Flatness and Roughness 

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It's all in the way you look at it!

Superficially, if you look at a piece of ordinary window glass, it looks flat and seems smooth.  However, our eye is not very good ad determining the quality of any surface. 

Under a microscope, such a smooth surface shows numerous scratches and other small imperfections.

Under an interferometer, we see that the surface is not flat; indeed it may be very wavy and irregular.

How can a surface be flat and yet rough?

There is considerable confusion over the meaning of flatness and roughness.  Really, it is all a matter of scale. The figures at the left attempt to explain the difference.

After we have defined some surface types, we will look at how they are measured.  We will also see that any definition of flatness or roughness depends upon which type of tool we use to measure it -- and, of course, it is all very relative!
 
A surface that is both flat and smooth is a special case -- the ideal type of surface that is so often sought in the world of optics.
Example: a high quality optical flat.
Most optical surfaces fall short of the ideal. Many are relatively flat but with some roughness-- usually in the form of scratches and digs or pits.
Example: most flat optical surfaces
Then there is a general class of surfaces that may have a relatively smooth surface, but with subtle curves or "waviness" that can not be considered flat. Example: a piece of high quality float glass
Some surfaces are really beyond classification with no particular surface figure -- flat or otherwise, and have a rough surface texture.
Example: most surfaces including optical glass during the grinding process.

One way of visualizing the properties of a surface that is both flat and smooth is to imagine such a surface being inclined slightly as shown at the left.  Now a smaller block also with a smooth flat surface is placed on the inclined plane and observe that it easily slides along.  No bumps and little friction.
A similar experiment with a surface that is flat but a little rough shows that the small block with a smooth flat surface likewise has little problem sliding along the inclined surface -- provided that the block is not small enough to drop into one of the pits!
When we take the same surface and allow a small ball to roll down, it may or may not make it all the way.  The image at the left shows such an experiment where the ball ultimately gets caught in one of the pits. Note that the results of this experiment depend upon the size of the ball!
This short treatise scarcely covers such a complex subject, but perhaps it will set the stage for further understanding.  There is such variation in surface texture, from very smooth to very rough, with semi-matte and matte surfaces in between.  Smooth, polished surfaces are readily measured using a standard Fizeau Interferometer, while semi-matte and matte finished surfaces can be measured using grazing incidence interferometers.  We invite you to explore the capabilities of these interferometers which ar described in detail throughout this website.  If you still need assistance with your measurement problem, don't hesitate to contact Gordon Graham: Phone (818) 700-1263  E-mail: techinfo@grahamoptical.com
Graham Optical Systems, 9530 Topanga Canyon Blvd., Chatsworth, California 91311
Copyright © 2013 Graham Optical Systems  All Rights Reserved  This page last updated April 22, 2013