Self-referencing Interferometer Research Articles

A self-referenced interferometer for in situ cryogenic wafer curvature measurements.

A self-referenced interferometer to measure time-varying curvature in mechanically unstable environments is needed in many applications. One application that demands this measurement technique with fast data acquisition, 2D sensitivity, and insensitivity to vibration is the measurement of thermal strain in thin films in operational environments. The diverging beam interferometer described here demonstrates an angular sensitivity to the local curvature using interferograms captured by a CMOS camera. Two-dimensional Fourier analysis is used to extract curvature changes. The interferometer demonstrates an experimental sensitivity to curvature changes on the order of 10-4 m-1 and is used to measure thermal stresses in a cryogenic environment of a polycrystalline titanium nitride thin film on a silicon wafer that exhibits anisotropic curvature.

Optical frequency domain polarimetry based on a self-referenced unbalanced Mach-Zehnder interferometer.

Optical frequency domain polarimetry (OFDP) is an emerging distributed polarization crosstalk rapid measurement method with an ultrawide dynamic range. However, interferometric phase noise induced by the laser source and ambient noise results in a trade-off between measurement length and dynamic range. In this Letter, we solve this problem with a self-referenced unbalanced Mach-Zehnder interferometer. The features of long distance (9.8 km), ultrawide dynamic range (107.8 dB), short measurement time (2 sec), and signal-to-noise ratio improvement against ambient noise are experimentally demonstrated. The method makes it possible to evaluate a long polarization-maintaining fiber in an environment whose state changes rapidly.

Generation of Stokes singularities using polarization lateral shear interferometer.

Lateral shear interferometer, being a self-referenced interferometer, has proven to be an important tool in scalar optics. Here we employ a vectorial counterpart - polarization lateral shear interferometer, in which the two interfering beams apart from being derived from the test wavefront, are in orthogonal states of polarization. Therefore when the test wavefront has spatially varying phase gradient across the beam cross-section, the resulting shearogram produces polarization fringes instead of intensity fringes. Further, the shearogram becomes inhomogeneously polarized. This polarization lateral shear interferometer may have potential uses in metrology, but in this article we demonstrate the ability of the interferometer in the generation of all Stokes singularities in the single beam by launching a phase singular beam into it. It is found that a vortex dipole is formed along with other generic Stokes singularities. Experimental observations support the results and they are discussed in the article.

Multi-tasking geometric phase element array based self-referenced vortex interferometer for three-dimensional topography.

Interferometry is a basic physical method to record and reconstruct the three-dimensional (3D) topography of a complex object. However, mainstream interferometers using two beams can be unstable in a volatile environment. Here, we present a self-referenced optical vortex interferometer employing multi-tasking geometric phase elements. Compared with conventional devices, the multitasking elements can enable vortex filters while deflecting the interference beams to achieve high mode purity in broadband. We use the proposed system to reconstruct the 3D topography of a sample while determining its surface elevations and depressions accurately and conveniently in one static interference pattern.

Direct f-3f self-referencing using an integrated silicon-nitride waveguide.

We have achieved the simultaneous generation of a 2.6-octave-wide supercontinuum (SC) spectrum over 400-2500 nm and third-harmonic light solely by a dispersion-controlled silicon-nitride waveguide (SiNW). To increase the visible intensity of the SC light component, we fabricated low-loss 5-mm-long deuterated SiNWs with spot-size converters by low-temperature deposition. We succeeded in measuring the carrier-envelope-offset (CEO) signal with a 34-dB signal-to-noise ratio because this short deuterated SiNW provides a large temporal overlap between the f and 3f components. In addition, we have demonstrated this method of CEO locking at telecommunications wavelengths with f-3f self-referencing generated solely by the SiNW without the use of highly nonlinear fiber and an additional nonlinear crystal. Compared with the method of CEO locking with a highly nonlinear fiber and a standard f-2f self-referencing interferometer, this method is not only simple and compact but also stable.

Integrated self-referencing single shot digital holographic microscope and optical tweezer

Digital holographic microscopy is a single-shot technique for quantitative phase imaging of samples, yielding thickness profiles of phase objects. It provides sample features based on their morphology, leading to their classification and identification. However, observing samples, especially cells, in fluids using holographic microscopes is difficult without immobilizing the object. Optical tweezers can be used for sample immobilization in fluids. The present manuscript provides an overview of our ongoing work on the development of a compact, low-cost microscopy system for digital holographic imaging of optically trapped samples. Integration of digital holographic microscopy system with tweezers is realized by using the optical pickup unit extracted from DVD burners to trap microsamples, which are then holographically imaged using a highly compact self-referencing interferometer along with a low-cost, in-house developed quadrant photodiode, providing morphological and spectral information of trapped particles. The developed integrated module was tested using polystyrene microspheres as well as human erythrocytes. The investigated system offers a multitude of sample features, including physical and mechanical parameters and corner frequency information of the sample. These features were used for sample classification. The proposed technique has vast potential in opening up new avenues for low-cost, digital holographic imaging and analysis of immobilized samples in fluids and their classification.

Spatial Wavefunction Characterization of Femtosecond Pulses at Single-Photon Level.

Reading quantum information of single photons is commonly realized by quantum tomography or the direct (weak) measurement approach. However, these methods are time-consuming and face enormous challenges in characterizing single photons from an ultrafast light source due to the stringent temporal mode matching requirements. Here, we retrieve the spatial wavefunction of indistinguishable single photons from both a continuous wave source and a femtosecond light source using a self-referencing interferometer. Our method only requires nine ensemble-averaged measurements. This technique simplifies the measurement procedure of single-photon wavefunction and automatically mode matches each self-interfering single photon temporally, which enables the measurement of the spatial wavefunction of single photons from an ultrafast light source.

Deep-turbulence wavefront sensing using digital holography in the on-axis phase shifting recording geometry with comparisons to the self-referencing interferometer.

In this paper, we study the use of digital holography in the on-axis phase-shifting recording geometry for the purposes of deep-turbulence wavefront sensing. In particular, we develop closed-form expressions for the field-estimated Strehl ratio and signal-to-noise ratio for three separate phase-shifting strategies-the four-, three-, and two-step methods. These closed-form expressions compare favorably with our detailed wave-optics simulations, which propagate a point-source beacon through deep-turbulence conditions, model digital holography with noise, and calculate the Monte Carlo averages associated with increasing turbulence strengths and decreasing focal-plane array sampling. Overall, the results show the four-step method is the most efficient phase-shifting strategy and deep-turbulence conditions only degrade performance with respect to insufficient focal-plane array sampling and low signal-to-noise ratios. The results also show the strong reference beam from the local oscillator provided by digital holography greatly improves performance by tens of decibels when compared with the self-referencing interferometer.

Reduced pulse energy for frequency comb offset stabilization with a dual-pitch periodically poled lithium niobate ridge waveguide

The pulse energy for stabilizing the carrier-envelop offset frequency of an Er-doped fiber laser was reduced by a dual-pitch (DP-) periodically poled lithium niobate (PPLN) ridge waveguide implemented in a 2f-to-3f self-referencing interferometer (SRI). The pulse energy requirement was less than half that for a single-pitch PPLN ridge waveguide implemented in an f-to-2f SRI. We also found that environmental noise could be reduced by adjusting the pulse energy for frequency stabilization with the DP-PPLN ridge waveguide, as estimated from the phase noise of an out-of-loop interferometer.

Complex amplitude reconstruction for dynamic beam quality M2 factor measurement with self-referencing interferometer wavefront sensor.

A real-time complex amplitude reconstruction method for determining the dynamic beam quality M2 factor based on a Mach-Zehnder self-referencing interferometer wavefront sensor is developed. By using the proposed complex amplitude reconstruction method, full characterization of the laser beam, including amplitude (intensity profile) and phase information, can be reconstructed from a single interference pattern with the Fourier fringe pattern analysis method in a one-shot measurement. With the reconstructed complex amplitude, the beam fields at any position z along its propagation direction can be obtained by first utilizing the diffraction integral theory. Then the beam quality M2 factor of the dynamic beam is calculated according to the specified method of the Standard ISO11146. The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment, including the static and dynamic beam process. The experimental method is simple, fast, and operates without movable parts and is allowed in order to investigate the laser beam in inaccessible conditions using existing methods.

Measurement of M²-Curve for Asymmetric Beams by Self-Referencing Interferometer Wavefront Sensor.

For asymmetric laser beams, the values of beam quality factor and are inconsistent if one selects a different coordinate system or measures beam quality with different experimental conditionals, even when analyzing the same beam. To overcome this non-uniqueness, a new beam quality characterization method named as M2-curve is developed. The M2-curve not only contains the beam quality factor and in the x-direction and y-direction, respectively; but also introduces a curve of versus rotation angle α of coordinate axis. Moreover, we also present a real-time measurement method to demonstrate beam propagation factor M2-curve with a modified self-referencing Mach-Zehnder interferometer based-wavefront sensor (henceforth SRI-WFS). The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment in multimode beams. The experimental results showed that the proposed measurement method is simple, fast, and a single-shot measurement procedure without movable parts.

Self-referenced interferometer for cylindrical surfaces.

We present a new interferometric method for shape measurement of hollow cylindrical tubes. We propose a simple and robust self-referenced interferometer where the reference and object waves are represented by the central and peripheral parts, respectively, of the conical wave generated by a single axicon lens. The interferogram detected by a digital camera is characterized by a closed-fringe pattern with a circular carrier. The interference phase is demodulated using spatial synchronous detection. The capabilities of the interferometer are experimentally tested for various hollow cylindrical tubes with lengths up to 600mm.

Frequency stabilization of an Er-doped fiber laser with a collinear 2f-to-3f self-referencing interferometer

We report the stabilization of the carrier-envelope offset (CEO) frequency of an Er-doped fiber laser with a collinear 2f-to-3f self-referencing interferometer. The interferometer is implemented by a dual-pitch periodically poled lithium niobate ridge waveguide with two different quasi-phase matching pitch sizes. We obtain a 52-dB signal-to-noise ratio in the 100-kHz resolution bandwidth of a heterodyne beat signal, which is sufficient for frequency stabilization. We also demonstrate that the collinear geometry is robust against environmental perturbation by comparing in-loop and out-of-loop Allan deviations when the in-loop CEO frequency is stabilized with a phase-locked loop circuit.

LSPV+7, a branch-point-tolerant reconstructor for strong turbulence adaptive optics.

Optical wave propagation through long paths of extended turbulence presents unique challenges to adaptive optics (AO) systems. As scintillation and branch points develop in the beacon phase, challenges arise in accurately unwrapping the received wavefront and optimizing the reconstructed phase with respect to branch cut placement on a continuous facesheet deformable mirror. Several applications are currently restricted by these capability limits: laser communication, laser weapons, remote sensing, and ground-based astronomy. This paper presents a set of temporally evolving AO simulations comparing traditional least-squares reconstruction techniques to a complex-exponential reconstructor and several other reconstructors derived from the postprocessing congruence operation. The reconstructors' behavior in closed-loop operation is compared and discussed, providing several insights into the fundamental strengths and limitations of each reconstructor type. This research utilizes a self-referencing interferometer (SRI) as the high-order wavefront sensor, driving a traditional linear control law in conjunction with a cooperative point source beacon. The SRI model includes practical optical considerations and frame-by-frame fiber coupling effects to allow for realistic noise modeling. The "LSPV+7" reconstructor is shown to offer the best performance in terms of Strehl ratio and correction stability-outperforming the traditional least-squares reconstructed system by an average of 120% in the studied scenarios. Utilizing a continuous facesheet deformable mirror, these reconstructors offer significant AO performance improvements in strong turbulence applications without the need for segmented deformable mirrors.

Carrier-envelope offset locking with a 2f-to-3f self-referencing interferometer using a dual-pitch PPLN ridge waveguide

We demonstrate that a 2f-to-3f self-referencing interferometer (SRI) becomes a useful tool for stabilizing a carrier-envelope offset frequency of an Er-doped fiber laser. A dual-pitch periodically poled lithium niobate (PPLN) ridge waveguide, consisting of two monolithically integrated segments with different quasi-phase matching pitch sizes, allows us to generate third-harmonic light with high efficiency. By using this device, we obtain a 45-dB signal-to-noise ratio in 100-kHz bandwidth of a heterodyne beat signal and instability of the in-loop f CEO of 8 × 10(-18) at 1 s of averaging time. This result is important for f CEO stabilization of a frequency comb, for which it is difficult to obtain a one-octave supercontinuum spectrum.

Phase-noise characteristics of a 25-GHz-spaced optical frequency comb based on a phase- and intensity-modulated laser

We investigated phase-noise characteristics of both a phase/intensity-modulated laser with 25-GHz mode spacing and a mode-locked fiber laser with carrier-envelope-offset (CEO) locking. As the separation from the frequency of the continuous wave (CW) laser diode (LD) for a seed light source increases, the integrated phase noise of each comb mode of both the phase/intensity-modulated laser and supercontinuum light originating from it increases with the same slope as a function of mode number. The dependence of the integrated phase noise on mode number with the phase/intensity-modulated laser is much larger than with the mode-locked fiber laser of the CEO locking. However, the phase noise of the phase/intensity-modulated laser is extremely lower than that of the mode-locked fiber laser with CEO locking in the frequency region around the CW LD. The phase noise of the phase/intensity-modulated laser with 25-GHz mode spacing and that of the mode-locked fiber laser with the CEO locking could be estimated and were found to be almost the same at the wavelengths required in an f-to-2f self-referencing interferometer. Our experimental results indicate the possibility of achieving an offset-frequency-locked frequency comb with the phase/intensity-modulated laser.

Self-referenced rectangular path cyclic interferometer with polarization phase shifting

A polarization phase shifting interferometer using a cyclic path configuration for measurement of phase nonuniformities in transparent samples is presented. A cube beam splitter masked by two linear polarizers is used to split the source wavefront into two counter propagating linearly polarized beams that pass through the sample. At the output of the interferometer, the two orthogonally polarized beams are rendered circularly polarized in the opposite sense through the use of a quarter wave plate. Finally, phase shifting is achieved by rotating a linear polarizer before the recording plane. In a rectangular path interferometer, although the two counter propagating wavefronts are laterally folded with respect to each other in the interferometer arms, the beams finally emerge mutually unfolded at the output of the interferometer. This phenomenon is utilized to create a reference if the sample is introduced in one lateral half of the beam in any one of the interferometer arms. The polarization phase shifting technique is used to generate four phase-shifted interferograms, which are utilized to evaluate the phase profile of the phase sample. Experimental results presented validate the proposed technique.

Collective coherent phase combining of 64 fibers

A new architecture for active coherent beam combining of a large number of fibers is demonstrated. The approach is based on a self-referenced quadriwave shearing interferometer and active control with arrays of electro-optic ceramic modulators. Coherent phase combining of 64 independent amplified fibers is obtained. This is to our knowledge the highest reported number of combined fibers. A Strehl ratio degradation less than 2dB is achieved with a residual phase error <λ/10 rms.

Detection of carrier-envelope offset frequency in an Er-doped fiber femtosecond laser

It is the inevitable trend of the development for the optical frequency comb based on the Ti: sapphire femtosecond laser to be replaced by that based on the Er: fiber femtosecond laser. The detection of the carrier-envelope offset f0 in the femtosecond laser is a key to the realization of an optical frequency comb. In this paper, the structure of the optical part of an Er: fiber optical frequency comb is introduced. The optical pulses from an Er: fiber femtosecond laser with a repetition of 230 MHz are first amplified with a two stage amplifiers, spectrally broadened in a highly nonlinear fiber, and then pass through a single-beam f—2f self-referencing interferometer. By optimizing the optical parameters, the f0 with a signal-to-noise ratio of 30 dB is obtained in the Er: fiber femtosecond laser, which is favorable for the realization of an Er: fiber frequency comb.

Adaptive control in an adaptive optics experiment

This paper presents results from an adaptive optics experiment in which an adaptive control loop augments a classical adaptive optics feedback loop. Closed-loop wavefront errors measured by a self-referencing interferometer are fed back to the control loops, which drive a membrane deformable mirror to correct the wavefront. The paper introduces new frequency-weighted deformable mirror modes used as the control channels and new wavefront sensor modes for analyzing the performance of the control loops. The corrected laser beam also is imaged by a diagnostic target camera. The experimental results show reduced closed-loop wavefront errors and correspondingly sharper diagnostic target images produced by the adaptive control loop as compared with the classical AO loop.