Common-path Interferometer Research Articles

One-grating common-path phase-shifting interferometer for quantitative phase imaging

A one-grating common-path phase-shifting interferometer for quantitative phase imaging is proposed as an improvement over the original interferometer design. In the original version, the setup is long, involving a grating pair, and requires precise mechanical translation of the grating, which poses difficulties for practical applications. The proposed interferometer utilizes grating multiplexing to reduce the length of the optical setup and uses a phase-only spatial light modulator to implement pinhole filtering and phase shifting simultaneously without any moving parts, making it more conducive for the realization of a practical version.

Automated phase-visibility modulating interferometry

This paper presents the Phase-Visibility Modulating Interferometry (PVMI) method automated by a microcontroller and three servomotors, under inhomogeneous out-of-phase amplitude modulation (OPAM) in the On-Off Modulation (OOM) mode. PVMI is implemented in a triple-aperture common-path interferometer (TACPI), based on a 4f optical imaging system. The high mechanical stability of the TACPI and the properties of the PVMI technique make the present method immune to noise, robust, fast, and convenient for measuring complex amplitude with high resolution and accuracy. PVMI does not preprocess and post-process the experimental irradiances and does not need a phase step shifter or a carrier frequency. Therefore, a calibration is unnecessary, there are no detuning errors, and no bandwidth reduction. The great advantage of automated PVMI is explained and demonstrated experimentally for three translucent objects. The focal length estimation of a lens with a percentual deviation of 0.14 to validate the automated PVMI, and the evaluation of two arbitrary translucent objects with high resolution and accuracy.

Thermally compensated common-path differential interferometer with reduced long-term zero-drifts

Abstract Laser interferometers have served as the workhorses in the metrology of length for several decades. Their broader application brings further challenges, especially for longer measurement time-frames or outside the laboratory environment with strictly controlled conditions. As a part of our team’s activities aiming at characterizing and eliminating the effects of unstable temperature on interferometric length measurements, we report on successfully remodelling a differential interferometer’s optical arrangement focused on increasing resilience against temperature changes. The experimental characterization under constant temperature and subsequently under thermal load proved a tenfold decrease in short-term fluctuations and reduced sensitivity to temperature changes by a factor of 100.

One-shot self-calibrating phase-shifting interferometry by direct normalization of interferograms

Dynamic phase measurement is a valuable technique applied across various scientific and technological domains due to its high accuracy, non-contacting method, and numerous practical applications. In this manuscript, we present a phase retrieval method capable of measuring the object’s phase in real-time. Our proposal is based on a double aperture common-path interferometer adapted for polarization modulation in the input windows, enabling the superposition of two fields with orthogonal circular polarizations. Two interferograms and two intensities are captured in a single shot, showcasing the possibility of obtaining two normalized interferograms directly and straightforwardly. This allows for the derivation of expressions for phase recovery and, additionally, the determination of the arbitrary phase step. We demonstrate that this method is easy to implement, highly accurate, and sufficiently fast for real-time applications. To validate the effectiveness of the method, we conduct numerical error analysis and laboratory experiments.

Enhancing hyperspectral imaging through macro and multi-modal capabilities

Hyperspectral imaging (HSI) has emerged as an effective tool to obtain spatially resolved spectral information of artworks by combining optical imaging with spectroscopy. This technique has proven its efficacy in providing valuable information both at the large and microscopic scale. Interestingly, the macro scale has yet to be thoroughly investigated using this technology. While standard HSI methods include the use of spatial or spectral filters, alternative methods based on Fourier-transform interferometry have also been utilised. Among these, a hyperspectral camera employing a birefringent common-path interferometer, named TWINS, has been developed, showing a high robustness and versatility. In this paper, we propose the combination of TWINS with a macro imaging system for the study of cultural heritage (CH). We will show how the macro-HSI system was designed, and we will demonstrate its efficient capabilities to collect interferometric images with high visibility and good signal of both reflectance and fluorescence on the same field of view, even on non-flat samples. Our hyperspectral camera for macro studies of both reflectance and fluorescence data is a completely new asset in the CH panorama and beyond. The relevance of the macro technology is demonstrated in two case studies, aiding in the analysis of biofilms on stone samples and of the degradation of dyed textiles.

Synthesizing polarization singularity lattices using phase ramps

In this paper, a novel methodology for generating polarization singularity lattices using ramp phase structures in a polarization interferometer is presented. By applying differential tilts to distinct regions within the wavefront using a spatial light modulator, a phase-discontinuity line separating the two regions is formed. During propagation along this line, phase vortices are formed at discrete points about which the phase difference on either side of the ramp is π. This wavefront with phase vortices is superimposed with a plane wave in orthogonal polarization in a polarization interferometer, giving rise to polarization singularities. A common-path polarization interferometer is constructed using a spatial light modulator to reduce errors and complexity. Polarization fringes instead of intensity fringes obtained in this interferometer host polarization singularities. Lattices made up of a linear chain of polarization singularities—unusually of the same index polarity—are found here. Experimental results corroborate the theoretical predictions. This study shows that singularities can be produced with non-spiral phase plates by using linear phase ramps. The method discussed in this paper may find potential applications in optical trapping and particle steering.

Generation of interferometrically stable pulse pairs from a free-electron laser using a birefringent interferometer

We present a compact, intrinsically stable common path interferometer for the seeding of free-electron lasers (FELs). The interferometer can handle the required ultraviolet seed wavelengths and features an excellent phase stability of 10 mrad at 265 nm. By seeding the FEL FERMI, we demonstrate the generation of extreme ultraviolet (XUV) pulse pairs with tunable delay and a delay stability of 6 as at 52.5 nm. Prospective applications are Fourier transform spectroscopy, nonlinear spectroscopy and coherent control experiments in the XUV and x-ray domain.

Single-protein optical holography

Light scattering by nanoscale objects is a fundamental physical property defined by their scattering cross-section and thus polarizability. Over the past decade, a number of studies have demonstrated single-molecule sensitivity by imaging the interference between scattering from the object of interest and a reference field. This approach has enabled mass measurement of single biomolecules in solution owing to the linear scaling of image contrast with molecular polarizability. Nevertheless, all implementations so far are based on a common-path interferometer and cannot separate and independently tune the reference and scattered light fields, thereby prohibiting access to the rich toolbox available to holographic imaging. Here we demonstrate comparable sensitivity using a non-common-path geometry based on a dark-field scattering microscope, similar to a Mach–Zehnder interferometer. We separate the scattering and reference light into four parallel, inherently phase-stable detection channels, delivering a five orders of magnitude boost in sensitivity in terms of scattering cross-section over state-of-the-art holographic methods. We demonstrate the detection, resolution and mass measurement of single proteins with mass below 100 kDa. Separate amplitude and phase measurements also yield direct information on sample identity and experimental determination of the polarizability of single biomolecules.

ANALYSIS OF NULL RESULTS OF HAMMAR EXPERIMENT BY CLASSICAL MECHANICS WITHOUT SPECIAL THEORY OF RELATIVITY

In optics interferometers are used for precision measurements. In interferometry two waves of light are superimposed to generate interference fringes. The interference pattern is observed and analyzed to measure physical process. Gustaf Wilhelm Hammar conducted an experiment in the year 1935 to test aether drag hypothesis. The null results of this experiment were interpreted in consistent with special theory of relativity. Hammar used common path interferometer and observed the changes in interference fringes due to motion of earth. The present work describes that when there is no aether and no medium drags the light in its direction of motion than what will be the behaviour of light.The analysis has been made according to classical mechanics keeping in view Huygen’s principle by tracking the pathways of both the rays of light.It is established that speed of light is independent of velocity of any object,apparatus or any observer and there is no effect of motion of earth.The null results of Hoek’s experiment and Hammar experiment are in consistent with classical mechanics.

Tight focusing through scattering media via a Bessel-basis transmission matrix.

The transmission matrix (TM) is a powerful tool for focusing light through scattering media. Here, we demonstrate a Bessel-basis TM that enables tight focusing through the scattering media and reduces the full width at half maximum of the focus by 23% on average, as compared to the normally used Hadamard-basis TM. To measure the Bessel-basis TM, we establish a common-path inter-mode interferometer (IMI), which can fully utilize the pixels of the spatial light modulator, leading to an enhancement in the peak-to-background intensity ratio (PBR) of the focus. Experimental results suggest that the Bessel-basis TM can achieve a tighter focus behind the scattering media, and the PBR of the focus obtained by the IMI is around 14.3% higher than that achieved using the normal peripheral reference interferometry.

A bolometric hyperspectral camera based on a birefringent interferometer for remote sensing in the thermal infrared

Remote sensing in thermal infrared bands (TIR) is largely dominated by cumbersome dispersive-type hyperspectral imagers, which usually require expensive and cryo-cooled quantum detectors to make up for their low optical throughput. Here, we present a compact and low-cost TIR hyperspectral camera based on the Fourier-transform approach. It combines an uncooled bolometer detector and a common-path birefringent interferometer made of calomel (Hg2Cl2). It features high optical throughput, an interferometric contrast greater than 90% even for incoherent radiation, spectral resolution tunable up to 4.5 cm-1, robust and long-term interferometric stability. Retrieving in a few minutes the infrared spectrum in all pixels of the TIR image, it could constitute a valuable tool for evaluating radiative cooling materials’ spatial and spectral properties over extended areas. We test the capabilities of the instrument by measuring the emissivity map of different butterfly wings, which provide a natural example of radiative cooling.

Adjustable accuracy of phase steps in a double-aperture common-path interferometer by rotating and displacing grating at Fourier plane

Detuning errors limit the accuracy of phase extraction in phase-shifting interferometry (PSI). To improve this accuracy, the systems to control the phase shifter dispositive must be highly accurate, involving high technology, exhaustive calibration, high cost, and constant maintenance. This manuscript presents a method for improving the accuracy of the phase step generated at the Fourier plane by rotating and displacing the grating in a double-aperture common-path interferometer. It is demonstrated that both the detuning errors and the phase extraction uncertainty decrease with the grating rotation angle. The experimental implementation is very simple, as it does not require any sophisticated mechanical system to improve the accuracy, no exhaustive calibration, and no additional mechanical and optical dispositive. With the present approach, the PSI method could be achieved very simply and with high accuracy by using a low-accuracy actuator. The theoretical model and experimental results are presented to demonstrate the present proposal.

Open fringes interferograms generation through the phase contrast technique

Phase contrast imaging is a proven technique for sensing optical wavefronts and obtaining qualitative and quantitative insights into phase disturbances. Traditionally, this method involves introducing a phase mask at the Fourier transform plane of the phase object to create a synthetic reference wave that interferes with the analyzed phase disturbance. In this study, we incorporate an intensity-dependent photorefractive material, facilitating the self-induction of a Zernike-type phase filter. We introduce an innovative modification by inducing an angular offset between the synthetic reference wave and the phase distribution of the object. Effective implementation necessitates an illumination area larger than the phase object's support. This method stands out due to its resilience to environmental factors, shared by all common-path interferometers. Furthermore, it leverages open fringe interferograms, consolidating all essential phase information into a single image. This innovation streamlines phase retrieval, eliminating the need for multiple images, and extends applicability beyond small-phase object perturbations. We present results demonstrating the recovered phase distribution using the well-established Takeda technique for open fringe interferograms. This novel approach promises to enhance phase distortion analysis, offering versatility and simplicity in a variety of applications.

Orientation-selective elliptic higher-order Poincaré sphere beam arrays

In this study, a new class of light-beam arrays, called orientation-selective elliptic higher-order Poincaré sphere (OS-EHOPS) beam arrays, is introduced as an extension of the scalar case reported in a previous study (Wang et al., 2020). For each beamlet of such beam arrays, the state of polarization represented by higher-/hybrid-order Poincaré spheres is spatially inhomogeneous, whereas the spatial profile takes on an elliptical shape with controllable orientation and ellipticity. The design procedure, which is rooted in multi-coordinate transformations, is comprehensively described and analyzed. Furthermore, we established an experimental setup involving a phase-only spatial light modulator that served as a Dammann grating and a common-path interferometer to effectively generate OS-EHOPS beam arrays. Two types of OS-EHOPS beam arrays, with hexagonal and double-ring-arranged structures, were synthesized to verify the feasibility of our method. Our design and optical system have potential applications in beam shaping and orientation-selective microfabrication.

Automatic experimental optimization of capture of interference patterns of a Double-Aperture Common-path interferometer to reduce negative effects of mechanical vibrations

Automatic experimental optimization of capture of interference patterns of a Double-Aperture Common-path interferometer to reduce negative effects of mechanical vibrations

Time gated Fourier transform spectroscopy as a technique for disentangling short- and long-lived luminescence

Overlapping short- and long-lived luminescence signals are often encountered and are not trivial to disentangle in a single measurement. Here, we demonstrate for a broad range of emitters that time gated Fourier transform spectroscopy can be used as a technique to simultaneously capture and temporally disentangle overlapping spectral features of luminescence signals. This allows us to concurrently measure the fluorescence and phosphorescence bands of an organic fluorophore, retrieve the emission of a quantum dot that is overshadowed by an autofluorescent serum solution, and for removing residual laser scatter and ambient room light in an optical filter free configuration. Time gated Fourier transform spectroscopy only requires the introduction of a common-path interferometer to the emission path of a standard time-correlated single photon counting setup; it can function as a technique to both discriminate signals as well as characterize properties of new materials.

Vortex phase deterioration common-path interferometry

Common-path interferometers (CPIs) are significant due to their compactness and vibration resistance. The usual challenge with CPIs arises due to a very small separation between reference and sample beams, where sending a reference beam through a sample is considered to be a limitation. However, this limitation also makes it difficult to probe the interaction of beams with materials as a function of their phase structure. This study paves the way for a new kind of interferometry that can provide unique phase signatures to study the sample. This paper proposes and demonstrates a novel approach based on thermo-optic refraction, to send both beams through the sample and probe the phase deterioration due to the relative interaction of beams in the material medium. Here, thermo-optic refraction interferometry allows the superposition of a higher-order vortex beam with a non-vortex beam through the phenomenon of thermal lensing. The non-vortex beam is made to expand in a controlled fashion by another laser. The relative interaction between the expanding non-vortex beam and the vortex beam within the sample, results in the output interferogram. The phase deterioration analysis of the output interferogram elucidates medium-driven phase changes. This technique is demonstrated using milk samples by recording the root-mean-square azimuthal phase deterioration of the orbital angular momentum beam.

Passive vibration suppression method based on frequency domain analysis in white light vertical scanning interferometer

Vibration in manufacturing environment can significantly affects the accuracy of surface measurements, especially for the white light vertical scanning interferometry (VSI), which requires mechanical scanning for full-field measurements. This paper proposes a passive vibration suppression technique that integrates a second common-path interferometer and uses frequency domain analysis to measure vibration and reconstruct surface topography. The method is feasible for suppressing vibrations with different frequencies and amplitudes, as verified by simulation and signal recovery analysis. An in-house developed interferometer with a common optical path is used to demonstrate the measurement performance experimentally. The mathematical formula relating the vibration amplitude, the vibration frequency, the frame rate of the camera and the scanning interval is presented. The experimental results show that the precision of plane measurement decreases with increasing vibration amplitude and frequency. Moreover, the step sample signals under a maximum vibration condition of 400 nm/5 Hz are recovered, with a standard deviation of 26.07 nm for the step height measurement. As the scanning interval increases, the system can suppress higher-amplitude vibrations.

Design and implementation of an electromechanical gear system for optimization of automatic phase-shifting of a Dual Aperture Common-Path Interferometer

In this work, we report experimental results of a proposed gear system for optimization of phase shifts used for extraction of phase between a reference and a test object in a Double Aperture Common Path Interferometer. The electromechanical approach is designed to increase the precision and control of automated transverse translation of a diffraction grating to obtain equidistant displacements, typically carried out manually. Calculations and analytics for the design and operation of the mechanical gear system are presented. The experimental results demonstrate significant error minimizing for equally spaced phase shifts compared to a previously reported implementation of our research group. The proposed system represents a reliable and low-cost implementation to improve the obtaining of suitable interferogram captures for equally spaced phase-shifting interferometry techniques.

Wavefront single-pixel imaging using a flexible SLM-based common-path interferometer

Wavefront single-pixel imaging (WSPI) is an important tool for simultaneously measuring the amplitude and phase of an unknown field, especially suitable for wavefront detecting in some special wavelengths where array detectors are immature or even unavailable. Here, a passive-detection-based WSPI method using a flexible SLM-based common-path interferometer is proposed, in which by detecting the zero-order diffraction of the SLM directly, the common-path phase-shift or off-axis technique can be flexibly realized by a “sandwich” structure consisting of a half-wave plate, a SLM, and a polarizer. The reference light can be conveniently chosen as the direct reflected light from the SLM, the unmodulated light from the pixels of the SLM, or the light from both of them. We experimentally verify the feasibility and advantages of the proposed method. We further demonstrate the method for wavefront measurement of a dragonfly wing, which suggests it can be used for quantitative phase imaging. It provides a high-resolution spatial wavefront passive detection technique, with a compact, stable, and flexible setup, which has lots of applications involving three-dimensional imaging, aberration correction, digital holographic measurement, and digital microscopy.