28 Sep 2005
Dynamic interferometry allows precise optical measurements to be made on the factory floor. Steve Martinek explains the principle and technology behind the technique.
The high-precision interferometry of optical components has always been a task that is relatively straightforward to perform in a quality control laboratory but that is a tough challenge elsewhere.
Conventional temporal phase-shifting interferometers can easily measure the surface shape and transmitted wavefront of optics with nanometre precision in a stable test environment. However, what happens when it is necessary to make precise measurements on the production floor or in a vacuum chamber? Or when the size and geometry of large astronomical optics make it impractical to isolate them from any environmental disturbances?
Unfortunately, the typical production environment is not stable on the nanometre scale. Architectural structures vibrate and resonate as a result of the motion caused by people, elevators, pumps, air-conditioning, noise and external traffic, for example. These mechanical perturbations couple into the test set-up and degrade the quality of measurements. Matters are made even worse owing to variations in the air's refractive index due to air currents and heating.
The result is that the fringes produced by interferometric test equipment are usually not sufficiently stable in the image plane to be measured. Relative distances between the interferometer and an optic under test can easily fluctuate by hundreds of nanometres, if not tens of micrometres, at frequencies of up to 100 Hz.
In the quality-control lab, the solution is simple: the environment is carefully controlled and any unwanted vibration is shielded by mounting the optical set-up onto a vibration-isolation table. But what happens when this isn't a practical option?
The answer is to shorten the data acquisition time dramatically and effectively freeze the fringe image during the measurement.
A conventional temporal phase-shifting interferometer typically requires the sequential acquisition of a minimum of four frames (∼120 ms) of video-rate data to make a measurement. "High"-precision measurement algorithms require as many as 13 more frames (which is equivalent to an additional 0.4 s). Keeping the fringes stable over this period of time without a vibration-isolation table is impossible.
However, reducing the acquisition time reduces the amount of relative motion and makes precise fringe measurements possible. Since the late 1980s, developments in phase-measuring interferometry have all tried to exploit this fact.
A number of methods have now been developed to achieve rapid data acquisition: high-speed static fringe, phase-shifting via high-speed camera, multiple simultaneous cameras, spatial carrier techniques and dynamic interferometry. Early implementations of these techniques were expensive, but recent developments have enabled affordable commercial products to enter the market. Methods that acquire just a single frame are the most efficient and two solutions will now be described in more detail.
Spatial carrier technique The spatial carrier technique is a single-frame phase measurement that works by introducing a tilt between the test and reference arms of the interferometer. The tilt is effectively used to provide the phase shift across three of four adjacent pixels.
In effect the method treats the fringe image as a mosaic of very small windows, each of which contains an individual tilted wavefront. It then measures their relative phases to reconstruct the information about the shape of the object under test.
The benefit of the approach is that it permits accurate data acquisition at camera frame rates with exposures possible in the order of a few milliseconds. The drawback is reduced spatial sampling and a limited measurement range of the local slope of the optical surface. In addition the method requires that the internal interferometer optics are well corrected to minimize off-axis aberrations.
By using Fourier transform algorithms to analyse spatial carrier measurements it is possible to reduce the required amount of tilt and relax the requirements of the internal optics. Spatial sampling is sacrificed, however, and care must also be taken to avoid the introduction of processing artefacts.
Dynamic polarization interferometry Another approach is to use polarization to generate the required phase shifts and to use multiple cameras, or multiple fringe images, on a single camera to acquire the data.
An example of a typical set-up is shown in figure 1. This dynamic interferometer is a polarization Twyman-Green configuration with a 2D grating at the exit pupil and a quadrant phase mask at the detector.
The imaging optics, grating and phase mask produce four images (phase-shifted interferograms) of the test object in parallel on a single high-resolution detector. This means that a single frame provides the four interferograms that are necessary to compute phase. The result is a phase-shifting interferometer with a sensor that is "exposure" limited rather than "frame-rate" limited.
To maintain sufficient spatial sampling of the object, a high-pixel-density camera is required. Fortunately, reasonably priced, commercially available megapixel cameras with integration times as short as 30 μs. With sufficient laser power it is possible to achieve data-acquisition times of a few microseconds by shuttering the source.
This design of phase sensor restricts data acquisition to a four-frame algorithm. That said, it has been shown that, in the presence of vibration, averaging multiple measurements gives an equivalent performance to that of a higher-frame algorithm.
Air turbulence over long path lengths can still degrade a single measurement, but as each interferogram sees the same perturbation averaging while mixing the air can quickly minimize this error contribution.
Recent improvements to the dynamic interferometer phase sensor have replaced the quadrant phase mask with a pixelated mask. In this configuration an array of phase-mask elements that match the pixel pitch of the camera are bonded directly to the camera sensor.
This mask creates a unit cell where the four phases are measured on four adjacent pixels and replicate this pattern over the entire sensor array. The 2D grating element is no longer required, and this phase mask is achromatic and allows operation at other wavelengths.
The pixelated phase mask can be exploited in Fizeau interferometer configurations as well. To operate at tens of microsecond exposures, these systems require fully coherent and custom-designed optical systems.
In conclusion, continual advancements in phase-shifting interferometry have now led to a dynamic method that can operate in the presence of environmental disturbances but preserves measurement accuracy.