Fringe Interpretation

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

 The arithmetic is simple.  The distance between the two red lines is the width of one fringe is “X“ (here measured to be 3.74 in arbitrary units) and the distance from the center of the top fringe to the blue line is “Y” (here measured as 1.93) The flatness of the test piece shown above is Y/X = 1.24/5.02 = 0.247 fringe                                                                                          = 3.08 millionths of an inch

 Another example -- flat to 6.4 millionths of an inch Just to illustrate another example, the flatness of this test piece is:  Y/X = 1.93/3.74 = 0.516 fringe        = 6.4 millionths of an inch. For some requirements, flatness is called out in waves, in micrometers, nanometers or in microinches.  A little calculation lets you manipulate these figures readily If these units are somewhat confusing, perhaps the following conversion tables will help  (hopefully not be more confusing!)

 English / Metric 1 inch = 1 microinch = 1 millimeter = 1 micrometer = 1 nanometer = Inches 1 .000001 inch .03937 inch .00003937 inch 00000003937 inch Microinches 1,000,000 microinches 1 39370 microinches 39.37 microinches 0.03937 microinch Millimeters 25.4 millimeters .0000254 millimeter 1 .001 millimeter .000001 millimeter Micrometers 25,400 micrometers .0254 micrometer 1,000 micrometers 1 001 micrometer Nanometers 25,400,000 nanometers 25.4 nanometer 1,000,000 nanometers 1,000 nanometers 1

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.

 Waves / Metric Fringes / Metric 1 wave = 1 fringe =  1/2 wave = 1/4 wave = 1/10 wave = 1/20 wave = Nanometers 632.8 nanometers 316.4 nanometers 158.2 nanometers 63.28 nanometers 31.64 nanometers Micrometers .6328 micrometers .3164 micrometers .1582 micrometer .06328 micrometer 0.03164 micrometer Millimeters .0006328 millimeter .0003164 millimeter .0001582 millimeter .00006328 millimeter .00003164 millimeter Microinches 24.913 microinches 12.457 microinches 6.228 microinches 2.3913 microinch 1.2457 microinches

Interferogram of a part which is concave
by 4 fringes (about 50 millionths of an inch)
I

Concentric ring-shaped fringes indicate either a concave or convex shaped part. This part happens to be concave.

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 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!

Interferogram of part flat to 2 fringes (~25 millionths of an inch)
Lapped Parts Flat to a Few Fringes

 Lapped Parts Flat to a Few Fringes These are the parts which are easiest to measure.  The interferometer is simply adjusted to show the minimum number of fringes achievable, and then the fringes are counted.  It's as simple as that.  If these parts are being evaluated using test flats, the part is brought into optical contact with the test flat and then the fringes are counted.  One of the problems with a test flat is that a certain amount of pressure is required to squeeze the air out of the gap.  It is difficult to know when true optical contact has been made. If the air gap is wedge shaped because of a piece of dirt or lint, then more fringes may appear than there should be, and the part will be under-evaluated.  In many cases such parts may be rejected, even though they really meets specification.  On the other hand, if too much pressure is applied in order to produce optical contact, actual distortion of both the part and the test flat may result, and a bad part may pass inspection when it should have failed. The result is that even for these simplest of evaluations (surfaces that are flat to a few fringes) serious errors can be made using test flats, particularly in inexperienced hands, whereas an interferometer always gives the same measurement, and can provide hard-copy verification of the data! There are so many factors involved in fringe interpretation, that it can, at times, be avery difficult task.  Certainly for high precision measurements that are repeatable, flatness interpretation needs a helping hand.  This is where computer-assisted interferometers play their part!

 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
Interferometer will provide higher accuracy and repeatability.

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.

GRAHAM OPTICAL SYSTEMS provides Durango Interferometry Software (both Static Fringe and Phase Measuring) with all of its interferometers.

GRAHAM OPTICAL SYSTEMS, 9530 Topanga Canyon Blvd., Chatsworth, California 91311
Phone (818) 700-1263