A.

Mirror Tilt Immunity

We have developed a simple novel optical design for a cat’s eye retro-reflector, developed specifically for a tilt insensitive interferometer with substantially unequal arms [1]. The new optical design behaves effectively as an ideal cat’s eye, but is referred to as a ‘quasi-cat’s’ eye’. As can be seen in Fig. 1, we have inverted the lenses in the quasi cat’s eye, compared with previous conventional designs [3]. Comparing the performance of the new design with a conventional cat’s eye optical configuration, it was shown that only the quasi cat’s eye is able to achieve the long working distance with unequal arm lengths required for this application (for more detail, see [1]).

Fig. 1.

Top: Diagram of a conventional cat’s eye. Bottom: The quasi cat’s eye, as used in nEUCLID.

The new cat’s eye has an extra term, δ, producing additional focusing of the beam. It was calculated that the δ term produces negligible errors in the optical path measurement [1]; however, it also causes an increase in radius of curvature, thus the interference pattern to be created of closely-spaced circular fringes. These can be very difficult to resolve, and cause the photodiode to average across the pattern, giving a low overall visibility. To solve this problem, we added a meniscus lens to the reference arm. This enlarged the radius of curvature of the reference beam to approximately that of the target beam, creating a much broader, clearer interference pattern (see Figs. 3 and 4). Section III contains more detail on how the δ term affects the output interference pattern.

This optical design is not limited to a target arm length of only 706 mm; theoretically, the cat’s eye design allows interferometers to be created with target arm lengths of several metres. However, as specified in Table 1, we were initially aimed at creating a prototype that would fit on a 1 m display rail.

Table 1.

The specifications and current design of nEUCLID.

B.

Layout of the interferometer

Fig. 3 shows a schematic diagram of the interferometer. Upon entry to the set-up, the beam is attenuated by a polariser. This attenuation prevents optical feedback, which causes laser instability. Once the beam has left the collimator it passes through a polarising beam splitter (PBS 1). The laser has been orientated to ensure the beam is only of one plane of polarisation (p-), thus all the intensity passes through PBS 1. The beam passes through a non-polarising beam splitter (NPBS), where it loses roughly 50% intensity. It passes through a half-wave plate (HWP) orientated to 22.5°, which rotates the plane of polarisation of the beam by 45°, which, upon having entered PBS 2, sends the p-polarisation to the reference arm and the s-polarisation beam to the target arm.

The target arm beam passes through a quarter wave plate (QWP) and on towards the target mirror. Having reflected off the target mirror, the target beam passes back through the QWP, causing it to now pass through PBS 2 as p-polarisation, and on to the cat’s eye lenses. The beam travels through the concave lens, followed by the convex lens, reflects off the mirror and returns back through the two lenses and through PBS 2 and the QWP again, to reflect off the target mirror. The target beam passes back through the QWP one more time, causing it to now reflect off PBS 2 (as s-polarisation) and back towards the laser. Here it recombines with the reference beam.

In the meantime, the reference beam has travelled through a polariser, which adjusts the intensity to create the best visibility at the photodiodes. The reference beam travels through the meniscus lens, to reflect off the reference mirror and return back through the polariser, and through PBS 2. Here it recombines with the target beam. The target beam has now accrued extra phase from the extra path length travelled.

With the two beams recombined, the beam passes back through the HWP and is split in half by the NPBS. Half the intensity travels onwards, and the other half is reflected through a second QWP and a third PBS. These two components act to separate the two polarisation components, with the QWP introducing a phase shift of π/2 between them. Each beam then passes on to a photodiode. The beam that travelled on from the NPBS is reflected by PBS 1 and passes onto a third photodiode.

The three photodiode signals are used to calculate the displacement of the target mirror, via the interference pattern produced. For more detail on this method, please refer to [4].

A.

Design Specification:

For space applications, a set of requirements was decided by Airbus Defence and Space. This meant we were constrained by these measurements when we built nEUCLID. The requirements and current prototype specifications are shown in Table 1 (including the electronics box, but discounting the aluminium rail mount shown in Fig. 2, which is purely for display purposes).

Fig. 2.

Left: Photograph of the nEUCLID optics in the laboratory. Right: Corresponding schematic diagram of the set-up, where l is the length of the target arm, and l_r the reference arm.

B.

Modelling the Output Interference Pattern:

The resulting interference pattern from nEUCLID was modelled to ensure the best possible visibility on the photodiodes. As explained in Section II, the meniscus lens was placed in the reference arm to counteract the effect of the δ term on the output beam. This ensured the reference and target beams were similar in radius of curvature, thus creating a better visibility (for more detail on the meniscus lens and its effects, refer to [1]).

The visibility of an interference pattern is defined as

where I_max is the maximum intensity value of the interference pattern, and I_min is the minimum intensity value.

A visibility of unity would be the best interference pattern possible. Figures 3 and 4 demonstrate what is predicted from nEUCLID and what we have actually observed.

Fig. 3.

Left: The predicted interference pattern with meniscus lens in reference arm. Right: Predicted interference pattern without meniscus lens in reference arm. (A width of 2.0 mm has been specified as this is the diameter of the photodiodes in the interferometer. The scale is smaller in the right-hand plot due to the tight fringe pattern).

Fig. 4.

Left: The theoretical and real interference pattern with the meniscus lens. Right: A close-up of the interference pattern without the meniscus lens. Again, a close-up was necessary to easily distinguish individual fringes in such a tight pattern.

With the meniscus lens, the visibility of the real data is 0.48, compared to 0.68 from the theoretical data. Without the meniscus lens, the visibility over this range (0.12 mm) for the real data is only 0.24, and 0.29 from the theoretical data.

C.

Component Specification:

A DFB fibre-fed laser is used, wavelength 1550 nm, connected from the purpose-built electronics box [5] to an FC/APC collimating lens via a polarising-maintaining, single-mode patch cord fibre. The polarisers on the input of the laser and in the reference arm are both made from material equivalent to Polaroid HR. The polarising and non-polarising beam splitters are 25.4 mm³ and IR-coated; the PBS made of N-SF1, and the NPBS of N-BK7. The three mirrors are 25.4 mm diameter protected aluminium, with a surface flatness of λ/10. The quarter-wave and half-wave plates are 25 mm in diameter, made of mica. The concave cat’s eye lens is 50.8 mm in diameter, the convex cat’s eye lens is 25.4 mm in diameter, and both are made from N-BK-7. All the optics are mounted on non-magnetic 303 series stainless steel posts on an anodised aluminium breadboard, attached to an aluminium rail. The photodiodes used are InGaAs and are 2 mm diameter.

Fig. 5 shows nEUCLID in its final configuration, as it is used in the laboratory. It is mounted on an aluminium rail of length 1 m, to allow the target mirror (on the right-hand side of image) to be moved easily towards/back from the interferometer. The electronics box (silver) [5] records the photodiode data and calculates the displacement, which is displayed on the laptop.

Fig. 5.

Photograph of nEUCLID in the laboratory.