Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.naic.edu/~phil/optics/compute/lnfeedphase.html
Äàòà èçìåíåíèÿ: Thu Sep 23 00:22:47 2004
Äàòà èíäåêñèðîâàíèÿ: Sat Dec 22 13:30:08 2007
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Ïîèñêîâûå ñëîâà: universe

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:

A=Rcos(za)
B=R/(2cos(za))
y=R/2 * (1./cos(za) - 1)
zamax=asin(500./870(radius)) = 35 degrees.

The plot shows these relationships for the 1000ft (305m) ao dish (f/D=.5)

Fig top. Intersection of linefeed at position y versus zenith angle za.
Fig 2nd. Intersection of linefeed at position y versus horizontal distance x from center of curvature.
Fig 3rd. The integrated phase needed from a position y on the linefeed to y=0 so that a plane wave is brought to a focus at the paraxial surface. This distance is P-(A+B) (see above image). A ray leaving the center of curvature travels P=R+R/2 so P=1.5R. The plot has y versus (1.5R-(A+B)). This value is less than the physical distance, so the phase velocity of the wave guide must be greater than c.
Fig Bottom. The 3rd figure was the integral of the phase from the y intersection of the ray to y=0. This can be written as

phaseIntegral=integral(velC/velWG*dy) y=0 to y

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