Parabolic dish and method of constructing same

Claim 1

The method of constructing a parabolic dish of focal length F and comprising narrow segments disposed side by side whose projection onto a plane normal to the principle axis of the dish and containing x and y coordinate axes intersecting at an origin on the principle axis is a plane figure divided into narrow increments parallel to the x-axis and spaced along the y-axis and each having a side adjacent and parallel to the x-axis which intersects the y-axis at an axis intersection point and terminates in end points on the perimeter of the figure, said method comprising the steps of: forming from relatively thin flexible sheet material an assembly of curved strips corresponding to said increments, respectively, and arranged side by side in the same order as said increments and each strip having a convex edge and an opposite concave edge, the convex edge of each strip conforming to a curve passing through said axis intersection point of said adjacent side of the corresponding increment and defined by the locus of points expressed by the parametric equations: ##EQU7## where: x o is any x coordinate value between and including the x coordinates of the end points of the adjacent side of the corresponding increment, y o is the y coordinate of the axis intersection point of the adjacent side of the corresponding increment, and the spacing w between said convex and concave edges of each strip parallel to said y-axis is uniform and equal to ##EQU8## where: w' is the width parallel to the y-axis of the corresponding increment; deforming said strips transverse to the plane of the strips to bring their adjacent convex and concave edges into contiguous relation wherein the strips conform to a parabolic curvature; and joining the contiguous strip edges.

Claim 2

The method of constructing a parabolic dish of focal length F and comprising narrow segments disposed side by side whose projection onto a plane normal to the principle axis of the dish and containing x and y coordinate axes intersecting at an origin on the principle axis is a plane figure divided into narrow increments parallel to the x-axis and spaced along the y-axis and each having a side adjacent and parallel to the x-axis which intersects the y-axis at an axis intersection point and terminates in end points on the perimeter of the figure, said method comprising the steps of: forming from relatively thin flexible sheet material an assembly of curved strips corresponding to said increments, respectively, and arranged side by side in the same order as said increments and each strip having a convex edge and an opposite concave edge, the convex edge of each strip conforming to a curve passing through said axis intersection point of said adjacent side of the corresponding increment and defined by the locus of points expressed by the parametric equations: ##EQU7## where: x o is any x coordinate value between and including the x coordinates of the end points of the adjacent side of the corresponding increment, y o is the y coordinate of the axis intersection point of the adjacent side of the corresponding increment, and the spacing w between said convex and concave edges of each strip parallel to said y-axis is uniform and equal to ##EQU8## where: w' is the width parallel to the y-axis of the corresponding increment; deforming said strips transverse to the plane of the strips to bring their adjacent convex and concave edges into contiguous relation wherein the strips conform to a parabolic curvature; and joining the contiguous strip edges.

Claim 3

The method of constructing a parabolic dish of focal length F comprising the steps of: generating a plane figure conforming to the projection of said dish onto a plane normal to the principle axis of the dish; establishing in said plane figure x and y coordinate axes intersecting at an origin located at the position of the principle axis; dividing said plane figure into narrow increments parallel to the x-axis and spaced along the y-axis and each having a side adjacent and parallel to the x-axis which intersects the y-axis at an axis intersection point and terminates in end points on the perimeter of the figure; forming from relatively thin flexible sheet material an assembly of curved strips corresponding to said increments, respectively, and arranged side by side in the same order as said increments and each strip having a convex edge and an opposite concave edge, the convex edge of each strip conforming to a curve passing through said axis intersection point of said adjacent side of the corresponding increment and defined by the locus of points expressed by the parametric equations: ##EQU9## where: x o is any x coordinate value between and including the x coordinates of the end points of the adjacent side of the corresponding increment, y o is the y coordinate of the axes intersection point of the adjacent side of the corresponding increment, and the spacing w between said convex and concave edges of each strip parallel to said y -axis is uniform and equal to ##STR1## where: w' is the width parallel to the y-axis of the corresponding increment; deforming said strips transverse to the plane of the strips to bring their adjacent convex and concave edges into contiguous relation wherein the strips conform to a parabolic curvature; and joining the contiguous strip edges.

Claim 4

The method of constructing a parabolic dish of focal length F comprising the steps of: generating a plane figure conforming to the projection of said dish onto a plane normal to the principle axis of the dish; establishing in said plane figure x and y coordinate axes intersecting at an origin located at the position of the principle axis; dividing said plane figure into narrow increments parallel to the x-axis and spaced along the y-axis and each having a side adjacent and parallel to the x-axis which intersects the y-axis at an axis intersection point and terminates in end points on the perimeter of the figure; forming from relatively thin flexible sheet material an assembly of curved strips corresponding to said increments, respectively, and arranged side by side in the same order as said increments and each strip having a convex edge and an opposite concave edge, the convex edge of each strip conforming to a curve passing through said axis intersection point of said adjacent side of the corresponding increment and defined by the locus of points expressed by the parametric equations: ##EQU9## where: x o is any x coordinate value between and including the x coordinates of the end points of the adjacent side of the corresponding increment, y o is the y coordinate of the axes intersection point of the adjacent side of the corresponding increment, and the spacing w between said convex and concave edges of each strip parallel to said y -axis is uniform and equal to ##STR1## where: w' is the width parallel to the y-axis of the corresponding increment; deforming said strips transverse to the plane of the strips to bring their adjacent convex and concave edges into contiguous relation wherein the strips conform to a parabolic curvature; and joining the contiguous strip edges.

Claim 6

The method of constructing a polarizing parabolic dish antenna reflector comprising the steps of: forming a parabolic dish of focal length F; generating a plane of figure conforming to the projection of said dish onto a plane normal to the principle axis of the dish; establishing in said plane figure x and y coordinate axes intersecting at an origin located at the position of the principle axis; dividing said plane figure into narrow increments parallel to the x-axis and spaced along the y-axis and each having a side adjacent and parallel to the x-axis which intersects the y-axis at an axis intersection point and terminates in end points on the perimeter of the figure; photoetching a sheet of relatively thin flexible material to define on the sheet a plurality of curved strips corresponding to said increments, respectively, and arranged side by side in the same order as said increments and each having a convex edge, an opposite concave edge, and a plurality of spaced electrically conductive polarized grid lines conforming substantially in curvature extending lengthwise of the strip in substantially parallel relation to said convex edge, the convex edge of each strip conforming to a curve passing through said axis intersection point of said adjacent side of the corresponding increment and defined by the locus of points expressed by the parametric equations: ##EQU10## where: x o is any x coordinate value between and including the x coordinates of the end points of the adjacent side of the corresponding increment, y o is the y coordinate of the axis intersection point of the adjacent side of the corresponding increment, and the spacing w between said convex and concave edges of each strip parallel to said y-axis is uniform and equal to ##STR2## where: w' is the width parallel to the y -axis of the corresponding increment; cutting said sheet along said strip edges to provide a strip assembly; and deforming said strip assembly into conformity with and bonding said strip assembly to the parabolic surface of said dish.

Claim 7

The method of constructing a polarizing parabolic dish antenna reflector comprising the steps of: forming a parabolic dish of focal length F; generating a plane of figure conforming to the projection of said dish onto a plane normal to the principle axis of the dish; establishing in said plane figure x and y coordinate axes intersecting at an origin located at the position of the principle axis; dividing said plane figure into narrow increments parallel to the x-axis and spaced along the y-axis and each having a side adjacent and parallel to the x-axis which intersects the y-axis at an axis intersection point and terminates in end points on the perimeter of the figure; photoetching a sheet of relatively thin flexible material to define on the sheet a plurality of curved strips corresponding to said increments, respectively, and arranged side by side in the same order as said increments and each having a convex edge, an opposite concave edge, and a plurality of spaced electrically conductive polarized grid lines conforming substantially in curvature extending lengthwise of the strip in substantially parallel relation to said convex edge, the convex edge of each strip conforming to a curve passing through said axis intersection point of said adjacent side of the corresponding increment and defined by the locus of points expressed by the parametric equations: ##EQU10## where: x o is any x coordinate value between and including the x coordinates of the end points of the adjacent side of the corresponding increment, y o is the y coordinate of the axis intersection point of the adjacent side of the corresponding increment, and the spacing w between said convex and concave edges of each strip parallel to said y-axis is uniform and equal to ##STR2## where: w' is the width parallel to the y -axis of the corresponding increment; cutting said sheet along said strip edges to provide a strip assembly; and deforming said strip assembly into conformity with and bonding said strip assembly to the parabolic surface of said dish.