LED light module for omnidirectional luminaire

Information

  • Patent Grant
  • 8360615
  • Patent Number
    8,360,615
  • Date Filed
    Wednesday, October 31, 2007
    16 years ago
  • Date Issued
    Tuesday, January 29, 2013
    11 years ago
Abstract
A light module including a single light emitting diode (LED) and a rotationally symmetrical reflective light transformer providing an omnidirectional pattern with a pre-calculated intensity distribution. In alternative embodiments the light module may consist of a plurality of LEDs and the reflective light transformer, having plurality of identical segments, provides an omnidirectional pattern with a pre-calculated intensity distribution as a result of superposition of the limited angle pattern reflected by each segment. In order to provide high efficiency the light transformer reflective surface profile is designed using a given LED's spatial intensity distribution and required intensity distribution across the emitted omnidirectional pattern as a design parameters.
Description
BACKGROUND OF THE INVENTION

1. Field of Invention


The present invention relates generally to light sources utilizing light emitting diodes (LEDs). In particular, the present invention relates to aviation signal lights providing omnidirectional patterns, such as a runway edge light, obstruction light and similar, where requirements for specific light distribution across the pattern are mandatory.


2. Discussion of Relevant Prior Art


Signal lights such as airfield lights and aviation obstruction lights require certification by the government (Federal Aviation Authority) or international organizations (ICAO). These specifications identify photometrics in detail. For example, ICAO specifications for medium intensity flashing red obstruction lights call for peak intensity minimum 2000 candelas + or −25% at horizontal level and allow maximum intensity limited by 75% of peak at −1%, with beam spread 3°. Application of solid-state technology (LEDs) as a light source because of the low power consumption, long lifetime, and smaller and lighter-weight design, makes it possible to overcome major disadvantages of conventional light sources, such as incandescent and halogen lamps. However, the solid-state technology's total efficiency in a luminaire, in practice, does not exceed 60%. This is why the performance of LED-based signal lights depends on implanted optics, specifically secondary optics light transformers which transforms light emitted by LEDs into light patterns required by specifications. In order to increase LED luminaire performance up to 85% to 90%, non-imaging light transformers, refractive and reflective (including total internal reflection properties) can be implemented. The method of design based on use, both the specifics parameters of the particular light source (such as LED spatial light distribution) and required light distribution across the pattern as a light transformer's design parameters are described in detail in U.S. Pat. No. 6,543,911.


BRIEF SUMMARY OF THE INVENTION

The present invention provides a LED light module (combination of LED and optic) based on light transformer with reflective surface profile (including total internal reflection surface profile) being calculated by taking into account specific LED parameters (spatial intensity distribution), required intensity distribution across emitted pattern and the geometrical relation of components. A single or multiple LED can be used to produce omnidirectional light distribution in a horizontal plane wherein the angle in the vertical plan remains limited. The LED module also can include an optical window and LED heatsink.


According to one aspect of the present invention the light module comprises at least one LED emitting light with a wide divergency and rotationally symmetrical reflective light transformer having a vertex located on the light transformer's axis of symmetry, which is coincidental with the LED axis. The light transformer reflective surface profile is determined by LED spatial intensity distribution across emitted pattern and light module geometry. The light transformer collects light emitted by the LED, compresses, redistributes, and directs the collected light with high efficiency in an omnidirectional pattern with pre-calculated intensity distribution.


According to the second aspect of the present invention, which is related to particular case when angular distribution is smaller than LED half-angle distribution, the reflective light transformer surface includes a plurality of circular facets, each facet profile being determined by LED spatial intensity distribution, required intensity distribution across emitted pattern and light module geometry. Each facet collects a portion of the light emitted by the LED, compresses, redistributes, and directs the collected light with efficiency in the same limited angle pattern in a vertical plane and a superposition of light pattern from all facets resulting in an omnidirectional pattern with pre-calculated intensity distribution.


In an alternative embodiment the light module comprising a plurality of LEDs, each LED emitting light with wide divergency, and reflective light transformer including a plurality of identical concave curved segments, each segment corresponds to an LED. The LED axes are parallel to the reflective light transformer axis. In a plane perpendicular to the LED optical axes the LED form a substantially circular array with the center of the circle located on the reflective light transformer axis. The concave curved segment's reflective surface profile is determined by the LED spatial intensity distribution, required intensity distribution across the emitted pattern and light module geometry. Each segment of the reflective light transformer collects light emitted by an associated LED, compresses, redistributes and directs the collected light with high efficiency in a limited angle in the plane perpendicular to the LED optical axis and superposition of pattern from a plurality of segments providing an omnidirectional pattern with a pre-calculated intensity distribution.


In another similar embodiment, the reflective light transformer's concave curved segment's surface includes a plurality of facets. Each facet reflective surface profile is determined by the corresponding portion of the LED spatial intensity distribution, required intensity distribution across emitted pattern and light module geometry. Each facet collects a portion of the light emitted by the corresponding LED from a circular array, compresses, redistributes, and directs the collected light with high efficiency in a limited angle pattern in the vertical plane and superposition of the light pattern from all facts in the vertical plane and all segments in the plane perpendicular to the LED optical axes resulting in an omnidirectional pattern with pre-calculated intensity distribution.


In another embodiment, the light module comprising a plurality of LEDs, each LED emitting light with wide divergence and a reflective light transformer including a plurality of identical concave curved segments. The LEDs optical axes are parallel to the reflective light transformer axis and in a plane perpendicular to LEDs optical axes wherein the LEDs are forming substantially polygon array with an equal number of LEDs in each polygon side, and the number of polygon sides are equal to number of concave curved segments, and each segment corresponds to a polygon side. The concave curved segments' reflective surface profile is determined by a combination of the spatial intensity distribution of all the LEDs located on a corresponding polygon side, required intensity distribution across emitted pattern and light module geometry. Each segment of the reflective light transformer collects light emitted by all the LEDs located on the corresponding polygon side, compresses, redistributes and directs collected light with high efficiency in a limited angle pattern in a plane perpendicular to the LEDS optical axes, and superposition of the pattern from a plurality of segments provides an omnidirectional pattern with pre-calculated intensity distribution.


Yet in another similar embodiment, the reflective light transformer's concave curved segment's surface consists of a plurality of facets. The facet's reflective surface profile is determined by combining the spatial intensity distribution of all LEDs located on the corresponding polygon side, required intensity distribution across emitted pattern and light module geometry. Each facet collects a portion of the light emitted by the LEDs located on the corresponding polygon side, compresses redistributes and directs collected light with high efficiency in a limited angle patter in the plane perpendicular to the LEDs optical axes and a superposition of the light pattern from all facets and all the segments resulting in an omni-directional pattern with pre-calculated intensity distribution.





BRIEF DESCRIPTION OF THE DRAWINGS

A clear understanding of the various advantages and features of the present invention, as well as the construction and operation of conventional components and mechanisms associated with the present invention, will become more readily apparent by referring to the exemplary, and therefore non-limiting, embodiments illustrated in the following drawings which accompany and form a part of this patent specification.



FIG. 1 is a perspective view of the light module for the omnidirectional luminaire.



FIG. 2 is an illustration of the method of reflective transformer design.



FIG. 3 is a cross-sectional diagram of the light module according to one embodiment.



FIG. 4 is a cross-sectional diagram of the light module according to another embodiment.



FIGS. 5(
a) and (b) are top view and perspective view of the light module according to another embodiment.



FIGS. 6(
a) and (b) are top view and perspective view of the light module according to another embodiment.



FIGS. 7(
a) and (b) are top view and perspective view of the light module according to another embodiment.



FIGS. 8(
a) and (b) are top view and perspective view of the light module according to another embodiment.





DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS


FIG. 1 is a perspective view of a light module for the omnidirectional luminaire 10. The light module 10 may comprise one or more LEDs 100 and a reflective light transformer 200. The light module 10 also can include an optical omnidirectional window 20 and a LED heat sink 30.


In operation, the light emitted by the LED 100 with given spatial intensity distribution is reflected by the reflective light transformer surface 230, transformed and directed omnidirectionally in 360° pattern 40, with a pre-calculated intensity distribution. In order to achieve high efficiency (80% and higher) the light transformer should be designed to take into account both the specifics of the light sources (such as the LED spatial intensity distribution) and the desirable light distribution across the emitted pattern.


The method of reflective light transformer surface profile design using light source spatial intensity distribution and required intensity distribution across the emitted pattern as design conditions is described in detail in U.S. Pat. No. 6,543,911 and illustrated in FIG. 2.


The optical axis 110 of light source (LED) 100 is coincidental with the axis of symmetry 210 of rotationally symmetrical reflective light transformer 200, having vertex 220 located on the axis of symmetry. The reflective light transformer's surface profile 230 is calculated as a step-by-step iterative procedure using a given light source spatial distribution in the emitted pattern. For example, arbitrary point 231 of reflective transformer surface reflects ray 120, emitted by light source 100 on an angular coordinate 130 relative to light source optical axis 110, belonging to the light source domain. To transfer the portion of the light energy corresponding to this direction into an emitted pattern, the reflected ray 250 must be reflected on an angular coordinate 260 relative to axis 241 in a pattern domain, which is orthogonal to the axis of symmetry 210. The orthogonal coordinates 211 and 241 are parallel to coordinates 210 and 240 respectively and the origin located in arbitrary point 231. As a result, the curvature of the reflective transformer surface profile in the arbitrary point 231 will be determined by the angular coordinate 280 of tangent 270 to the profile in the arbitrary point 231, relative to the transformer axis of symmetry 210.



FIG. 3 is a cross-sectional diagram of the light module 10 according to a preferred embodiment. The light module 10 can include a single LED 100 and a rotationally symmetrical reflective light transformer 200, having a vertex located on the light transformer axis of symmetry 210, which is coincidental with the LED 100 optical axis 110. In operation, a ray 121 emitted by the LED 100 at angular coordinate 131 with respect to LED's 100 optical axis 110 reflects from the arbitrary point 231 of light transformer's 200 reflective surface 230 as a ray 251, which is directed in a pattern domain 41 at an angular coordinate 261 with respect to axis 241 orthogonal to the light transformer's 200 axis of symmetry 210. Accordingly, a ray 122 emitted by the LED 100 at angular coordinate 132 with respect to the LED's 100 optical axis 110 reflects from arbitrary point 232 of light transformer's 200 reflective surface 230 as a ray 252, which is directed in pattern domain 41 at an angular coordinate 262 with respect to axis 242 orthogonal to the light transformer's 200 axis of symmetry 210. As a result, the reflective light transformer 200 redistribute given LED 100 intensity distribution from angular coordinate 131 to angular coordinate 132 into a pre-calculated pattern 41 with intensity distribution from angular coordinate 261 to angular coordinate 262.



FIG. 4 is a cross-sectional diagram of the light module 10 according to another embodiment. The light module 10 can include a single LED 100 and a rotationally symmetrical light transformer 200, having a vertex 220 located on the light transformer axis of symmetry 210, which is coincidental with the LED optical axis 110. The light transformer's 200 reflective surface consists of a plurality of circular facets 291, 292, 293, each facet profile is determined by the corresponding portion of the LED spatial intensity distribution, required intensity distribution across the emitted pattern, and the light module geometry. In operation, a portion of the light emitted by the LED 100 is redirected by each facet into pattern domain 42. For example, ray 111 is substantially coincident with the LED optical axis 110 and reflected from the vertex 220 as a ray 253. A ray 112, emitted by LED 100, reflects from the point 233 (which belongs to facet 291), as a ray 256. As a result, a portion of the light emitted by LED 100 in the spatial domain between rays 111 and 112 is redistributed and redirected in pattern domain 42. Similar, ray 113, which is almost coincident with ray 112 reflects from point 234 (which is next to point 233, but in contrast belongs to facet 292), as a ray 254. Further ray 114 reflects from point 235 as a ray 257, ray 115 reflects from point 236 (belonging to facet 293), as a ray 255, ray 116 reflects from point 237 as a ray 258, and so on. As a result, each facet collects a corresponding portion of the light emitted by the LED 100, compresses, redistributes and directs the collected light with high efficiency in the pattern domain 42 and superposition of light pattern from all of the facets results in an omnidirectional pattern with a pre-calculated intensity distribution.



FIGS. 5 (a) and (b) are top and perspective views respectively of the light module according to another embodiment. Light module 300 comprising a plurality of LEDs 400 and reflective light transformer 500, which consists of a plurality of identical concave curved segments 510, each segment corresponds to a LED 400. LED's 400 axes are parallel to the reflective transformer axis 520. The concave curved segment's reflective surface profile is determined by the LED 400 spatial intensity distribution, required intensity distribution across emitted pattern and light module 300 geometry. A surface profile of each of the concave curved segments is defined by an equation R[(α,β); θ]=F{Is(α,β); Ip(θ)} where R[(α,β);θ] is a surface profile of each of the concave curved segments, α, β are two dimensional angular coordinates belonging to a light source domain, θ is an angular coordinate relative to an orthogonal axis to an axis of symmetry of the reflective light transformer belonging to a pattern domain, Is(α,β) is spatial intensity distribution of the light source, Ip(θ) is a required intensity distribution across an emitted pattern, and F{ } is an arbitrary function determined by a method of design. Each segment 510 of the reflective light transformer 500 collects light emitted by corresponding LED 400, compresses, redistributes and directs the collected light with high efficiency in a limited angle pattern 600 in the plane perpendicular to the LEDs 400 optical axes and superposition of pattern 600 from the plurality of segments 510 provides an ominidirectional pattern with a pre-calculated intensity distribution.



FIGS. 6 (a) and (b) are top and perspective views respectively of the light module 310 according to another embodiment. The light module 310 comprising a plurality of LEDs 400 and a reflective light transformer 500, which consists of a plurality of identical concave curved segments 510, each segment corresponds to a LED 400. The LED's 400 axes are parallel to the reflective transformer axis 520. In a plane perpendicular to the LED 400 optical axes, the LEDs form a substantially circular array 410 with the center of the circle 420 located on the reflective light transformer's 500 axis 520. Each reflective light transformer's 500 concave curved segments 510 surface consists of a plurality of facets 530. The facets reflective surface profile is determined by the corresponding portion's required intensity distribution across emitted pattern and light module 310 geometry. Each facet 530 collects a portion of the light emitted by the corresponding LED 400 from the circular array 410, compresses, redistributes and directs collected light with high efficiency in a limited angle pattern 610 in the vertical plane, and superposition of light pattern 610 from all facets and light pattern 600 from all segments resulting in an omnidirectional pattern with a pre-calculated intensity distribution.



FIGS. 7(
a) and (b) are top and perspective views respectively of the light module 700 according to another embodiment. The light module 700 comprising a plurality of LEDs 400 and a reflective light transformer 800, which consists of a plurality of identical concave curved segments 810. The LED's axes are parallel to reflective transformer 800 axis 820. In a plane perpendicular to LEDs optical axes LEDs 400 form substantially a polygon array 430 with an equal numbers of LEDs in each polygon side, the number of polygon sides equal to the number of concave curved segments 810, and each segment 810 corresponds to a side of the polygon array 430. The polygon array center 440 located on reflective transformer's 800 axis 820. The concave curved segment's reflective surface profile is determined by combining the spatial intensity distribution of all the LEDs located on the corresponding polygon side, required intensity distribution across emitted pattern and the light module 700 geometry. Each segment 810 of the reflective light transformer 800 collects light emitted by all the LEDs, compresses, redistributes and directs the collected light with high efficiency in a limited angle pattern 900 in a plane perpendicular to the LEDs optical axes and superposition of pattern 900 from plurality of segments 800 providing an ominidirectional pattern with a pre-calculated intensity distribution.



FIGS. 8(
a) and (b) are top and perspective views respectively of the light module 710 according to another embodiment. The light module 710 comprising a plurality of LEDs 400 and a reflective light transformer 800, which consists of a plurality of identical concave curved segments 580. The LED's 400 axes are parallel to the reflective transformer 800 axis 820. In a plane perpendicular to LEDs optical axes, the LED 400 form a substantially polygon array 430 with equal numbers of LEDs in each polygon side, the number of polygon sides equal to the number of concave curved segments 810, and each segment 810 corresponding to a side of the polygon array 430. The polygon array 430 center 440 is located on the reflective transformer's 800 axis 820. The concave curved segment's 810 surface profile consists of a plurality of facets 830. The facet reflective surface profile is determined by a portion of the combined spatial intensity distribution of all the LEDs located on the corresponding polygon side, the required intensity distribution across the emitted pattern and the light module 710 geometry. A surface profile of each of the concave curved segments is defined by an equation R[(α,β); θ]=F{ΣnIs(α,β); Ip(θ)} where R[(α,β);θ] is a surface profile of each of the concave curved segments, α, β are two dimensional angular coordinates belonging to a light source domain, θ is an angular coordinate relative to an orthogonal axis to an axis of symmetry of the reflective light transformer belonging to a pattern domain, ΣnIs(α,β) is a combined spatial intensity distribution of all the LEDs located on a corresponding polygon side, n is a number of the LEDs on a polygon side, Ip(θ) is a required intensity distribution across an emitted pattern, and F{ } is an arbitrary function determined by a method of design. Each facet 830 collects a portion of the light emitted by all the LEDs located on the corresponding side of the polygon array 430, compresses, redistributes and directs the collected light with high efficiency in a limited angle pattern 910 in the vertical plane and superposition of light pattern 910 from all facets 830 in the vertical plane, and all limited angle pattern 900 in the plane perpendicular to the LEDs optical axes from a plurality of segments 810 provides an ominidirectional pattern with a pre-calculated intensity distribution.


While we have shown and described the preferred embodiments of my invention, it will be understood that the invention may be embodied otherwise than as herein specifically illustrated or described, and that certain changes in form and arrangement of parts and the specific manner of practicing the invention may be made within the underlying idea or principles of the invention.

Claims
  • 1. A light module comprising: at least one light emitting diode (LED) for emitting light with wide divergence; anda reflective light transformer being rotationally symmetrical and having a vertex located on an axis of symmetry coincident with an optical axis of the LED,wherein in order to obtain high efficiency, a surface profile of the reflective light transformer is defined by an equation R(α;θ)=F{Is(α);Ip(θ)}wherein R(α;θ) is the surface profile of the reflective light transformer, α is an angular coordinate relative to an axis of symmetry of the reflective light transformer belonging to a domain of the LED, θ is an angular coordinate relative to an orthogonal axis to the axis of symmetry belonging to a pattern domain, Is is a light source spatial intensity distribution, Ip(θ) is a required intensity distribution across an emitted pattern, and F{ } is an arbitrary functional determined by a method of design, wherein the reflective light transformer collects light emitted by the LED, compresses, redistributes, and directs collected light with high efficiency in an omnidirectional pattern with pre-calculated intensity distribution.
  • 2. The light module according to claim 1, wherein a surface of the reflective light transformer comprises a plurality of circular facets, each facet collects a portion of the light emitted by the LED, compresses, redistributes and directs the collected light with high efficiency in a same omnidirectional pattern, and wherein superposition of a light pattern from all facets results in an omnidirectional pattern with a pre-calculated intensity distribution.
  • 3. A light module comprising: at least one light emitting diode (LED); anda reflective light transformer being rotationally symmetrical and having a vertex located on an axis of symmetry coincident with an optical axis of the LED,wherein a surface profile of the reflective light transformer is designed based on a function of a light source spatial intensity distribution and a pre-calculated intensity distribution across a predetermined pattern,wherein the reflective light transformer collects rays of the light emitted by the at least one LED, redirects and redistributes the rays where some of the rays cross or merge paths, in the predetermined pattern.
  • 4. A light module comprising: at least one light emitting diode (LED); anda reflective light transformer being rotationally symmetrical and having a vertex located on an axis of symmetry coincident with an optical axis of the LED,wherein a surface profile of the reflective light transformer is designed based on a function of a light source spatial intensity distribution and a pre-calculated intensity distribution across a predetermined pattern,wherein the reflective light transformer collects rays of the light emitted by the at least one LED and transforms the collected light with an efficiency greater than or equal to 80 percent.
CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of and claims priority to U.S. patent application Ser. No. 10/277,230, filed Oct. 21, 2002 now U.S. Pat. No. 7,503,669; which is a continuation-in-part of U.S. patent application Ser. No. 09/566,521, filed May 8, 2000, now U.S. Pat. No. 6,543,911 and is herein incorporated by reference.

US Referenced Citations (79)
Number Name Date Kind
1676463 Ryan Jul 1928 A
1888995 Matter Nov 1932 A
2215900 Bitner Sep 1940 A
2589569 Peter et al. Mar 1952 A
3610912 Schwartz Oct 1971 A
3852584 Levin Dec 1974 A
3875561 Scarpino et al. Apr 1975 A
4337759 Popovich et al. Jul 1982 A
4355350 Mader Oct 1982 A
4382274 De Backer et al. May 1983 A
4617768 Gebelius Oct 1986 A
4678269 Pace Jul 1987 A
4767172 Nichols et al. Aug 1988 A
4768133 Simons et al. Aug 1988 A
4826273 Tinder et al. May 1989 A
4915484 Yamamoto Apr 1990 A
5103381 Uke Apr 1992 A
5105347 Ruud et al. Apr 1992 A
5134550 Young Jul 1992 A
5136483 Schoniger et al. Aug 1992 A
5161874 Benes Nov 1992 A
5180221 Yoder Jan 1993 A
5289356 Winston Feb 1994 A
5321717 Adachi et al. Jun 1994 A
5363469 Elderfield Nov 1994 A
5408395 Schmid et al. Apr 1995 A
5467335 Braat Nov 1995 A
5469347 Duve et al. Nov 1995 A
5471371 Koppolu et al. Nov 1995 A
5553174 Snyder Sep 1996 A
5556189 Wallis Sep 1996 A
5575550 Appeldorn et al. Nov 1996 A
5592578 Ruh Jan 1997 A
5621829 Ford Apr 1997 A
5629996 Rizkin et al. May 1997 A
5642933 Hitora Jul 1997 A
5661828 Riser et al. Aug 1997 A
5694112 VannRox et al. Dec 1997 A
5704709 Zwick et al. Jan 1998 A
5707130 Zwick et al. Jan 1998 A
5775792 Wiese Jul 1998 A
5785410 Branson, Sr. Jul 1998 A
5800050 Leadford Sep 1998 A
5813743 Naka Sep 1998 A
5854872 Tai Dec 1998 A
5926320 Parkyn, Jr. et al. Jul 1999 A
5929788 Vukosic Jul 1999 A
5931575 Yamamoto et al. Aug 1999 A
5951144 Gavigan et al. Sep 1999 A
6013985 Green et al. Jan 2000 A
6028535 Rizkin et al. Feb 2000 A
6048083 McDermott Apr 2000 A
6075650 Morris et al. Jun 2000 A
6097549 Jenkins et al. Aug 2000 A
6107916 Beck et al. Aug 2000 A
6132072 Turnbull et al. Oct 2000 A
6155703 Rizkin et al. Dec 2000 A
6168294 Erni et al. Jan 2001 B1
6210017 Miura et al. Apr 2001 B1
6217197 Siminovitch et al. Apr 2001 B1
6234646 Ito May 2001 B1
6334699 Gladnick Jan 2002 B1
6380864 Richard Apr 2002 B1
6402347 Maas et al. Jun 2002 B1
6450661 Okumura Sep 2002 B1
6464373 Petrick Oct 2002 B1
6547423 Marshall et al. Apr 2003 B2
6565239 Rizkin et al. May 2003 B2
6568827 Forster May 2003 B2
6637921 Coushaine Oct 2003 B2
6899443 Rizkin et al. May 2005 B2
7160004 Peck Jan 2007 B2
7568821 Peck et al. Aug 2009 B2
20020136027 Hansler et al. Sep 2002 A1
20030189832 Rizkin et al. Oct 2003 A1
20030193807 Rizkin et al. Oct 2003 A1
20050190559 Kragl Sep 2005 A1
20060209541 Peck Sep 2006 A1
20060268549 Oehlke Nov 2006 A1
Foreign Referenced Citations (27)
Number Date Country
87107021 Apr 1988 CN
2201574 Jul 1973 DE
4128995 Aug 1991 DE
4129094 Sep 1991 DE
4305585 Feb 1993 DE
4243175 Jun 1994 DE
19507234 Feb 1995 DE
19507234 Sep 1996 DE
29708858 May 1997 DE
19647094 Jun 1997 DE
19728354 Jan 1999 DE
19739173 Mar 1999 DE
0635744 Oct 1993 EP
0766115 Sep 1996 EP
0780265 Dec 1996 EP
0798788 Jan 1997 EP
0798788 Feb 1997 EP
0762515 Mar 1997 EP
0942225 Mar 1999 EP
61147585 Jul 1986 JP
61147585 Jul 1986 JP
63033879 Feb 1988 JP
1125719 May 1989 JP
9901695 Jul 1997 WO
9909349 Aug 1997 WO
0024062 Apr 2000 WO
WO 0024062 Apr 2000 WO
Non-Patent Literature Citations (18)
Entry
Trigonometric functions. (2003) In the Penguin Dictionary of Mathematics.
Office Action in U.S. Appl. No. 10/316,642 (USP 6,814,470), dated Feb. 20, 2004.
Notice of Allowability in U.S. Appl. No. 10/316,642 (USP 6,814,470), dated Aug. 10, 2004.
Examiner Interview in U.S. Appl. No. 10/316,642 (USP 6,814,470), dated Aug. 10, 2004.
Notice of Allowability in U.S. Appl. No. 10/620,524 (USP 6,902,291), dated Dec. 16, 2004.
Notice of Allowability in U.S. Appl. No. 11/930,423, dated Dec. 9, 2009.
Notice of Allowability in U.S. Appl. No. 10/391,327 (USP 6,951,418), dated Mar. 22, 2005.
Office Action in U.S. Appl. No. 10/391,327 (USP 6,951,418), dated Dec. 12, 2003.
Office Action in U.S. Appl. No. 10/391,327 (USP 6,951,418), dated Jun. 9, 2004.
Notice of Allowability in U.S. Appl. No. 10/408,923 (USP 6,899,443), dated Jan. 24, 2005.
Office Action in U.S. Appl. No. 10/408,923 (USP 6,899,443), dated Jul. 13, 2004.
Communication from EPO related to European Patent Application No. 06016404.3, dated Nov. 30, 2009.
EPO Examination in 019357631, dated Apr. 29, 2005.
EPO Search Report in 019357631, dated Dec. 29, 2004.
International Search Report for PCT/US04/23037, dated Mar. 28, 2005.
International Search Report for PCT/US03/33227, dated Sep. 1, 2009.
International Search Report for PCT/US2008/081981, dated Feb. 2, 2009.
Notice of Allowability in U.S. Appl. No. 11/930,423, dated Mar. 23, 2010.
Related Publications (1)
Number Date Country
20080192480 A1 Aug 2008 US
Continuation in Parts (2)
Number Date Country
Parent 10277230 Oct 2002 US
Child 11933248 US
Parent 09566521 May 2000 US
Child 10277230 US