Interferometry is one of the most widely used precision measurement techniques known to humankind. The precision provided by interferometers has enabled countless scientific discoveries and breakthroughs. These range from the Michelson and Morley Experiment in 1887, which lead to the discovery that electromagnetic waves could propagate through the vacuum of space without the need for an “aether” to the detection of gravitational waves in 2015 by the Laser Interferometer Gravitational-Wave Observatory (LIGO). In addition to these groundbreaking discoveries, interferometry is also used every day for applications including infrared spectroscopy, telecommunications, and metrology. It would be impossible to review all aspects of interferometry, so we are instead going to focus on an application that is of importance to laser engineers, testing surface flatness of optical elements with a technique called Firzeau Interferometry. In this blog we will briefly introduce the fundamental physical principles of interference, then we will get into the specifics of the Fizeau Interferometer and explain why this interferometer is uniquely suited for measuring the surface flatness of optical elements.
One of the unique physical properties of waves is their ability to be superimposed on top of each other. This arises from the fact that unlike solid matter two or more waves can exist in the exact same physical space, and while they do their amplitudes add together. As can be seen from the simulation below, when the two waves are perfectly in phase with each other, this superposition produces a resultant wave with twice the intensity of the original. On the other hand, when the two waves are perfectly out of phase, they cancel out. These two processes are known as constructive and destructive interference, respectively.
In an interferometer, two identical beams of light, typically but not always from a laser source, are split into two different legs and then recombined. If there is any difference in the optical path length between each of the legs of the interferometer, it will cause a pattern of constructive and destructive interference. This interference pattern is directly correlated to the difference in pathlength, and as the optical path length is varied by half of a wavelength of light, the pattern of bright and dark spots will invert. By counting the variation in the fringes this allows for sub-wavelength displacement measurement.
While there are many different types of interferometers used in optical testing, the Fizeau interferometer has become the standard for evaluating optical quality. In the Fizeau interferometer, the laser source is first spatially filtered to ensure that the beam quality is as close to perfect as possible, then the light is recollimated using a collimating lens and then directed to the reference surface which is precisely placed on top of the flat being tested, separated by narrow spacers. This reference surface must be made to exceptional optical quality typically with roughness less than a twentieth of a wavelength. The first surface of the reference flat is slightly angled to ensure that any light reflected doesn’t contribute to the resultant interference fringes, but the second surface is straight so that the reflected light travels back along the same path as the incident light. When the laser light which is transmitted through the reference surface is incident on the test flat, the reflected light from the flat will also propagate back along the same path as the reference surface. Therefore, if there are any surface defects this will result in a difference in optical phase between the two wavefronts and result in interference fringes. In the two images below, you can see a simplified example of a schematic diagram of a Frizeau interferometer, as well as an interferogram captured by Wanqing Xie, Et al. at the Harbin Institute of Technology in China using an interferometer from the Zygo Corporation. In the interferogram, you can clearly see surface deformation ranging from roughly +/- half a wavelength.
Curved optics such as lenses and curved mirrors can also be tested using this interferometer. For this measurement though, they require the addition of a transmission sphere which is a set of lenses whose power is specially designed to match the angle if the reflected rays from the test surface to re-collimate the light back into the interferometer. In the figure below, you can see an example of a Frizeau interferometer from Zygo Corporation showing the use of a transmission sphere (TS) to test a curved optic. It is important to note that these transmission spheres must be designed to be diffraction limited so that they do not add any additional aberration to the wavefront. Otherwise they will not produce an accurate interferogram.
Just as it is essential that the reference surface and the transmission sphere are designed so that they don’t add any additional aberration into the system, so must the laser beam itself. It is important that the laser be both single longitudinal mode and single spatial mode. Having a single longitudinal mode laser ensures that the coherence length is long enough that there are no phase discontinuities over the measurement length. This is extremely important for optical surface measurement, since many industrial Frizeau interferometers can be several meters long. As for the spatial mode profile, having a single TEM00 mode provides the same assurance over the entire optic. While all interferometers require single longitudinal mode, the fact that Frizeau interferometers expand the beam across the whole optic means they are far more sensitive to the laser’s spatial mode profile than most. Additionally, since the laser beam is spread so widely and, in many cases, only a small fraction of the laser light is reflected into the interferometer (for example when testing lenses and windows), these interferometers typically require higher laser powers as well.
Traditionally this has been achieved using costly stabilized HeNe lasers, but today solid-state options are not only available, but their performance is starting to outmatch those of even the highest end stabilized HeNe sources. For example, the Solo - 640/1000 single frequency diode pumped solid state (DPSS) laser from UnikLasers uses Bragg Range Michelson Mode Selector (BRaMMS) technology to produce output powers of up to 1 watt with perfect TEM00 spatial mode profile at 640nm. These lasers offer exceptional power stability of 1.5% over 4 hours with RMS noise (10Hz – 10MHz) less than 0.1%. Additionally, the Solo - 640/1000 offers actual single frequency performance with a laser linewidth less than 500kH and a coherence length greater than 100m, all within a compact footprint laser head of only 80 mm x 65 mm x 172.2 mm.
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