Laser velocimeter

• US 4,859,055 A
• Filed: 05/17/1988
• Issued: 08/22/1989
• Est. Priority Date: 05/17/1988
• Status: Expired due to Fees

• Current Assignee: Lockheed Missiles and Space Co Inc (Martin Marietta Corporation)
• Original Assignee: Lockheed Missiles and Space Co Inc (Martin Marietta Corporation)
• Inventors: Gal, George, Morrow, Howard E.
• Primary Examiner(s): Tarcza, Thomas H.
• Assistant Examiner(s): Wallace, Linda J.
• Application Number:
  US07/194,781
• Time in Patent Office: 462 Days
• Field of Search: 356/5, 356/28, 356/28.5, 73/861.05, 73/861.06, 350/463, 350/469, 350/473
• US Class Current: 356/28
• CPC Class Codes: G01P 5/20 using particles entrained by a fluid stream G01P5/22 takes precedence

Abstract

An aircraft velocimeter comprises means for projecting three pairs of independently generated ribbon-shaped laser beams to a measurement volume located at a predetermined distance from the aircraft with a predetermined separation being maintained between the two ribbon-shaped laser beams of each pair at the measurement volume. The times of flight of atmospheric aerosol particles between the two ribbon-shaped laser beams of corresponding pairs of laser beams are measured as the aerosol particles pass through the measurement volume. From the predetermined distance between the two ribbon-shaped laser beams of each pair and the measured time of flight of an aerosol particle across that predetermined distance, a component of velocity of the aerosol particle relative to the aircraft is calculated for each pair of ribbon-shaped laser beams. From the three components of velocity corresponding to the three pairs of ribbon-shaped laser beams projected to the measurement volume, a vector measurement of the velocity of the aircraft relative to atmospheric particles in the surrounding atmosphere is obtained using an on-board computer programmed with a conventional algorithm.

Claims

1. A method for determining velocity of an object relative to particles in a gaseous mass surrounding said object, said method comprising the steps of:

(a) projecting a plurality of pairs of beams of optical radiation from said object to a measurement volume that is spaced apart from said object, each pair of said plurality of pairs of beams consisting of two beams that are generally ribbon-shaped and substantially parallel to each other and that are separated from each other by a predetermined distance at the measurement volume, the two beams of each pair of said plurality of pairs of beams being nonparallel to the beams of every other pair of said plurality of pairs of beams at the measurement volume, the particles in said gaseous mass at the measurement volume scattering optical radiation from the two beams of each pair of said plurality of pairs of beams;

(b) gathering a portion of the optical radiation scattered by said particles in said gaseous mass surrounding said object from the two beams of each pair of said plurality of pairs of beams at the measurement volume;

(c) discriminating the gathered optical radiation scattered from each of the two beams of each pair of said plurality of pairs of beams at the measurement volume from the gathered optical radiation scattered from every other beam of said plurality of pairs of beams at the measurement volume;

(d) generating a plurality of pairs of electrical signals, each electrical signal being related to the scattering of optical radiation from a corresponding beams of said plurality of pairs of beams at the measurement volume;

(e) processing said plurality of pairs of electrical signals to measure time intervals required for said particles to traverse the predetermined distance between the two beams of each pair of said plurality of pairs of beams at the measurement volume, and to calculate components of velocity of said particles relative to said object; and

(f) determining a velocity vector for said object relative to said particles from said calculated components of velocity.

2. The method of claim 1 wherein the step of projecting said plurality of pairs of beams of optical radiation from said object to the measurement volume comprises generating three pairs of ribbon-shaped laser beams, and focussing the two beams of each of said three pairs of beams so as to be separated from each other by said predetermined distance on a projection plane at the measurement volume.

3. The method of claim 2 wherein each beam of said three pairs of ribbon-shaped laser beams is produced by:

(a) energizing a corresponding semiconductor laser device having an active region with an edge portion that emits said beam so as to have a generally rectangular cross section, a first dimension of said cross section being larger than a second dimension of said cross section, said second dimension being perpendicular to said first dimension;

(b) anamorphically expanding said beam to provide a greater magnification for said first cross-sectional dimension than for said second cross-sectional dimension, thereby causing said beam to assume a generally ribbon-shaped configuration;

(c) focussing the anamorphically expanded beam onto an intermediate focal plane so as to produce an elongate image of said edge portion of said active region of said semiconductor laser device; and

(d) re-imaging said elongate image of said edge portion of said active region of said semiconductor laser device on said projection plane.

4. The method of claim 3 wherein said three pairs of ribbon-shaped laser beams intersect said projection plane in three corresponding pairs of line segments, the line segments corresponding to a particular pair of said three pairs of ribbon-shaped laser beams being parallel to each other and being nonparallel to the line segments corresponding to the other two pairs of said three pairs of ribbon-shaped laser beams, the components of velocity of said particle relative to said object being referred to a three-dimensional coordinate system whose axes are determined by respective orientations of said three corresponding pairs of line segments.

5. The method of claim 1 wherein the step of gathering a portion of the optical radiation scattered from each beam of each of said plurality of pairs of beams at the measurement volume comprises collecting said portion of the radiation scattered from each beam, and focussing said portion of the radiation so collected onto a corresponding detection means.

6. The method of claim 5 wherein the step of discriminating the gathered radiation scattered from each of the two beams of each pair of said plurality of pairs of beams at the measurement volume from the gathered radiation scattered from every other beam of said plurality of pairs of beams at the measurement volume comprises positioning a plurality of field stops so that each field stop transmits the radiation scattered from a corresponding one of said beams at the measurement volume.

7. An apparatus for determining velocity of an object relative to particles in a gaseous mass surrounding said object, said apparatus comprising:

(a) means for projecting a plurality of pairs of beams of optical radiation from said object to a measurement volume that is spaced apart from said object, each pair of said plurality of pairs of beams consisting of two beams that are generally ribbon-shaped and substantially parallel to each other and that are separated from each other by a predetermined distance at the measurement volume, the two beams of each pair of said plurality of pairs of beams being nonparallel to the beams of every other pair of said plurality of pairs of beams at the measurement volume, the particles in said gaseous mass at the measurement volume thereby scattering optical radiation from the two beams of each pair of said plurality of pairs of beams;

(b) means for gathering a portion of the optical radiation scattered by said particles in said gaseous mass surrounding said object from the two beams of each pair of said plurality of pairs of beams at the measurement volume;

(c) means for discriminating the gathered optical radiation scattered from each of the two beams of each pair of said plurality of pairs of beams at the measurement volume from the gathered optical radiation scattered from every other beam of said plurality of pairs of beams at the measurement volume;

(d) means for generating a plurality of pairs of electrical signals, each electrical signal being related to the scattering of optical radiation from a corresponding beam of said plurality of pairs of beams at the measurement volume;

(e) means for processing said plurality of pairs of electrical signals to measure time intervals required for said particles to traverse the predetermined distance between the two parallel beams of each pair of said plurality of pairs of beams at the measurement volume, and to calculate components of velocity of said particles relative to said object; and

(f) means for determining a velocity vector for said object relative to said particles from said calculated components of velocity.

8. The apparatus of claim 7 wherein said means for projecting said plurality of pairs of beams of optical radiation from said object to the measurement volume comprises means for generating three pairs of ribbon-shaped laser beams and for focussing the two beams of each of said three pairs of beams so as to be separated from each other by said predetermined distance on a projection plane at the measurement volume.

9. The apparatus of claim 8 wherein said means for generating said three pairs of ribbon-shaped laser beams and for focussing the two beams of each of said three pairs of beams on the projection plane comprises:

(a) three pairs of semiconductor laser devices, each of said semiconductor laser devices having an active region with an edge portion that emits a corresponding beam of generally rectangular cross section, a first dimension of said cross section being larger than a second dimension of said cross section, said second dimension being perpendicular to said first dimension;

(b) means for anamorphically expanding each beam of said three pairs of beams emitted by the edge portions of the active regions of said three corresponding pairs of semiconductor laser devices to provide a greater magnification for said first cross-sectional dimension than for said second cross-sectional dimension of each beam of said three pairs of beams, thereby causing each beam of said three pairs of beams to assume a generally ribbon-shaped configuration;

(c) means for focussing each of said anamorphically expanded beams onto an intermediate focal plane so as to produce corresponding elongate images of said edge portions of said active regions of said corresponding semiconductor laser devices; and

(d) means for re-imaging said elongate images of said edge portions of said active region of said corresponding semiconductor laser devices on said projection plane.

10. The apparatus of claim 9 wherein said means for anamorphically expanding each beam of said three pairs of beams, and said means for focussing each of said anamorphically expanded beams, comprise corresponding groups of lens elements in an optical train aligned with the active region of a corresponding one of said laser devices.

11. The apparatus of claim 7 wherein said means for gathering said portion of the optical radiation scattered from the two beams of each pair of said plurality of pairs of beams at the measurement volume comprises a lens system for collecting said portion of said scattered radiation and for focusing the radiation so collected onto a corresponding detector means.

12. The apparatus of claim 11 wherein said means for discriminating the gathered radiation scattered from each of the two beams of each pair of said plurality of pairs of beams at the measurement volume from the gathered radiation scattered from every other beam of said plurality of pairs of beams at the measurement volume comprises a plurality of fields stops, each field stop being positioned so as to transmit the radiation scattered from a corresponding one of said beams at the measurement volume.

13. An apparatus mountable on an aircraft for measuring velocity of said aircraft relative to atmospheric aerosol particles in an air mass surrounding said aircraft, said apparatus comprising:

(a) means for generating three pairs of ribbon-shaped laser beams;

(b) means for focussing said three pairs of ribbon-shaped laser beams onto an intermediate focal surface to form three corresponding pairs of intermediate focal surface to form three corresponding pairs of intermediate image, the intermediate images formed by the two beams of each pair of said ribbon-shaped laser beams being separated from each other on said intermediate focal surface by a specified distance;

(c) means for expanding said three pairs of ribbon-shaped laser and for focussing the expanded beams onto a projection surface in a measurement volume located at a predetermined distance from said aircraft, so that the two beams of each pair of said ribbon-shaped laser beams are substantially parallel to each other at the measurement volume, and so that the images formed on the projection surface by the two beams of each pair of said ribbon-shaped laser beams are separated from each other by a distance that is related to the separation between the corresponding intermediate images formed by the two beams of the same pair of said ribbon-shaped laser beams on the intermediate focal surface in accordance with a predetermined magnification ratio, the two beams of each pair of said ribbon-shaped laser beams being nonparallel to the beams of each of the other pairs of said ribbon-shaped laser beams at the measurement volume, aerosol particles in said measurement volume scattering light from the two beams of each pair of said ribbon-shaped laser beams;

(d) means for gathering a portion of the light scattered by said aerosol particles in said measurement volume from the two beams of each pair of said ribbon-shaped laser beams;

(e) a field stop plate having three pairs of field stops, said field stops being positioned with respect to each other on a field stop array surface so that each field stop can transmit the scattered light that has been gathered from a corresponding one of said ribbon-shaped laser beams, each field stop thereby discriminating the scattered light that has been gathered from the corresponding one of said ribbon-shaped laser beams from the scattered light that has been gathered from every other one of said ribbon-shaped laser beams;

(f) means for generating three pairs of electrical signals, each electrical signal being responsive to scattered light gathered from the corresponding one of said ribbon-shaped laser beams and transmitted by a corresponding one of said field stops;

(g) means for processing said three pairs of electrical signals to measure time intervals required for said aerosol particles to traverse the distance between the two parallel beams of each pair of said ribbon-shaped laser beams at the measurement volume, and to calculate velocity components in three dimensions for said aerosol particles relative to said aircraft; and

(h) means for determining a velocity vector for said aircraft relative to said aerosol particles from said calculated velocity components.

14. The apparatus of claim 13 wherein both said intermediate focal surface on which said intermediate images are formed and said field stop array surface which said field stops are positioned are formed on a common structural member of said apparatus, a fixed relationship between said intermediate focal surface and said field stop array surface thereby being maintained with respect to said projection surface as said aircraft passes through said air mass.

15. The apparatus of claim 13 wherein said means for generating said three pairs of laser beams comprises three corresponding pairs of laser devices, each of said laser devices having an active region that emits a corresponding beam with a generally rectangular cross section.

16. The apparatus of claim 15 wherein said means for focusing said three pairs of ribbon-shaped laser beams onto said intermediate focal surface comprises:

(a) lens means for collimating the beam of rectangular cross section emitted from a corresponding one of said laser devices;

(b) lens means for anamorphically expanding the collimated beam of rectangular cross section emitted from said corresponding one of said laser devices so that a greater magnification is provided for a first dimension of said rectangular cross section than for a second dimension of said rectangular cross section, said first and second dimensions of said rectangular cross section being orthogonal to each other, the anamorphically expanded beam thereby assuming a generally ribbon-shaped configuration; and

(c) lens means for refracting the ribbon-shaped anamorphically expanded beam from said corresponding one of said laser devices so as to be capable of forming a corresponding intermediate image.

17. The apparatus of claim 16 further comprising a prismatic means for folding the refracted ribbon-shaped anamorphically expanded beam from said corresponding one of said laser devices so that the corresponding intermediate image is formed on said intermediate focal surface.

18. The apparatus of claim 16 wherein said lens means for collimating the beam of rectangular cross section emitted from said corresponding one of said laser devices comprises a collimator group consisting of five lens elements that are configured and positioned with respect to each other along an optic axis according to an optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (measured) ______________________________________ 0 ∞

1.58 Air 1 -11.549 10.77 LAFN2 1.731759 2 -8.128 0.24 Air 3 36.309 1.92 SF3 1.721101 4 13.927 4.38 BAKl 1.565285 5 -18.720 1.34 Air 6 56.060 1.92 SF3 1.721101 7 9.390 4.38 BAKl 1.565285 8 -298.400 4.27 Air 9 ∞

Air ______________________________________

where optically significant surfaces of said collimator group in the direction of propagation of light along said optic axis are numbered consecutively in the column headed "Surface No.";

where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thicknesses of lens element and spacings bounded by adjacent surfaces in said direction of propagation of light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces;

where entries in the column headed "Material" identify air gap spacings that are bounded by corresponding adjacent surfaces by the designation "Air", and identify optical glass lens elements that are bounded by corresponding adjacent surfaces by manufacturer'"'"'s designations; and

where the column headed "N.sub..83 (measured)" provides refractive index values with reference to a base wavelength of 0.83 micron a supplied by the optical glass manufacturer.

19. The apparatus of claim 18 wherein said lens means for anamorphically expanding said collimated beam comprises a beam-expander group consisting of five lens elements that are configured and positioned with respect to each other along said optic axis according to an optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (measured) ______________________________________ 1 -9.000 2.000 SF11 1.763321 2 ∞

1.000 Air 3 -9.000 2.000 SF11 1.763321 4 ∞

4.305 Air 5 -34.595 1.600 LF7 1.564422 6 ∞

3.000 PSK3 1.545105 7 -11.078 0.500 Air 8 ∞

3.000 PSK3 1.545105 9 -20.487 Air ______________________________________

where optically significant surfaces of said beam-expander group in the direction of propagation of light along said optic axis are numbered consecutively in the column headed "surface No.", where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thicknesses of lens elements and spacings bounded by adjacent surfaces in said direction of propagation of light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces where entries in the column headed "Material" identify air gap spacings that identify optical glass lens elements that are bounded by corresponding adjacent surfaces by manufacturer'"'"'s designations; and

where the column headed "N.sub..83 (measured)" provides refractive index values with reference to a base wavelength of 0.83 micron as supplied by the optical glass manufacturer.

20. The apparatus of claim 19 wherein said lens means for refracting said ribbon-shaped anamorphically expanded beam comprises an imager group consisting of three lens elements that are configured and positioned with respect to each other according to an optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (measured) ______________________________________ 1 46.563 4.000 SK11 1.556329 2 -30.940 2.000 SF4 1.735245 3 -1172.490 0.250 Air 4 33.561 3.500 BK7 1.510288 5 -680.212 (to image) Air 6 ∞

Air (image surface) ______________________________________

where optically significant surfaces of said imager group in the direction of propagation of light along said optic axis are numbered consecutively in the column headed "Surface No.", where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thicknesses of lens element and spacings bounded by adjacent surfaces in said direction of propagation of light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces;

where entries in the column headed "Material" identify air gap spacings that are bounded by corresponding adjacent surfaces by the designation "Air", and identify optical glass lens elements that are bounded by corresponding adjacent surfaces by manufacturer'"'"'s designations; and

where the column headed "N.sub..83 (measured)" provides refractive index values with reference to a base wavelength of 0.83 micron as supplied by the optical glass manufacturer.

21. The apparatus of claim 13 wherein said means for expanding said three pairs of ribbon-shaped laser beams and for focussing the expanded beams onto said projection surface comprises:

(a) lens means for separating the two beams of each pair of said ribbon-shaped laser beams so as to be substantially parallel to each other at the measurement volume, and for magnifying the intermediate image so that said images formed on said projection surface are larger than corresponding intermediate images formed on said intermediate focal surface in accordance with said predetermined magnification ratio; and

(b) prismatic means for aligning the two beams of each pair of said ribbon-shaped laser beams with corresponding images of said field stops on said projection surface.

22. The apparatus of claim 21 wherein said lens means for separating the two beams of each pair of said ribbon-shaped laser beams comprises two lens elements that are configured and positioned with respect to each other along an optic axis according to an optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (measured) ______________________________________ 1 467.256 5.000 SF1 1.699628 2 117.490 0.500 Air 3 117.490 9.500 SKll 1.556329 4 -164.160 (to image) Air ______________________________________

where surfaces of said two lens elements in the direction of propagation of light along said optical axis are numbered consecutively in the column headed "Surface No.";

where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thicknesses of said two lens elements and of an intervening air gap bounded by corresponding adjacent surfaces in said direction of propagation of light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces where entries in the column headed "Material" identify optical glass lens elements that are bounded by adjacent surfaces by manufacturer'"'"'s designations; and

where the column headed "N.sub..83 (measured)" provides refractive index values with reference to a base wavelength of 0.83 micron as supplied by the optical glass manufacturer.

23. The apparatus of claim 21 wherein said prismatic means comprises a pair of prism elements spaced apart from each other, said prism elements being mounted for rotation in opposite directions with respect to each other to permit adjustable deviation for the two beams of each pair of said ribbon-shaped laser beams, whereby said ribbon-shaped laser beams can be aligned with said corresponding images of said field stops on said projection surface.

24. The apparatus of claim 23 wherein each of said prism elements is made of Schott K5 glass, and wherein each of said prism elements has a thickness of approximately 4.00 mm at its center and a wedge angle of approximately 2.19 degrees.

25. The apparatus of claim 13 wherein said means for gathering a portion of the light scattered by said aerosol particles in said measurement volume from the two beams of each pair of said ribbon-shaped laser beams comprises a collecting lens system for focussing light scattered from each beam by said aerosol particles onto a corresponding field stop on said field stop plate.

26. The apparatus of claim 25 wherein said collecting lens system gathers background light as well as light scattered from said ribbon-shaped laser beams, and wherein said field stop plate also has a guardband field stop, said guardband field stop being positioned with respect to said three pairs of field stops that transmit scattered light gathered from corresponding ones of said ribbon-shaped laser beams so that said guardband field stop can transmit only background light, said apparatus further comprising means for subtracting the background light transmitted by said guardband field stop from the scattered light transmitted by said three pairs of field stops, said three pairs of electrical signals responsive to scattered light gathered from corresponding ones of said ribbon-shaped laser beams thereby being substantially unaffected by background light.

27. The apparatus of claim 25 wherein said collecting lens system comprises three lens elements that are configured and positioned with respect to each other along an optic axis according to an optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (measured) ______________________________________ 0 ∞

2450.708 Air 1 229.283 24.000 BK7 1.509924 2 -589.788 0.500 Air 3 193.853 26.880 BK7 1.509924 4 -309.321 0.800 Air 5 -314.091 12.500 SF6 1.783366 6 507.365 264.202 Air ______________________________________

where optically significant surfaces of said collimator group in the direction of propagation of light along said optic axis are numbered consecutively in the column headed "Surface No.";

where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thicknesses of lens element and spacings that are bounded by adjacent surfaces in said direction of propagation of light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces;

where entries in the column headed "Material" identify air gap spacings that are bounded by corresponding adjacent surfaces by the designation "Air", and identify optical glass lens elements that are bounded by corresponding adjacent surfaces by manufacturer'"'"'s designations; and

where the column headed "N.sub..83 (measured)" provides refractive index values with reference to a base wavelength of 0.83 micron as supplied by the optical glass manufacturer.

28. The apparatus of claim 13 wherein said means for generating said three pairs of electrical signals comprises:

(a) three pairs of photodetectors; and

(b) optical means for relaying to each one of said photodetectors the scattered light that has been gathered from the corresponding one of said ribbon-shaped laser beams at the measurement volume and transmitted by the corresponding one of said field stops.

29. The apparatus of claim 28 wherein said optical means comprises:

(a) three pairs of bundles of optical fibers, a first end of each bundle of optical fibers being aligned with said corresponding one of said field stops; and

(b) three pairs of relay lens systems, a second end of each bundle of optical fibers being aligned with a corresponding one of said relay lens systems, each one of said relay lens systems being positioned to transmit light from a corresponding one of said bundles of optical fibers to the corresponding one of said photodetectors.

30. The apparatus of claim 29 wherein said means for generating said three pairs of laser beams comprises three corresponding pairs of laser devices, each one of said laser devices emitting a beam of different wavelength, and wherein each one of said relay lens systems comprises an optical filter matched to the wavelength of a corresponding one of said beams.

31. The apparatus of claim 29 wherein each of said optical fibers has a substantially square transverse cross-sectional configuration.

32. The apparatus of claim 29 wherein the optical fibers comprising each one of said bundles are arranged in a linear array at said first end and in a nonlinear array at said second end, said linear array being aligned with said corresponding one of said field stops, said nonlinear array being aligned with said corresponding one of said relay lens systems.

33. The apparatus of claim 32 wherein the optical fibers are arranged in a array at said first end of each bundle, and in a array at said second end of each bundle.

34. The apparatus of claim 29 wherein each of said relay lens systems comprises:

(a) a collimator group of lens elements for collimating light transmitted by the corresponding one of said field stops;

(b) a filter assembly having a relatively narrow bandpass with a center wavelength that is matched to a measured wavelength of the corresponding ribbon-shaped laser beam from which light is scattered by said aerosol particles in said measurement volume; and

(c) an imager group of lens elements for imaging the second end of the corresponding bundle of optical fibers onto the corresponding one of said photodetectors.

35. The apparatus of claim 34 wherein said collimator group of lens elements comprises four lens elements, said filter assembly comprises a plane-parallel filter plate, and said imager group of lens elements comprises five lens elements, said lens elements and filter plate being configured and positioned with respect to each other along an optic axis according to an optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (measured) ______________________________________ 0 ∞

3.635 Air 1 -18.217 2.500 SF14 1.741403 2 18.217 4.550 BK7 1.510206 3 -5.931 5.500 Air 4 46.010 2.000 SF14 1.741403 5 14.940 4.350 BK7 1.510206 6 -14.940 1.000 Air 7 ∞

2.000 BK7 1.510206 8 ∞

1.000 Air 9 48.750 3.485 BK7 1.510206 10 -14.285 1.567 Air 11 -11.146 1.600 SF4 1.735580 12 -41.135 6.391 Air 13 11.557 3.840 K10 1.494296 14 -11.557 2.000 SF6 1.782732 15 -19.431 3.178 Air 16 4.770 3.907 LAFN2 1.731382 17 6.840 0.500 Air 18 ∞

1.200 K10 1.494296 19 ∞

1.142 Air 20 (Image) ______________________________________

where optically significant surfaces of said collimator group in the direction of propagation of light along said optic axis are numbered consecutively in the column headed "Surface No.";

where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thicknesses of lens element and spacings bounded by adjacent surfaces in said direction of propagation of light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces;

where entries in the column headed "Material" identify air gap spacings that are bounded by corresponding adjacent surfaces by the designation "Air", and identify optical glass lens elements that are bounded by corresponding adjacent surfaces by manufacturer for a nominal operating wavelength of 0.83 micron.

36. A collimating lens system comprising five lens elements configured and positioned with respect to each other along an optic axis according to an optical prescription substantially as follows

37. An anamorphic beam-expander lens system comprising five lens elements configured and positioned with respect to each other along an optic axis according to an optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (measured) ______________________________________ 1 -9.000 2.000 SF11 1.763321 2 ∞

1.000 Air 3 -9.000 2.000 SF11 1.763321 4 ∞

4.305 Air 5 -34.595 1.600 LF7 1.564422 6 ∞

3.000 PSK3 1.545105 7 -11.078 0.500 Air 8 ∞

3.000 PSK3 1.545105 9 -20.487 Air ______________________________________

where optically significant surfaces of said beam-expander group in the direction of propagation of light along said optic axis are numbered consecutively in the column headed "Surface No.";

where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thickness of lens elements and spacings bounded by adjacent surfaces in said direction of propagation of light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces;

where entries in the column headed "Material" identify air gap spacings that are bounded by corresponding adjacent surfaces by the designation "Air", and identify optical glass lens elements that are bounded by corresponding adjacent surfaces by manufacturer'"'"'s designations; and

where the column headed "N.sub..83 (measured)" provides refractive index values with reference to a base wavelength of 0.83 micron as supplied by the optical glass manufacturer.

38. An imaging lens system comprising three lens elements configured and positioned with respect to each other along an optic axis according to an optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (measured) ______________________________________ 1 46.563 4.000 SK11 1.556329 2 -30.940 2.000 SF4 1.735245 3 -1172.490 0.250 Air 4 33.561 3.500 BK7 1.510288 5 -680.212 (to image) Air 6 ∞

Air (image surface) ______________________________________

where optically significant surfaces of said imager group in the direction of propagation of light along said optic axis are numbered consecutively in the column headed "Surface No.";

where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thickness of lens elements and spacings bounded by adjacent surfaces in said direction of propagation of light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces;

where entries in the column headed "Material" identify air gap spacings that are bounded by corresponding adjacent surfaces by the designation "Air", and identify optical glass lens elements that are bounded by corresponding adjacent surfaces by manufacturer'"'"'s designations; and

where the column headed "N.sub..83 (measured)" provides refractive index values with reference to a base wavelength of 0.83 micron a supplied by the optical glass manufacturer.

39. A magnifying lens system comprising two lens elements configured and positioned with respect to each other along an optical axis according to an optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (measured) ______________________________________ 1 467.256 5.000 SF1 1.699628 2 117.490 0.500 Air 3 117.490 9.500 SK11 1.556329 4 -164.160 (to image) Air ______________________________________

where surfaces of said two lens elements in the direction of propagation of light along said optic axis are numbered consecutively in the column headed "Surface No.";

where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thickness of said two lens elements and of an intervening air gap bounded by corresponding adjacent surfaces in said direction air gap bounded by corresponding adjacent surfaces in said direction of propagation of light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces;

where entries in the column headed "Material" identify optical glass lens elements that are bounded by adjacent surfaces by manufacturer'"'"'s designations; and

where the column headed "N.sub..83 (measured)" provides refractive index values with reference to a base wavelength of 0.83 micron as supplied by the optical glass manufacturer.

40. An imaging lens system comprising three lens elements configured and positioned with respect to each other along an optic axis according to an optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (measured) ______________________________________ 0 ∞

2450.708 Air 1 229.283 24.000 BK7 1.509924 2 -589.788 0.500 Air 3 193.853 26.880 BK7 1.509924 4 -309.321 0.800 Air 5 -314.091 12.500 SF6 1.783366 6 507.365 264.202 Air ______________________________________

where optically significant surfaces of aid collimator group in the direction of propagation of light along said optic axis are numbered consecutively in the column headed "Surface No.";

where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thicknesses of lens element and spacings bounded by adjacent surfaces in said direction of propagation o light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces;

where entries in the column headed "Material" identify air gap spacings that are bounded by corresponding adjacent surfaces by the designation "Air", and identify optical glass lens elements that are bounded by corresponding adjacent surfaces by manufacturer'"'"'s designations; and

where the column headed "N.sub..83 (measured)" provides refractive index values with reference to a base wavelength of 0.83 micron a supplied by the optical glass manufacturer.

41. A relay lens system comprising a plurality of lens elements configured and positioned with respect to each other along an optic axis according to a optical prescription substantially as follows:

space="preserve" listing-type="tabular">______________________________________ Surface Radius Thickness No. (mm) (mm) Material N.sub..83 (catalog) ______________________________________ 0 ∞

3.635 Air 1 -18.217 2.500 SF14 1.741403 2 18.217 4.550 BK7 1.510206 3 -5.931 5.500 Air 4 46.010 2.000 SF14 1.741403 5 14.940 4.350 BK7 1.510206 6 -14.940 1.000 Air 7 ∞

2.000 BK7 1.510206 8 ∞

1.000 Air 9 48.750 3.485 BK7 1.510206 10 -14.285 1.567 Air 11 -11.146 1.600 SF4 1.735580 12 -41.135 6.391 Air 13 11.557 3.840 K10 1.494296 14 -11.557 2.000 SF6 1.782732 15 -19.431 3.178 Air 16 4.770 3.907 LAFN2 1.731382 17 6.840 0.500 Air 18 ∞

1.200 K10 1.494296 19 ∞

1.142 Air 20 (Image) ______________________________________

where optically significant surfaces of said collimator group in the direction of propagation of light along said optic axis are numbered consecutively in the column headed "Surface No";

where the columns headed "Radius" and "Thickness" provide axial radii of curvature and thicknesses of lens element and spacings bounded by adjacent surfaces in said direction of propagation o light;

where positive and negative designations for the radii correspond to positive and negative curvatures of the surfaces;

where entries in the column headed "Material" identify air gap spacings that are bounded by corresponding adjacent surfaces by the designation "Air", and identify optical glass lens elements that are bounded by corresponding adjacent surfaces by manufacturer'"'"'s designations; and

where the column headed "N.sub..83 (catalog)" provides refractive index values as supplied by the optical glass manufacturer for a nominal operating wavelength of 0.83 micron.