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A very flat surface -- parallel straight fringes  Analysis
of Surface Fringes
Volumes have been written about fringe interpretation and the subject can be treated as either an art or a science — it is a little of both. The simplest way to approach the matter is to provide the operator of an interferometer with some examples of various fringe patterns, or “interferograms”, together with a clear description of their meaning. A more analytical method is required in many cases and an attempt will be made to provide a very simplified and abbreviated demonstration of the techniques involved. The interferograms and drawings that follow are intended to familiarize the reader with the methods of fringe interpretation. Topographical Maps of a Surface One can think of an interferogram as a topographical map, only instead of the lines representing surface levels in feet, the contour lines are separated by one-half wavelength of light, 0.3164 microns (12.46 millionths of an inch) for interferometers with a Helium-Neon Laser source. So at the position of each contour line or “fringe” is at a level of 12.46 millionths of an inch above or below the fringe adjacent to it. When a surface is not very flat, one sees a lot of fringes — just as one sees the tightly packed contour lines surrounding a mountain or a steep valley. When examining this kind of surface, the tilt-table of the interferometer is simply adjusted to achieve the minimum number of fringes possible. This really just means adjusting the tilt of the test piece until it is as parallel as possible to the reference surface of the interferometer. These fringes are then counted, thus yielding some number such as “flat to 4 fringes” or “flat to 2 fringes per inch” When the surface is very flat, such as in a shallow valley or plain, the spacing between contour lines may be very large — indeed there may be only one contour line, or even less than one contour line, over an extended region. This corresponds to a very flat optical surface which may be flat to a very small fraction of a fringe. If the operator simply adjusts the tilt-table to achieve the minimum number of fringes possible, there would not be ANY fringes at all! The surface would appear either black or white, but without any fringe pattern. Therefore we must have a way of measuring such “fractional fringes”. Flat Parts When the interferometer can be adjusted to show less than one fringe, then one must resort to “Fringe Splitting” as shown above in order to evaluate flatness to fractional fringe accuracy. Very Flat Parts --Evaluation of Straight Fringes When a part is very flat, to less than 1/5 fringe as shown above, the fringes are so straight and uniformly spaced, that it becomes very difficult to accurately measure the fringe pattern without computer analysis. Thus, for routine measurements of parts that are this flat, the use of a computer equipped with either Fringe Analysis or Phase Analysis Software becomes a necessity if reliable, repeatable measurements are to be made. Some experts are able to
accurately determine the flatness of such parts without the use of a computer,
but these individuals are rare, and often two such experts will not entirely
agree on the flatness of a part. In addition, such measurements,
although they may be accurate, do not provide any hard numerical data that
can be verified and documented.
Not-so-flat Parts: “Fringe Splitting” When a surface is flatter
than one fringe, it cannot be evaluated by adjusting the interferometer
to see the minimum number of fringes. Suppose that a surface is flat
to 1/2 fringe. Trying to see 1/2 fringe using an interferometer would
result in the interferogram being either all black or all white, and would
not result in any precise measurement. In the drawing above, we see
a number of curved fringes with some lines drawn through them. The
two red lines are drawn to be tangent to the center of two adjacent fringes.
The green line is drawn to pass through the center of each fringe where
it cuts the edge of the test piece.
If
using a Fizeau Interferometer (with Helium-Neon laser with wavelength 632.8
nanometers) to measure a surface by reflection, the following table may
be helpful
Interferogram
of a part which is concave
by 4 fringes (about 50 millionths of an inch)
The fringe pattern of a convex part would look very much the same, but the difference can be determined by the way that the fringes move as described below. Is the Surface Concave or Convex? Concave and convex surfaces can only be distinguished by noting which way the fringes move during adjustment of the interferometer tilt-table. In all cases the procedure is the same: The interferometer tilt-table is adjusted to reveal a conveniently small number of fringes say 4 to 10. Then one of the tilt-table adjust screws is adjusted to move the part upward toward the interferometer. On a concave surface, the fringes will pour down into the valley On a convex surface the fringes will flow down the outside of the hill. The rule is simple: Raising the tilt-table toward the interferometer causes the fringes to run downhill — just like water.
Interferogram
of part flat to 2 fringes (~25 millionths of an inch)
Lapped Parts Flat to a Few Fringes
Computer-assisted Interferometers For highly precise and repeatable measurements of flatness, a computer evaluation of the interferogram is recommended. Two basic types of computer analysis are available: Static Fringe Analysis and Phase-Measuring Analysis, Static Fringe Interferogram Analysis In these systems, the Interferometer's CCD camera is connected directly to a “Frame Grabber” board in the computer. At the press of a button, all of the interferogram’s imaging data is dumped into the frame grabber so that the computer can begin elaborate data processing of the fringe position and straightness. Whereas with the simple approach described previously, we might make a flatness evaluation based upon the position and shape of 2 or 3 fringes, the Static Fringe Software looks a hundred or more data points on the fringes and performs sophisticated data reduction techniques to produce hard figures of rms flatness, peak-to-valley flatness, irregularity, etc. This permits the generation of elaborate graphical output of surface contour., showing 3-dimensional isometric plots, cross-sections, etc. Any basic interferometer with a CCD camera, can be up-graded to perform Static Fringe Analysis at any time. Phase Measuring Interferogram Analysis In Phase-Measuring interferometers, the frame grabber board captures five images of the interferogram, with the fringes in each image being shifted 1/4 wavelength of the laser source. This is accomplished by means of a piezoelectric transducer which actually moves either the reference flat or the test part in a number of small steps , each 1/4 wavelength long. The mathematical reduction of this data looks at 60,000 data points or more (depends upon size of sample) on the interferogram, yielding extremely high accuracy and repeatability, with a number of advantages over the Static Fringe method. Since special equipment is required to perform Phase-Measuring, it is not always possible to up-grade existing interferometers which are not properly equipped to handle the additional hardware required. Static Fringe or Phase-Measuring? The choice between these two types of systems is dependent on a number of factors: Phase-Measuring Interferometers are substantially more expensive than Static Fringe Systems
Although the same type of data and graphic output is provided by both systems,
the Phase-Measuring
With a Static Fringe Interferometer, it is necessary to place a synthetic aperture around the part being measured as well as a synthetic obscuration about any holes in the part. This is required to tell the software “where not to look.” Placing these apertures and obscurations is the responsibility of the operator, and can be a slow and nearly impossible task with some complex test pieces. With a Phase-Measuring Interferometer, this is unnecessary, since it looks at phase data, it never requires a synthetic aperture or obscuration. Not only does this save a lot of time and effort, but it also guarantees a higher level of accuracy. Since the Static Fringe Interferometers do not change the distance between the test piece and the reference surface, it is not possible to tell the difference between concave and convex. (Remember our prior discussion: when the test piece is moved toward the reference surface, the fringes run downhill — just like water. ) Phase-Measuring Interferometers
do not face this problem. Since they move either the test piece or
the reference flat the system can determine whether the test piece is concave
or convex.
Copyright
© 2008 Graham Optical Systems All Right Reserved
This page last updated June 28, 2008
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Concentric
ring-shaped fringes indicate either a concave or convex shaped part. This
part happens to be concave.
Interferogram
of a part with an area that is convex near the upper left-hand corner.
Some parts show very complex fringe patterns with both convex and concave
regions. Some are saddle shaped or shaped like potato chips!
