between the reference surface and the surface of the test piece is called
light reaches the reference surface of the Transmission flat, most of the
light passes through the surface and travels on to the surface of the piece
being tested. The rest of the light reflects from the reference surface
and begins the return journey back into the interferometer. This is the
piece is normally mounted on a tip/tilt device that permits adjustment
so that the surface under test can be made parallel to the reference surface.
condition is achieved, the light reflected from the test piece returns
to the interferometer where it interferes with the light that was reflected
from the reference surface. This is the Test Beam
of interference occur: Constructive Interference and Destructive
interference. When the Test Beam is in phase (i.e. in step) with
the Reference Beam, there is Constructive Interference -- the two intensities
"add" to each other and the light intensity is increased. This makes a
bright area in the interferogram. When the two beams are 180 degrees
out of phase, there is Destructive Interference and a dark area occurs.
where the two beams are out of phase by some other angle, say 45 degrees
or 90 degrees, there will be gray areas -- perhaps brighter than normal
or darker than normal dependent on the phase angle.
often think of the black areas of the interferogram as Fringes, but actually
a fringe consists of one dark and one light area. Each fringe amounts
to phase differences of 180 degrees. The entire phase cycle of a
wave of light is 360 degrees, so each fringe is equal to one half wave.
This is true for the Fizeau interferometer setup being described, but for
some setups, and for other types of interferometers, there can be other
values, such as one fringe per wave.
interference at the reference surface, the resultant beam returns to the
beam splitter where half of the beam is reflected into the CCD camera where
the interferogram is detected and displayed on the computer monitor.
this happens regardless of whether the interferometer employs phase shifting
or not. But without the advantage of phase shifting, or at lease
static fringe analysis, the operator is faced with the problem of interpreting
the interferogram and reducing the data to usable numerical values.
|In a phase
shifting interferometer, under software control, piezo-electric transducers
actually move the reference surface in a number of predetermined steps--
usually 1/4 wave steps towards the test piece. At each position,
the interferometer's Frame Grabber Board captures an interferogram
and stores it for analysis by the software. In Figure 2 above, with
each step of the phase shifter, you can see the fringes move 1/4 wave to
frame data are then processed by the computer to calculate optical wavefront
errors. The software finds aberrations and computes both peak-to-valley
(PV) and Root Mean Square (rms) values. The operator has the option
to subtract tilt, power, astigmatism, coma, and spherical aberrations from
the data. Interactive computer graphics make it easy to interpret
the output and numerical data provides quantitative results.
2 above, with each step of the phase shifter, you can see the fringes move
1/4 wave to the right. These straight "well behaved" fringes are
indicative of a flat surface, and the phase analysis of this interferogram
indicates that the test surface being measured is flat to better than 1/20
Figure 3, the test piece is actually slightly concave and irregular, The
fringes appear to spill down into the concavity. The advantage of
phase shifting is that it can determine whether the curved surface is concave
of convex by the direction that the fringes move. As the reference
surface is moved toward the test piece, the fringes will flow downhill
-- just like water. Attempting to interpret the meaning
of this fringe pattern is substantially more difficult than when the fringes
are better behaved. That is why phase-shifting interferometers are preferred
to accurately evaluate surface configurations of any but the simplest surfaces.
well as eliminating any ambiguity as to whether the surface is concave
or convex, the phase software is capable of analyzing extremely complex
surfaces and providing numerical values for Peak to Valley distances (PV)
and root mean square (rms) values. It also can provide highly accurate
information on aberrations such as astigmatism. Colorful graphics are presented
to help with the visualization and interpretation of surface contours
it is always desirable to obtain fringes of the highest possible contrast
in order to obtain the best analyses. The contrast seen in an interferogram
is dependent on the relative intensity of the reflections from the reference
surface and the test piece. The reflection from the reference surface
is dependent upon the reflective coating (or lack of a coating).
An uncoated fused silica surface will reflect about 4% of the light back
into the interferometer. If the test piece is made of almost any
glass, the reflectance from it will also be around 4 to 5%.
produced by the interferometer will display the highest contrast image
if the reflectance of the reference surface and the reflectance of the
test piece are not grossly different. If the goal is to measure highly
reflective surfaces such as that of a mirror, the interferometer will produce
better contrast if the reference surface also has a higher reflectance
coatings can be applied to the reference surface to improve the fringe
contrast over wide ranges of test piece reflectance.
covers the use of a Fizeau Interferometer making measurements of surfaces
that are approximately flat. Interferometers are also used to measure curved
surfaces by comparing the surface to a highly precise spherical surface
known as a Transmission Sphere. This will be dealt with in
a separate tutorial.
are also used to measure transmitted wavefronts through a substrate, and
can be used to determine the homogeneity and optical quality of an optical
component or a train of components. This will also be dealt with
in a separate tutorial.
Shifting Without Piezo Transducers -- Frequency Shifting
The availability of Diode
Lasers allows Interferometers to be phase-shifted by frequency modulation
of the laser source. By applying the appropriate voltage signal to the
Diode Laser driver, small changes in the laser frequency can be produced.
These frequency changes are small enough to make little difference to the
precision of the measurement, but do result in a train of moving fringes
that permit interferometry software to perform the phase measurement operation
with little difference from the standard method using piezo transducers.
There are a number of advantages to phase-shifting by frequency modulation
-- some of them outlined below.
of piezo transducers results in a much simpler and less costly method of
phase-shifting. Not only are piezos relatively expensive, but to achieve
more than minimal displacement of the reference surface, some type of voltage
amplification is required with resultant increase in complexity and cost.
interferometers, with their longer wavelength require larger displacements
if the phase shift is to result in a movement of several fringes. Again,
it is much easier to cover this requirement by frequency modulating the
laser than to do so using piezo transducers.
of larger aperture, the additional mass of the larger Transmission Flat
or Transmission Sphere present a greater challenge to a smooth operation
by a group of piezo transducers. Hysteresis is always a concern when moving
any mass with a spring-loaded device, but is particularly evident when
the mass being moved is relatively large. The effect of hysteresis
can be to cause subsequent phase-shift sequences to differ slightly from
each other -- resulting in small measurement and calibration errors.
caused by Frequency shifting is virtually zero and is independent of the
aperture of the interferometer or the weight of the T-Flat or T-Sphere
being used. After many thousands of phase-shifting cycles, piezo
transducers can exhibit some fatigue, and may ultimately fail or operate
under diminished capacity. No such problem exists when Diode Lasers
are frequency modulated. They continue to exhibit extremely long
life -- for many years, with no degradation.
Interferometers which utilize Diode Lasers incorporate our EndoPhazeTM
system of phase-shifting. Interferometers using HeNe Lasers and other non-diode
lasers, still require piezo transducers for phase shifting.