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A new balanced-path homodyne I/Q-interferometer scheme using a specially designed polarizing beam displacer (PBD) is described. The PBD is designed for splitting the s- and p-polarization components of the input beam into two parallel output beams which can be used as two beams of a balanced-path interferometer. The interferometer has a very simple optical arrangement because all of seven optical components used for interfacing two arms of the interferometer into the I/Q-demodulator in the previous schemes are replaced by the single PBD. A simple optical arrangement makes the interferometer less susceptible to environmental perturbations. It will be shown that the RMS fluctuations during a long-term phase noise measurement for 24 hours is ~7 × 10−5 rad. in an open lab environment. In addition, the separation between two arms of the interferometer is adjustable which makes the interferometer very flexible for many sensor applications. Potential use of our new interferometer as an interferometric sensor will be demonstrated by employing a displacement sensor arrangement.
© 2017 Optical Society of America
1. Introduction
There have been significant progresses in instrumentations for the interferometric sensors. Implementations of a homodyne or a heterodyne I/Q-demodulation scheme makes an interferometric sensor more versatile and useful. It has been shown that an interferometer can be operated at the optimum sensitivity without any feedback control of optical path length difference between the probe beam (PB) and the reference beam (RB) to keep the interferometer at the quadrature demodulation condition [1–8,14], which makes the operation of the interferometer very simple and easy. Moreover, the I/Q-interferometer can measure both the amplitude and phase changes induced on the probe beam, which is very useful in many applications such as a scanning interferometer microscope. It has been shown that a topography of a surface under test can be imaged by using the phase information obtained while the inhomogeneity of the same surface can be mapped on the surface by making use of amplitude information obtained during the scanning [7–9].
Another progress in the interferometer sensor scheme is to employ a clever design that makes the interferometer geometrically balanced [10–13]. In this arrangement, two parallel beams, the PB and RB, are coming out from the interferometer and sending back into the interferometer by using either two independent mirrors or one mirror, which will be referred as two-mirror arrangement (TMA), and one-mirror arrangement (OMA), respectively [10]. The PB and RB can also be reflected by using two patterned mirrors coated on one substrate. The phase of the RB is fixed in the TMA while, unless a sample is inserted in the PB path, the PB and RB have the same phase in the OMA. It has been shown that common vibration noise can be rejected significantly in many readout sensor schemes, for which the OMA can be applicable [10,11].
Despite these innovations mentioned above, an interferometer sensor is still difficult to implement because of the complexity in optical arrangement for providing the parallel PB and RB. It requires not only many optical components including one beam splitter, two polarizing beam splitters (PBSs), one mirror, and two half-wave plates (HWPs) for providing the two parallel beams orthogonally polarized with respect to each other, but also precision alignments between these components. Therefore, a tedious and time consuming alignment procedure is needed in these interferometer schemes. Moreover, these optical components must be securely mounted and kept at an isolated environment to make the interferometer stable and immune to environmental perturbations.
In this paper, we present a novel interferometer which has a very simple optical arrangement for providing the PB and RB by using a specially designed beam displacer (PBD). The PBD is the polarizing beam splitter for which two output faces are properly angled so that the two orthogonal polarized output beams are running parallel with respect to each other. We will show that all five optical components in the previous arrangement can be replaced by the one PBD. As pointed out in the previous works [10,11], the balanced path interferometer can have many applications because either a transmission or reflection geometry can be used as the sensor geometry. Details about the sensitivity and noise characteristics of the OMA and TMA are discussed. Potential as a high sensitivity sensor will be demonstrated by employing a displacement sensor arrangement.
2. Interferometer and experimental arrangement
The optical layout of the polarizing beam displacer is shown in Fig. 1.(a). It is simply the polarizing beam splitter for which the output faces are angle polished so that the output beams are running parallel with respect to each other. It can be shown easily that the half apex angle of the PBD is given by
where is the corner angle shown in Fig. 1. (a) and n is the refractive index of the PBD. As shown in the figure, the s-polarization of the input beam is reflected and the p-polarization is transmitted through the PBD. The output beams can be sent back into the PBD along the same path by using the arrangement shown in Fig. 1. (a). The returning beams make double passes in the quarter-wave plate (QWP) and the plane of polarizations are rotated by 90°. The returning beams are then recombined by the PBD and exiting in the remaining port of the PBD as shown in Fig. 1. (a). It has a big advantage that the separation between the two output parallel beams is adjustable. In order to make the corner angle and, thereby, the adjustable range of the beam separation reasonably large, a high refractive index glass N-SF1 (n = 1.7125 @633nm) was used as the material for the PBD and the corner angle was 9.88°. The manufacturing tolerance for the PBD is not that much critical for the TMA because the parallelism between the two beams can be finely adjusted by using a precision tilt-rotation stage. For the OMA, however, although the angle between the two beams can be adjusted, since the input and two output beams must be coplanar, the beam splitting surface and two output faces must be aligned properly within 10ths of arc minutes, which gives less than 1% wave front mismatch for a 10cm arm length and 1mm beam diameter. The PBD was custom manufactured by the Thorlabs: It has the same specifications as the commercial PBS (Thorlabs, PBS201), but the output faces are angled to make the output beams parallel. The separation between two beams can be varied from 6mm to 9mm by displacing the PBD, which is a big advantage in many readout sensor applications. It should be emphasized that a commercial PBD, which is making use of the birefringence in a crystal, cannot be used in this application, because, as will be shown in the next paragraph, the polarizations of the returning PB and RB must be rotated by 90° and the returning beams will not follow the initial paths when they reenter the conventional PBD as shown in Fig. 1.(b).A schematic of the optical arrangement of the proposed interferometer is shown in Fig. 2. The interferometer is designed in a way that the output beam does not return to the laser source. In practice, however, because of the imperfect optical components, it is inevitable that a small portion of the output light, typically less than 1%, is returning to the laser source. An optical isolator OI with a 55dB return loss is used for blocking the returning stray reflected beam. The laser and the OI are aligned properly so that the plane of polarization (PoP) of the incident beam to the interferometer is oriented at 45° to the preferred axes of the PBD. The transmitted p-polarization and reflected s-polarization are refracted at the properly angled faces so that the output beams are running parallel. The beams are circularly polarized but have opposite handedness by using a 0th order quarter-wave plate, QWP1. As in the case of an archetypal two-beam interferometer sensor scheme, one of the beams, the reflected beam at the PBD in this arrangement, is used as the PB and the other beam as the RB. The PB and RB are sent back into the PBD by using either TMA or OMA. One example of the TMA is the displacement sensor arrangement which is shown in the dotted box (a) in Fig. 2. In this arrangement, one mirror, the reference mirror (RM), is mounted on a fixed block while the other mirror, the target mirror (TM), is mounted on a moving object, the PZT (Thorlabs, PE4) or step motor (Oriental Motor, PMM33BH2) driven stage in our present work. The interferometer is used for measuring the displacement of the TM. The OMA is very useful for reading out extremely small changes in optical properties, the complex refractive index, for example, of a sample under test in the PB path [10,11]. In our present work, as shown in the dotted box (b) of Fig. 2, the one mirror was mounted on the PZT stage to investigate the noise rejection in this arrangement. As the result of double passes in the QWP1, the PoPs of the returning PB and RB are rotated by 90° with respect to the corresponding initial PoPs of the PB and RB. Therefore, the orthogonally polarized PB and RB are combined at the PBD and exit along the path orthogonal to the input beam path. The PBD, RM and TM are aligned properly so that the PB and RB are propagating along the same path.
Fig. 2 Experimental arrangement. The TMA for a displacement sensor arrangement and OMA for noise evaluation are shown in the dotted rectangle (a) and (b), respectively. A schematic of optical arrangement of the homodyne I/Q-demodulator is shown in (c).
The PB and RB are then sent to the homodyne I/Q-demodulator sown in the dotted box (c) of Fig. 2, in which the induced phase and amplitude changes of PB are measured. The Details about the I/Q-demodulator can be found in [7, 11]; It consists of two identical balanced mixers but the output interference signals from the corresponding differential amplifiers DA1 and DA2 have a 90° phase difference induced by the QWP2. Therefore, if the output signal from the DA1 is given by
then the output signal from the DA2 is given bywhere and are the responsivity of the photodetector, probe beam power, reference beam power and the phase difference between the PB () and RB (). In here, we assumed that the responsivities of the photodiodes are the same. These signals are interfaced to a computer by using a 24-bit A/D converter model (National Instruments, NI PCI-4462). The phase difference and the amplitude of the PB are measured by taking the following operations in the computer, respectively:andAs shown in Eq. (4), it does not require any calibration procedure for measuring the phase difference and, thereby, the path length difference between the PB and RB. In the case of the displacement sensor arrangement, since the RM is fixed, the phase difference is determined by the position of the PM. The displacement between the two consecutive measurements and can be calculated in the computer by using the following equation:where the measurement interval between and is determined by the bandwidth of the filter. For a full-bandwidth measurement, the interval is determined by the sampling time of the A/D-converter.3. Evaluation results of the proposed interferometer
To show a potential of the proposed interferometer as an interferometer sensor, the TM was sinusoidally displaced by applying a 40Hz and 150mV driving voltage to the PZT. The measured displacement of the TM is shown in Fig. 3, which is in good agreement with the calculated value based on the manufacturer’s specification of the PZT stage. This result shows that the proposed I/Q-interferometer scheme is suitable for interferometer sensor applications. The frequency spectrum of the phases measured by using the displacement sensor arrangement is shown as the grey (red online) trace in Fig. 4. In addition, the corresponding frequency spectrum for the OMA shown in the dotted box (b) in Fig. 2 is shown as the black trace in Fig. 4. Since the TM and RM are moving together in the latter arrangement, the phase difference between the two measurements at the modulated frequency represents the common vibration rejection for the balanced path arrangement. These results show that there is at least a 30dB rejection of common vibrations along the direction parallel to the beam propagation in the OMA. Moreover, the results in Fig. 4 show that the low frequency noise level for the OMA is significantly lower than that of the TMA. Since the PB and RB have the same geometrical arrangement for the OMA and TMA, the noises induced by the local environmental perturbations on these two separated beams are statistically the same for both cases. Therefore, the additional low frequency noises in the grey trace in Fig. 4, the frequency spectrum for two-mirror arrangement, are merely resulted from uncorrelated motions between the two separated mirrors. The frequency spectra of the corresponding phase measurements for the OMA and TMA when all moving parts are securely locked are shown as black and grey (red on-line) traces, respectively, in Fig. 5, which represent the spectral noise on the corresponding phase measurements. These results and the corresponding spectra in Fig. 4 tell us that the noises are almost the same whether mirrors were in motion or locked, but the OMA has much lower noise level than the TMA. It can also be noted from the TMA spectra in Fig. 4 and 5, that there is a band of noise peaks around 1kHz, which does not go away but just become smaller even when the mirrors are fixed. The PB and RB have the same optical arrangement for both the OMA and TMA, which ensure us that the localized fluctuations such as atmospheric turbulence along the PB and RB paths are statistically the same. Therefore, we can claim that the additional noises in the TMA are resulted from the uncorrelated mechanical motions of the two different mounting stages. In all, we found that the TMA has a significantly higher noise, at least a 10dB at frequencies lower than a few tens of Hz, than that of the OMA, which is related to the mounting mechanisms of the mirrors.
Fig. 4 Frequency spectra representing the common vibration rejection at 40 Hz: the gray (red online) and black traces represent the frequency spectra by using the TMA shown in Fig. 2.(a) and OMA shown in Fig. 2.(b), respectively.
Fig. 5 Spectral noise measurements: the gray (red online) and black trace represent the frequency spectra represent the frequency spectra for TMA and OMA, respectively, when all moving parts are locked.
In most of readout sensor applications of the interferometer, TM and RM do not need to be separated. Therefore, although the requirement on manufacturing tolerance becomes tight, it is desirable to employ the OMA in a readout sensor or a scanning interferometer application. In principle, the sensitivity is limited by photon noise, but, in our current arrangement, the sensitivity is limited by the resolution of the 24-bit A/D converter, ~2π/224 = 2.14 × 10−5 deg., which is specified as the dashed line in Fig. 5. The corresponding displacement is 1.88 × 10−14m. A long-term stability of the OMA was tested for 24 hours and the result is shown in Fig. 6. The RMS phase fluctuation is ~4 × 10−3 deg., which is equivalent to ~7 × 10−12m. This result shows a significant improvement over the long-term stability obtained in the previous work, 1.26 × 10−2 deg., presented in [10] and even for the 5-minute stability, 5 × 10−3 deg. in [11]. We believe that the stability can be improved significantly if the interferometer is operated in well controlled environment. A long stroke displacement was measured by using a step motor driven stage and the result is shown in Fig. 7. The measured values are shown as dots and the best linear fit to the applied displacement is shown as the solid line. The slope and R2 of the fit are 0.9984 and 99.99%, respectively.
4. Summary and Conclusion
In summary, a novel interferometer scheme has been introduced. The proposed scheme has the following advantageous features; Firstly, it has a very simple optical arrangement by using the specially designed PBD. The PBD not only makes the optical arrangement very simple, but also makes the interferometer highly immune to noises related to independent motions of the optical components in the conventional interferometers which may be resulted from local environmental perturbations. Secondly, it has the geometrically balanced and closely spaced PB and RB which can be used for either a transmission or a reflection geometry. Thirdly, the separation between the PB and RB can be adjusted by simply displacing the PBD. The last two features make the interferometer very flexible to use in many sensor applications: a displacement sensor, vibrations sensor, scanning interferometer, and many readout sensor applications.
Funding
National R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2014M1A7A1A01029956).
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