Multifacet substantially paraboloidal collimator and method for making same

Claim 1

A collimator having a substantially paraboloidal surface and formed of a plurality of juxtaposed facets, each having a substantially paraboloidal surface, comprising: a. each facet surface being defined by two paraboloidal radii in orthogonal planes; b. the radii being calculated for a known paraboloid from the equations: where Rs is the short radius, Rc is the long radius, F iS the focal length of the paraboloid, and theta is an angle between the parabolic axis and a line normal to a tangent through the center point of each facet, said line and axis being in a first of said orthogonal planes normal to a respective tangent: the angle being determinable from the equation: theta tan 1 (U/2F): where U is the distance from the center point of each facet along a line normal to the parabolic axis, the latter line and axis being in the same plane: c. each of said facets being predetermined squares when viewed along lines parallel to said parabolic axis, each square having at least one adjacent corner with another square; d. at least one of said facets having a diagonal lying in its second orthogonal plane; e. the distance of the center point of said last facet from the parabolic axis being predetermined; f. the parabolic axis and the center point of each facet lying in the second orthogonal plane of the respective facet; g. the position of the second orthogonal plane in each facet other than that second plane of said one facet being determinable by the equation; phi tan 1 (X/Y); where phi is the angle between said second plane of said one facet and the plane to be determined; X is the length of a line normal to said second plane of said one facet to the center point of the respective facet and along a diagonal thereof and Y is the length of a line in said second plane from said parabolic axis to and normal to said last line, X and Y being determinable as diagonals or parts thereof of known squares.

Claim 3

A method for making a collimator having a substantially paraboloidal surface formed of a plurality of substantially paraboloidal facets on individual plates, each facet being defined by two paraboloidal radii in orthogonal planes, comprising: a. determining the location of each facet to form said collimator having a predetermined paraboloidal surface; b. determining the shape and dimensions of each facet plate along its edges viewed parallel to the parabolic axis; c. determining the angles between the parabolic axis and lines normal to tangents through center points of each respective facet, each of said lines being in a first orthogonal plane normal to said tangent for each facet; d. determining the position of the second orthogonal plane for each facet; e. determining the respective radii for each facet; f. preparing a respective jig face for each of said facets by putting steps on a jig plate from a central axial apex downwardly toward opposite sides symmetrically to nadir outer edge positions, g. said steps extending in an axial position relative to the axis of a cylindrical curve adapted to extend transversely on the edges of said steps; h. the depth of each step from the apex being determined from the equation; where dh is the depth of each step; C is the transverse distance normal to said cylindrical axis from the axial apex to each step edge, arbitrarily selected; Rc is one of said respective radii for each facet to be used as a cutting radius to cut a spherical face as a part of a respective facet in each facet plate and which is in said second orthogonal plane; and Rs is the other of said respective radii which defines the finished facet and which is in said first orthogonal plane: i. tilting each plate at an angle with the horizontal equal to the respective angle formed by the parabolic axis and the line normal to the tangent at the respective center point of each respective facet and positioning the plate in accordance with the respective orthogonal planes of the facet in relationship to a reference plane in the collimator so that the orthogonal planes will be in the proper positions in relation to the position of the facet in the collimator, then cutting the edges of each plate vertically to sHape and dimension it according to the predetermined shape and dimensions viewed parallel to the parabolic axis: j. placing each facet plate on a corresponding jig depending upon the radii of the respective facet; k. positioning and securing each facet plate on its respective jig in accordance with the respective orthogonal planes of the facet in relationship to the cylindrical axis of the jig with respect to said reference plane so that the plate is deformed within its elastic limit on the curve of said steps and so that the planes will be in the proper positions in relation to the position of the facet in the collimator; l. cutting said spherical surface on each facet using a respective Rc radius; m. releasing each facet plate from its jig to permit the plate to return to its undeformed shape and thereby forming a second curved surface having the Rs radius in the first orthogonal plane, the Rc radius being in the second orthogonal plane; n. finishing each facet to produce a highly reflective surface; and o. securing said facets together to form said collimator in accordance with the predetermined location of each facet, and to have a substantially paraboloidal reflective surface.

Claim 4

A method for making a collimator having a substantially paraboloidal surface formed of a plurality of substantially paraboloidal facets on individual plates, each facet being defined by two paraboloidal radii in orthogonal planes, comprising: a. determining the location of each facet to form said collimator having a predetermined paraboloidal surface; b. determining the shape and dimensions of each facet plate along its edges viewed parallel to the parabolic axis; c. determining the angles between the parabolic axis and lines normal to tangents through center points of each respective facet, each of said lines being in a first orthogonal plane normal to said tangent for each facet; d. determining the position of the second orthogonal plane for each facet; e. determining the respective radii for each facet; f. preparing a respective jig face for each of said facets by putting steps on a jig plate from a central axial apex downwardly toward opposite sides symmetrically to nadir outer edge positions, g. said steps extending in an axial position relative to the axis of a cylindrical curve adapted to extend transversely on the edges of said steps; h. the depth of each step from the apex being determined from the equation; where dh is the depth of each step; C is the transverse distance normal to said cylindrical axis from the axial apex to each step edge, arbitrarily selected; Rc is one of said respective radii for each facet to be used as a cutting radius to cut a spherical face as a part of a respective facet in each facet plate and which is in said second orthogonal plane; and Rs is the other of said respective radii which defines the finished facet and which is in said first orthogonal plane: i. tilting each plate at an angle with the horizontal equal to the respective angle formed by the parabolic axis and the line normal to the tangent at the respective center point of each respective facet and positioning the plate in accordance with the respective orthogonal planes of the facet in relationship to a reference plane in the collimator so that the orthogonal planes will be in the proper positions in relation to the position of the facet in the collimator, then cutting the edges of each plate vertically to sHape and dimension it according to the predetermined shape and dimensions viewed parallel to the parabolic axis: j. placing each facet plate on a corresponding jig depending upon the radii of the respective facet; k. positioning and securing each facet plate on its respective jig in accordance with the respective orthogonal planes of the facet in relationship to the cylindrical axis of the jig with respect to said reference plane so that the plate is deformed within its elastic limit on the curve of said steps and so that the planes will be in the proper positions in relation to the position of the facet in the collimator; l. cutting said spherical surface on each facet using a respective Rc radius; m. releasing each facet plate from its jig to permit the plate to return to its undeformed shape and thereby forming a second curved surface having the Rs radius in the first orthogonal plane, the Rc radius being in the second orthogonal plane; n. finishing each facet to produce a highly reflective surface; and o. securing said facets together to form said collimator in accordance with the predetermined location of each facet, and to have a substantially paraboloidal reflective surface.