h, and gq, in the best bivariate fit at pixel separation distances x = 2 (solid), 16 (dashed), and 256 (dotted).

Figure 11: Contour plot of the log histogram of wavelet coefficient pairs for natural optical images.

Figure 10: Contour plots of the log histograms of wavelet coefficient pairs for range images.

Figure 12: Contour plots of the log histogram of wavelet coefficient pairs, calculated from range images scaled down by taking the minimum of 2X2 blocks.

Figure 13: Contour plots of the log histogram of wavelet coefficient pairs, calculated from range images scaled down by taking the average of 2 x 2 blocks.

Figure 14: An equi-surface of a 3D joint histogram of horizontal, vertical and diagonal wavelet coefficients in range images, viewed from three different angles.

descriptionView Paper arrow_downwardDownload

An optical technique for remote focusing in microscopy

by Edward J Botcherby

2008, Optics Communications

We describe the theory of a new method of optical refocusing that is particularly relevant for confocal and multiphoton microscopy systems. This method avoids the spherical aberration that is common to other optical refocusing systems. We... more

Fig. 1. Imaging four point sources in the meridional plane using (a) a perfect imaging system, (b) a system obeying the sine condition and (c) a system obeying the Herschel condition. FREE OTA ERe.aort Laven meee NTAY Relay ERE M EE rnern a Tune eran see Erne eal ag Veen timer eS EARN OTTO OE A © SEMEL Slew Maeve SEreiy gyn mWeRre ere we rece The requirement of perfect three-dimensional imaging imposes quite a constraint on the design parameters of such Most microscopes are designed according to the sine condition, however, and in Fig. 1b we show how such a system behaves when imaging the same array of point sources. Here we see that points lying in a unique plane, shown as a dashed line in object space, are imaged stigmat- ically in image space with a lateral magnification of whereas points displaced axially form non-stigmatic images. The paraxial rays still converge, however, with an axial magnification of M?m,/n2, whereas the rays traveling

Fig. 2. A general microscope system. We now take a closer look at the specific geometry of a high NA microscope objective which can be modelled as a pair of principal surfaces that are spherical and planar in shape as shown in Fig. 2. A point source, placed at the ori- gin of object space, emits a spherical wave which, upon crossing the principal sphere, is transformed into a plane wave in the pupil. A low NA tube lens not shown) can then be used to focus this plane wave stigmatically to a point in image space. A point placed at some different loca- tion, r = (x,y,z), also emits a spherical wave but in this case different parts of the wavefront cross the principal sphere at

Fig. 3. Demonstration of odd parity pupil functions. where the coordinate system is defined in the diagram. If the 4f system mapping the pupil planes together has magnification: Due to the reciprocal nature of ray optics we also note that if a wavefront could be generated at the pupil plane with the same form as that in Eq. (9) but traveling into the lens then there would be stigmatic convergence to a single point. Such wavefronts could be manufactured with a deformable mirror. However, a simpler method can be inferred by considering the situation in Fig. 3. If the ori- entation of the second lens were reversed and the pupil function from the first lens was imaged into the pupil plane of the second lens then the wavefront would be of

Fig. 5. Two systems comprising a perfect imaging system and a further microscope for magnification.

Fig. 6. (a) The Strehl ratio and (b) the coefficient of defocus as a function of point source position for the system shown in Fig. 4

Fig. 7. Systems used to measure detection PSFs where z is the axial coordinate in the focal region of objective lens LI. We began by measuring the PSF of a microscope objec- tive that obeys the sine condition to illustrate how spherical aberration is introduced when trying to refocus to different depths in the sample by moving the detector axially. We

Fig. 8. Detection PSFs measured with the systems in Fig. 7.

descriptionView Paper arrow_downwardDownload

A Survey of Camera Self-Calibration

by Elsayed Hemayed

2003

This paper surveys the developments of the last 10 years in the area of camera self-calibration. In order to solve this problem, researches have used the camera intrinsic constraints separately and in conjunction with the camera motion... more

descriptionView Paper arrow_downwardDownload

Second-harmonic generation frequency-resolved optical gating in the single-cycle regime

by Douwe Wiersma

1999, IEEE Journal of Quantum Electronics

The problem of measuring broad-band femtosecond pulses by the technique of second-harmonic generation frequency-resolved optical gating (SHG FROG) is addressed. We derive the full equation for the FROG signal, which is valid even for... more

descriptionView Paper arrow_downwardDownload

Parametric interactions in the organic salt 4-N,N-dimethylamino-4[sup ʹ]-N[sup ʹ]- methyl-stilbazolium tosylate at telecommunication wavelengths

by Peter Gunter

1998, Journal of Applied Physics

We show that the organic salt 4-N,N-dimethylamino-4Ј-NЈ-methyl-stilbazolium tosylate, originally developed for electro-optic applications, is also a very interesting material for phase-matched parametric interactions such as... more

descriptionView Paper arrow_downwardDownload

A UTD propagation model in urban microcellular environments

by Athanasios Kanatas and

1997, IEEE Transactions on Vehicular Technology

This paper presents a three-dimensional (3-D) propagation model for path-loss prediction in a typical urban site, based on geometrical optics (GO) and uniform theory of diffraction (UTD). The model takes into account numerous rays that... more

descriptionView Paper arrow_downwardDownload

A Laguerre geometric approach to rational offsets

by Helmut Pottmann

1998, Computer Aided Geometric Design

Laguerre geometry,provides a simple approach,to the design of rational curves and surfaces with rational offsets. These so-called PH curves and PN surfaces can be constructed from arbitrary rational curves or surfaces with help of a... more

descriptionView Paper arrow_downwardDownload

Nonlocal Surface-Wave Solitons

by Carmel Rotschild

2007

We demonstrate, experimentally and theoretically, surface-wave solitons occurring at the interface between a dielectric medium (air) and a nonlinear material with a very long-range nonlocal response. These surface solitons are always... more

descriptionView Paper arrow_downwardDownload

The slab geometry laser - Part II: Thermal effects in a finite slab

by Robert L. Byer

2000, IEEE Journal of Quantum Electronics

This paper presents two methods for calculating the thermally induced stress, focusing, and depolarization in a pumped zigzagslab solid-state laser. A computer program capable of detailed calculations of thermal effects in the general... more

Fig. 1. Zigzag geometry slab laser. The terminology for the slab surfaces, the coordinate system, and the slab dimensions are defined. The origin of the coordinate system (x, y, z) = (0, 0, 0) is at the center of the slab, halfway between all faces.

Fig. 2. Stress distribution for a pumped slab in the x-y plane. The length of a cross-bar indicates the magnitude of the stress, and the orientation of the cross indicates the orientation of the axes of the stress tensor. The top to bottom asymmetry is an artifact of the plotting procedure. TABLE I

Fig. 4. (a) Caltulated depolarization in a pumped LHG-S slab, Display shows one-half of the slab aperture, with the dark pattern of depolari- zation being near the side of the slab. (b) Measured (dots) and calculated (solid line) depolarization versus position along line w and (c) along line t, which passes through the region of peak depolarization.

The change in optical path lengh for one reflection is found by multiplying (29) by 2” sin @ where n is the index of refraction and @ is the angle between the slab and the ray path, as shown in Fig. 1. The factor of 2” occurs be- cause any bulge of the surface is traversed twice in a me- dium of index n. The factor of sin 6 expresses the reduc- tion of path length difference that takes place as the angle of the beam approaches glancing incidence. For N reflec- tions, the path length change is given by The temperature difference from average, T'(x, y), does not depend on x for the ideal finite case, and may thus be dropped. It is significant if the slab is nonideal, and is dealt with in the next section. The stress o,, must average to zero over a full traverse of the slab if there is to be no net force across a plane containing the zigzag path. For an unaccelerated slab with no external forces, this must be the case. Thus, using the overbar to signify an average over y, we get

Fig. 6, Numerical calculation of the normalized distortion of the slab sur- . face for slabs of aspect ratio A. This plot may be used to calculate the focusing proportional to stress in a uniformly pumped slab of any size or material, at any power level.

Fig. 7. Calculated slab depolarization as a function of N, the number of elemental slabs, with the power per elemental slab held constant. As the number of elements (or internal reflections) goes up, the depolarization fluctuates around a fixed value. slightly from dn/dT,,,,p. Both values are tabulated for a number of materials in Table II, for @ = 20°.

‘ig. 8. Distribution of the slab depolarization constants M and M for abor 100 calculated slab configurations. Pump powers, material constants, an slab dimensions varied over three orders of magnitude.

Note that the argument in (C.1) is x, not x’ as was the case for (14). Equation (21) gives the edge stress for a slab with a emperature distribution given by (14) and a very large aspect ratio. If (C.1) is used for the temperature distribu- ‘ion, and if the effect of side cooling on the average tem- erature is considered, then a smaller stress estimate re- sults. We assume that the temperature at any point in the slab is given by (13) with 7(x) given by (C.1). The average »ver the whole slab is found by averaging 7(x) over x. The result is

Properttes OF SoME NeopyMiuM Hosts. | TPascal = 10.2 x 10° kg/em’. TABLE II (Note that this is not the definition we used in [5]. Our definition there had the opposite sign; here we return to the established convention.) The stress o.. does not aver- age to zero, and according to (18) it can be written

Prof. Byer is a member of the American Association for the Advance- ment of Science and the American Physical Society, a Fellow of the Optical Society of America, and President of the IEEE Lasers and Electro-Optics Society for 1985. SEES: el ah ae RR ET SE Re ee MOLE ee FP Meee = NEP es aD de eS ie aeh F His early and continuing interest has been nonlinear interactions, in- cluding harmonic generation and parametric oscillators. After joining the Department of Applied Physics at Stanford, he initiated research into re- mote sensing using tunable laser sources, which led to the development of the unstable resonator Nd:YAG laser and to high-power tunable infrared generation in an LiNbO, parametric tuner, In 1974. he and his colleagues

descriptionView Paper arrow_downwardDownload

Composite real-time image processing for railways track profile measurement

by Vincenzo Piuri

2000, IEEE Transactions on Instrumentation and Measurement

Checking railway status is critical to guarantee high operating safety, proper maintenance schedule, and low maintenance and operating costs. This operation consists of the analysis of the rail profile and level as well as overall... more

Fig. 5. Algorithmic prefiltering: (a) the image, (b) the intensity distributior in columns A (typical) and B (with saturation), and (c) the convolution value: along these columns. Fig. 4. Composite processing approach: (a) algorithmic filtering, and (b) neural processing.

“ig. 6. Derivative prefiltering: the convolution values along the columns.

Fig. 7. Learning error: (a) the training image, (b) nonuniform sampling, and (c) uniform sampling.

Fig. 11. Generalization ability versus spread: (a) the error deviation and (b) the number of neurons required to perform identification. Fig. 10. Successful identification with error <0.5 pixel by selecting widths every (a) 0.5 and (b) 0.1 pixels in the range of 4-5 pixels.

descriptionView Paper arrow_downwardDownload

Relations between Hermite and Laguerre Gaussian modes

by Luis Elias

1993, IEEE Journal of Quantum Electronics

Relations between Hermite (HG) and Laguerre (LG) Gaussian modes are derived. With these, a LG mode is written as a sum of HG modes, and vice versa. These mode relations are derived from addition identities between a Laguerre polynomial... more

For configurations with cylindrical symmetry the LG modes are the natural choice. The LG modes with radial number p and azimuthal parameter m can be written as a function of the polar radius p = (x? + y?)'/? and the azi- muthal angle ¢ as [1] In this expression as usual k = 2 a/) and the Rayleigh length zg, the beam ‘‘radius’’ w(z) and the radius of cur- vature R(z) are given by

Fig. 1. Symbolic representation of (7). The LG mode a? contains the HG modes ¥, 4, ¥3,2 and ¥; 9; each one multiplied by its coefficient in (7). In the figure, each mode is pictorially represented by its intensity distribution. mode relations, let us write down (4) and (5) for the par- ticular cases p = 1,m = Oandp = 1,m=3

This last relation (7) is illustrated in Fig. 1. The shading density of the first picture was obtained by adding the modular square of the three terms on the right-hand side of (7), and it coincides precisely with the intensity of °A?. The other three pictures show, in the same way, the intensities of each of the component HG modes.

In these relations, the sum of the subindices of ¥ is equal to 2p + m. Then, the Guoy phases are the same on both sides of the equation, as it should be. In the next section HG modes will be written in terms of LG modes. In this section we will derive an expression giving the LG modes (1) as a sum of HG modes (3). This can be accom- plished by the use of the relations derived in Appendix A. From (A7) one gets By counting the possible different subindices, we see that (p + 1 + [m/2]) HG modes are required to describe the LG mode ‘A;’, while *A;’ contains (p + 1 + [Ga + 1)/2]) HG modes Y; ,. As examples of the LG to HG

As the second step towards having Laguerre polyno- mials with positive superindices only, even and odd k in- dex cases in (A6) and (A7), have to be treated separately. From (B6) we get

When using these identities one should remember the fol- lowing boundary conventions for the binomial coefficients

descriptionView Paper arrow_downwardDownload

Multiple-scattering scheme useful for geometric optical modeling

by Sylvain Leblanc

2001, IEEE Transactions on Geoscience and Remote Sensing

Geometrical optical (GO) models have been widely used in remote sensing applications because of their simplicity and ability to simulate angular variation of remote sensing signals from the earth's surface. GO models are generally... more

descriptionView Paper arrow_downwardDownload

Automated sensor planning for robotic vision tasks

by Konstantinos Tarabanis

1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation

In this paper, we present a method to determine viewpoints for a robotic vision system for which object features of interest will simultaneously be visible, inside the field-of-view, in-focus and magnified as required. As part of our... more

descriptionView Paper arrow_downwardDownload

Wave analysis of Airy beams

by Ehud Heyman

2010, Optics express

The Airy beams are analyzed in order to provide a cogent physical explanation to their intriguing features which include weak diffraction, curved propagation trajectories in free-space, and self healing. The asymptotically exact analysis... more

Fig. 1. Ray description of the Airy beam plotted on a background of the intensity of the Airy beam in Eq. (3) (in Colors). As discussed after Eq. (7), the z and x axes are normalized with respect to z; and W, respectively. Here and in all other figures, A = 0.5m, x) = 200A, giving W = 139.4A and z;- = 2kW? = 24.4104. The following ray species are depicted (see discussion after Eq. (11)): the @;* species (black solid lines) that converge to a caustic (thick dashed line); the @, species (dashed-dotted lines); the artificial shadow boundaries SB* of the @% ray species, introduced by the aper- ture truncation at Xep [see Eq. (5)]. Regions I = shadow of the caustic; Regions II = lit side of the caustic and also lit side of SB*; Regions II = shadow side of SB* and of SB’; Re- gions IV = lit side of SB~. At a typical observation point in region II (shown in the figure), there are two ray contributions: “ray 1”, which has yet to touch the caustic, and “ray 2”, which has already touched it. Note that additional rays of the @, species emerging from points at the aperture which are located beyond the figure frame (on the left hand side) have been removed for clarity.

Fig. 2. The intensity |U, 7 of the field radiated by the main lobe of the Airy beam initial distribution (solid blue line), compared with the intensity |U ? of the total field calculated from the paraxial closed-form solution in Eq. (3) (solid magenta line), and the intensity |Ucs|? of the Gaussian beam that has the same effective width as the main lobe of the Airy beam initial distribution (see discussion after Eq. (7); dashed green line). All intensities are normalized with respect to the maximal intensity of the close-form solution. The fields are calculated at several ranges from the aperture: (a) z = 0; (b) z= V3zp; and z = V/8zp. At z = V3z, the effective width of the GB doubles whereas the effective width of the U, field increases by a factor of 2.3. At z = /8z; the effective width of the GB and the U, field increase by a factor of 3 and 3.6, respectively.

Fig. 3. Definition of the ray coordinates (p;>,x,,, 0,2) for rays 1 and 2 (green lines) that are shown in Fig. 1. Also shown (in magenta) are the coordinates of the diffracting ray (Pa,Xep, 94) and (in black) the shadow boundaries angles 6, defined in Sec. 4.2. p are the distances traversed by the rays, 6 are the ray exit angles and x’ are the ray exit points. where J = O(x,z)/O(p,x’) is the Jacobian for the transformation (p,x’) — (x,z) evaluated it the observation point r, and Jo is the Jacobian at the exit point. We also identify p, = cos? 6/04 y, as the distance from x’ to the caustic (note that ok y; <0 so that p, > 0). 3q. (14) fails near the caustic at p © p,. For p > p-, the square root in Eq. (14) becomes ~i|1 —p/p-|~!/*. The caustic coordinates are obtained by setting p — p; in Eq. (11) for each *xit point x’.

where Ai’ is the derivative of the Ai function with respect to its argument. The parameters in Eq. (16) are functions of r and defined in terms of the GO parameters via Fig. 4. Exit points of the rays corresponding to certain observation points at the observation plane z = 10z,. The observation points are tagged by their location in the Ist, 2nd, or 3rd lobes of the field at this observation plane. As a reference, we also show the intensity of the initial field distribution on the z = 0 plane.

Figure 6 compares the paraxial closed form solution of Eq. (3) to the UGO solution. An excel- lent agreement between the two is seen. Fig. 5. The intensities of the fields radiated by the main lobe of the initial distribution (lU, ? — blue line) and by the rest of the initial distribution (\U3|? —red line), calculated at the observation plane z = 10z-. The intensity of their sum |U; + U;|? (black line) agrees extremely well with the intensity of the total field |U | calculated from the paraxial closed- form solution in Eq. (3) (magenta line); a difference is seen only near the peak of the main lobe. The locations of the caustic and of the artificial shadow boundary are indicated by tags on the x-axis.

Fig. 6. The intensity |Uygo|* of the UGO field (green line) compared to the intensity |U|* of the total field calculated from the paraxial closed-form solution in Eq. (3) (magenta line), at the observation plane z = 10z, . The two results are indistinguishable within the scale of the figure. The location of the caustic is indicated by a tag on the x-axis.

descriptionView Paper arrow_downwardDownload

Lorentz beams and symmetry properties in paraxial optics

by Sergio Severini

2006, Journal of Optics A: Pure and Applied Optics

A new kind of tridimensional scalar optical beams is introduced. These beams are called Lorentz beams because the form of their transverse pattern in the source plane is the product of two independent Lorentz functions. Closed-form... more

descriptionView Paper arrow_downwardDownload

Multifed Printed Reflectarray With Three Simultaneous Shaped Beams for LMDS Central Station Antenna

by Manuel Arrebola

2000, IEEE Transactions on Antennas and Propagation

A two-layer reflectarray is proposed as a central station antenna for a local multipoint distribution system (LMDS) in the 24.5-26.5 GHz band. The antenna produces three independent beams in an alternate linear polarization that are... more

descriptionView Paper arrow_downwardDownload

Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials

by David Schurig

2006, Optics Express

We perform an experimental study of the phase and amplitude of microwaves interacting with and scattered by two-dimensional negative index metamaterials. The measurements are performed in a parallel plate waveguide apparatus at X-band... more

descriptionView Paper arrow_downwardDownload

Terrain mapping for a walking planetary rover

by Eric Krotkov

1994, IEEE Transactions on Robotics and Automation

descriptionView Paper arrow_downwardDownload

Data mining for improving a cleaning process in the semiconductor industry

by Armin Shmilovici

2002, Semiconductor Manufacturing, IEEE …

setting where data is scarce. The paper suggests that data mining methodologies may be particularly useful when data is scarce and the various physical and chemical parameters that affect the process exhibit highly complex interactions. A nother impli- cation is that on-line monitoring of the cleaning process using data mining may be highly effective. capillary, and electrostatic forces. Although the relative amount of these forces depends on the nature and chemical composition of both the particle and the wafer surface, they are proportional to the particle diameter. The removal force, on the other hand, is proportional to the square or the cube of the diameter [18], [19]. Therefore, it is harder to overcome adhesion forces for smaller particles.

Fig. 2. Contamination map. Left: Before cleaning. Right: After cleaning.

Fig. 3. Simplified decision tree for experiment 1 with target function % Moval.

Fig. 4. Composite classifier architecture. Stacked Generalization: Stacked generalization [14] as- sumes that we have a two-layer architecture in which the classifiers to be combined are called level-0 classifiers, and the combining classifier is the level-1 classifier (the layering can be enlarged to more than two layers). The basic idea is that we have been given a set of n level-0 leaming algorithms components), a level-1 learning (combining) algorithm, and a training set of TJ classified instances. The n level-0 learning algorithms should be distinct, so that diverse level-0 classifiers are obtained, for the reasons specified earlier. The algorithm has usually two phases [14], [22]:

TYPICAL RECORDS * FROM THE CLEANING EXPERIMENTS Due to the commercial confidentiality of the process some of the data have been uniformly altered.

it ttt A PORTION OF THE DECISION TREES GENERATED FOR EXPERIMENT 3 afar 7 * RULES GENERATED FOR EXPERIMENT 3 (TARGET FUNCTION %MOVAL & %REMOVAL)

clustering of the instances in the feature space. As neural net- works can deal with continuous class values, the instances have been entered with their original success rates of %Moval and %Removal. The SOM network resulted in 3 categories. The highest-ranking class was class c and the lowest was class a. The instances have been classified according to those categories and run through C4.5 for classification. This produced an equiva- ent classification accuracy to that of experiment 3 (which also has three classes). This experiment validates the efficiency of using SOM for determining a “natural” number of classes when a human expert is not available. A portion of the generated de- cision tree is illustrated in Table V. éfaeee A SIMPLIFIED DECISION TREE GENERATED WHEN USING SOM

COMPOSITE CLASSIFIER OF C4.5 DECISION TREES FOR PREDICTING %REMOVAL, %MOVAL TABLE VII CHARACTERISTICS OF THE NEURAL NETWORKS USED IN STACKED GENERALIZATION- 1

seven decision trees (for % Removal) and six decision trees (for % Moval) have been generated. up tails, then apply C, to new instances until C’, makes a cor- rect classification. In either case, add the triggering (mistaken or correct) instance to a training set for Cz. This process of flip- ping a coin and adding a training instance is repeated until a sufficient number of examples have been collected to train C2. Finally, new instances are drawn from a distribution of training instances, and are classified by C, and Cy. If they disagree the instance is added to a training set for C3. When C3 has been trained of a sufficient number of examples, the training stops. The composite classifier is applied by taking a majority vote of C1, Cz and C3. An extension of this method (called A daptive Boosting or Adaboost [16]), which can combine a large number of weak component classifiers, has been applied in this paper.

DIFFERENT COMPOSITE CLASSIFIER EXPERIMENTS FOR PREDICTING %REMOVAL AND %MOVAL TABLE IX

descriptionView Paper arrow_downwardDownload

High-Q conical polymeric microcavities

by Cristian Gohn-Kreuz

2010, Applied Physics Letters

We report on the fabrication of high-Q microresonators made of low-loss, thermoplastic polymer poly͑methyl methacrylate͒ ͑PMMA͒ directly processed on a silicon substrate. Using this polymer-on-silicon material in combination with a... more

FIG. 1. (Color online) Process steps for fabricating high-Q conical micro- cavities. After exposure (a) and development (b) of PMMA, the silicon substrate is etched using XeF, (c). A thermal reflow (d) then forms the conical geometry of the cavities. By heating the sample for 30 s on a hotplate at a tem- perature of 125 °C slightly above the glass transition tem-

FIG. 4. (Color online) Simulated mode structure of a conical microcavity. The intensity distribution and resonance wavelength of the WGMs are cal- culated. The azimuthal mode number m of the presented WGMs is 105.

descriptionView Paper arrow_downwardDownload

Cerium fluoride, a new fast, heavy scintillator

by Stephen Derenzo

1989, Nuclear Science, IEEE …

We describe the scintillation properties of Ceriuin Flue ride (CeF3), a newly discovered, heavy (6.16 g/cm3), in-organic scintillator. Its fluorescence decay lifetime, mea-sured with the delayed coincidence method, is described by a... more

descriptionView Paper arrow_downwardDownload

Directional Effects in a Daily AVHRR Land Surface Temperature Dataset Over Africa

by Ana Privette

2004, IEEE Transactions on Geoscience and Remote Sensing

Land surface temperature (LST) is a key indicator of the land surface state and can provide information on surface-atmosphere heat and mass fluxes, vegetation water stress, and soil moisture. Split-window algorithms have been used with... more

descriptionView Paper arrow_downwardDownload

Reflections on shading

by Andrew Zisserman

1991, IEEE Transactions on Pattern Analysis and Machine Intelligence

descriptionView Paper arrow_downwardDownload

A method to track cortical surface deformations using a laser range scanner

by Valérie Duay

2005, IEEE Transactions on Medical Imaging

This paper reports a novel method to track brain shift using a laser-range scanner (LRS) and nonrigid registration techniques. The LRS used in this paper is capable of generating textured point-clouds describing the surface... more

descriptionView Paper arrow_downwardDownload

Hamiltonian-Preserving Schemes for the Liouville Equation with Discontinuous Potentials

by XIN WEN

2005, Communications in Mathematical Sciences

In this paper, we construct two classes of Hamiltonian-preserving numerical schemes for a Liouville equation with discontinuous local wave speed. This equation arises in the phase space description of geometrical optics, and has been the... more

descriptionView Paper arrow_downwardDownload

Radio caustics from localized interstellar medium plasma structures

by James Cordes

1987, Nature

descriptionView Paper arrow_downwardDownload

Dielectric Lens Antennas

by Jorge Costa and

2016, Handbook of Antenna Technologies

Dielectric lens antennas are attracting a renewed interest for millimetre-and sub-millimetre wave applications where they become compact, especially for configurations with integrated feeds usually referred as integrated lens antennas.... more

descriptionView Paper arrow_downwardDownload

Polarization diffraction grating produced by femtosecond laser nanostructuring in glass

by Peter Kazansky

2010, Optics Letters

We demonstrate polarization sensitive diffractive optical element fabrication by femtosecond direct writing in the bulk of silica glass. Modulation of the anisotropic properties is produced by controlling light-induced self-assembled... more

descriptionView Paper arrow_downwardDownload

Review of 20 Years of Research on Microwave and Millimeter-wave Lenses at “Instituto de Telecomunicações”

by Eduardo Lima and

2005

Starting from a challenge in the early 1990s to develop a highly shaped beam dielectric lens antenna for a pilot 150 Mb/s cellular mobile broadband system operating in the 60-GHz band, several new developments have been accomplished over... more

descriptionView Paper arrow_downwardDownload

Dynamic Appearance Modeling for Human Tracking

by Hwasup Lim

2006

Dynamic appearance is one of the most important cues for tracking and identifying moving people. However, direct modeling spatio-temporal variations of such appearance is often a difficult problem due to their high dimensionality and... more

descriptionView Paper arrow_downwardDownload

A Laser Range Scanner Designed for Minimum Calibration Complexity

by xing chen

2001

Laser range scanners are a popular method for acquiring three-dimensional geometry due to their accuracy and robustness. Maximizing scanner accuracy while minimizing engineering costs is a key challenge to future scanner designs.... more

descriptionView Paper arrow_downwardDownload

Optical propagation in tissue with anisotropic scattering

by John Tulip

1988, IEEE Transactions on Biomedical Engineering

Understanding the distribution of light in tissue is necessary for dosimetry in photodynamic therapy of malignant tumors. The Dunning R3327-AT rat prostate solid tumor model was the specific tissue chosen for experimental and theoretical... more

descriptionView Paper arrow_downwardDownload

Bidirectional NDVI and atmospherically resistant BRDF inversion for vegetation canopy

by crystal schaaf

2002, IEEE Transactions on Geoscience and Remote Sensing

The normalized difference vegetation index (NDVI) has been widely applied in optical remote sensing. However, it has been demonstrated that NDVI is still partially affected by atmospheric path scattering and bidirectional (illumination... more

descriptionView Paper arrow_downwardDownload

Independent Motion Detection in 3D Scenes

by Harpreet Sawhney

2000, IEEE Transactions on Pattern Analysis and Machine Intelligence

AbstractÐThis paper presents an algorithmic approach to the problem of detecting independently moving objects in 3D scenes that are viewed under camera motion. There are two fundamental constraints that can be exploited for the problem:... more

descriptionView Paper arrow_downwardDownload

Constant resolution omnidirectional cameras

by jose gaspar

2002

In this paper we present a general methodology for designing mirrors of catadioptric onmidirectional sensors encompassing linear projection properties, the so called constant resolution cameras. The linearity is stated between 3D... more

descriptionView Paper arrow_downwardDownload

Log In

Geometrical Optics

Related Topics