Old interferometer layout

Gams4 used a simple Michelson layout to measure the axis angles as illustrated in Figure 4.1. The HP5501B laser provides the two frequencies within the same beam, separated by perpendicular linear polarization. In the interferometer, the laser beam is split at the central polarising beam splitter cube a. This provides the frequency splitting for each interferometer branch. Both beams are guided by mirror prisms d,e,f to two retro reflectorsl,m sitting on each end of the goniometer arm. Each beam path continues

4.1. INTERFEROMETER

to a roof prism j,k which reflects the beam by 180° but displaced in height. The beams return their way through the retro reflectors back to the splitter cubea which now serves as beam combiner. From there the beam goes on to the detector. Some λ

2-retarder plates

b,c, which are passed only once, rotate the beam polarization, and thus the beam is de- viated to the detector instead of going back to the laser. Two Glan-Thompson prisms i,h

are used to clean for components of the wrong polarization and thus the wrong frequency. A compensating element g ensures that both beams pass through the same amount of glass. This is important as optical path length is heavily influenced by the refractive index of the material. This changes with temperature. For usual materials it influences the optical path length stronger than the thermal expansion.

An exact copy of this is used to measure the angle of the second goniometer arm.

Weak points

The central beam splitter which provides the frequency separation is cube-type. The sep- aration power is far from being sufficient. Additionally the frequency separation, provided by the HP5501B-laser, is hardly better than -50 dB. This leads to frequency mixing and thus to periodic non-linearity in the interferometer response function on the nanometre level [LK00].

The layout of each interferometer was chosen such that the optical path length in the zero position as well as all paths in glass are the same for both branches. Hence they will compensate for global temperature changes and consequent changes of the refractive index. However, this layout is not able to compensate movements of the optical elements themselves. Any of such a drift would falsify the measurement without a possibility for the experimenter to notice.

This is probably the dominating effect of the Gams4 instrument instability. The optics were mounted on asymmetric alignment elements and bonded with a humidity sensitive glue. A stability test showed a correlation with humidity. See section 3.4 for details. Furthermore, the old set-up consisted of two separate interferometers mounted on individ- ual support plates. If these plates drift with respect to each other, the angle measurement will be wrong, again without any mean to notice.

The reference signal was taken right at the laser, which is some optical elements and distance away from the interferometer. Any change of the birefringence in the optics may introduce a phase shift and hence a wrong measurement.

The laser was placed under the interferometer, and hence introduces thermal gradients and probably also thermal instability.

Figure 4.1: Gams4 _{interferometer layout. The goniometer arms with the diffraction crystals are}

on the very left and very right. See text for an explanation. Graph taken from [Kes+01]

(a) Interferometer layout for one side or axis only. It is a combination of Michelson and Mach- Zehnder interferometer. The laser is injected at one spot; the two frequencies must be separated by perpendicular polarization.

(b) Layout for two sides or axes. The same polar- izing mirrors are used for both sides. A second laser also providing two frequencies – again sep- arated by polarization – is injected at a different spot. It may be a copy of the first one, created by a non-polarizing beam splitter. Beams for left and right axis may overlay.

Figure 4.2: Scheme of heterodyne interferometer. The moving mirrors (solid black lines) on the sides can be replaced by corner cubes to obtain a goniometer. Only four polarizing mirrors (dashed

black lines) are necessary for both interferometers. Retarder plates (λ/4– thin black lines, λ/2–

thin black double-lines) are used to guide the different frequencies to the correct path. The laser source must provide two frequencies, separated by perpendicular polarization. For simplicity, the retro-reflectors are illustrated by two flat mirrors (thick black lines).

4.1. INTERFEROMETER

(a) Layout for one side or axis only. Monochro- matic laser light is injected at one spot. After passing the measuring path, it is frequency shifted by AOMs (grey boxes) to two different frequen- cies. They overlap in the detector and induce a beating signal.

(b) Two sides or axes. A second laser is injected at a different spot. The AOMs are used from both sides. The beams for left and right axis may over- lay.

Figure 4.3: Interferometer layout using AOMs inside the interferometer. The monochromatic laser source provides a single frequency. The light is still homodyne when passing through displacement mirrors. It is shifted by AOMs into two different frequencies before recombination.

(a) Layout for one side or axis only. (b) Layout for two sides or axes. The beams for

left and right axismust overlay. Frequency sepa-

ration is done by polarization.

Figure 4.4: Interferometer layout with no AOM inside. Two lasers with slightly different frequencies are injected at two different spots.