CLAIM 1 - A beam director comprising: a beam source rotatable about a longitudinal axis, an actuator for rotating the beam source about the longitudinal axis, whereby the beam source rotates and reflects the beam at a constant angle to the longitudinal axis; an annular reflector encircling the beam source coinciding with the longitudinal axis of the rotating actuator; constantly facing the beam source at a constant angle; a second reflector including a reflective surface at an acute angle to the longitudinal axis for reflecting the beam, configured to reflect the beam towards a work surface at a constant angle thereto; and a beam corrector comprising a reflective surface on the second reflector for modifying the beam dimensions; whereby when the beam is activated and the actuator rotates the beam source, the beam strikes the reflector rotating the beam and reflecting the beam to the work surface; the beam then following a curved path relative to the work surface, tracing out an arc on the work surface; and wherein the beam corrector comprises a reflective surface on the second reflector with curvature correction in the first (x’) direction and in the second perpendicular direction

(y)·

2 - A beam director comprising: a rotatable first reflector rotatable about a longitudinal axis for receiving a beam from a beam source along the longitudinal axis, the first reflector including a reflective surface at an acute angle to the longitudinal axis for reflecting the beam; an actuator for rotating the first reflector about the longitudinal axis, whereby the first reflector rotates and reflects the beam at a constant angle to the longitudinal axis; an annular second reflector encircling the first reflector, a center of the first reflector coincides with the longitudinal axis of the first reflector, constantly facing the first reflector at a constant angle; the second reflector configured to reflect the beam towards a work surface at a constant angle thereto; a beam corrector comprising a reflective surface on the second reflector for modifying the beam dimensions; whereby when the beam is activated and the actuator rotates the first reflector, the beam strikes the rotating first reflector rotating the beam and reflecting the beam to the second reflector, which reflects the beam to the work surface; the beam then following a curve path relative to the work surface, tracing out an arc on the work surface; wherein the reflective surface of the first and second reflectors changes the beam dimensions to a desired dimension in either a first (x’) direction or in a second perpendicular direction (y’) or in both; wherein the first reflective surface comprises a lying on a first plane orthogonal to a second curve lying on a second plane where the first and second planes are orthogonal and vertex’s of the first and second curves meet at the longitudinal axis; wherein the second reflector includes a toric surface where the toric surface is a surface swept out when a function z(y) is rotated about an axis that is parallel to local y axis represented by: wherein the function is rotated at a distance 1/Cx’ where Cx’ is the reciprocal of the radius of the circle in the xz plane; wherein Asph is a value representing a departure from a sphere shape; wherein polynomials coefficients A. for any j from 0 to 14 is 0 when C is non zero or when

C is zero then at least one of the A. coefficient is non zero; wherein the polynomial coefficients provide a higher degree of definition to the rotated function z(y); and where C is the curvature defining the rotated function.

3. The beam director according to claim 1 , wherein the second reflector comprises a toroidal surface with curvature C1 in a first direction and curvature C2 in a second perpendicular direction; wherein the beam source is a distance d from a toroidal origin and rotatable along the C1 surface; and wherein the longitudinal axis is parallel with a toroidal vertical axis.

4. The beam director according to claim 2 wherein the first mirror comprises a rotating flat mirror at an acute angle of 45 degrees from the longitudinal axis, and wherein the beam source is positioned along the longitudinal axis, whereby the beam source directs the beam to the first reflector and the first reflector reflects the beam to the toroidal surface, whereby, the beam is activated according to the equations: where the second mirror comprises a toroidal surface where V is the toroidal vertex where C1 is the first center of a first toroidal with a radius R’ laying on the zy plane where C2 is a second center for a second toroidal radius r’ laying on the xy plane where the beam source is perpendicular to a line connecting C1 ,V and C2 where the beam source optical axis is on C2 where the beam is reflected from the first reflector striking at the second reflector at M2 of the Toroidal surface and in a distance d from the source optical axis where q is the distance from the second reflector M2 to a point I at the work surface where q = d+h and the angle in the triangle M2 C1 V is Q R’ is calculated by: and r’ is calculated by:

5. The beam director according to claim 2, wherein the second reflector comprises a paraboloid surface, and wherein the first reflector comprises a biconic surface, wherein a first surface comprises a spherical surface, and an orthogonal second curved surface with an aspherical surface value between 0 and -1 , and pitch in about 45 degrees.

6. The beam director according to claim 2, wherein the first reflector is a biconic surface comprises a spherical surface, and a second surface comprising an aspherical surface, and wherein the aspherical surface and the spherical surface meet at a vertex.

7. [Original] The beam director according to claim 2, wherein the second reflector is configured to focus the beam only in one direction; and wherein the one direction is used to construct a logical pixel.

8. The beam director according to claim 2, wherein the first reflector comprises a first paraboloid surface, and second spherical plane wherein the second reflector comprise a second paraboloid surface; and wherein the first surface is pitched at about 45 degrees. wherein the vertex of the first reflector is facing an off-axis portion of the second reflector at around P where P is the second reflector focal point on the paraboloid plane.

9. The beam director according to claim 8, wherein the first reflector paraboloid surface is substantially identical to the second reflector paraboloid surface.

10-The beam director according to claim 2, wherein the second reflector comprises a conical surface,

31 wherein the first reflector comprises a biconic surface; wherein a first curvature of a first biconic surface is about twice a second curvature of a second biconic surface; and wherein the aspherical value for the first biconic surface is about -0.8 wherein the aspherical value for the second surface is about 1 wherein the first reflector is pitched in an acute angle ~45 degrees.

11 - A beam director comprising: a rotatable first reflector rotatable about a longitudinal axis for receiving a beam from a beam source along the longitudinal axis, the first reflector including a reflective surface at an acute angle to the longitudinal axis for reflecting the beam; an actuator for rotating the first reflector about the longitudinal axis, whereby the first reflector rotates and reflects the beam at a constant angle to the longitudinal axis; an annular second reflector encircling the first reflector, a center of the first reflector coincides with the longitudinal axis of the first reflector, constantly facing the first reflector at a constant angle; the second reflector configured to reflect the beam towards a work surface at a constant angle thereto; a beam corrector comprising a reflective surface on the second reflector for modifying the beam dimensions; whereby when the beam is activated and the actuator rotates the first reflector, the beam strikes the rotating first reflector rotating the beam and reflecting the beam to the second reflector, which reflects the beam to the work surface; the beam then following a curve path relative to the work surface, tracing out an arc on the work surface; wherein the reflective surface of the first and second reflectors changes the beam dimensions to a desired dimension in a first (x’) direction and in a second perpendicular direction (y’); wherein the first reflective surface comprises a biconic surface where the first curve is lying on a first plane orthogonal to a second curve lying on a second plane where the first and second planes are orthogonal and vertex’s of the first and second curves meet at the longitudinal axis;

32 wherein the second reflector includes a toric surface where the toric surface is a surface swept out when a function z(y) is rotated about an axis that is parallel to local y axis represented by z(y).

12. The beam director according to claim 11 , wherein the second reflector comprises a paraboloid surface z(y), and wherein the first reflector comprises a biconic surface, wherein a first plane curve comprises a spherical surface, and an orthogonal second plane curve comprises a surface with an aspherical value between 0 and -1 , and pitch in about 45 degrees.

13. The beam director according to claim 11 , wherein the second reflector is configured to focus the beam only in one direction; and wherein the one direction is used to construct a logical pixel where the logical beam size is controlled by the beam speed.

14. The beam director according to claim 2, wherein the second reflector comprises a conical surface, wherein the second reflector is configured to focus the beam only in one direction; and wherein the one direction is used to construct a logical pixel, where the logical beam size is controlled by the beam speed.

15. The beam director according to claim 12, wherein the vertex of the first reflector is facing an off-axis portion of the second reflector at around P where P is the second reflector focal point on the paraboloid plane.

16. The beam director according to claim 11 , wherein the first reflector paraboloid surface is substantially identical to the second reflector paraboloid surface.

17. The beam director according to claim 11 , wherein the first reflector comprises a first paraboloid surface, and second spherical plane, wherein the second reflector comprise a cone surface; and

33 wherein the first surface is pitched at about 45 degrees. wherein the vertex of the first reflector is facing an off-axis portion of the second reflector at around P where P is the second reflector focal point on the paraboloid plane.

18. The beam director according to claim 11 , wherein the first reflective surface comprises a first spherical curve lying on a first plane orthogonal to a second parabolic curve lying on a second plane where the first and second planes are orthogonal and vertex’s of the first and second curves meet at the longitudinal axis.

20 The beam director according to claim 11 , wherein the second reflector includes a toric surface where the torse surface is composed of a surface swept out at a distance Cx^J when a function z(y)=y is rotated about an axis that is parallel to the local y axis.

21 , The beam director according to claim 11 , wherein the second reflector includes a toric surface where the toric surface is composed of a surface swept out at a distance Cx* when a function z (y) = 4 *P *y² is rotated about an axis that is parallel to the local y axis; and wherein the first reflector is positioned at about p distance from the vertex of the second reflector, where P is the focal point of the function,

22, The beam director according to claim 11 , wherein the second reflector includes a toric surface where the toric surface is composed of a surface swept out at a distance Cx* when a function z² +y² ------ r² rotated about an axis that is parallel to the local y axis, where r is the radius of the sphere surface.

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