How to optimize interferometer performance

Interferometers are generally easy-to-use instruments for measuring the surface figure of optical elements and the transmitted wavefront performance of optical systems. Their "push-button" ease of use may actually be a shortcoming in the operator`s ability to obtain accurate measurements in a given test situation. In order to maximize the measurement capabilities of an interferometer system, it is important to have a good understanding of the measurement process, as well as a familiarity with th

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Interferometers are generally easy-to-use instruments for measuring the surface figure of optical elements and the transmitted wavefront performance of optical systems. Their "push-button" ease of use may actually be a shortcoming in the operator`s ability to obtain accurate measurements in a given test situation. In order to maximize the measurement capabilities of an interferometer system, it is important to have a good understanding of the measurement process, as well as a familiarity with the materials and design of the surfaces and systems to be tested.

Understanding the measurement process entails more than just an understanding of how the interferometer system works-it also requires knowledge of what can affect the accuracy and the repeatability of the measurement. Interferometer systems are very sensitive to changes in the test environment. Changes can be the result of vibration, acoustic noise, air turbulence, temperature, and humidity.

Any change in the test environment can cause noise in the measurement. Noise in the measurement process is any difference in the data that is not directly attributable to the surface or system being measured. The sources of measurement noise-for example, vibration and sound energy-can be identified, and countermeasures can be put in place to minimize their effects on the measurement process.

Damping vibrations and acoustic noise

Several sources of error in the test environment can have substantial effects on the accuracy and reliability of interferometric data. Vibration in particular is the largest and most obvious error source in an interferometric test situation. Vibration is present in all environments and is typically the product of operations inside and outside of the physical plant. Internal vibrations can emanate from machinery, air conditioning, heating systems, and processing equipment. Vibrations from external sources include road traffic, railroads, and the machinery and processing equipment at the plant next door or down the street. The magnitude of vibrations from external sources is dependent on a number of variables, including the magnitude of the source, the frequency, and how well the ground conducts the sound energy.

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FIGURE 1. Vibration and acoustically coupled noise usually appear in computer-plotted interferometer data as ripples in the contour and isometric plots.
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The most effective countermeasure for vibration is to make sure that the interferometer is located in a quiet area of the building and is supported on a vibration-isolation table. Several manufacturers produce vibration-isolation systems that can isolate a given equipment setup from floor vibrations down to approximately 1.8 Hz. Usually this will take care of most of the low-frequency noise coupled through the floor.

Acoustic noise can also be a significant source of error in a measurement. Acoustic noise is basically sound pressure waves that travel through the air. These waves have varying energies, but in general, the lower the frequency of the noise, the greater the amplitude. Acoustic noise affects the interferometric cavity by "driving" elements of the test setup-the mounts, the part, the part holder, even the interferometer mainframe itself.

Interferometers are particularly sensitive to vibrations and acoustic noise in the range from 0 to 30 Hz, with the lower-frequency noise having the most dramatic effect (see Fig. 1). The ripples seen in contour and isometric plots typically have a frequency approximately two times the fringe frequency. The most effective countermeasure for acoustically coupled noise is to design the test setup such that the part or system to be tested is rigidly mounted and the mount supporting the part is stable and robust. Ideally, the mount, in combination with the part to be tested, should have a resonant frequency higher than 30 Hz.

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FIGURE 2. Software-based environmental qualification routine allows the user of an interferometer to determine the frequency spectrum of environmental vibrations/noise.

Normally, sophisticated measurement tools and techniques are required to measure and quantify vibration and acoustic noise sources. Because of the cost, this equipment is not always readily available, and it is not always practical to measure each test environment. Some PC-based interferometer systems have an environmental qualification routine built into the software. This software tool enables an operator to qualify the measurement environment by directly measuring the effects of vibration and noise on the interferometric cavity (see Fig. 2).

Minimizing air turbulence

Perhaps the most difficult task for the operator is determining when the measurement is reliable and accurately reflects the true characteristics of the component or system being measured. Air turbulence, material stability, index stability, and temperature gradients in the cavity also affect the accuracy and reliability of interferometer measurements.

The movement of air in the interferometric cavity produces a transmission medium that varies in density across the measurement aperture. The differences in air density causes small, local differences in the index of refraction of the air, which produces differences in optical path (OPD) within the cavity. The varying OPD in the cavity combines with the OPD of the measurement wavefront, introducing errors.

Sometimes, it is helpful to enclose the test cavity to isolate it from the airflow in the room. There are some cautions that need to be observed when doing this. If the edges of the enclosure are very close to the edge of the beam path, there can be some effect from the air boundary layer at the wall of the enclosure. To avoid this, make sure that the walls of the enclosure are at a distance at least half the beam diameter from the edge of the measurement beam.

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FIGURE 3. Repeated measurements of peak-to-valley and rms wavefront values determine whether the measurement cavity is stable enough for reliable data to be taken.
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Averaging can be used to minimize the effects of random air turbulence. A high-quality interferometer system will provide both intensity and phase averaging. The difference is that in intensity averaging, the raw camera intensity data are accumulated and averaged. In phase averaging, wavefront data are averaged after the intensity data are converted to phase. Because the intensity averaging takes place before any calculations are made, the time period for each data set is very short. The averaging time period is somewhat longer for phase averaging.

Phase averaging and intensity averaging can be used alone or in conjunction with each other. For example, an operator may specify that the measurement will consist of eight phase averages, each consisting of the average of 16 intensity data sets. The advantage is that a combination of averages can sometimes be used to negate the effects of purely random turbulence over a wide range of periodicity.

A modern, computer-based interferometer will have statistical tools available that enable an operator to look at the distribution of data from a number of measurements. Using these tools, the operator can create control charts for the peak-to-valley and rms values for the measurement. The control charts will show the variation in these values over a number of measurements. When the peak-to-valley and rms values stabilize, that is, when the trend is flat, the operator has a good indication that the measurement cavity is stable. If the cavity is stable, then reliable interferometric data can be taken (see Fig. 3).

Controlling temperature variations

Variations in temperature can cause differences in air density across the measurement aperture, thermal air movement, and changes in the surface or system being measured. Thermal effects in the air can be handled in the same fashion as air turbulence. Thermal effects in the part being measured are more difficult to deal with.

In the case of a surface measurement on a mechanically and thermally stable sample, there is relatively little error introduced by distortion of the part due to temperature variations. For most other materials, including crown and flint glasses and transmitted wavefront measurements of systems or single components, the material can change with temperature, which can lead to erroneous measurements.

All materials, optical and nonoptical, have a coefficient of thermal expansion and contraction and a coefficient of thermal conductivity. The coefficient of thermal expansion dictates how much the material will change with temperature, and the coefficient of thermal conductivity determines how fast the material will respond to changes in temperature. Knowing both of these parameters can be useful in determining whether the interferometric data are reliable.

Surface measurement is probably the most common application for an interferometer system. Most optical surfaces are polished wet, using an abrasive agent suspended in water, or some other carrier medium. The polishing takes place on some type of lap, which controls the basic shape of the piece being worked. In the polishing process, the temperature of the slurry medium may be different from the ambient temperature in the work area. In addition, cleaning of the surface with solvents prior to measurement can cause a large difference between the temperature of the part and the ambient environment. This is primarily due to evaporative cooling of the solvent from the surface. The cleaning process may also introduce temperature gradients across the surface of the part, caused by nonuniform cooling of the surface. Depending upon the characteristics of the material being polished, the temperature gradients can influence the surface measurement data if ample time is not allowed for the test piece to come to thermal equilibrium prior to measurement.

Although there are some optical materials that have very low coefficients of thermal expansion, most optical materials require some time to come to thermal equilibrium. The data sheets for an optical glass will always include a number that defines the coefficient of expansion and contraction for that particular material, the coefficient of thermal conductivity, and the index change with temperature. The amount of time required for a sample to come to thermal equilibrium depends greatly on the size of the sample-a small sample will come to equilibrium far more quickly than a large sample of the same material.

Changes in temperature also produce changes in the index of refraction of optical materials. In some materials the change is negligible; in others, the change is large enough to cause substantial errors in the wavefront measurement. In an optical system, such as an imaging lens, temperature changes can cause changes in power and can cause distortions in the internal element, producing variations in the wavefront performance. It is more important to allow an optical system to come to thermal equilibrium prior to taking qualification data for these systems than it is for surfaces.

Humidity, too, can influence accuracy of interferometer readings, but in most instances, the humidity of the air in the test environment will have a negligible effect on the data.

PHILIP ARMITAGE is a senior engineer at Zygo Corp., Laurel Brook Rd., Middlefield, CT, 06455.

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