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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 onehalf wavelength
of light, 0.3164 microns (12.46 millionths of an inch) for interferometers
with a HeliumNeon 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 tilttable 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 tilttable 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.
Notsoflat
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 HeliumNeon 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
ringshaped 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 tilttable. In all cases the procedure is the
same:
The
interferometer tilttable is adjusted to reveal a conveniently small number
of fringes say 4 to 10.
Then
one of the tilttable 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 tilttable 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 lefthand 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 underevaluated. 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 hardcopy 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 computerassisted interferometers play their part!

Computerassisted
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 PhaseMeasuring
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, peaktovalley
flatness, irregularity, etc. This permits the generation of elaborate graphical
output of surface contour., showing 3dimensional isometric plots, crosssections,
etc. Any basic interferometer with a CCD camera, can be upgraded
to perform Static Fringe Analysis at any time.
Phase
Measuring Interferogram Analysis
In PhaseMeasuring 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 PhaseMeasuring, it is not
always possible to upgrade existing interferometers which are not properly
equipped to handle the additional hardware required. 
Static
Fringe or PhaseMeasuring?
The
choice between these two types of systems is dependent on a number of factors:
PhaseMeasuring Interferometers are substantially more expensive than Static
Fringe Systems
Although the same type of data and graphic output is provided by both systems,
the PhaseMeasuring
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 PhaseMeasuring 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. )
PhaseMeasuring 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.
For further information
on how Phase Interferometers
work, click here.
GRAHAM
OPTICAL SYSTEMS, 9530 Topanga Canyon Blvd., Chatsworth, California 91311
Phone
(818) 7001263
Copyright
© 2014 Graham Optical Systems All Rights Reserved
Durango
is a trademark of Diffraction International
This
page last updated February 19, 2014
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