Displacement interferometry is widely used for accurately characterizing nanometer and subnanometer displacements in many applications. In many modern systems, fiber delivery is desired to limit optical alignment and remove heat sources from the system, but fiber delivery can exacerbate common interferometric measurement problems, such as periodic nonlinearity, and account for fiber-induced drift. In this Letter, we describe a novel, general Joo-type interferometer that inherently has an optical reference after any fiber delivery that eliminates fiber-induced drift. This interferometer demonstrated no detectable periodic nonlinearity in both free-space and fiber-delivered variants. © 2011 Optical Society of America OCIS codes: 120.0120, 120.2650, 120.3180, 120.3930, 120.4570, 120.4820. Heterodyne displacement measuring interferometry is a widely applied tool used in gravitational wave detection and conditioning the measurement environment can mitigate the effects of laser frequency instability and refractive index fluctuations. However, periodic nonlinearity in the measurement is more difficult to eliminate because it arises from a combination of source mixing, manufacturing tolerances, and imperfect alignment. Fiber delivery will inherently decrease polarization stability and add timevarying effects, which further complicates the signal processing for interferometers susceptible to periodic nonlinearity [17].Several heterodyne interferometer configurations have been developed that limit the chances for periodic nonlinearity [18][19][20][21][22][23]. These interferometers generally use a spatially separated source and limit all reference and measurement beam overlaps until the final interfering surface prior to detection.In this Letter, we present a general, fiber-coupled Joo-type interferometer with a novel design based on previous Joo-type retroreflector (RR) and plane mirror target interferometers [21,23], which is more suitable for multiaxis systems and has the same footprint on the measurement target as a typical Michelson plane mirror interferometer. Additionally, we compare the results from periodic error analyses between fiber-and free-space-delivered variants and characterize the nominal drift from fiber-induced Doppler shifts. Figure 1 shows a schematic of the general Joo-type interferometer. Two spatially separated beams, horizontally polarized with slightly different optical frequencies ðf 1 ; f 2 Þ are used as the input. When fiber coupling is employed, the phase of the respective optical frequencies ðθ 1 ; θ 2 Þ, vary in time.Both beams enter a beamsplitter (BS), where they are split equally. The reflected beams diagonally cross in a large RR due to the RR's point symmetry. They then travel back to the BS, where they interfere with their respective measurement arms.The initially transmitted beams at the BS also transmit through the polarizing beamsplitter (PBS) and pass through the quarter-wave plate (QWP) oriented at 45°a bout the azimuthal angle. The measurement beam reflects from a mirror (M...

Many error sources can affect the accuracy of displacement measuring interferometer systems. In heterodyne interferometry two laser source frequencies constitute the finally detected wavefront. When the wavefronts of these source frequencies are non-ideal and one of them walks off the detector, the shape of the detected wavefront will vary. This leads to a change in measured phase at the detector resulting in increased measurement uncertainty. A new wavefront measurement tool described in this publication measures the relative phase difference between the two wavefronts of the two source frequencies of a coaxial heterodyne laser source as used in commercial heterodyne interferometer systems. The proposed measurement method uses standard commercial optics and operates with the same phase measurement equipment that is normally used for heterodyne displacement interferometry. In the presented method a bare tip of a multimode fiber represents the receiving detection aperture and is used for locally sampling the wavefront during a line scan. The difference in phase between the beating frequency of the scanning fiber and a reference beating frequency that results from integration over the entire beam, is used for the reconstruction of the wavefront. The method shows to have a phase resolution in the order of ~25 pm or ~λ/25000 for λ 632.8 nm, and a spatial resolution of ~60 µm at a repeatability better than 1 nm over one week.

Periodic nonlinearity (PNL) in displacement interferometers is a systematic error source that limits measurement accuracy. The PNL of coaxial heterodyne interferometers is highly influenced by the polarization state and orientation of the source frequencies. In this Letter, we investigate this error source and discuss two interferometer designs, designed at TU Delft, that showed very low levels of PNL when subjected to any polarization state and/or polarization orientation. In the experiments, quarter-wave plates (qwps) and half-wave plates (hwps) were used to manipulate the polarization state and polarization orientation, respectively. Results from a commercial coaxial system showed first-order PNL exceeding 10 nm (together with higher order PNL) when the system ceased operation at around 15°hwp rotation or 20°qwp rotation. The two "Delft interferometers," however, continued operation beyond these maxima and obtained first-order PNLs in the order of several picometers, without showing higher order PNLs. The major advantage of these interferometers, beside their high linearity, is that they can be fully fiber coupled and thus allow for a modular system buildup. Laser interferometry is an often applied measurement method in several fields of research, since it allows for noncontact measurements. It is especially preferred in the field of metrology, because of its direct traceability to the length standard [1]. Interferometry is also used in lithography machines in the semiconductor industry, gravitational wave detection [2], coordinate measuring machines, and as a calibration tool for other measurement devices, such as capacitive sensors, inductive sensors, and optical encoders. Many types of displacement interferometer systems can be distinguished; this publication deals with heterodyne displacement interferometry using a stabilized He-Ne laser (λ 632.8 nm) combined with two acoustooptic modulators for generating two (fixed-offset) source frequencies.Industrial manufacturing processes currently operate with measurement errors at the subnanometer level and will require even smaller errors in the near future [3]. When operating at this level, a heterodyne interferometer system is hampered by many error sources. The main error sources are the frequency stability of the laser source, noncommon optical pathway variations due to variations in the refractive indices of optical transport media, system alignment (i.e., cosine error, Abbé error), optical wavefront quality combined with beam walkoff [4], and periodic nonlinearity (PNL) in the measured phase [5][6][7][8][9][10]. Operating in vacuum will improve the obtained measurement error. However, PNL in the measurand remains a substantial error source.PNL manifests itself primarily in traditional heterodyne systems with coaxial beams. Such beams contain two linearly polarized frequencies that are orthogonally oriented. These frequencies may mix (due to "frequency leakage"), resulting in periodic errors that are superimposed on the obtained displacement data. This type ...

Due to the distance limitation of quantum communication via ground-based fibre networks, space-based quantum key distribution (QKD) is a viable solution to extend such networks over continental and, ultimately, over global distances. Compared to Low Earth Orbits (LEO), QKD from a Geostationary Orbit (GEO) offers substantial advantages, such as large coverage, continuous link to ground stations (cloud cover limited), 24/7 operation (background limited), and no tracking required. As a downside, QKD from GEO comes with large link losses due to the space-ground distance, lowering the achievable key rates. From our feasibility and conceptual design study it is concluded that although link losses are high, QKD from GEO is technically feasible, and a favourable solution if the satellite needs to act as an untrusted node (that is, no security assumptions required for the space segment). However, the optimal solution, generating a higher value-for-money, is to have the possibility to operate it in trusted mode as well, as higher key rates can be obtained. But this will be at the cost of security as key material needs to be (temporarily) stored on board of the satellite. In order to arrive at a minimum required secure bit rate of ~1 bit/s in untrusted mode, two ~0.5m diameter telescopes in the space segment are required with <0.65μrad pointing accuracy each, a >1GHz entangled photon pair generation rate, in combination with ~2.5m diameter telescopes on ground, operating at 810nm wavelength. In trusted mode, with the same optical system but only using one telescope in the space segment, a factor of ~300 to ~10000 more key can be obtained. Details on our assumptions and results and drawings of the high level system design are presented, as well as a description of the required technology improvements and building blocks needed, which is applicable to non-GEO applications as well.

This paper presents the first test results of a novel Fine Steering Mirror (FSM) for optical communication terminals. The FSM utilizes efficient variable reluctance actuators, tailored for the specific application, making it highly compact and power efficient. The test results demonstrate a high dynamical performance of >1.7kHz closed-loop bandwidth, and an optical angular range of more than ±2˚ in two axes. The actual optical angular jitter is less than 1.5 μrad. These numbers demonstrate that this FSM is highly suitable for the evolving field of inter-satellite laser communications.