Mirau interferometer
A Mirau interferometer or Mirau lens is a white light interferometer that consists of a microscope lens , a semi-transparent mirror and a reference mirror. It is mostly used for optical measurement and classification of reflective surfaces. It was applied for a patent on March 3, 1949 by the French optician André Henri Mirau .
principle
Figure 1 shows the beam path of a Mirau objective. The objective is used in reflected light microscopy . The object is illuminated through the lens. As a result, the illumination and observation beam paths in the lens are the same. The white light from the light source (not shown), which is incident through the lens (1) from above, first hits the semi-transparent mirror (2). Part of the light passes through at (5) and is reflected by the object (3) at (7). The other part of the light takes its way from (5) to the reference mirror (4) and from there is reflected back to the semi-transparent mirror (2).
At (6) the object beam and the reference beam finally unite and get back into the lens as an overlay. The objective images this overlay as interference in the eyepiece or a camera used for observation .
The prerequisite for the observation of interference phenomena is that the optical path lengths of the light paths (5-4-6) and (5-7-6) differ by a maximum of the coherence length of the white light used for illumination. In order to function, it is therefore necessary that the partially transparent mirror (2) is half the focus distance in front of the lens and that the object is in focus .
Effects
If you observe a mirror that is slightly tilted to the optical axis with a Mirau lens (Fig. 2), you can see parallel interference fringes around the focal plane, which are the most contrasting in the focal plane and are modulated weaker and weaker to the sides. Figure 3 shows the intensity profile along the horizontal axis for clarity.
This picture becomes easier to understand if one looks at only a single point of the mirror and slowly pushes the mirror through the focal plane. The theoretical intensity profile at this point then corresponds to the blue curve (3) in Fig. 4.
Applications
A Mirau interferometer can be used for a variety of purposes.
Flatness check
Mirau initially designed the system for mobile use, as Fig. 5 from his patent document shows. The interference fringes on the sample surface allow a very simple, but precise, visual flatness test: if the strips run parallel through the image, the sample is flat, if they are curved, it is uneven. The method is preferably used on metallic surfaces and optical components.
Profile measurement
In order to measure a three-dimensional profile of a surface with a Mirau interferometer, one observes a point on the sample while sliding it through the focus along the optical axis. The brightness changes several times from light to dark and back according to the blue curve (3) from Fig. 4. The exact position of the surface coincides with the maximum of the envelope curve (1). If you measure the brightness curve of the interference over the focus position and fit a mathematical model of the function - for example using the least squares method - into the measured values, the height of this surface point can be localized very precisely to less than a hundredth of the mean wavelength . In the case of visible light with an average wavelength of around 500 nanometers, this is less than 5 nanometers.
literature
- ^ André Henri Mirau : Interferometer , French patent No. 152151 of March 3rd. 1949 and U.S. Patent No. 2612074 filed March 27. 1950.