--  welcome to

The Spot Test

By   John Sherman

    The Spot Test is an improved way to test telescope mirrors, complete telescopes, and other optical equipment. A century and a half ago Jean Bernard Léon Foucault showed the world a way to see errors measuring into the millionths of an inch. In his time other people had already been examining telescope mirrors from their radius of curvature (roc)  with a pinhole and an eyepiece.  (A telescope mirror's reflecting surface is curved, right? So if you think of that curve as part of a sphere, the radius of curvature is the center point of the sphere.)  
Foucault setup
    Foucault got the idea to cut a knife edge into the light beam. This great advance facilitated the more accurate making of telescope mirrors. His test and variations thereof are still in wide use today.

   In this diagram the spot marked with an X is the roc of the mirror. Any light which leaves this point and hits the spherical mirror will return exactly to this point. Foucault put a light source at the top red dot. The light (red) shines on the mirror (blue) and returns to form an image of the light source, in this case it is another red dot. This way the condition of the mirror can be determined by examining the image it makes. Foucault (green eyeball) did it with a knife-edge.

    Since that time many variations of his test have appeared. All of them were straight-edge tests, one dimensional to some degree. There is no sensitivity in the direction of the knife, only perpendicular to its edge. For example, you can use a straight-edge to null test a sphere. But you are limited to one dimension, so if the mirror had astigmatism you might not know it.

astigmatism in a paraboloid
You can barely see the astigmatism in this photo.

   Many of the straight-edge tests can also be done in 2D by using a curved edge. It is the second dimension in testing. A very-strongly-curved edge is best, one with a very short radius. The result is a tiny spot, as small as your light source will allow. With a spot you can null test an otherwise spherical mirror in 2D and astigmatism is immediately and automatically apparent. Just as it is with the 2D pinhole/eyepiece test.

   In the photograph on the left, the shadow of the spot is not exactly in the center, and there is a disturbance in the diffraction pattern on its right. If I adjust the setup in order to center the spot, then the dark ring shifts over and is not centered. This persistence is a demonstration of the astigmatism caused by the small lateral separation between the source and the spot of an inch or so. A straight-edge device is not likely to show you that.

   Most of the many versions of the Foucault test can be done in two-dimensions. This mini website will briefly describe some of them. Presented are my findings, some or all of which may be in error. After all, I am just a beginner at all of this. Please do not think that I am an expert. There are no formulas, math or rigorous analysis here. Most of that stuff has already been figured out in relation to the 1D tests. Those familiar with mirror testing should not have a problem understanding how to do it in 2D.

   The essence of the Spot test is to illuminate the mirror with a round pinhole, and examine its image with a round spot on a piece of glass. The setup is the same as in the diagram above. A spot has an edge pointing in every direction, and functions as a 360° "knife" edge. The Spot test is not actually a new test, it is just a way to convert the existing tests into two dimensions. You still do the same test you've been doing, except now you have your eye wide open.

Happy telescope making!!


Page 2 shows testing methods at the radius of curvature
Page 3 are methods inside or outside of the radius of curvature
Page 4 deals with astigmatism in a spheroid mirror
Page 5 deals with astigmatism in a paraboloid
Page 6 gives my ideas for a robo-tester
Page 7 is about measuring zones


copyright 2002 - 2004 by John Sherman