Common-path Interference Research Articles

Detection limit improvement for a gas concentration measurement system using space-domain active fiber cavity ring-down sensing technology

Trace gas sensors have received extensive attention and have become particularly attractive for applications in toxic gas detection, medical diagnostics, pollution monitoring, industrial emission measurement, and so on. However, it is still a critical challenge for gas sensors to simultaneously achieve high sensitivity and low detection limits while performing well in stability. Here, a space-domain active fiber cavity ring-down (FCRD) gas sensing technique was proposed to develop a high-performance gas sensor. Taking advantage of the active FCRD sensing technique and frequency-shifted interferometry, the proposed gas sensor exhibited a high sensitivity of 1.122km−1/%. Importantly, introducing a bidirectional EDFA into the fiber cavity further enhances the light–gas interaction, resulting in a low detection limit of 55 ppm, which is much lower than that of most reported gas sensors. Moreover, a good stability of 0.58% can be achieved due to the combined effect of the proposed technology using differential detection to eliminate DC noise, as well as common-path interference to eliminate common-mode noise and the use of continuous light to stabilize the optical power in the fiber cavity for suppressing the gain fluctuations of EDFA.

Encoding the Intensity and Phase Gradient of Light Beams with Arbitrary Shapes

We present an approach for engineering the intensity trajectory and phase gradient of light beams with arbitrary shapes by estimating their parametric equations using Freeman chain code and by applying the fast Fourier transform. The analysis of the electric field distribution expected for a given curve allows the phase extraction over each local coordinate, generating a phase pattern to be displayed over a spatial light modulator. The intensity and phase gradient of eight different shapes is encoded during our experiments. The far field intensity profiles are captured and compared in shape to those designed, while the encoded phase is demonstrated by implementing a common path interference setup with a pair of beams from the spatial light modulator. The designed beams, initially drawn either by hand or generated with software, exhibit both the intensity and phase profiles encoded onto them.

Fiber Optic All-Polarization Weak Magnetic Field Sensor Based on Sagnac Interferometer

A novel fiber-optic magnetic field sensor, based on a Sagnac structure, is proposed with the approach of polarization interference detection. The sensor takes advantage of common path interference, combining with a high magnetic field sensitivity sensing unit, composed of magneto-optical crystal, and magnetic field concentrators, to achieve high resolution, high stability, and large dynamic measurement of DC magnetic field signals. In this paper, the theoretical model is established and the related theory is derived in detail. The key technologies in the system are thoroughly investigated and verified. Experimental research on the proposed system is demonstrated and the results show that a DC magnetic field resolution of 5.6 nT and a dynamic range of larger than 70 dB is achieved. Furthermore, the linearity of the system is greater than 99.8% and the instability is less than 0.5%.

Dual-modality quantitative phase-contrast microscopy based on pupil phase modulation (DQPCM)

Phase-contrast optical microscopy that converts phase modulation of transparent samples into intensity modulation plays an indispensable role in biomedical research. In this study, we propose a dual-modality quantitative phase contrast microscopic (DQPCM) platform that integrates quantitative differential interference phase-contrast microscopy (qDIC-PCM) and quantitative Zernike phase-contrast microscopy (qZ-PCM) in the same microscopy. Both imaging modalities are realized through spatial light modulator (SLM) based pupil phase modulation, and switching between the two imaging modes is performed by rotating two polarizers. Both imaging modalities have the merits of high stability and low coherent noise due to their common path interference structure and partially coherent illumination. The experimental results indicate that qDIC-PCM is superior to qZ-PCM in quantitative phase imaging of samples with certain scattering, while qZ-PCM has higher spatial resolution than qDIC-PCM. The proposed technique will be very helpful for imaging the dynamic processes of biological samples with high spatiotemporal resolution.

Single-shot terahertz polarization detection based on terahertz time-domain spectroscopy

This paper presents a novel design for single-shot terahertz polarization detection based on terahertz time-domain spectroscopy (THz-TDS). Its validity has been confirmed by comparing its detection results with those of the THz common-path spectral interferometer through two separate measurements for the orthogonal components. Our results also show that its detection signal-to-noise ratios (SNRs) are obviously superior to those of the 45° optical bias THz-TDS by electro-optical sampling due to its operation on common-path spectral interference rather than the polarization-sensitive intensity modulation. The setup works without need of any optical scan, which does not only save time, but also efficiently avoids the disturbances from the fluctuations of the system and environment. Its single-shot mode allows it to work well for the applications with poor or no repeatability.

Kilohertz retinal FF-SS-OCT and flood imaging with hardware-based adaptive optics.

A retinal imaging system was designed for full-field (FF) swept-source (SS) optical coherence tomography (OCT) with cellular resolution. The system incorporates a real-time adaptive optics (AO) subsystem and a very high-speed CMOS sensor, and is capable of acquiring volumetric images of the retina at rates up to 1 kHz. While digital aberration correction (DAC) is an attractive potential alternative to AO, it has not yet been shown to provide resolution allowing visualization of cones in the fovea, where early detection of functional deficits is most critical. Here we demonstrate that FF-SS-OCT with hardware AO permits resolution of foveal cones, imaged at eccentricities of 1° and 2°, with volume rates adequate to measure light-evoked changes in photoreceptors. With the reference arm blocked, the system can operate as a kilohertz AO flood illumination fundus camera with adjustable temporal coherence and is expected to allow measurement of light-evoked changes caused by common path interference in photoreceptor outer segments (OS). In this paper, we describe the system's optical design, characterize its performance, and demonstrate its ability to produce images of the human photoreceptor mosaic.

Hybrid vector beams with non-uniform orbital angular momentum density induced by designed azimuthal polarization gradient**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0303800), the National Natural Science Foundation of China (Grant Nos. 11634010, 61675168, 91850118, 11774289, and 11804277), the Fundamental Research Funds for the Central Universities, China (Grant No. 3102019JC008), and the Basic Research

Based on angular amplitude modulation of orthogonal base vectors in common-path interference method, we propose an interesting type of hybrid vector beams with unprecedented azimuthal polarization gradient and demonstrate in experiment. Geometrically, the configured azimuthal polarization gradient is indicated by intriguing mapping tracks of angular polarization states on Poincaré sphere, more than just conventional circles for previously reported vector beams. Moreover, via tailoring relevant parameters, more special polarization mapping tracks can be handily achieved. More noteworthily, the designed azimuthal polarization gradients are found to be able to induce azimuthally non-uniform orbital angular momentum density, while generally uniform for circle-track cases, immersing in homogenous intensity background whatever base states are. These peculiar features may open alternative routes for new optical effects and applications.

Spectral resolution enhanced static Fourier transform spectrometer based on a birefringent retarder array.

The principle and experimental demonstration of a spectral resolution enhanced static Fourier transform spectrometer (SESFTS) is presented. The device, which is based on a birefringent retarder array and a Wollaston prism, offers significant advantages over previous static Fourier transform (FT) implementations. Specifically, its use of an ultra-compact common-path interference structure creates a simple and robust spectral resolution enhanced spectrometer while preserving their high throughput and wide free spectral range. The operation principle of the device is explained in detail with a design example with a spectral resolution of 7 cm-1, which is nearly two orders of magnitude higher than that of a conventional static FT spectrometer with a similar CCD detector. An experimental demonstration is performed by the measurement of a gas charge lamp and three diode laser sources with a SESFTS prototype working in 400-1000 nm with an approximate 25 cm-1 spectral resolution.

Common-path interferometry with tilt carrier for surface measurement of complex optics.

We propose a novel common-path non-null interference system for the surface measurement of complex optics. Because of the common-path structure, systematic errors are mostly eliminated and the complexity of system calibration is reduced for the proposed setup. However, optical design of common-path non-null interference systems is of great difficulty because many off-axis beams are used to compensate for the local gradient of the measured piece. Different from the classical common-path interferometers, which pay more attention to the beam quality of the on-axis field of view (FOV), the proposed system requires better quality for both on-axis and off-axis outgoing beams. In the proposed setup, the lens groups with wide FOVs afford wave aberrations better than 0.1λ for the on-axis and off-axis FOVs. Simultaneously, the off-axis beams are prevented from generating pseudo reference beams by optimizing the parameters of the lenses and the aperture. In addition, multiple tilted test beams are generated by a point-source generator based on a fiber array, which is more versatile than a lens-array-type point-source generator. Further, a universal measurement system with high accuracy and time savings is formed, as evidenced by the measurement results of a parabolic mirror and different types of cylindrical mirrors.

Surface profilometry using vortex beams generated with a spatial light modulator

We present a common path interference setup for detection of surface depth differences of the order of 200 nm, using a vortex and a Gaussian beam generated with a spatial light modulator. The phase of a vortex with a topological charge +1 and the phase of a lens are encoded next to each other onto the spatial light modulator. Both beams are incident onto a surface with a step feature; the Gaussian beam is incident onto a flat mirrored surface, while the vortex beam scans through the step. Upon interaction with the testing surface, both beams are superposed and their interference pattern is captured, collecting a set of images as a result of the scanning process. A phase detection algorithm is applied to these images and by tracking the vertical positions of the phase singularity along the scanning, the depth variations are estimated. The proposed set up is able to detect a 179 nm step feature, working with light at a wavelength of 830 nm and using a vortex with a diameter of 177μm.

A low threshold nanocavity in a two-dimensional 12-fold photonic quasicrystal

In this article, a low threshold nanocavity is built and investigated in a two-dimensional 12-fold holographic photonic quasicrystal (PQC). The cavity is formed by using the method of multi-beam common-path interference. By finely adjusting the structure parameters of the cavity, the Q factor and the mode volume are optimized, which are two keys to low-threshold on the basis of Purcell effect. Finally, an optimal cavity is obtained with Q value of 6023 and mode volume of 1.24×10-12cm3. On the other hand, by Fourier Transformation of the electric field components in the cavity, the in-plane wave vectors are calculated and fitted to evaluate the cavity performance. The performance analysis of the cavity further proves the effectiveness of the optimization process. This has a guiding significance for the research of low threshold nano-laser.

Shot noise in systems with semi-Dirac points

We calculate the ballistic conductance and shot noise of electrons through a two-dimensional stripe system (width W ≫ length L) with semi-Dirac band-touching points. We find that the ratio between zero-temperature noise power and mean current (the Fano factor) is highly anisotropic. When the transport is along the linear-dispersion direction and the Fermi energy is fixed at the semi-Dirac point, the Fano factor has a universal value F = 0.179 while a minimum conductivity exists and scales with L1∕2. Along the parabolic dispersion direction, the Fano factor at the semi-Dirac point has a contact-independent limit exceeding 0.9, which varies weakly with L due to the common-path interference of evanescent waves. Our findings suggest a way to discern the type of band-touching points.

Band-Gap tuned oscillatory conductance in bilayer graphene n-p-n junction

We study transmission of quasiparticles through a bilayer graphene n-p-n junction when the particle energy lies within the band gap produced by external gate fields. The dispersion relation of eigenspectrum allows two pairs of complex-conjugate wave vectors inside the barrier region, so that two types of common paths, [R. Nandkishore and L. Levitov, Proc. Natl. Acad. Sci. 108, 14021 (2011)] one with decaying amplitude and the other with growing amplitude, contribute to the transmission. Each common path produces interference effect of oscillatory transmissions, with vanishing tunneling probabilities at certain values of the band gap and incident angles. We explain this interference effect by using a semiclassical approximation of path integral approach and show that multiple reflection of forward and backward propagations inside the barrier does not destroy the common-path interference. As a result of the interference, we demonstrate that the conductance through the barrier oscillates as a function of the band gap.

Common path interference in Zener tunneling is a universal phenomenon

We show that the probability of electric field induced interband tunneling in solid state systems is generically a non-monotonic (oscillatory) function of the applied field. This unexpected behavior can be understood as arising due to a common path interference between two distinct tunneling solutions. The phenomenon is insensitive to magnetic field, and arises whenever the low energy dispersion relation contains higher order terms in addition to the usual $p^2$ term. Such higher order terms are generically present, albeit with small co-efficient, so that the oscillatory Zener tunneling is a universal phenomenon. However, the first `Zener oscillation' occurs at a transmission probability which is exponentially small when the co-efficient of the higher order terms is small. This explains why this oscillatory aspect of Zener tunneling has been hitherto overlooked, despite its universality. The common path interference is also destroyed by the presence of odd powers of $p$ in the low energy dispersion relation. Since odd powers of $p$ are strictly absent only when the tunneling barrier lies along an axis of mirror symmetry, it follows that the robustness of the oscillatory behavior depends on the orientation of the tunneling barrier. Bilayer graphene is identified as a particularly good material for observation of common path interference, due to its unusual nearly isotropic dispersion relation, where the $p^4$ term makes the leading contribution.

High-resolution corneal topography and tomography of fish eye using wide-field white light interference microscopy

Topography and tomography of fish cornea is reconstructed using high resolution white light interference microscopy. White light interferograms at different depths were recorded by moving the object axially. For each depth position, five phase shifted interferograms were recorded and analyzed. From the reconstructed phase maps, the corneal topography and hence the refractive index was determined and from amplitude images the cross-sectional image of fish cornea was reconstructed. In the present method, we utilize a nearly common-path interference microscope and wide field illumination and hence do not require any mechanical B-scan. Therefore, the phase stability of the recorded data is improved.

Common-path interference and oscillatory Zener tunneling in bilayer graphene p-n junctions.

Interference and tunneling are two signature quantum effects that are often perceived as the yin and yang of quantum mechanics: a particle simultaneously propagating along several distinct classical paths versus a particle penetrating through a classically inaccessible region via a single least-action path. Here we demonstrate that the Dirac quasiparticles in graphene provide a dramatic departure from this paradigm. We show that Zener tunneling in gapped bilayer graphene, which governs transport through p-n heterojunctions, exhibits common-path interference that takes place under the tunnel barrier. Due to a symmetry peculiar to the gapped bilayer graphene bandstructure, interfering tunneling paths form conjugate pairs, giving rise to high-contrast oscillations in transmission as a function of the gate-tunable bandgap and other control parameters of the junction. The common-path interference is solely due to forward-propagating waves; in contrast to Fabry-Pérot-type interference in resonant-tunneling structures, it does not rely on multiple backscattering. The oscillations manifest themselves in the junction I-V characteristic as N-shaped branches with negative differential conductivity. The negative dI/dV, which arises solely due to under-barrier interference, can enable new high-speed active-circuit devices with architectures that are not available in electronic semiconductor devices.

X-ray phase micro-tomography using an interference microscope with zone plates

Using an x-ray common-path interference microscope with two zone plates at SPring-8 BL20XU, quantitative phase imaging was investigated by the fringe-scanning method. The phase sensitivity was estimated to be λ/62. Tomographic three dimensional phase image of diamond particles and polystyrene beads of 2.8 μm in diameter could be clearly reconstructed.

An Enhanced Common Path Interference Measurement Method for Optical Refractive Indices

This study presents an enhanced common path interference system designed to measure the refractive index of crystal optical components. The proposed system is based on the classic Michelson interferometer and comprises a frequency stabilized helium-neon (He-Ne) laser, a beam splitter, a fixed mirror, an adjustable mirror, and a light detection system. The waveplate of interest was clamped to a rotatory motor and positioned between the beam splitter and the fixed mirror. The refractive index of the waveplate was then derived from the change in rotational angle of the waveplate as it moved from one position of minimum interference to the next. The measurement system proposed in this study is simple in construction, straightforward in operation, and robust to the effects of experimental noise. Furthermore, the system is a non-contact measurement system, and hence does not damage the optical component of interest. The experimental results are found to be in good agreement with the theoretical results. Therefore, the proposed system provides a viable means for the rapid experimental evaluation of the optical characteristics of quartz components.

An enhanced common path interference optic measurement system for refractive indices and thickness

This study proposes a common path interference optical system for the measurement of refractive indices and thickness of uniaxial crystal material. The measurement system comprises an accurate Mach–Zehnder laser interferometer, a single-axis rotary stepping motor, and a computer. The laser interferometer is composed of a single-frequency He–Ne laser, two-beam splitters and two reflectors. The Mach–Zehnder laser interferometer measures the optical length difference by using its linear measurement accuracy. The proposed solution procedure enables both the refractive indices and the thickness of the optical waveplate to be obtained. The proposed design differs from conventional designs in that it does not use a heterodyne modulator with a lock-in technique. It is shown that the refractive indices and thickness of the tested optical elements can be measured rapidly and accurately.

Investigation of common-path interference profilometry

The principle of laser common-path interference profilometry based on the theory of Gaussian beams is analyzed and its measure- ment equation is deduced. From the measurement equation, the main factors that affect the vertical resolution of the profilometer are dis- cussed. According to the conclusions of the analysis, laser common-path interference profilometry can be used to measure microprofiles of fine surfaces with subnanometer vertical resolution. © 1997 Society of Photo- Optical Instrumentation Engineers. (S0091-3286(97)02911-5)