So how do you read these images? The knife edge was moved
back a bit between each image (roughly 3 hundredths of an inch each time).
As the Foucault test diagram showed,
the test images show (nearly) an extremely exaggerated relief view of how
high the surface is relative to a given sphere. When the knife
edge is moved forward or back, you are changing the radius of the sphere
you are comparing your surface to. Note that all of the pictures
resemble the descriptions of what
various parabolas look like relative to different spheres. Does this
mean we have a parabola? Unfortunately not. Hyperboloids and
half of all ellipsoids also show qualitatively similar images. To
be sure we have a parabola, we need to make some measurments of how certain
parts of the images look depending on the position of the knife edge.
There are a few ways to do this. The most common is to block or "mask"
most of the surface so that you're only looking at areas at a given range
of distance from the center. Now if you used the Foucault test on
a perfect sphere, and if the knife edge was positioned just right (essentially
at the center of curvature of the sphere), then all the light would reflect
back exactly to the edge of the blade. Then if you moved the knife
edge to the left or right, you would either be cutting the light off completely
or uncovering it completely, so the image would get completely bright or
completely dark, all at once. At other positions, the mirror will
go dark from one side to the other. The idea of using a mask is that
you move the knife edge forward and back, while simultaneously moving it
left or right, until you find the right knife edge distance where the exposed
parts of the surface go completely bright or completely dark, all at once
when you move the blade sideways (this is what the word null refers to
in the above picture labels, the "zones" refer to a particular range of
distance from the center). This means the exposed parts of the surface
have the same slope angle, and thus the same curvature, as a sphere whose
radius corresponds to the knife edge position. Checking this at several
distances from the center of the mirror to the edge can tell you if the
surface is really a parabola. The details of the math are included
in any good book on amateur telescope mirror making.
The focograms show a few scratches. This was due to the fact that we streched the process over such a long period of time, generally working only a few hours each weekend. This allowed dust to build up in our work area, which contaminated the rouge and scratched the mirrors. The bright dashes in the center are reflections off the back surface of the mirror.
The bright thin line around the dark left edge in the images is a good sign: it is a diffraction effect that occurs only if the mirror doesn't have a turned edge.
Although the measuring and math involved in reading focograms are among
the most scientific parts of the process of producing optics, reading focograms
is also a bit of an art. The measurements can tell you the shape
within the required 1/8 wave criterion (though often only barely with most
amateur test equipment, and it strains your ability to detect differences
in light/shading levels), but the 1/8 wave criterion is only part of the
story. Overall smoothness is also very important. A mirror
that has been fine-tuned to death in the figuring process will likely not
be very smooth on a smaller scale.
Finally both mirrors were finished...