Hi Mark76,

Right... I think I'm aware of all the effects you mentioned. Just don't have time to go into all of it right now.

If you look at Verhoeven's notes (early chapter(s) plus appendix I think), you will see that he talks about multiple-faceted knife edges on the laser goniometer. So the laser shines on both the micro-bevel and the back-bevel. So typically, you get a total of four spots (two on each side).

Normally, the multiple facets (micro bevel, back bevel, and then the side of the knife) form a convex polygonal cross section. So the microbevel has the largest included angle, and deflects the light the most, producing the widest two spots. Next, the included angle of the back-bevel is a bit smaller, and creates two spots which are closer together. Finally the sides of the knife have the smallest included angle of them all, and creates the spots which are closest to gether. In this example, there would be a total of six laser spots (three on each side, from microbevel, back-bevel, and the side of the knife).

If the cross-section of the knife is not convex (ie: a hollow grind), then the order of the spots can be changed around.

Maybe (?) one way to avoid confusion is simply to cover the sides of the knife with black tape, then the reflections will only be from the micro-bevel and back-bevel? Don't know if this works well in practice or not.

Curved surfaces act like having a million little faceted bevels. So you get a "smear" of spots. This is interesting, but makes things harder to understand. The "smear" is caused by two things, I think. The first is a curved bevel (such as a convex bevel). The second is scratches and unevenness in the surface. Ignoring the surface-scratches/texture, let's assume the convex edge has a mirror polish. Then the smeared out reflections represent the range of angles along the convex bevel. Each point in the smear, can be thought of as representing the angle of an infinitesimal tiny bevel facet (where the smooth convex bevel is thought of as being composed of an infinte number of tiny facets, just like a circle can be thought of as a polygon with an infinite number of sides).

Sorry, leaving out some details, and I'm not explaining things very well. But I think this is enough that all the details can be figured out without too much trouble. If not, I'll have a more detailed post for you guys.

In the goniometer that I want to build, I'm hoping to use some optics to shrink the diameter of the laser beam, so that you are only checking the angles for a small spot on the knife. Not sure about the pratical issues of this, but you could easily use a binocular which is say, 8x magnification, to shrink the beam diameter by a factor of 8. In a real lab, they have "beam expanders" that they could run backwards to shrink the beam, and they have fancy collimator lenses, etc. But all that's too expensive, I'm going to use a pair of cheapo $20 binoculars. Just shine light into the main aperature, and out the eyepiece will be a thinner beam. You may have to play with the focus a bit, though.

btw, NEVER EVER (never never, ever ever) look into an optical instrument of _any_ kind when working with laser light. The optics can focus the power of the laser to an extreme degree, which can much more easily cause eye-damage than an unfocused laser. Remember, your laser pointers are "safe" under normal conditions; looking at a laser through optics is NOT normal!

The real issue I'm worried about is how to deal with smearing in the reflected beam that is caused by surface texture (such as scratch patterns). Right now, I'm thinking to take multiple measurements of the reflected beam, where the twist of the knife (along it's long axis) is changed several times. There is the whole issue of precision versus accuracy in such measurements, where the smear due to surface texture is, in a way, kind of hurting our precision.
en.wikipedia.org/wiki/Accuracy_and_precision

If the surface-texture were isotropic (ie: look like it was sand-blasted), then this is easier to think about. But the scratch pattern is not isotropic; it's anisotropic, meaning it has direction (such as parallel scratch patterns) and will smear out the reflection in some directions more than others. The sand-blasted texture is, on average, uniform and directionless, so we can consider it to be basically isotropic, and it would (on average) spread out the reflection in all directions equally. I'm oversimplyfing slightly, but this is the easiest way I know how to give the general idea without going into the details of the bidirectional-reflectance-distribution-function (BRDF) etc.
en.wikipedia.org/wiki/Bidirectional_refl...istribution_function

Finally, there may be issues with the laser being a coherent light source with a sngle wavelength, and therefore revealing diffraction and interference problems more readily. I think this isn't so much of an issue, but I've not experimented, so I don't know.

So my main question is: how to tell the difference between smearing due to geometry (such as convexing) from smearing due to surface texture (such as scratch marks)?

Hopefully I have more free time this week (or next) to discuss and experiment with everyone and everything in full detail.

Sincerely,
--Lagrangian

P.S. Another way to get precise knife angles is to use a mold of the knife (say using epoxy). You then remove the mold, cut a cross section, and then take a photograph of the mold using a microscope. Then measuring the photo, you can get the angle rather precisely. For example, most USB microscopes have tools for measuring lengths etc. in the image. This method was mentioned by Phil Wilson, and I also think by Cliff Stamp and/or Ankerson (of www.BladeForums.com). But I think it was someone else (sorry that I forget who) in bladeforums.com who first tried it (he talked about using WD-40 as an anti-sticking agent and W-B Weld Putty as the epoxy for making the mold). Perhaps one could compare the results of the mold-method to the laser-goniometer to see what's going on with the smeared out reflected beams?

P.S. My favorite joke for hobbyists who play with lasers above 5 milli-watts of power is a sign that reads:

You can buy this sign from United Nuclear:
unitednuclear.com/index.php?main_page=index&cPath=29_60