How Phase Interferometers work 
(With and without Piezo Transducers)

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 Phase Shifting With Piezo Transducers

Figure 1 below is a schematic drawing of the most important features of a Fizeau Interferometer. The light path begins at the laser which produces a coherent beam of small diameter (typically less than 1 mm).  A beam that is coherent can be imagined as one in which all of the individual waves of light are in step. Before this small diameter beam can be of any use in the interferometer it must pass through and reflect from several critical components.  It is convenient to break the light's journey down into individual steps:
 

The laser beam passes through a spatial filter and a beam expander which increases the diameter of the beam so that it will fill the aperture of the interferometer -- in the illustrated case, a 4-inch aperture Fizeau.  The purpose of the spatial filter is to remove "noise" from the laser beam and minimize "speckle" -- an annoying feature of laser light.
The expanding beam now passes through a "beam splitter" which literally divides the beam into two beams -- one which passes through the beam splitter, and one which reflects from it at an angle of 90 degrees.
The beam which passes through the beam splitter continues to expand as it travels on to the "collimator" -- a special lens which is positioned so that after the expanding beam passes through the collimator, it emerges as a parallel beam 4-inches in diameter.  This parallel, or "collimated" beam still consists of highly coherent laser light -- with all of the waves in step.
The collimated beam of light now passes through a plate of high quality fused silica usually called a Transmission Flat, which has two highly precise surfaces.  The first surface that the light encounters is sometimes coated with an anti-reflection coating to eliminate any unwanted reflections, but most often, the two surfaces are deliberatelymade to be at a slight angle to each other. 
With this configuration, the interferometer can be aligned with its second surface perpendicular to the axis of the collimated beam.  This second surface is the "reference surface" which will be used to produce the interferogram of the test piece.  With the second surface aligned perpendicular to the collimated beam, obviously the first surface is not, because of the small angle between the two surfaces. This condition prevents any "unwanted" reflections from the first surface spoiling the interferogram.
Figure 1
Figure 2
Adjusting the tip tilt of the test piece brings the surface nearly parallel to the reference surface, and reduces the number of fringes.		 Figure 3
This is an interferogram of a flat surface.  As the reference surface is phase shifted, the fringes move in 1/4 wave steps		 Figure 4
This one isn't so flat; its concave. As the reference surface is phase shifted, the fringes move inward -- down into the concave surface!
The region between the reference surface and the surface of the test piece is called the "cavity" 
When the 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 Reference Beam.
The test 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.
When this 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
Two types 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. 
In between, 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.
People 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.
So after 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.
All of 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 the right.
The 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. 
In Figure 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 wave! 
 In 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. 
As 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
In Interferometry 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%. 
The interferogram 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 coating.
Special coatings can be applied to the reference surface to improve the fringe contrast over wide ranges of test piece reflectance.
This description 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.
Interferometers 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.
Phase 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.
The elimination 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.
Infrared 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.
With interferometers 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.
Hysteresis 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.
All Graham 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.
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This page last updated April 23, 2013