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Center Null
Below are the focogram images for the (nearly finished) left mirror. To the discerning eye (not mine yet!-EH), you will see that the mirror appears somewhat flat from about half to three quarters of the way from the center to the edge. This means that part of the mirror is still spherical and the mirror as a whole is still undercorrected (ie, it hasn't been changed all the way from a sphere to a paraboloid). (Note to experienced or potential opticians- the "zone numbers" shown below were used only for convenience and do not quantitatively match the standard zones).

Zone 2 Null

Zone 3 Null
Zone 4 Null
Outer Zone Null
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.
(approximate) zone mask used on our mirrors
This is actually a multiple-zone mask that can be used to check 5 zones
rather than checking each zone with a separate mask.
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...