Integrated Phase along linefeed vs offset position.

sept 2004

    A linefeed for the AO spherical dish (with Radius R=870ft) is placed R/2 feet below the center of curvature. Concentric rings on the dish focus energy at different places on the line feed. The edge of the dish focuses at the bottom of the line feed while points directly below the line feed (ignoring blockage) focus at the top of the line feed.  The picture below is for a plane wave at the center of curvature of the dish. It shows the path for a ray of radius x feet from the center of curvature.

    The ray goes along line A (blue),hits the dish, reflects back along  ray B (magenta), and then intersects the line feed a distance y (red line) from the paraxial point (R/2 feet below the center of curvature). The distance P=A+B+y must be a constant for all values of x along the plane wave. Remember that there is an axis of symmetry so x needs to be rotated (or integrated) around a ring of 360 degrees.
    A summary of the computations are: The plot shows these relationships for the 1000ft (305m) ao dish (f/D=.5)