|Publication number||US6717745 B2|
|Application number||US 10/143,215|
|Publication date||Apr 6, 2004|
|Filing date||May 9, 2002|
|Priority date||May 9, 2001|
|Also published as||US7167321, US20030021037|
|Publication number||10143215, 143215, US 6717745 B2, US 6717745B2, US-B2-6717745, US6717745 B2, US6717745B2|
|Original Assignee||George Nemes|
|Export Citation||BiBTeX, EndNote, RefMan|
|Patent Citations (7), Non-Patent Citations (13), Referenced by (15), Classifications (12), Legal Events (5)|
|External Links: USPTO, USPTO Assignment, Espacenet|
This application claims the priority date of U.S. Provisional Patent Application No. 60/290,157, filed May 9, 2001, which is herein incorporated by reference.
The invention relates to optical systems and methods for magnifying images or controlling the sizes of laser spots or optical images, and in particular to optical systems and methods employing rotating cylindrical lenses and/or mirrors.
Microscopes, image projectors, industrial laser optical systems, and various other optical systems have been used to control the sizes of images at a target location. Many such optical systems employ lenses and/or mirrors which are translated relative to each other along the optical axis of the system in order to control the output image size. In some systems, changing the size of the image alters the location of the plane at which the image is in focus. Moreover, some conventional systems can be relatively bulky, and require complex mechanical components.
The present invention provides an optical system comprising a first cylindrical optical element for receiving an input light beam, and a second cylindrical optical element positioned at a round spot location optically subsequent to the first cylindrical optical element. At least one of the cylindrical optical elements is rotatable about the optical axis so as to adjust an angle between the principal axes of the cylindrical optical elements to symmetrically scale a light beam spot at a target location.
Further provided is an optical method comprising: generating a symmetrically-scalable spot on a target positioned at a working location by passing a light beam sequentially through a first cylindrical optical element and a second cylindrical optical element, the second cylindrical optical element being separated from the first cylindrical optical element by a distance chosen such that an input beam forms a circular spot at the second cylindrical optical element after passing through the first cylindrical optical element; and symmetrically scaling the spot at the working location by adjusting an angle between a principal axis of the first cylindrical optical element and a principal axis of the second cylindrical optical element by rotating at least one of the first cylindrical optical element and the second cylindrical optical element.
The foregoing aspects and advantages of the present invention will become better understood upon reading the following detailed description and upon reference to the drawings where:
FIG. 1 is a schematic diagram of an optical system comprising two cylindrical lenses, according to a presently preferred embodiment of the present invention.
FIGS. 2-A and 2-B are schematic diagrams illustrating the passage of a light beam through the system of FIG. 1, for two extreme angular lens positions, respectively.
FIG. 3 illustrates another system configuration according to the present invention.
FIG. 4 shows another system configuration according to the present invention.
FIG. 5 shows yet another system configuration according to the present invention.
FIGS. 6-A and 6-B are schematic diagrams illustrating the passage of a light beam through yet another system configuration according to the present invention, for two extreme angular lens positions, respectively.
FIG. 7 is a schematic diagram of a system configuration including a cylindrical lens and a cylindrical mirror, according to another embodiment of the present invention.
FIG. 8 is a schematic diagram of a system configuration including two cylindrical mirrors, according to another embodiment of the present invention.
FIG. 9 illustrates in a longitudinal sectional view an implementation of mechanical components suitable for rotating one cylindrical lens with respect to another, according to an embodiment of the present invention.
In the following description, it is understood that, unless explicitly specified otherwise, all recited distances are optical distances, which may or may not be equal to physical (free space) distances between optical elements. The terms “round spot” and “circular spot” are not limited to spots of uniform intensity, and are understood to encompass modulated, symmetrically-scaleable images encoding patterns/pictures. Such images may be projected on a target screen for example. A “round spot” position of an optical element of a system is understood to be a position at which an input round spot is transformed to an output round spot by the part of the optical system optically preceding the optical element. Adjusting angles between the cylindrical axes of optical elements refers to adjusting optical angles, i.e. angles between the cylindrical axis of the elements and the direction of the transverse (vertical or horizontal) axis at the cylindrical element location. The statement that a second optical element is rotatable with respect to a first optical element is understood to encompass rotating either or both of the optical elements.
The following description illustrates embodiments of the invention by way of example and not necessarily by way of limitation.
The general terminology and concepts employed in the ensuing description are discussed below.
Terminology and Concepts
An optical system comprising spherical and cylindrical lenses and/or mirrors, and sections of free spaces, can be described mathematically by a 4×4 real matrix called the ABCD matrix. For simplicity, such a system can be considered to be made of centered, aligned, lossless, passive, and aberration-free elements. The ABCD matrix has specific mathematical properties (called symplecticity) which can limit the maximum number of the independent matrix elements to ten. In a first order approximation, most optics belong to this category. These optical systems are called ABCD-type systems. The beams propagate aligned to the ABCD-type optical systems.
A beam is a distribution of light in free space that does not depart too far away from a reference axis. Such a distribution can be termed a paraxial distribution. The reference axis coincides with the beam axis. The beam axis is rigorously determined by using the first-order moments of the beam irradiance (sometimes termed “intensity”). For consistency, in the following discussion the z-axis is the beam axis, and the x- and y-axes represent the horizontal and the vertical transverse laboratory axes, respectively.
The main physical quantities characterizing the simplest beam can be defined using the second-order moments of the beam irradiance. They are, according to the International Standard Organization (ISO): the beam waist radius w0 (half-diameter), the beam waist size (full diameter) D0, the waist location z0, the beam divergence (full angle) θ, the Rayleigh range zR, (zR=D0/θ), and the beam propagation parameter M2. The beam propagation parameter is also named the times-diffraction-limit factor. These quantities are defined for a stigmatic (ST) beam, which is rotationally-symmetric about the z-axis, and forms a round spot everywhere in free-space propagation.
These quantities do not rigorously apply to the so-called pseudo-stigmatic beam, which is also rotationally symmetric in free-space propagation, but contains a hidden non-symmetrical parameter. This hidden parameter may not manifest itself in beam propagation through any rotationally symmetric optics, including the free-space, but it may appear in beam propagation through cylindrical optics. The beam propagation parameter M2 remains constant in beam propagation through rotationally-symmetric ABCD-type optical systems, and therefore represents a beam characteristics. It has a value which is always ≧1. Generally, the closer the beam parameter value is to 1, the better the beam quality is considered to be.
Consider the beam parameter product, or the product between the waist size and the divergence angle for a ST beam:
where λ is the wavelength of the laser light or the average wavelength of the white light. The lower the M2 value, the smaller the “beam parameter product,” and the better localized the laser beam in the near-field (w0 or D0) and the far-field (θ) simultaneously.
The physical properties of a beam can be described mathematically by a 4×4 real, symmetric, and positive definite beam matrix containing all the beam second-order moments. There are a maximum of ten independent such moments. The relevant information on the beam propagation properties and on the beam physical parameters is contained in this beam matrix. The 4×4 matrix is usually written as four 2×2 submatrices. The symmetry of these 2×2 submatrices determines the beam symmetry properties.
A stigmatic (ST) beam is a beam which has its four 2×2 submatrices proportional to the identity matrix. Therefore a ST beam has at most three independent parameters. It has also a rotational symmetry in free space. Not all rotationally symmetric beams are necessarily ST beams.
An aligned simple astigmatic (ASA) beam is a beam which has all its four 2×2 submatrices diagonal. Therefore an ASA beam has at most six independent parameters: three for each transverse coordinate, x and y. An ASA beam has different propagation and physical parameters in the two independent transverse directions, x and y. An ASA beam has two beam propagation parameters, M2 x and M2 y, which for some beams are equal (intrinsic stigmatic, or IS, beams), and for some other beams are not equal (intrinsic astigmatic, or IA, beams). An ASA beam has an orthogonal symmetry of its transverse irradiance (“intensity”) profile everywhere along its axis in free-space propagation. An ASA beam keeps the same ASA symmetry and preserves its M2 x and M2 y factors by propagation through aligned cylindrical optics and rotationally-symmetric optics.
A general astigmatic (GA) beam is a beam which has two 2×2 non-symmetrical submatrices. Some GA beams may have non-orthogonal symmetry in their transverse irradiance profile in free-space propagation. Such beams are called twisted-irradiance beams, or simply, twisted beams. There are also GA beams with rotational symmetry and GA beams with orthogonal symmetry in propagation through free-space and spherical optics, but not through cylindrical optics. Such beams are generally called pseudo-symmetrical beams, or more specifically pseudo-ST (PST), and pseudo-ASA (PASA) beams, respectively, or twisted-phase beams. The maximum number of independent elements of the GA beam matrix is ten.
Any GA beam can be transformed (detwisted, or decoupled) up to an ASA beam (with M2 x≠M2 y) or up to a ST beam (with M2 x=M2 y=M2), by using spherical and cylindrical lenses, mirrors, and sections of free-space or ABCD-type optics.
The intrinsic astigmatism parameter, a, is an invariant beam parameter which is a function of all ten second-order moments of a beam, which discriminates between the only two existing disjoint classes of beams: intrinsic stigmatic (a=0), and intrinsic astigmatic (a>0). The intrinsic astigmatism parameter a remains constant at beam propagation through ABCD-type optics, even though the beam symmetry changes during its propagation. The intrinsic astigmatism parameter a is a measure of the difference between the two beam propagation parameters, M2 x≠M2 y, defined for the beam transformed into its simplest, ASA-type symmetry:
An intrinsic stigmatic (IS) beam is a beam which, irrespective of its symmetry in free space (round, orthogonal, or even non-orthogonal), is obtained from or can be transformed into a ST beam by using only ABCD-type optics. An intrinsic astigmatic (IA) beam is a beam which cannot be obtained from (or transformed into) a ST beam by using only ABCD-type optics. An IA beam has a>0, and therefore cannot normally be transformed into a beam with a=0 by using the above mentioned ABCD-type optics. A collimated beam is a beam for which its Rayleigh range is much greater (usually at least 10 times greater) than all the characteristic lengths of intervening optics (free-spaces and focal lengths of the lenses).
The systems and methods described below preferably employ IS, collimated beams, either with ST symmetry (round shape in free space), or with ASA symmetry (orthogonal symmetry in free space with the elliptical spot aligned to the horizontal and vertical axes). Typical examples of ST beams are the collimated beams of virtually all types of lasers, including beams from diode lasers which are passed through low-order mode fiber and then collimated to become ST beams. Typical examples of IS beams with ASA symmetry are the collimated beams with elliptical beam spots in free space of index-guided diode lasers without fiber optics.
The degree to which a beam is intrinsic stigmatic is approximate. The degree depends on the errors of measuring its parameters, and to the degree to which we want to obtain the desired parameters, especially spot roundness. An IS beam can be defined as that one for which the parameter a is much less than the square of the geometrical mean (and therefore also of the arithmetic mean) of the two beam propagation parameters, M2 x and M2 y:
Alternatively, an IS beam can be defined as a beam having the ratio between the two different M2 x,y close to one, or more precisely:
where ε is a positive small number, ε<<1, to be conventionally specified. A collimated beam having in any transverse section a spot with the aspect ratio (the ratio between the major and the minor axis of the transverse irradiance spot) of 1.15:1, is considered a round beam everywhere along its axis according to ISO 11146 document. This beam is approximately an IS beam. The above criterion gives approximately ε≈0.15 and also
For example, using the above criteria to test whether a beam is IS or IA, a high power YAG:Nd laser with some intrinsic astigmatism, M2 x=40 and M2 y=46, can still be considered IS, having a=18<18.4, and ε=0.15; however, if the beam has slightly different values of M2, i.e. 40 and 50, then it is IA, because a=50 is not <20, and ε=0.2>0.15. Similarly, a beam from a diode laser having M2 x32 1.5 and M2 y=1.7 can be considered also IS, having a=0.02<0.026, and ε=0.13<0.15. Alternatively, a beam from a pulsed N2 laser having M2 x=9 and M2 y=12 is an IA one, because a=4.5 which is not <1.08, and ε=0.33>0.15.
The description of preferred embodiments below will ordinarily employ the thin lens approximation, which neglects the physical thickness of any lenses relative to their focal lengths. The optics (lenses, mirrors) will be considered aberration-free. Each optical element and the whole optical system is considered an ABCD-type system.
All the concepts and optical configurations will be illustrated specifically for laser beams, i.e., for coherent electromagnetic waves with wavelength in the range of 0.1 micrometers to 100 micrometers. Similar optical configurations can be implemented for coherent electromagnetic waves with longer wavelengths, in the millimeter and centimeter microwave range called the quasi-optical domain, by using specific components for the quasi-optics equivalent to the ABCD-type optical systems.
Two main beam configurations will be treated in sequence: collimated ST beams (with rotational symmetry), and collimated ASA beams (with orthogonal symmetry). Each of these beam configurations has several different embodiments, depending on the operation mode: image-mode, projection-mode, and focus-mode. For each main case, a generating configuration will be described first, to allow an analysis of the properties of this configuration, and allow an easy understanding of subsequent configurations and embodiments based on that generating configuration.
(I) Configurations for Collimated Stigmatic (ST) Beams
1. Image Mode
FIGS. 1-A and 1-B show schematic isometric and side views, respectively, of a two-lens optical system configuration 20 according to the present invention. The optical axis (z-axis) is shown at 22. A first (input) cylindrical lens 24 is placed along optical axis 22 such that lens 24 is converging along the x axis. First lens 24 is a positive-focus lens, and has a cylindrical focal length f1. A second (output) cylindrical lens 26 is placed along optical axis 22, approximately at an optical distance 2 f 1 behind lens 24, as discussed below. As illustrated in FIGS. 1-A and 1-B, lenses 24 and 26 are preferably separated by free space. In general, one or more lenses and/or mirrors could be placed between lenses 24, 26, while still allowing the positioning of second lens 26 at the round-spot location following first lens 24. Second lens 26 can be a positive or negative focus lens, and has a cylindrical focal length f2. The cylindrical axis of lens 26 is rotated about the z-axis with an angle a with respect to the cylindrical axis of first lens 24.
Consider an incoming collimated, ST, rotationally symmetric beam incident on first lens 24, with a waist of diameter Do at first lens 24. The beam has an elliptical cross-section in the space between lenses 24, 26. Second lens 26 is located in the plane where there is again a round spot after first lens 24, at or very close to a distance 2 f 1 from first lens 24. If the incoming beam is ideally collimated, second lens 26 is exactly 2 f 1 away from first lens 24. If the incoming beam is slightly convergent (or divergent), the round spot is situated at a distance slightly shorter (or longer) than 2 f 1. Second cylindrical lens 26 is placed in the plane of this round spot after first cylindrical lens 24.
There is always a round spot after first lens 24 if the incoming beam is a ST, rotationally symmetric, collimated beam. In classical optics this round spot is also called the circle of least confusion for the ASA beam created by first lens 24. An output round spot of an adjustable diameter D(α) is generated at an output transverse plane or screen 30 located at a fixed distance d20 after second lens 26, provided the following conditions are met:
Conditions [6.1-3] specify, respectively, that second cylindrical lens 26 is converging, second cylindrical lens 26 is more powerful than first cylindrical lens 24, and the output round spot is after second lens 26, and real, i.e., can be seen on screen 30.
The distance d20 at which the real spot is round can be called the image distance. The distance d20 is given by:
The diameter of the real round spot is adjustable by changing the angle α of second cylindrical lens 26 according to the equation (exact formula):
Eq. [8.1] can be rewritten as:
where K(α)>1 is the variable magnification factor, or variable scale factor.
For well collimated beams (f1/ZR→0), in the geometrical optics approximation (marked by the index g), eq.  becomes:
The minimum output spot size corresponds to α=0, i.e. an orientation of the cylindrical axis of second cylindrical lens 26 parallel to the cylindrical axis of first lens 24. The minimum spot size Dm=D(0) is given by:
In the geometrical optics approximation, eq. [10.1] can be rewritten as:
The maximum spot size corresponds to α=90°, i.e. an orientation of the cylindrical axis of second cylindrical lens 26 perpendicular to the cylindrical axis of first lens 24. The maximum spot size is given by:
In the geometrical optical approximation the maximum spot size is:
which is >D0.
If we define the dynamic range factor K as the ratio of the maximum to the minimum spot size,
we obtain (exact formula):
In the geometrical optics limit, eqs. [12.1-2] can be rewritten as:
A dynamic range K of 2-20 can be readily obtained by appropriately selecting the values of f1 and f2.
By placing a transparency (object) either on the first cylindrical lens 24, or on the second lens 26, in a fixed, aligned position with respect to the x and y axes, an adjustable size, proportional image is generated at screen 30. The image at screen 30 is rotated by an angle 2α. If the transparency/image is placed on the second cylindrical lens 26 and rotated together with it, the image at screen 30 is a fixed, aligned image, with a variable scale factor depending on α according to the equations above. For a laser beam, a certain transverse irradiance profile at the waist on the first cylindrical lens 24 can be replicated at screen 30 with an adjustable scale factor given by the equations above. The input irradiance profile can be for example a circular top-hat (uniform, rotationally-symmetric) profile, which is of particular use in industrial and medical laser applications.
The configuration shown in FIGS. 1-A and 1-B is useful for replicating and scaling a certain irradiance profile with an adjustable scale factor K(α)=2-20 at a fixed distance d20, or to project some images at a fixed distance d20 with an adjustable scale factor K(α).
If in the above generating configuration the second cylindrical lens 26 is either positive but weaker than the first one, f2>f1, or is negative, f2=−|f2|, the distance d20 becomes negative, i.e., the beam after the second lens 26 is never round. However, there is a virtual round spot located before the second lens 26, which can be converted into a real round spot by using an additional spherical relay lens L after the second lens 26. The virtual round spot located at −|d20| becomes a virtual object for the spherical lens L which, with appropriate focal length and positioning, can give a real image of the round spot. Overall, the adjustable virtual round spot is transformed into a real adjustable round spot. The specific values of the “virtual image distance”−|d20|, and of the “virtual round spot size” Dv(α) are relevant in this configuration, because the image location and size after the relay lens L (or after any imaging system) can be determined straightforwardly.
For a positive but weaker second cylindrical lens, f2>f1, the distance from the second cylindrical lens to the virtual round spot plane located before the second lens is:
The adjustable virtual round spot size is (exact formula, where the index v stands for “virtual”):
which can be rewritten as
For collimated beams, or geometric optics approximation (f1/zR→0), eq. [15.2] becomes
The minimum virtual spot size Dvm is given by (for α=0, exact formula):
In the geometric optics approximation the minimum virtual spot is:
The maximum spot size is given by (for α=90°, exact formula):
In geometrical optics approximation the maximum spot size is:
The dynamic range factor Kv (exact) or Kvg (geometrical optics) is:
For a negative second cylindrical lens 26, f2=−|f2<0, the focal length of the second cylindrical lens 26 is unrestricted by the focal length of the first cylindrical lens 24. The distance from the second cylindrical lens 26 to the virtual round spot plane located before second lens 26 is:
The adjustable virtual round spot size Dv(α) is (exact formula):
which becomes for collimated beams, or geometric optics approximation (f1/zR→0):
Equations [18.2-3] can be rewritten as:
The minimum virtual spot size Dvm is obtained for α=90° and is given by:
In geometric optics approximation it is:
The maximum virtual spot size is given by (for α=0):
In geometric optics approximation it is:
The dynamic range factor Kv (exact formula) and its counterpart Kvg in geometrical optics are:
While it is possible to use a relay spherical lens also for a real round spot, in the configuration of FIGS. 1-A-B, for practical applications any of the configurations with a virtual round spot can be more advantageous because they allow a relatively shorter overall length of the total configuration (two cylindrical lenses and a spherical lens).
A negative first cylindrical lens can be used in conjunction with a positive or negative second cylindrical lens, by positioning an appropriate spherical lens between the two cylindrical lenses such that the second cylindrical lens is situated in the round-spot plane following the first spherical lens.
2. Projection Mode
In the configuration of FIGS. 1-A and 1-B, the image distance d20 can be chosen to be infinity, d20→∞, by having both cylindrical lenses 24, 26 positive and of equal focal length, f. A real round spot of adjustable size is then located far away from the second cylindrical lens 26. That spot has all the properties of the real round and adjustable spot from a finite image distance. Therefore, a variable size image can be projected on a screen located far away from the second cylindrical lens 26.
Consider the optical system of FIGS. 1-A-B, with f1=f2=f>0. FIGS. 2-A and 2-B show a schematic geometric optics illustration of the passage of a light beam through system 20, for two extreme angular positions of second lens 26, respectively. FIG. 2-A corresponds to parallel cylindrical axes for the two lenses 24, 26, while FIG. 2-B corresponds to mutually perpendicular cylindrical axes.
An incoming, perfectly collimated round beam has a diameter D0 and substantially zero divergence. The beam divergence, D0/zR, is close to zero for a well-collimated beam. In the parallel-orientation configuration shown in FIG. 2-A, first lens 24 focuses the x-distribution 40 a of the incoming beam at a distance f, and leaves the y-distribution 40 b of the incoming beam unaltered. Second lens 26 recollimates the x-distribution 40 a, and leaves unchanged the y distribution of the beam (with dotted line in FIG. 2). After passage through second lens 26, the output light beam is collimated.
In the perpendicular-orientation illustrated in FIG. 2-B, the second cylindrical lens 26 is rotated perpendicular to the first cylindrical lens 24. First lens 24 acts only on the x-distribution 44 a of the light beam, while second lens 26 acts only on the y-distribution 44 b of the light beam. The x-distribution 44 a of the beam is focused by the first cylindrical lens 24, and remains divergent after the second cylindrical lens 26. The y-distribution 44 b of the beam is collimated until the second cylindrical lens 26, and then leaves the second cylindrical lens as a converging, and then diverging y-distribution. At a distance far enough from the second cylindrical lens 26, both x-distribution 44 a and y-distribution 44 b have the same maximum divergence, which is, in geometrical optics approximation, θM=D0/f. By rotating the second cylindrical lens 26, a variable divergence can be varied between a minimum value (D0/zR, which is near zero,) and a maximum value (D0/f). A rigorous result can be obtained from Eqs.  and  by defining the variable divergence θ(α) as the limit (for d20→∞, or for f2→f1=f):
In geometrical optics approximation the following variable divergence θg(α) results:
which gives correct results for α≠0. For α=0, the exact formula below gives the correct result of the minimum divergence:
where θin is the initial divergence of the incoming beam.
Note that in the geometrical optics approximation we have the non-physical result:
The maximum divergence is obtained for α=90° and is given by (the exact formula and the geometrical optics, respectively):
The dynamic range factor K, defined as K=θM/θm (exact formula) and its geometrical optics counterpart Kg are given by:
Desired values for the ratio K or Kg in Eqs. [19.6-9] between the maximum and minimum image size at a certain distance d can be obtained by using the optical system of FIGS. 1-A-B to project an image with variable magnification as described above. The maximum, DM, and the minimum, Dm, image size at the distance d, such as f<<d<<zR, are given by multiplying the maximum and the minimum divergence with the distance d:
Consider now a projection-mode optical system with positive and negative cylindrical lenses of equal absolute power, f2=−f1=−f. FIG. 3 shows an isometric view of a system 120 having two such lenses 124, 126 placed as close to each other as mechanically possible. The optical axis of system 120 is illustrated at 122. Either one or both of the two lenses can be rotated with respect to each other as described above. The system of FIG. 3 is functionally similar to a projection-mode system implemented in the configuration shown in FIGS. 1-A-B. The system of FIG. 3 can act either as a variable divergence optical system for a laser beam, or as a variable magnification projection system. In such a variable-magnification projection system, a collimated white light beam can be used at its input, and a transparent object can be attached to the rotating lens. The target projection screen is preferably positioned at a distance at least ten times larger than the magnitude of the focal length f. Ideally, in the system of FIG. 3, the two cylindrical lenses 124, 126 are infinitely thin and superimposed at the same physical location. In practice, cylindrical lenses such as lenses 124, 126 have finite thicknesses. As a result, lenses 124, 126 may not cancel each other when aligned.
FIG. 4 shows a schematic side view of an optical system 220 which images a focal plane 246 of a positive input cylindrical lens 224 to a focal plane 248 of a negative output cylindrical lens 226. Two identical, positive-magnification spherical lenses 250 a-b of focal length f0 are positioned between cylindrical lenses 224, 226 in a −1 magnification afocal configuration. Lenses 250 a-b are separated by a distance 2f0. The first principal plane 246 of the first cylindrical lens 224 coincides with the front focal plane of a first spherical lens 250 a. The first principal plane 248 of the second cylindrical lens 226 coincides with the back focal plane of the second spherical lens 250 b. The total physical length of the configuration is approximately 4f0. The first principal planes of lenses 224, 226 coincide. Similarly, the second principal planes of lenses 224, 226 coincide.
3. Focus Mode
FIG. 5 shows a schematic isometric view of a focus-mode optical system 320 according to another embodiment of the present invention. The optical axis of system 320 is illustrated at 322. System 320 includes first and second cylindrical lenses 324, 326 of focal length f, and a spherical lens 360 of focal length f0, situated after second lens 326. At least one of lenses 324, 326 is capable of rotation about the optical axis 322. An output plane or screen 330 is situated in the back focal plane of spherical lens 360, at a distance f0 away from spherical lens 360. The working distance of system 320 is equal to f0. Cylindrical lenses 324, 326 are separated by an optical distance 2 f, as described above with reference to FIGS. 1-A-B. Spherical lens 360 is situated a distance s≈0 after second cylindrical lens 326. Spherical lens 360 can be attached to the second, rotating cylindrical lens 326 in order to reduce the total length of system 320.
Irrespective of the placement of a focusing spherical lens in an incoming beam, the spot size at its back focal plane, Df, is proportional to the divergence of the incoming beam, θin:
where f0 is the focal length of the convergent spherical lens. The variable spot size Df (α) in the focal plane of spherical lens 360 is given by the (exact) formula:
In a geometrical optics approximation the variable spot size Dfg(α) is given by:
D fg(α)=D 0(f 0 /f) sin(α)=D 0 K g(α) [20.3]
The minimum spot size is obtained for α=0 and is given by:
The minimum spot size of Eq. [20.4] is the minimum spot size which would be obtained in the focal plane of the same spherical lens of focal length f0, without any intervening cylindrical optics, for an identical incoming beam having an incoming divergence θin. In pure geometrical optics the following non-physical result is obtained:
The maximum spot size DfM corresponds to α=90° and is given by the exact relations:
For a well collimated beam (geometrical optics approximation) the maximum spot size is:
The exact dynamic range factor K and the geometrical optics dynamic range factor Kg are given respectively by:
A remarkable feature of the “focus-mode” arrangement shown in FIG. 5 is its large achievable dynamic range factor. Dynamic range factor values of 50 to 400 are readily achievable. The design of FIG. 5 is also remarkably flexible. The desired working distance determines the focal length of spherical lens 360. The desired dynamic range factor determines the required incoming beam collimation (the value of its Rayleigh range zR) and the cylindrical lens characteristics. For a lower value of K and a large Rayleigh range, the positive-negative cylindrical lens configuration of FIGS. 3-4 can be more convenient than the positive-positive configuration of FIGS. 1-A-B. The depth of focus, or the extent over which the beam maintains approximately a round spot, can be a relevant parameter in certain applications. An estimate for this range is by considering the true Rayleigh range of the focused beam when the minimum spot is obtained, zRDm, given by:
One can estimate a deviation from the round spot within this “quasi-Rayleigh range” of about 10%, for the entire range of spot sizes at the working distance.
Focus-mode optical systems such as the system 320 shown in FIG. 5 can be particularly useful in beam delivery systems for industrial and medical lasers. The input beam can be collimated accordingly before entry into system 320, either using discrete lenses and free-spaces, or using optical fibers and collimating lenses. System 320 allows the use of a single laser for a relatively wide range of applications, by allowing relatively wide variations in the laser spot size at the target and thus allowing adjustments of the laser power density or the laser energy density at the target plane. Applications such as cutting and surface treatment for industrial lasers, and medical applications in dermatology and ophthalmology would benefit from variable spot size optical systems such as the ones described above.
A focus-mode system can be constructed by modifying the configuration shown in FIG. 3, by positioning a convergent spherical lens adjacent to the second cylindrical lens 126 opposite the first cylindrical lens 124. The target location where a symmetrically-scalable round spot is formed is then situated a distance f0 away from the spherical lens, where f0 is the focal length of the spherical lens.
(II) Collimated, Aligned Simple Astigmatic (ASA) Beams
Collimated ASA beams of intrinsic stigmatic type can be obtained by collimating an index-guided diode laser. The extent of such a beam over one of the transverse axes, for example the x-axis, is several times larger than the extent of the beam over the other transverse axis. A beam aspect ratio of 3:1 to 5:1 is typical.
There are in principle two ways of generating a variable-size round spot at a desired working distance (say, at infinity) using a laser source with a collimated elliptical beam. One way is to enlarge the small axis of the elliptical beam until it equals the large axis, and then to transform the resulting round, collimated laser beam into a variable-divergence beam. The second way is to reduce the large axis of the elliptical beam to make it equal to the small axis, and subsequently to transform the resulting round, collimated beam into a variable-divergence beam. Assume for example that we are interested in enlarging the small axis of the beam until it becomes as large as the larger axis. The enlargement could be achieved by using a negative-positive pair of cylindrical lenses, or a positive-positive pair. Reducing the larger axis of the beam can be achieved by switching the direction of light travel through the lens pair used for enlargement (i.e. switching the system input and output). Therefore, there are four different configurations that could be used to generate a round spot at a desired distance using an incoming ASA beam: small-to-large configuration using negative and positive cylindrical lenses (Galilean magnifying telescope with the positive lens rotating); small-to-large configuration using positive and positive cylindrical lenses (Keplerian magnifying telescope with rotating second lens); large-to-small configuration using positive and negative cylindrical lenses (Galilean demagnifying telescope with rotating negative lens); and large-to-small configuration using positive and positive cylindrical lenses (Keplerian demagnifying telescope with rotating second lens). Only one of the four possible configurations will be analyzed in detail below. The other three configurations will be readily apparent to the skilled artisan from the discussion below.
FIGS. 6-A-B show schematic views of a small-to-large cylindrical telescope 420 having a first, fixed, negative focus cylindrical lens 424, and a second, rotatable, positive focus cylindrical lens 426. Although the discussion below focuses on a projection-mode, variable divergence system, corresponding focus-mode systems can be constructed by adding an output spherical lens as described above. First lens 424 has a focal length f1=−|f1|, while second lens 426 has a positive focal length f2. First lens 424 is oriented so as to act only along the smaller beam size direction, or the y-direction. Second lens 426 is situated at the location where the light beam is round after first lens 424. This position corresponds approximately to a distance f2−f1 after first lens 424.
The incoming beam is collimated on both the x- and y-directions, and has both its x- and y-waists at first lens 424. The beam has a larger waist size along the x-axis, D0x, than along the y-axis, D0y. When second lens 426 is parallel with first lens 424, i.e. when second lens 426 acts also only along the y-axis, the configuration is a Galilean magnifying telescope (or afocal system), as illustrated in FIG. 6-A. The x-distribution 440 a of the beam passes undisturbed through both cylindrical lenses 424, 426 and retains its size Dox. The y-distribution 440 b is enlarged by f2/|f1|>1 by the Galilean afocal system. To obtain a collimated round spot after second lens 426, the magnification ratio of the telescope should equal the ratio of the beam sizes along the x- and y-directions:
The divergence of the beam with both lenses in parallel position acting on y is minimum (zero in geometric optics limit), or equal to the smaller divergence of the larger axis, x:
FIG. 6-B illustrates the effect of rotating second cylindrical lens 426 by 90°. As shown, both the x- and y-distributions 444 a-b of the light beam become divergent, with the maximum divergence angle θM given by:
The cylindrical Galilean afocal optical system 420 with the rotating second lens 426 is a variable divergence source of light for a collimated ASA beam of intrinsic stigmatic type. The other three possible configurations can be analyzed similarly.
As the skilled artisan will appreciate from the preceding discussion, it is possible to construct projection-mode optical systems with variable spot sizes at large distances for collimated ASA beams of intrinsic stigmatic type. Adding a spherical lens after the second cylindrical lens allows generating focus-mode, variable spot sizes at a fixed working distance. Applications such as coupling to a fiber, material processing, or medical applications (dermatology) can benefit from the designs described above.
(III) Systems Using Cylindrical Mirrors
Generally, the lenses described above can be replaced by suitably-chosen mirrors. In the far infrared spectral domain, reflective optics are sometimes less expensive than refractive optics. Mirrors can also be of particular use when the chromatic aberrations are of concern. In general, many configurations using mirrors or mirrors and lenses can be conceived.
FIG. 7 shows a configuration 520 using a first (input) cylindrical lens 524, and a second (output) cylindrical mirror 526 situated along the optical axis 522 of the incoming beam. Lens 524 is a converging lens of focal length f, acting along the y-axis. Mirror 526 is a converging, rotatable cylindrical mirror with a focal length f and a cylindrical radius of curvature 2 f. A polarizing cube beam splitter (PCBS) 550 and an attached quarter-wave plate (QWP) 552 are positioned in the optical path between lens 524 and mirror 526.
An input ST, collimated beam, linearly polarized along the vertical direction, is incident on lens 524. The optical distance between the cylindrical lens 524 and the cylindrical mirror 526 is 2 f. Thus, mirror 526 is positioned in the round spot of the light beam after its passage through PCBS 550. The incoming beam is p-polarized inside PCBS 550 and is transmitted almost completely toward mirror 526. The beam reflected from mirror 526 becomes s-polarized inside PCBS 550 by passing a second time trough QWP 552, and is reflected almost completely downwards within PCBS 550. With mirror 526 oriented parallel to lens 524 (with both acting along the y-direction), the reflected beam after mirror 526 has a minimum divergence equal to that of the incoming beam. With mirror 526 rotated by 90° about the optical axis 522, the outgoing beam has a maximum divergence. The configuration shown in FIG. 7 otherwise satisfies the equations set forth above for the system shown in FIGS. 1-A-B, with f1=f2=f.
FIG. 8 shows a configuration 620 including a first cylindrical mirror 624 and a second cylindrical mirror 626 situated along an optical axis 622. First mirror 624 has focusing power along the y- (vertical) axis, and has a focal length f and a cylindrical radius of curvature 2 f. Second mirror 626 is rotatable about the vertical axis of FIG. 8, and has the same focal length f and cylindrical radius of curvature 2 f. A polarizing cube beam splitter (PCBS) 650 and two attached quarter-wave plates (QWP) 652, 654 are positioned in the optical path between mirrors 624, 626. The optical distance between each mirror 624, 626 and the center of PCBS 650 is f.
A collimated ST beam, linearly polarized along the vertical direction, is incident on PCBS 650 along optical axis 622. The beam axis path through PCBS 650 is established by the polarization state of the beam. The incoming beam is p-polarized and is transmitted almost completely to first mirror 624 through the first QWP 652. After reflection by mirror 624, the light beam passes again through first QWP 652 and becomes s-polarized. The s-polarized beam is reflected upwards by PCBS 650, through second QWP 654 and toward second mirror 626. The beam reflected by second mirror 626 arrives inside PCBS 650 after a second pass through second QWP 654. The beam, now p-polarized inside PCBS 650, is transmitted almost completely downward toward the system output.
The divergence of the output beam is minimal and equal to the divergence of the incoming collimated beam for the mirrors in the position as drawn. The maximum divergence of the output beam is obtained for the second mirror 626 rotated with 90° about its optical axis in FIG. 8. Second mirror 626 is located at an optical distance equal to 2 f from first mirror 624, where the round spot after first mirror 624 is located. Thus the incident beam will be affected by the pair of mirrors 624, 626 according to the equations described above for the configuration of FIGS. 1-A-B, with f1=f2=f.
(IV) Mechanical, Electrical and Computer Elements
The distances between the cylindrical lenses/mirrors affect the performances of all configurations, and are also slightly dependent on the input beam characteristics. Ideally, an optical system as described above is designed so as to allow a fine adjustment of these distances after the lenses/mirrors are assembled. Because this adjustment is done only once, during the assembly of the real device, expensive fine mechanisms can generally be avoided. A translational adjustment allowing a range of +/−3% of the nominal length would be of particular use. After the adjustment, a simple locking system (screws or glue) can be used to fix the translational position of the optical elements.
Suitable mechanical and/or electrical components can be provided for controlling and driving the relative rotation of the cylindrical elements. The spot size depends nonlinearly of the rotation angle α, as discussed in the detailed analysis of the configurations presented. Therefore, a fine rotation mechanism with good reproducibility and ideally no backlash is desirable. A rotating ring rigidly attached to the rotating lens/mirror holder can suffice. The holder should be well centered to the mechanical axis of the whole device, which should be coincident with the optical axis. An elastic washer can be provided to allow the necessary friction such as to avoid losing the desired position of the ring during operation, and therefore to keep the spot size at the desired value. If desired, several discrete angular positions corresponding to several discrete magnifications can be selected by appropriate ring indentations. A mechanical stop to limit the whole rotation range to 90 degree can be used. Thin line graduations on the outer tube and a mark on the rotating ring can also be used to control the angular position of the lens(es). More precise solutions may use gears to control the rotation of the ring, and stepper motors driven by appropriate electronics and computer software. Special software can be implemented to allow the precise control of the spot size by using a spot size optical detector (based, for example on pinhole/quadrant detectors) which will give a feedback signal to the computer to control and maintain the spot size at the desired value. Fine rotation control, with approximately 1 minute of angle resolution and reproducibility (especially when small spots are desired to be controlled in focus-mode configurations) can be obtained by using levers attached to the rotation ring and activated by fine translation mechanisms, as micrometric or differential screws. A focus-mode configuration coupled with a small spot size measuring system can be used as a sensor for very small angular movements, with a resolution in the range of 1 second of arc, for a limited range (several degrees) of angular movements.
FIG. 9 shows a side sectional view of a mounting/control arrangement suitable for controlling the operation of a three-lens system as described above. An optical system 920 includes a first cylindrical lens 924 rigidly mounted within a protective housing 980. Lens 924 is mounted within a fixed cylindrical lens holder 982, which is in turn fixedly attached to housing 980. A block holder 984 is fixedly mounted within lens holder 982. The translational position of block holder 984 is adjusted during the assembly of system 920 to ensure that a second cylindrical lens 926 is positioned at a desired distance (2 f) away from first lens 924. Once block holder 984 is positioned at the desired location, it is affixed to lens holder 982 by inserting screws through a set of holes 994 defined in the wall of lens holder 982, and pressing the screws to the surface of block holder 984.
Second cylindrical lens 926 and an attached spherical lens 960 are rigidly mounted on a rotatable lens holder 986. The translational position of lens holder 986 is held fixed by a locking flange 988 which holds lens holder 986 against block holder 984. A rotatable handling ring 990 is rigidly coupled to lens holder 986, for coupling an external rotational driving force to lens holder 986 so as to rotate second lens 926.
Cylindrical lenses 924, 926 are identical, and have a focal length f=50 mm. The spherical lens 960 has a focal length f0=140 mm. The device acts on a 3-4 mm diameter collimated, low power laser beam (red laser diode), and provides at the working distance a round spot continuously adjustable from a minimum of approximately 50 μm to a maximum of approximately 12 mm.
It will be clear to one skilled in the art that the above embodiments may be altered in many ways without departing from the scope of the invention. Accordingly, the scope of the invention should be determined by the following claims and their legal equivalents.
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|Citing Patent||Filing date||Publication date||Applicant||Title|
|US7167321 *||Jan 30, 2004||Jan 23, 2007||George Nemes||Optical systems and methods employing adjacent rotating cylindrical lenses|
|US7369334 *||Jul 14, 2005||May 6, 2008||Cyberoptics Corporation||Optical device with alignment compensation|
|US7599591||Jan 12, 2007||Oct 6, 2009||Optimedica Corporation||Optical delivery systems and methods of providing adjustable beam diameter, spot size and/or spot shape|
|US8029637 *||Nov 29, 2007||Oct 4, 2011||Hitachi Global Technologies Netherlands, B.V.||System, method and apparatus for ultraviolet curing of adhesives with light beam shaping in disk drive manufacturing|
|US9017316 *||Jul 25, 2011||Apr 28, 2015||Lumenis Ltd.||Distance estimation between a fiber end and a tissue using numerical aperture modulation|
|US9639066 *||Dec 26, 2014||May 2, 2017||Lenovo (Beijing) Co., Ltd.||Display device and electronic apparatus|
|US20020168147 *||Mar 15, 2002||Nov 14, 2002||Case Steven K.||Optical circuit pick and place machine|
|US20050243275 *||Apr 30, 2004||Nov 3, 2005||Curatu Eugene O||Wavefront sensor and relay for optical measurement and associated methods|
|US20050249464 *||Jul 14, 2005||Nov 10, 2005||Case Steven K||Optical device with alignment compensation|
|US20070189664 *||Jan 12, 2007||Aug 16, 2007||Andersen Dan E||Optical delivery systems and methods of providing adjustable beam diameter, spot size and/or spot shape|
|US20080297912 *||Jun 1, 2007||Dec 4, 2008||Electro Scientific Industries, Inc., An Oregon Corporation||Vario-astigmatic beam expander|
|US20090139652 *||Nov 29, 2007||Jun 4, 2009||Hitachi Global Storage Technologies Netherlands Bv||System, method and apparatus for ultraviolet curing of adhesives with light beam shaping in disk drive manufacturing|
|US20130123769 *||Jul 25, 2011||May 16, 2013||Lumenis Ltd.||Distance Estimation Between a Fiber End and a Tissue Using Numerical Aperture Modulation|
|US20150279254 *||Dec 26, 2014||Oct 1, 2015||Lenovo (Beijing) Co., Ltd.||Display Device and Electronic Apparatus|
|US20150323788 *||Dec 26, 2014||Nov 12, 2015||Lenovo (Beijing) Co., Ltd.||Display Device and Electronic Apparatus|
|U.S. Classification||359/710, 359/670|
|International Classification||G02B27/09, G02B27/30|
|Cooperative Classification||G02B27/09, G02B27/30, G02B27/0933, G02B27/0966|
|European Classification||G02B27/09, G02B27/30, G02B27/09M, G02B27/09S2L2|
|Jan 23, 2007||CC||Certificate of correction|
|Sep 13, 2007||FPAY||Fee payment|
Year of fee payment: 4
|Nov 21, 2011||REMI||Maintenance fee reminder mailed|
|Apr 6, 2012||LAPS||Lapse for failure to pay maintenance fees|
|May 29, 2012||FP||Expired due to failure to pay maintenance fee|
Effective date: 20120406


The final college all-star game of the season is televised on Friday evening at 5:00 p.m. CT on CBS Sports Network.
"Pigskin" Paul Guillemette checks in from Mobile, Ala. to discuss potential Packers draft targets.
According to a report at NFL.com, the Packers interviewed the Mississippi State guard in Mobile, Ala. this week.
The Packers have reportedly shown interest in Vanderbilt safety Kenny Ladler and Stanford linebacker Trent Murphy while in Mobile.
Live coverage of practice from Mobile, Ala. takes place on the NFL Network starting at 2:00 p.m. CT.
"Pigskin" Paul Guillemette checks in from the site of the college football all-star game in Florida to talk Packers prospects.
Fans can see what Packers scouts are seeing at the site of the college football all-star game on ESPNU on Thursday.
NFL draft prospects Texas A&M quarterback Johnny Manziel and Clemson wide receiver Sammy Watkins headline our annual All-Bowl team.
Freshman quarterback Jameis Winston will expose Auburn's pass defense on the way to breaking the SEC's seven-game national-championship streak.
Looking for potential Green Bay Packers prospects? Notre Dame defensive lineman Stephon Tuitt and North Carolina tight end Eric Ebron are two players you might want to watch Saturday.
The Alabama quarterback is the CFWP's second annual recipient given to a college football player for outstanding performance over the course of his career. It's the four-year Heisman.
The Heisman Trophy will be handed out Saturday evening, and the Florida State quarterback is CFWP's prediction as the winner.
Mizzou is predicted to win the SEC championship. Now all Ohio State (or Florida State) has to do is lose and the Tigers are heading to Pasadena for the BCS title game.
Ohio State, Michigan State and Wisconsin can hang with the big boys, but programs like Michigan and Nebraska are holding the conference back.
Some of the best teams in the nation feature an outstanding group of linebackers like Alabama, Florida State, Michigan State and Stanford.
Credit David Cutcliffe for directing Duke to a 7-2 record heading into Saturday's matchup against Miami in an ACC matchup.
Baylor is in the national-championship hunt, and Oregon is not after the biggest Thursday night in college football history.
If any of Oregon, Florida State, Ohio State or Baylor are undefeated at the end of the season, the deserve to be in the BCS national championship ahead of a one-loss Alabama.
The Tigers and Red Raiders are national-title contenders as long as they remain among the undefeated, but their schedules are about to get a whole lot tougher.
College football fans are the biggest winners when they're able to watch Johnny Manziel, Marcus Mariota and Jameis Winston excel at the quarterback position.
The NFL draft stock of South Carolina's Jadeveon Clowney and Colt Lyerla, formerly of Oregon, is slipping after poor choices.
With Lane Kiffin and Paul Pasqualoni already getting axed at their respective institutions, the coaching merry-go-round is on its first revolution.
There's a trio of terrific SEC games, highlighted by LSU at Georgia, where College GameDay is broadcasting from.
Wisconsin can learn a lesson from Arizona Cardinals head coach Bruce Arians in learning to hand the ball to the official when learning to run the two-minute drill.
The Crimson Tide will roll into College Station looking for payback from the game that catapulted Manziel to the Heisman Trophy last year.
Jadeveon Clowney and the South Carolina Gamecocks take on the Georgia Bulldogs in a key SEC East showdown on Saturday afternoon.
The fact that Manziel is suspended for the first half of the season opener is a joke. The NCAA has to change it archaic rules or college football as we know it will cease to exist.
Cheesehead TV's very own "Pro Football Draft Preview" drops in just over a week. Take a look at how our guide is shaping up.
Wisconsin center Travis Frederick is among the top-rated centers in this year's NFL Draft class. Could the Packers spend their first round pick on him?
"Pigskin" Paul Guillemette joins Railbird Central to preview Saturday's Senior Bowl all-star game in Mobile, Ala.


text:
No deal, event, offer, or promotion found for CODE BLACK COFFEE. Add some if you know any. Otherwise, here are some we've found from other businesses...
Milano Espresso Bar - Early bird special! Small coffee with Milano's famous egg and bacon roll for $9 from 6:30am to 10:30am on weekdays!
Queen Street Rescue - $6.5 Basic Spirits, All Week, -
Terrace Deli On Little Collins - Muffin or Slice served with Coffee/ tea or Hot Chocolate $4.50 avaible, Mon Tue Wed Thu Fri, 06:00-16:00
The Hidden Spot Cafe - Come in and try out our BIG breakfast for only $12!
Queen Street Rescue - $5 gls house wine, All Week, -
The Phoenix Hotel - $15 Weekday Lunch Specials in the a la carte Bistro!
When is this happening?

domain: food


Urban travel requirements are constantly changing, and so are the challenges that cities face in keeping their inhabitants mobile. In an interview with URBANET, Roger Behrens (University of Cape Town) talks about the importance of accessibility, the challenges for local governments and the changing travel dynamics in South Africa.
In a four-part series, URBANET takes a closer look at specific projects that contribute to making cities more liveable. This third part describes efforts to better integrate and reintegrate migrants, refugees and returning migrants into local life in Morocco.
What do cities in India need to be more livable? In the four part series "Spotlight on livable cities", ISOCARP Vice-President Shipra Narang Suri aims to answer this question by approaching it from various angles, giving examples from different areas of urban planning. In this second part, she talks about urban building master plans, the land housing market in India's cities and the urban poor.
The German government pushes for a New Urban Agenda oriented towards the vision of the “lebenswerte Stadt”, i.e. a city worth to live in, but is mostly translated with “liveable city”. But how do we define “liveable”? Our authors Alexandra Linden, Astrid Ley and Alexander Jachnow contend that it goes beyond “freedom from fear” and “freedom from want” as proposed by the UN. Liveability, construed as Quality of life shouldn’t just be determined by indicator models, but within a specific local context and in conjunction with international standards.
Three weeks after the Habitat III conference in Quito, Ecuador, the 22nd Conference of the Parties (COP 22) to the UN Framework Convention on Climate Change (UNFCCC) is currently taking place in Marrakesh, Morocco. Sarah Schneider and Lisa Lebershausen look at the the international climate change conference through an urban lense.
In the run-up to the German Habitat Forum in June 2016, people from all over the world were asked how they imagine the city of the future, what they expected from local, national and international authorities for their city, and how their city has evolved. The series "Voice on Habitat" projects an image of the
“Make cities and human settlements inclusive, safe, resilient and sustainable” - this is the call to action formulated in Sustainable Development Goal 11. Although this reflects an awareness of urban governance issues in regard to sustainable development, our author argues that many of these issues are still neglected and need to be further elaborated.
In the run-up to the German Habitat Forum in June 2016, people from all over the world were asked how they imagine the city of the future, what they expected from local, national and international authorities for their city, and how their city has evolved. The series "Voice on Habitat" projects an image of the issues that the New Urban Agenda has to tackle, and gives a voice to the people who will be directly affected by its implementation.
Commentary by Dr. Christoph Beier, Vice-Chair of the GIZ Management Board.
A key recommendation of the German Habitat Forum held in May 2016 in Berlin was that “cities need to be empowered as actors”. Urbanization not only implies geographical changes, but also a political change in order to manage growth. This is where local governments are most needed.
A colourful video overview how local governments in Ghana can increase their Internally Generated Funds and what benefits they provide.
What are the challenges Ghanaian cities face in achieving sustainable development? Isaac Ashai Omdatten, Mayor of Tema, describes how he makes his city more livable.
“Those innovative instruments are now recognised as effective instruments to finance urban development”
Subnational Pooled Financing Mechanisms (SPFMs) are expected to play an increasingly strategic role in financing sustainable development. Jean-François Habeau, Executive Director of the international cities network FMDV, talks about the benefits and specific challenges of Subnational Pooled Financing Mechanisms for developing countries.
To be able to achieve good governance, local governments must not only work together with communities, but also grant them a certain amount of responsibility. In an interview with URBANET, Diana Mitlin, Managing Director of the Global Development Institute at the University of Manchester, talks about the importance of community-led development and the value grassroots organisations can add to local communities.


Briefs: Grease thrown at man in dispute over glasses
Oakland County Sheriff's deputies are looking for a man who allegedly threw hot grease in a Pontiac man's face.
Join the discussion below, or Read more at Detroit News.
#1 Jan 22, 2013
Certainly an interesting story. I heard that some glasses company in Ottawa replaced the man's glasses free of charge after hearing the story. http://mcleodoptometryclinic.ca
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From the Czech Republic comes the beautiful Fel Cassieli.
Fel Cassieli is from the visually intriguing city of Prague and has worked and lived in Hamburg, Munich, Milano, Paris, Barcelona, Cape Town, Istanbul, the list continues. An international beauty with a fantastic career outside of the USA.
Having started modeling at the age of 21, she began her career late in the model-fashion world. But she is making up for lost time with her busy work schedule around Europe.
Fel works out and adheres to a semi-strict diet “My diet is about healthy foods, salads and fish. But I love to eat so I prefer to have some gastronomic fun and later burn it all at the gym.”
Photo by Danielle Klopper
She loves wine, beer and coconut water (don’t all models love coconut water and sushi?) This beauty also studied media communications and has aspirations of opening a restaurant in the future. Her appreciation for fine dining and culture demands she opens her own gastronomic brasserie.
She has worked with brands such as; Garnier, Triumph, Gossard, Vasto and featured in magazines such as Lash and Zut! (mainly she has been active in the European market)
“I love traveling of course. Thanks to my job I have seen so many beautiful places. Actually there is nothing that I dislike.”
Follow Fel on Tumblr: http://felcassieli.tumblr.com/
and don’t forget to follow us REDHOTPRSOCIETY as well.

domain: artistic


I have visited the binder file for the 40m wiring file in the control room.
The 12V power supply on 1Y1 is for the CCD cameras. So we still want to keep the 12V 0.8A power and the side connections for these. It is not necessary to be Sorensen. Can we replace it with an AC-DC adapter with +12V/1A for example? BTW, the video matrix and quads are AC-powered.
The mysterious thick cables and cross-connects (green wires) on the side panel (labeled AP1/AP2/SP/IMCREFL) are for "EO shutters". It was meant for the protection of the PDs from bright beams.
I don't think they have been used. And we don't need them.


text:
US STOCKS SNAPSHOT - Wall St edges lower in thin trade
NEW YORK Dec 24 (Reuters) - U.S. stocks edged lower on Monday after the S&P 500 suffered its worst drop since mid-November on continued worry legislators will be unable to reach a deal to avert the "fiscal cliff."
The Dow Jones industrial average dropped 27.95 points, or 0.21 percent, to 13,162.89. The Standard & Poor's 500 Index dropped 2.55 points, or 0.18 percent, to 1,427.60. The Nasdaq Composite Index dropped 6.23 points, or 0.21 percent, to 3,014.78.
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- Scotland's pro-independence campaign gains on final TV debate - poll
- Cameron says he's 'nervous' over Scottish independence vote
- China and Hong Kong poised for showdown over democracy
- Ukraine says Russian tanks flatten town; EU to threaten more sanctions |
- UPDATE 1-Cricket-One Day International England v India scoreboard

domain: economics


text:
Arsenal star Hector Bellerin has NO intentions of Emirates stay next season and wants to quit for Real Betis transfer
HECTOR Bellerin wantsto leave Arsenal and return to Real Betis permenently this summer, reports claim.
The 27-year-old played for the La Liga side on loan this season as they won the Copa del Rey.
And Bellerin want to make his move there permanent, claims journalist Fabrizio Romano.
He reports that the player has zero intentions of playing for the Gunners again.
However a transfer to Manuel Pellegrini's side may prove difficult due to financial reasons.
Bellerin is a boyhood Real Betis fan and after playing his last home match at the club he was in tears on the pitch.
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His parents then joined him on the Estadio Benito Villamarin turf.
He has become a popular figure at the Spanish club and his teammate Borja Iglesias stated on Twitter that he wants to start a crowdfunding page in order to get him to stay.
This was then endorsed by Betis man Aitor Ruibal too.
Also in an emotional farewell message posted by the official Betis account it described Bellerin as "pure Betis".
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The Spaniard remains an Arsenal player and has been since 2013, featuring an incredible 239 times.
However he has not played for the North London side since March 2021.
And since the signing of Takehiro Tomiyasu, it seems unlikely Bellerin will be able to force his way back into the Arsenal starting XI.
His contract expires at the Emirates Stadium at the end of next season with a rumoured fee of £8million being Arsenal's asking price according to Goal.
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Zilean is one of the most popular champions in the game League of Legends. The champion is a Support Mage, which means he is capable of dealing tremendous amounts of damage while also providing a lot of utility. His versatility and power make him a must-have champion in most team compositions in the game.
In this article, we’ll discuss all that you need to know about this champion, from his abilities and playstyle, to his strengths and weaknesses:
Overview of Zilean
Zilean is a champion in the popular game League of Legends, created by Riot Games. He is a part of the Chronokeeper group, powerful beings who manipulate time itself to help or harm other beings in the world.
Zilean is a powerful support character, capable of granting healing and shielding to his allies while also slowing his enemies with his inherent powers over time. He is has high mobility, excellent crowd-control potential and multiple unique spells at his disposal.
Overall, Zilean has an interesting playstyle which focuses on either providing support to other carries or controlling the fight through crowd-control abilities and area of effect damage spells. With maximum cooldown reduction, he can often be found cycling between these two roles throughout the course of a game depending on what will benefit his team most significantly in any given situation. His kit provides excellent utility for pushing objectives and fighting enemy teams even without building items outside of standard support spell items such as Archangel’s staff or Redemption.
In any matchup, it can often be beneficial for the team to have Zilean as their primary support character as he provides both damage output and crowd-control for whichever side holds him.
Zilean is a champion in League of Legends who excels at offering utility, control, and lane dominance. He can be played both offensively or defensively depending on the lane matchup. He is also able to help teamfights with his ability to slow and speed up allies/enemies.
Passive: Heightened Learning
Heightened Learning grants Zilean three additional ability power or attack damage per level, as well as an extra 25% experience gain when he kills an enemy unit.
Q: Time Bomb
Time Bomb is Zilean’s primary damage dealing ability. When cast it will place a bomb on the target that detonates after a few seconds for magic damage and slows enemies near the blast radius. If Zilean recasts this ability on a previously placed bomb it will detonate instantly, dealing more damage and slowing even more enemies in the area.
Rewind enables Zilean to reduce the cooldown of all his other spells by 8 seconds whenever he uses it. This enables him to chain combos of spells very quickly and make plays that would normally not be possible.
E: Time Warp
Time Warp is Zilean’s signature spell which allows him to grant sped up movement speeds or reduced movement speeds to allies or enemies respectively whenever casted on them for 2-3 second durations which makes it better at getting into or out of fights or even zone out priority targets in teamfights.
R: Chrono Shift
Chrono Shift gives Zilean’s teammates a layer of safety net before death as they will be went back in time before they died with all their health restored back while they were invulnerable while being shifted back in time for 6 seconds enabling them escape most trysts at death easily if used correctly.
Zilean is a great champion to use in League of Legends for a number of reasons. His time-manipulating abilities allow him to turn the tide of fights and his spells have great utility in team fights and skirmishes. His kit is packed with powerful abilities that can make him a valuable asset in any team composition. Let’s take a closer look at Zilean to explore his strengths and capabilities.
Ability to Stun Enemies
One of Zilean’s unique abilities as a champion is his crowd control capability. He has the ability to counteract enemy skill shots, disrupt coordinated attacks, and secure kills with his Chronoshift support ult. His main stun comes from his E ability “Time Bomb” which causes an area of effect damage and stuns enemies for the duration of 1 second.
This ability does not rely on attack speed to be effective, because the additional attack speed that Zilean rolls don’t increase the duration or damage, so it maintains its same usage throughout a match.
To use this correctly you must keep in mind that Time Bomb has a very short range and requires you to get close to enemies in order to apply it. It is useful as both an initiation tool, as well as an extension tool when mixed with other crowd control abilities due its short duration despite decent range. It can be used while chasing down enemies, or setting up ganks. Additionally, Time Bomb is great for escape tools coupled with Zilean’s passive “Time Warp” that speeds up allies and slows down enemies for two seconds. This gives Zilean immense control over team fights if used correctly!
Ability to Heal Allies
Zilean is a highly versatile and powerful support character in League of Legends inspired by a legendary chronokeeper. His primary strength lies in his ability to heal allies both in the laning and mid-late game stages. He can restore health, revive recently slain allies, and supplement crowd control abilities with his low cooldown basic abilities.
His Time Warp ability allows him to bestow an ally or himself with an additional burst of speed for three seconds. Zilean can also use the Chronoshift ultimate to revive the closest dead ally at full health after a short channeling period. This can be used either offensively to initiate fights early on or defensively in later game stages against enemies who have taken down members from your team.
Zilean’s passive ability Time Lord grants increased Health Regeneration as well as bonus Ability Power and Movement Speed on leveled up Q (Time Bomb) cast which makes it even easier to keep allied heroes alive both through healing spells and bonus stats granting extended survivability in fights. Not only does this make him one of strongest supports due to his allies sustain capabilities but also a possible contender for mid lane solo roams when paired with appropriate itemization.
Ability to Slow Enemies
One of Zilean’s key abilities is to slow enemies within a large radius. He does this by using his powerful time spells, Chronoshift and Time Warp.
These two abilities give him the ability to slow his opponents and gain a distinct advantage in combat.
Chronoshift is Zilean’s ultimate ability and it allows him to freeze an allied champion in time. This champion, who must be chosen carefully, will be given all of the benefits of his Chronoshift including an increase in health, armor, speed and magic resist. The frozen champion also has their attack damage increased making them formidable in battle. Enemies who come too close to this champion will also be slowed by Zilean’s Time Warp spell allowing him to gain an advantage over them before they can react.
Time Warp is Zilean’s second ability and it slows enemies as well as heals allies when cast on them. This ability has both offensive and defensive uses that are extremely advantageous for the team if used effectively by the player controlling Zilean. It can be used to:
- Assist allies escape from ganks.
- Reposition themselves for better crowd control during team fights.
- Pair offensively with Chronoshift, creating a deadly combination that allows allies time to land devastating attacks while enemies cower beneath its power.
Zilean is a champion in League of Legends who is known for his versatility and high damage output. However, like all champions, Zilean has his weaknesses. In this article, we will explore the weaknesses of Zilean and how they can affect his performance in the game.
We will look at how his low mobility and low health pool can be exploited by enemies, as well as how his lack of crowd control abilities can be used against him. By understanding these weaknesses, players can learn how to better counter Zilean in their next game.
Lack of Mobility
One of Zilean’s weaknesses is a lack of mobility in comparison to other champions. His only method of movement is Eulogic Shift (W), which allows him to gain movement speed, but it is on a relatively long cooldown. As such, zoning and crowd control abilities can lay him up and make it difficult for him to turn fights in his favor. Moreover, since Eulogic Shift only lasts for a few seconds at maximum, even if he manages to escape danger with it, Zilean may not be able to fully realize the advantage gained. As such, Zilean players need to carefully choose the moments when they engage the enemy or try to retreat from dangerous situations.
Zilean also has no escapes built into his kit and relies heavily on his allies for support in team fights or skirmishes. When pushing ahead or attempting a difficult all-in maneuver, it is important he communicates with his team prior so they can help cover any potential retreats. Although the safety benefit may not always apply due to the extended cooldowns on his abilities; having an aware ally nearby can help tilt any unfavorable situations back into Zilean’s favor.
Besides this strategic disadvantage, Zilean lacks both physical and magical damage capabilities in terms of dealing direct DPS as most of his damage will come through bombs and slows:
- No escapes built into his kit
- Rely heavily on allies for support in team fights or skirmishes
- Needs to communicate with team prior to pushing ahead or attempting a difficult all-in maneuver
- Lacks both physical and magical damage capabilities
- Most of his damage comes through bombs and slows
Weak Early Game
Zilean’s weaknesses are primarily focused on his early game performance. He is very mana hungry and lacks waveclear, which makes it difficult for him to stay relevant in the early game. He is vulnerable to ganks due to his slow base movement speed, lack of an escape, and low health pool.
His kit offers few trading opportunities and requires careful positioning to maximize individual effectiveness.
At all stages of the game, Zilean needs sustained protection from his team, as he can be easily bursted down in fights due to his squishy nature and inability to engage safely. His ultimate also requires him to be in the thick of the fight for maximum impact, making him a potential target for enemy burst crowd control. Zilean does not provide any form of lane sustain either – and can be easily harassed by most common ADC matchups.
His skill-floor is relatively low due even if he underperforms early on; however overall effectiveness is tempered by a high skill-ceiling and strategic play pattern – primarily relying around teamfight positioning and ability usage timing/comboing.
Low Damage Output
One of the biggest weaknesses of playing as Zilean in League of Legends is that he does not have very much damage output. Zilean’s main form of damage dealing is his Time Bomb ability, which deals an initial burst of damage when placed on an enemy and detonates a second time to deal 30 (+20% AP) additional magic damage. While this burst can be very effective in setting up a gank or finishing off an enemy, it pales in comparison to most other mages who have access to more powerful spells that can deal significantly more burst damage.
In addition, Zilean lacks the ability to consistently poke opponents with auto-attacks, making it difficult for him to trade effectively compared to most other mages in lane.
Best Items for Zilean
Whether you’re new to League of Legends or have been playing for a while, playing Zilean well requires knowledge of what items are best to buy. There are a lot of items that work well on Zilean, and understanding which of these items give him the most power is key to being successful in game. Here, we will discuss the best items for Zilean and how to use them to maximize his potential:
Boots of Swiftness
Boots of Swiftness are a great choice for Zilean. With his passive, Time in a Bottle, Zilean can instantly restore some cooldowns and move around quickly, making Boots of Swiftness the right choice. These boots grant +50 movement speed and additional +10 movement speed when out of combat. The Tenacity passive Ability reduces the duration of stuns and slows by 35%, allowing Zilean to chase after enemies and make quick escapes when necessary. This makes Boots of Swiftness an excellent choice when playing Zilean in League of Legends.
Rabadon’s Deathcap is an essential item for Zilean, granting immense amount of Ability Power. Rabadon’s Deathcap amplifies all other Ability Power gained, resulting in an exponential increase in damage output. With 155 base Ability Power, this item gives a whopping 30% additional ability power to items with flat Ability Power such as Archangel’s Staff. As with all ability power items, it grants a 15% cooldown reduction to skills when fully stacked.
In addition to this, Rabadon’s Deathcap has additional passive Bonuses: Incarnation and Spellblade. Incarnation increases Zilean’s base ability power by 30% – allowing him to deal more damage from the start – while Spellblade grants bonus physical and magical damage on basic attacks and abilities after using an ability.
Overall, considering how important ability power is for boosting Zilean’s burst damage potential and his consistency in dealing massive amounts of spell-oriented damage on a regular basis makes Rabadon’s Deathcap the most important item for him.
Morellonomicon is a powerful magic item for the champion Zilean in the popular video game League of Legends. It provides a low-cost source of ability power for Zilean, as well as bonus cooldown reduction and reduced mana costs when using his abilities. The passive effect of this item is also extremely useful, granting Zilean an immense power boost whenever he kills one of his enemies. This makes Morellonomicon an essential tool for any competitive Zilean player’s inventory.
Morellonomicon’s other effects include:
- -15% Cooldown Reduction on all spells
- -10% Spell Vamp
- -15 Ability Power
- -Reduced Mana Cost on Abilities by 15%
- -Grants bonus 5 Magic Resist and 30 Health per level up to 99 (+21 Magic Resist and 126 Health at level 18)
- -Passive : Upon obtaining 40 Ability Power, converts 20% of damage taken from champions into true damage for up to 5 seconds (maximum 3 times increased). Recharges every 45 seconds with no cooldown reduction.
Best Strategies for Zilean
Zilean is a powerful champion in League of Legends and has many different playstyles depending on how you build and position him. Knowing when and how to use Zilean’s abilities, such as his Rewind and Time Warp spells, can give you a huge advantage in the game.
In this article, we’ll cover the best strategies for playing Zilean, his best builds and team compositions, and how you can counter him and play around him:
Harass Enemies with Q
Harassing enemies with Zilean’s Q, Time Bomb, is a great strategy for maximizing your damage output in team fights. Time Bomb’s low cooldown and its explosion on both cast and recast makes it one of the most powerful abilities in Zilean’s kit. When a target is afflicted with the Time Bomb, casting it again within 3 seconds will cause it to explode for additional damage, healing or shielding effects depending on how many bombs are present.
When using your Q, keep in mind that it can reach longer distances than most abilities so you should aim to place your bombs away from enemy creeps and structures to maximize their effectiveness. Additionally, Zilean can mark enemy champions more frequently than other similar champions since he can carry up to three time bombs at once with fully maxed out Time Lord stacks. Use this to your advantage; try focusing on chipping down enemy health bars during lane phase by placing bombs where they are least expecting them and causing unnecessary pressure on enemies so your team can capitalize off of those situations later in game.
Time Warp Allies with W
Utilizing Zilean’s W, Time Warp, is an important tool for those looking to craft a viable strategy with the Chronokeeper. Time Warp provides an ally with a large increase in move speed that lasts for a few seconds before fading. This helps allies close in on enemies or flee from engagement when needed.
Due to the nature of this ability, it’s best used on champions like ADC/Marksmen, Assassin’s, fighters and tanks that excel at getting up-close and personal with their opponents. With the power of movement speed and Time Warp active, allies can chase down fleeing targets or escape dangerous situations with ease. Having this level of momentum control will open up opportunities and create some serious headaches for your opponents.
When possible it is best to apply a charge of this spell twice on your intended target during team fights for maximum efficiency; however if you are unable to recharge your ability between casts then one charge should be enough if applied correctly. Finally, do not underestimate Time Warp’s application either early game or late game as movespeed provides invaluable tools during laning phase when maneuvering around minions and players alike come into play as well providing momentary reprieve in teamfight repositioning allowing allies to flee (or warps) quickly without losing too much health points while doing so!
Use E to Slow Enemies and Escape
Zilean is a great solo-laner in League of Legends with many tools at his disposal to overwhelm enemies fights and help teammates out. His E ability, Time Warp, gives him the ability to slow or speed up friendly or enemy champions respectively. Using his E ability on enemies that are trying to dive or focus you down can be great for your survivability and in conjunction with flash can give you enough time to escape any sticky situations.
Time Warp not only slows down your enemies but also increases their casting time which makes them very vulnerable during teamfights. In addition, Zilean’s Q grants him bonus attack speed which when combined with his E can give him a great advantage when engaging fights against enemies as well as disengaging from them. The bonus attack speed quaffiness up the rest of your cooldowns, allowing you to use all of your abilities quickly and efficiently, giving you an edge in any fight.
Time Warp can not only be used offensively but also defensively by using it on your allies so they won’t get caught out in those intense teamfights or ganks mid-lane. Zilean’s ultimate is a global heal that allows him to share his health pool with multiple allies at once so they do more damage without taking too much damage themselves, giving you the edge in many different scenarios like teamfights, chases, sieges and tower dives. Use this powerful combination of abilities to capitalize on enemy mistakes and come out on top of any situation!
Frequently Asked Questions
Q1: What abilities does Zilean have in LoL?
A1: Zilean has the following abilities: Time Warp, Time Bomb, Chronoshift, and Rewind. Time Warp increases the movement speed of an ally champion or himself. Time Bomb deals magic damage and slows enemies. Chronoshift revives a dead ally champion and gives them bonus health. Rewind reduces Zilean’s cooldowns.
Q2: What is Zilean’s role in LoL?
A2: Zilean is a support champion in League of Legends. His primary role is to provide assistance to his team in fights by providing crowd control and aiding in objective control. He is also able to provide healing to his allies, as well as revive them with Chronoshift.
Q3: What is Zilean’s playstyle in LoL?
A3: Zilean’s playstyle is that of a utility-based support champion. He should be focusing on keeping his allies alive and providing them with the resources they need to succeed in fights. He should also be controlling objectives such as dragon and Baron Nashor, as well as providing vision control with his Time Bomb.

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