Home | Page3 | Page4 | Page5 | Page6 | Page7 |

Here are some test methods which function at the radius of curvature with a single spot.


Spherical Spot test

   All you do is examine the image of a pinhole with a tiny spot. If you have a perfect sphere then the entire mirror is in the same zone. This causes the entire mirror to darken at the same time. Foucault tsphere with zones -- knife edgeest users are quite familiar with this principle. A lot of surface detail can be seen in the null. This is not more sensitive than when using a straight knife edge, but using two dimensions improves the view because, if you have astigmatism it will be instantly visible.

    This test uses only a pinhole and a spot. The smaller the pinhole and the spot, the more sensitive the null will be. It is very low cost to make, and easy to setup and perform. You can move both pinhole and spot by hand.

   Here is an image of an 8" f/5 spheroid being null tested with a knife edge, the way Foucault described (left). Unfortunately my camera doesn't like the low light levels caused by the non-aluminized and spheroid mirror, and the dim led shining through the little ~0.005" pinhole, so these images sphere with zones -- spot testare noisy. It is probably best to back up and look at them from about ten feet away. The knife is cutting in from the right, so the surface of the mirror appears to be illuminated from the left. The mirror has a hole in the center and a big raised zone at the 60% radius (which looks like a donut).

   The next photo is the same mirror but now it is being null tested with a spot (right). The same zones are illuminated differently. Both sides are the same, and appear to be illuminated from the center. The big raised zone at about 60% radius is bright on the inside and dark on the outside. For this image I used a spot which is slightly larger than the pinhole. That means also that the spot is slightly larger than the image of the pinhole which the mirror forms.

sphere with zones -- spot test    So if you put this large spot exactly at the roc it would block all the light (except that you will still see diffraction effects). This image was made with the spot just outside the roc, so that some light can escape around the edge of the spot and be seen. Now, if the spot was moved just inside the roc, the big zone would appear illuminated from the outside in. Just as in the left half of the top image.

   The third photo is also the same mirror null tested with a spot (left). This time the spot is about half the size of the pinhole. That means the spot can be placed exactly at the image of the pinhole, and since it will be smaller than the image then about half of the light will still get past. The same zones can be seen, but the contrast is less. Very tiny spots are the most sensitive, but generally require a true point source of light to maintain good contrast.


Star Spot test

    The Spherical Spot test is wonderfully sensitive because it is a null test. This means that when you do the test every part of the mirror is (supposed to be) at the same zone. Any part of the mirror which is at a different zone stands right out. You can get the same results from a complete telescope by using a real star as the light source.

    Assemble your telescope, wait for some great seeing, and point to a star. You will need a sturdy mount for your telescope. Keep the star centered and remove the eyepiece (dob users usually prefer Polaris). You can start with a knife edge cutting in the cone of light, move the focuser to find the focal point of the telescope. This is a 1D null test and it is very sensitive. Many people have done this before. Now merely replace the knife edge with a very small spot. Since the star is a true point source, you will be able to use a spot as small as 0.001" for greater sensitivity.

    Bring the spot to the focal point (keep the star centered). There is a null point there which will show you the quality of the wavefront exiting the telescope in graphic detail. But be aware, this test is severe. It tests the entire optical system. Not just the mirrors and/or lenses, but also the air the light travels through. It might even be as brutal as the regular star test (with an eyepiece; it shows the change in the diffraction pattern due to image aberrations). Certainly they should be used together. The star test can tell if you have errors, the Star Spot test will show you most of those errors directly.



Axial Spot test

knife-edge on a paraboloid

    Now I'll show three methods which work at the roc of an asphere. These photographs are of a 22" f/4.5 paraboloid mirror illuminated by the blue led shining through the ~0.005" pinhole. The purpose of these methods is to determine the relative length of the roc of each zone on the mirror. The data can then be combined to determine how far your mirror is from the perfect parabola, or whatever shape you're trying to achieve.

    To measure zones here I'm using a mask with notches across the top, spaced at one inch apart. The first photo (right) uses Foucault's knife-edge tester. The knife cuts in from the right. You will notice two bright areas and two dark areas. The dark areas are the shadow of the knife. Separating them is a gray circle, and a gray vertical line which is the edge of the knife. This gray circle intersects the 8" zone on my notchstick.

    This means the edge of the knife touches the mirror's optical axis at the same point where the rays from the 8" zone cross the optical axis. The knife is at the roc (radius of curvature) of the 8" zone, so that zone appears gray (nulled). The knife is inside the roc of the outer zones, so they are dark on the right half. The knife is outside the roc of the inner zones, so the image is reversed and the knife's shadow appears on the left side of the vertical gray line.

   To do the test, I would write down how far from the mirror the knife is, then I would move the knife along the optical axis causing the gray ring to get larger wire test on a paraboloidor smaller. Every time the ring is centered on a zone I record the distance from the mirror for that zone. From this data the shape of the mirror can be determined.

   In the image above, the gray circle with the gray vertical line through it resembles the Greek letter Phi. So we call it the Phi symbol. For this next picture (left) I replaced the knife with a thin wire, about 0.005" thick. This represents just the edge of the knife-edge, so light gets past on both halves of the image. Now the Phi symbol is unmistakable. However, it is still one-dimensional like the knife-edge. Since it is tied to the vertical bar, no measurements can be made in the vertical direction. Once again, the wire is currently at the 8" zone on the notchstick (the mirror has a radius of 11").

   To do Kent's Wire test you move the wire longitudinally along the optical axis and measure the zones, just as with the tests above and below. Some folks might use one edge of the dark ring shadow to mark the zone with, but I believe that is inaccurate. It is better to use the center of the dark ring.

   Next I'll replace the wire with a spot about 0.005" diameter. The spot is only blocking the light from the part of the mirror with a roc equal to the position of the spot test on a paraboloidspot, which causes the dark ring shadow, and the out-of-focus spot itself blocks the center (right). The spot has an edge pointing in every direction, meaning that it is working in two dimensions. Light from the inner and the outer zones all get past the spot, only the 8" zone is blocked. The test is performed and reduced the same as the tests above.

   The last two photos on this page are the same setups as the previous two photos, except that the mask is removed and the light source is now a bright red led. The red led is a laser diode fixed so that it doesn't lase. The physical size of the opening which emits the light is very small, much smaller than my pinholes. That means that the edges of the shadows will be sharper, but the cost is a lot of diffraction effects.

    In some cases the extra diffraction can be a good thing. You can see that the dark ring now has a thin, bright, diffraction-caused line splitting it into two dark rings. It is especially easy to line up this narrow bright ring with the notches (or with a pinstick, if you prefer).

   In the left image (below) the diffraction patterns from the wire and from the ring interfere with each other. In the Spot test photo the ring is smooooth and two-dimensional. You might notice that the shadow of the spot in the center is slightly off-center. This is the astigmatism introduced by the small lateral separation of the source and the spot.

wire test on a paraboloid      spot test on a paraboloid


Here are some tips on spot-making:

   First, examine your pinhole with a very strong magnifying glass, like, a loupe or an inverted 25mm Plossl eyepiece will do. Make sure it is very round and clean, you don't want any burrs, etc. (You cannot use a slit light source as the test would then be constrained to one dimension.) The hole could be about 0.004" diameter (1/250 inch). The hole can be much smaller, but diffraction effects can become annoying.

   Now acquire a thin piece of glass, like, a microscope slide. Tiny spots can be made by very lightly misting with a can of spray paint. The spots should be perfectly round and about 0.004" diameter or so (0.1mm). There should be a variety of sizes, you will experiment with all of them. One of the sizes will be just right for the test you're currently running.

   I start with the glass several inches inside the roc, where it is easy to find. I bring the glass closer till I can see the small spots all over, then just move the glass over to center a spot I like. It's normally best to have the spot on the side of the glass facing the light, away from your eye. To measure diameters I have a machinists ruler with increments down to 0.010". Each line and each space between the lines is 0.005". Some of my spots are so small that I can barely see them with the naked eye. They are mere specks, about 0.001" or so.  You can pick up a tiny drop of liquid paint with a small nail and make a big spot next to your favorite tiny spot.

   So far the smallest spots I've played with are the specks of dust landing on a clean glass slide. For spot grids I made a file in Photoshop and let the local camera store print the digital file directly onto slide film with their fancy machine.

   Please be careful!! Glass has sharp edges which can reach out and cut you. I don't want to hear of anyone shaving off their corneas or needing their noses sewn back on. As you may have learned from the Foucault knife-edge tester, it hurts when you cut yourself.

Have fun, eh?



copyright ©2002 - 2004 by John Sherman