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In Table 1 the first column is the radius of the various zones, the centre. the first tested (k/2) and thereafter every " inch

The second column gives the zonal difference, or the distance of the focus of that zone from the focus of the centre zone when the light source is stationary. This is denoted by "y" . It is zero for a sphere, while for a paraboloid its value is r ^/R where "r" is the radius of the zone and "R" is the radius of curvature of the centre zone.

The third column gives these figures less the figure for the first zone, whose radius is K/2. This figure, denoted by "m" is the distance of the focus of each zone from the focus of the first zone.

The forth column gives these figures for the third column plus the distance "d". This is now the spacing. At this distance increased the apparent spacing of the shadow bands decreases inversely. So the spacing "w" of the shadow bands at any zone is w = Kd/n which are the figures given in the fifth column.

Using the equations above I made calculations of the band spacings for a 6" diameter mirror with a radius of curvature of 96". A 100 lines per inch Ronchi grid was to be used and a maximum band spacing of 1.5" These are set out below.


My intention was to drill holes in an aluminium plate and drive in roll-pins to curve a wire around. The diameter of the wire and the roil-pin had to be allowed for. Using 1/16" dia. wire and 3/32" dia. roll-pins, .156" had to be subtracted from the spacings above. The plate was set up on a Bridgeport milling machine and the holes accurately positioned. The plate was removed and roilpins inserted in all the holes. A piece of 1/16" dia. welding wire which is stiff was curved around the pins and tied together at each end to hold them firmly in place. Short pieces for ties were laid across the wires and silver soldered to them. The wire grid was then lifted off the plate. One end of the wires was then bent at 90 deg. at the appropriate position so that it could be hung on the mirror.

All this is illustrated in the duiagram below. This procedure results in a very accurate.