Adjustable phase control in stabilized interferometry

Background-free correlation spectroscopy using an infrared mode-locked laser

The recent advances in infrared laser technology are expanding the capabilities and applications of vibrational spectroscopy. A promising approach utilizing broadband infrared mode-locked lasers is background-free (BF) absorption spectroscopy. This method captures the free-induction decay (FID) of excited molecules while suppressing the background light. It is unique in that the signal strength increases with input optical power but eventually struggles with detector noise when targeting fewer molecules. In this paper, we present a novel method of multiplexed background-free spectroscopy using a spectral mask whose transmittance has a strong correlation with the absorption spectrum of a target molecule. We successfully demonstrate an order of magnitude increase in the sensitivity due to multiplexing as well as a high molecular contrast due to the spectral correlation. The presented results indicate the promising potential of the method for sensitive and selective detection of trace molecules.

Broadband dispersion spectroscopy using interferometric phase modulation under background light suppression

This Letter presents a dispersion spectroscopy method that achieves simultaneous detection of molecular vibrational dispersion over a broad spectral range. The method is implemented with an infrared mode-locked laser, a dispersion-compensated Michelson interferometer, and a multichannel detector. Synchronous detection under interferometric phase modulation near the destructive interference condition is employed to achieve a high signal-to-noise ratio. We successfully demonstrate the method by measuring the dispersion of carbon monoxide gas, achieving a noise-equivalent dispersion of 1.3 × 10-8 cm and a corresponding noise-equivalent absorbance of 6.5 × 10-4 with a measurement time of 2.2 s.

Apparatus for attosecond transient-absorption spectroscopy in the water-window soft-X-ray region

We present an apparatus for attosecond transient-absorption spectroscopy (ATAS) featuring soft-X-ray (SXR) supercontinua that extend beyond 450 eV. This instrument combines an attosecond table-top high-harmonic light source with mid-infrared (mid-IR) pulses, both driven by 1.7-1.9 mJ, sub-11 fs pulses centered at 1.76 [Formula: see text]m. A remarkably low timing jitter of [Formula: see text] 20 as is achieved through active stabilization of the pump and probe arms of the instrument. A temporal resolution of better than 400 as is demonstrated through ATAS measurements at the argon L[Formula: see text]-edges. A spectral resolving power of 1490 is demonstrated through simultaneous absorption measurements at the sulfur L[Formula: see text]- and carbon K-edges of OCS. Coupled with its high SXR photon flux, this instrument paves the way to attosecond time-resolved spectroscopy of organic molecules in the gas phase or in aqueous solutions, as well as thin films of advanced materials. Such measurements will advance the studies of complex systems to the electronic time scale.

Active stabilization of a pseudoheterodyne scattering scanning near field optical microscope

Scattering scanning near-field optical microscopes (s-SNOMs) based on pseudoheterodyne detection and operating at ambient conditions typically suffer from instabilities related to the variable optical path length of the interferometer arms. These cause strong oscillations in the measured optical amplitude and phase comparable with those of the signal and, thus, resulting in dramatic artifacts. Besides hampering the comparison between the topography and the optical measurements, such oscillations may lead to misinterpretations of the physical phenomena occurring at the sample surface, especially for nanostructured materials. Here, we propose a stabilizing method based on interferometer phase control, which improves substantially the image quality and allows the correct extraction of optical phase and amplitude for both micro- and nanostructures. This stabilization method expands the measurement capabilities of s-SNOM to any slowly time-dependent phenomena that require long-term stability of the system. We envisage that active stabilization will increase the technological significance of s-SNOMs and will have far-reaching applications in the field of heat transfer and nanoelectronics.

Broadband background-free vibrational spectroscopy using a mode-locked Cr:ZnS laser

We demonstrate high-sensitivity vibrational absorption spectroscopy in the 2-micron wavelength range by using a mode-locked Cr:ZnS laser. Interferometric subtraction and multichannel detection across the broad laser spectrum realize simultaneous background-free detection of multiple vibrational modes over a spectral span of >380 cm^-1. Importantly, we achieve detection of small absorbance on the order of 10^-4, which is well below the detection limit of conventional absorption spectroscopy set by the detector dynamic range. The results indicate the promising potential of the background-free method for ultrasensitive and rapid detection of trace gases and chemicals.

Robust correction of interferometer phase drift in transmission matrix measurements

A complex-valued transmission matrix describing a scattering medium can be constructed from a sequence of many interferometric measurements. A major challenge in such experiments is to correct for rapid phase drift of the optical system during the data acquisition process, especially when the phase drifts significantly between consecutive measurements. Therefore, a new method is presented where the exact phase drift between two measurements is characterized and corrected using a single additional measurement. This approach removes the need to continuously track the phase and significantly relaxes the phase stability requirements of the interferometer, allowing transmission matrices to be constructed in the presence of fast and erratic phase drift.

Simple digital system for the stabilization of holographic recordings of a slow grating in photorefractive materials

We report on a digital system for the stabilization of an interference pattern of light fringes. This system uses a Raspberry Pi computer to operate a continuously stabilized setup and, because of the particular features of this stabilization setup, it is possible to record slow gratings in photorefractive materials. Our system proved to be effective, less expensive, and easy to operate, compared to the frequently employed setup with a lock-in amplifier, as it does not require specific equipment and/or specialized personnel.

Frequency locking of a field-widened Michelson interferometer based on optimal multi-harmonics heterodyning

A general resonant frequency locking scheme for a field-widened Michelson interferometer (FWMI), which is intended as a spectral discriminator in a high-spectral-resolution lidar, is proposed based on optimal multi-harmonics heterodyning. By transferring the energy of a reference laser to multi-harmonics of different orders generated by optimal electro-optic phase modulation, the heterodyne signal of these multi-harmonics through the FWMI can reveal the resonant frequency drift of the interferometer very sensitively within a large frequency range. This approach can overcome the locking difficulty induced by the low finesse of the FWMI, thus contributing to excellent locking accuracy and lock acquisition range without any constraint on the interferometer itself. The theoretical and experimental results are presented to verify the performance of this scheme.

Active stabilization of a fiber-optic two-photon interferometer using continuous optical length control

The practical realization of long-distance entanglement-based quantum communication systems strongly rely on the observation of highly stable quantum interference between correlated single photons. This task must accompany active stabilization of the optical path lengths within the single-photon coherence length. Here, we provide two-step interferometer stabilization methods employing continuous optical length control and experimentally demonstrate two-photon quantum interference using an actively stabilized 6-km-long fiber-optic Hong-Ou-Mandel interferometer. The two-step active control techniques are applied for measuring highly stable two-photon interference fringes by scanning the optical path-length difference. The obtained two-photon interference visibilities with and without accidental subtraction are found to be approximately 90.7% and 65.4%, respectively.

Active stabilization of a Michelson interferometer at an arbitrary phase with subnanometer resolution

We report on the active stabilization of a Michelson interferometer at an arbitrary phase angle with a precision better than 1° at λ=632.8  nm, which corresponds to a precision in the optical path difference between the two arms of less than 1 nm. The stabilization method is ditherless, and the error signal is computed from the spatial shift of the interference pattern of a reference laser, measured in real-time with a CCD array detector. We discuss the usefulness of this method for nanopositioning, optical interferometry, and quantum optical experiments.

High-efficiency holograms fixed in lithium niobate after recording using a digital fringe stabilization system

We used a digital feedback control loop system to produce reproducible fixed volume transmission holograms of high diffraction efficiency. Different strategies were investigated to obtain holograms of good quality and the highest refractive index modulation depth. Using this control system, we were able to record holograms with stationary fringes. Additionally to using the stationary fringe recording, a double recording-fixing schedule resulted in being the most appropriate one to produce reproducible holograms of better characteristics. This strategy is discussed and compared with other already established ones.

All-fiber interferometry: design and analysis

This paper presents a design procedure for a fiber interferometer, the optical system, and its associated electronic control. Analog and digital circuits were optimized to achieve an inexpensive and compact system. The lock-in amplifier required for phase control was designed using a field programmable gate array that was also configured to carry out the required phase stepping. The interferometer was built into two stages. The first stage used only one wavelength to measure samples with step heights in the hundreds of nanometers, with improvements in accuracy through averaging of data. The next stage included two measurement wavelengths to extend the measurement range to a few hundreds of micrometers. The paper conducts a systematic study of sources of errors. A least squares method that minimizes measurement time but retains accuracy has been used to measure height.

Free-space optical delay interferometer with tunable delay and phase

A free-space optical delay interferometer (DI) featuring a continuously tunable time delay, polarization insensitive operation with high extinction ratios and accurate phase and time delay monitoring scheme is reported. The polarization dependence is actively mitigated by adjusting a birefringent liquid-crystal device. The DI has been tested for reception of D(m)PSK signals.

Active feedback regulation of a Michelson interferometer to achieve zero-background absorption measurements

An active phase-controlling scheme based on a proportional-integral-derivative-controlled piezoelectric transducer is presented with the purpose of stabilizing a quasi-zero-background absorption spectrometer. A fiber-based balanced Michelson interferometer is used, and absorption due to a gas sample in one of its arms results in an increased light signal to a detector, which otherwise, thanks to destructive interference, experiences a very low light level. With the presented approach, the sensitivity of already potent absorption measurement techniques, e.g., based on modulation, could be improved even further.

Phase-shift extraction for phase-shifting interferometry by histogram of phase difference

We propose a non-iterative approach to extract the unknown phase shift in phase shifting interferometry without the assumption of equal distribution of measured phase in [0,2π]. According to the histogram of the phase difference between two adjacent frames, the phase shift can be accurately extracted by finding the bin of histogram with the highest frequency. The main factors that influence the accuracy of the proposed method are analyzed and discussed, such as the random noise, the quantization bit of CCD, the number of fringe patterns used and the bin width of histogram. Numerical simulations and optical experiments are also implemented to verify the effectiveness of this method.

Stabilization of a long-armed fiber-optic single-photon interferometer

We report on single-photon interference experiments in a Michelson-type interferometer built with two 6-km-long fiber spools, as well as on the active stabilization of the interferometer. A weak coherent light signal was (de-) multiplexed with a strong reference light using wavelength-division multiplexing technique, and real-time feedback control technique was applied for the reference light to actively stabilize the phase fluctuation in the long-armed fiber interferometer. The stabilized interferometer showed phase stability of 0.06 rad, which corresponds to an optical path length fluctuation of 15 nm between the 6-km-long interfering arms. The raw visibility obtained without subtracting noise counts in the single-photon interference experiment was more than 98% for stabilized conditions.

Active control of grating interferometers for extended-range low-noise operation

An active control method is proposed and demonstrated to improve grating-based laser interferometry to achieve low-noise (subpicometer resolution) and multiwavelength unambiguous range of operation simultaneously. The method modifies a recurrent calibration-based path stabilization algorithm to extract high-resolution and low-resolution data in parallel. This extended range recurrent calibration method is experimentally verified by implementing it on the micromachined scanning grating interferometer (microSGI).

Resolving fringe ambiguities of a wide-field Michelson interferometer using visibility measurements of a noncollimated laser beam

An actively stabilized interferometer with a constant optical path difference is a key element in long-term astronomical observation, and resolving interference fringe ambiguities is important to produce high-precision results for the long term. We report a simple and reliable method of resolving fringe ambiguities of a wide-field Michelson interferometer by measuring the interference visibility of a noncollimated single-frequency laser beam. Theoretical analysis shows that the interference visibility is sensitive to a subfringe phase shift, and a wide range of beam arrangements is suitable for real implementation. In an experimental demonstration, a Michelson interferometer has an optical path difference of 7 mm and a converging monitoring beam has a numerical aperture of 0.045 with an incidental angle of 17 degrees. The resolution of visibility measurements corresponds to approximately 1/16 fringe in the interferometer phase shift. The fringe ambiguity-free region is extended over a range of approximately 100 fringes.

Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts

A random phase-shifting interferometry insensitive to environmental noises is proposed. The relationship between intensity and phase in each pixel is obtained from a large amount of phase-shifting interferograms. In the phase-solving algorithm, the phase shift step length is not taken as a parameter, but the temporal intensity maximum and minimum in each pixel are needed. For finding the extreme values, random passive phase shifts caused by environmental noises are adopted to make the intensity ergodic. Supplementary active phase shifts, which are not accurately controlled or calibrated, are performed to shorten the measurement cycle. Finally, averaging statistically uncorrelated data over a long enough period of time can effectively reduce most random errors. A minitype Fizeau interferometer applying this random phase-shifting method demonstrated the feasibility of it.

Vibration-compensated interferometry system using phase-modulating interference fringe subdivision technology

An innovative vibration-compensation method, with phase-modulating interference fringe subdivision technology, is described. It simulates fringe movement by the phase difference of signals and can detect the fringe movement with an accuracy of 1/400 fringe spacing using this subdivision technology. A closed-loop vibration-compensation system is built, and the measurement of an interference fringe movement and a vibration-compensation test are successfully demonstrated. Because of this new method and a new feedback algorithm that was introduced, interference fringes can be stabilized at any preset phase position in real time. Compared with known methods, this method is simple and inexpensive, as well as effective.

Full-field quantitative phase imaging by white-light interferometry with active phase stabilization and its application to biological samples

We report a Koehler-illumination-based full-field, actively stabilized, low-coherence phase-shifting interferometer, which is built on a white-light Michelson interferometer. By using a phase-stepping technique we can obtain full-field phase images of the sample. An actively stabilized phase-lock circuit is employed in the system to reduce phase noise. An application to human epithelial cells (HeLa cells) is achieved in our experiment. The advancement of this technique rests in its ability to take images of unstained biological samples quantitatively and on a nanometer scale.

Regimes of feedback-controlled beam coupling

The introduction of certain electronic feedback loops into photorefractive wave-coupling schemes makes them noise free and leads to dramatic changes of the whole nonlinear behavior. The familiar steady states can be transformed into periodic states that are characterized by ultimately high and low values of the diffraction efficiency eta of the recorded index grating or into quasisteady states with small values of eta. These transformations possess thresholds with respect to controllable experimental parameters like the coupling strength and the input intensity ratio. We present a general analysis of the threshold behavior for different modes of the feedback operation and different types of the nonlinear photorefractive response. The results obtained (analytical and numerical) allow one to predict the regions of stability for feedback-controlled steady states and the observable characteristics of the system, including the output amplitudes and diffraction efficiency of the spatial grating, beyond these regions. They extend strongly the potentialities of the feedback-controlled wave coupling.

Quantitative phase imaging using actively stabilized phase-shifting low-coherence interferometry

We describe a quantitative phase-imaging interferometer in which phase shifting and noise cancellation are performed by an active feedback loop using a reference laser. Depth gating via low-coherence light allows phase measurement from weakly reflecting biological samples. We demonstrate phase images from a test structure and living cells.

Closed-loop phase stepping in a calibrated fiber-optic fringe projector for shape measurement

Active homodyne feedback control can be used to stabilize an interferometer against unwanted phase drifts introduced by, for example, temperature gradients. The technique is commonly used in fiber-optic sensors to maintain the fiber at its most sensitive (quadrature) position. We describe an extension of the technique to introduce stabilized, pi/2-rad phase steps in a full-field interferometer. The technique was implemented in a single-mode, fiber-optic interference fringe projector used for shape measurement and can be easily applied to other fiber- or bulk-optic interferometers, for example, speckle pattern and holographic interferometers. Fresnel reflections from the distal fiber ends undergo a double pass in the fibers and interfere at the fourth port of a directional coupler. The interference intensity (and hence phase) is maintained at quadrature by feedback control to a phase modulator in one of the fiber arms. Stepping between quadrature positions (separated by pi rad for light undergoing a double pass) introduces stabilized phase steps in the projected fringes (separated by pi/2 rad for a single pass). A root-mean-square phase stability of 0.61 mrad in a 50-Hz bandwidth and phase step accuracy of 1.17 mrad were measured.

Adaptive systems in speckle-pattern interferometry

The concept of adaptivity in television holography is discussed, and various realizations of adaptivity are presented. In one possible variation, functions of the components of the optical arrangement may be changed to adapt them to measurement conditions. An additional peculiarity of the technique is that reference waves are produced by holographically reconstructed virtual images. A method, believed to be new, is introduced for synthesizing the phase front of the master object beam that is produced by a simple holographic optical element and is used as a smooth or a speckled reference beam in the electronic speckle-pattern interferometer. An adaptive interferometer is presented as a measuring device for various measuring tasks. Selected applications are shown, demonstrating different aspects of adaptivity.

Surface profilometry with laser-diode optical feedback interferometer outside optical benches

A simple and robust interferometer with a laser diode subject to optical feedback from the interferometer is presented for surface testing of a spherical mirror. The fringe phase can be locked by the optical feedback within less than 0.2pi (peak-to-valley value) even when the interferometer is placed on a wooden table. The fringe locking is caused by the change of lasing wavelength that suppresses the net phase change to be much less than 2pi. The locked fringe pattern with spatial carriers can be analyzed by a fringe analyzer at a video rate, and the measurement results of the spherical mirror showed the same result as on an optical bench.

Analysis of fringe locking in a laser diode interferometer under injection-current modulation

A theoretical analysis has been performed that explains a fringe-locking phenomenon observed in a two-beam interferometer in which a laser diode was subjected to optical feedback and modulation of its injection current. The dependence of wavelength change on the injection-current variation is calculated by use of a model of coupled resonators consisting of the laser cavity and the interferometer. The fringe phase change caused by modulation of the injection current is derived from this model and has proved to be suppressed within much less than 2pi in excess of an integer multiple of 2pi if the path difference of the interferometer is longer than 10 mm. The calculated phase fluctuation agrees well with those observed in experiments.

Incremental holographic recording in lithium niobate with active phase locking

Angular-multiplexed hologram recording in iron-doped lithium niobate crystals was carried out with near-infrared light. An incremental recording schedule with active phase locking of the light pattern onto the hologram was used. Continuous and reproducible recording of holograms of equal efficiency was achieved, and a hologram multiplexing number, M/#=2 , for a 5-mm-thick crystal was obtained at a 760-nm wavelength of light.

Parametric Extension of the Classical Exposure-Schedule Theory for Angle-Multiplexed Photorefractive Recording over Wide Angles

The gradual reorientations in crystal geometry encountered during angle-multiplexed holographic recording with obliquely incident recording beams can create significant parametric exposure-time and recording-angle dependencies in both grating writing- and erasure-time constants. We present a parametric extension of the classically derived backward-recursion algorithm that compensates for the intermingling effects of recording geometry, writing-beam intensity variations, and unique crystal behavior. We present experimental data for a sequence of 301 holograms recorded with the goal of equal hologram strength and, separately, the same sequence recorded with the goal of equal hologram reconstruction intensity-which are different cases for a steeply incident readout beam.

Avoiding hologram bending in photorefractive crystals

Dynamic coupled-wave theory predicts the bending of recorded hologram phase planes in most photorefractive crystals. Bent holograms occur in LiNbO(3) and other photovoltaic crystals that are particularly interesting as holographic storage media and result in a reduced overall diffraction eff iciency. We show that hologram bending in LiNbO(3) can be avoided or at least sensibly reduced by use of an actively stabilized recording technique.