very flat surface -- parallel straight fringes
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.
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”.
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.
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.
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
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
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
these units are somewhat confusing, perhaps the following conversion tables
not be more confusing!)
using a Fizeau Interferometer (with Helium-Neon laser with wavelength 632.8
nanometers) to measure a surface by reflection, the following table may
/ Metric Fringes / Metric
of a part which is concave
4 fringes (about 50 millionths of an inch)
ring-shaped fringes indicate either a concave or convex shaped part. This
part happens to be concave.
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
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
interferometer tilt-table is adjusted to reveal a conveniently small number
of fringes say 4 to 10.
one of the tilt-table adjust screws is adjusted to move the part upward
toward the interferometer.
a concave surface, the fringes will pour down into the valley
a convex surface the fringes will flow down the outside of the hill.
rule is simple: Raising the tilt-table toward the interferometer causes
the fringes to run downhill — just like water.
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!
of part flat to 2 fringes (~25 millionths of an inch)
Parts Flat to a Few Fringes
Parts Flat to a Few Fringes
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.
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.
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!
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!
Fringe or Phase-Measuring?
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
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.
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.
choice between these two types of systems is dependent on a number of factors:
Phase-Measuring Interferometers are substantially more expensive than Static
Although the same type of data and graphic output is provided by both systems,
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. )
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
SYSTEMS provides Durango Interferometry Software (both Static Fringe and
Phase Measuring) with all of its interferometers.
For further information
on how Phase Interferometers
work, click here.
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page last updated February 19, 2014