Optical Path Difference Variation Research Articles

Influence of the tilted arm glass on the temperature and wind velocity inversion for a static wind imaging interferometer

In a static wind imaging Michelson interferometer (SWIMI) developed by us, two-arm glasses are used to achieve the achromatic thermally compensation. The arm glass is cemented with the beam splitter. The tilt of the arm glass would cause a change to the optical path difference (OPD), thereby reducing the visibility of the interferogram and introducing phase error to the SWIMI system, which eventually responsible for errors in the inversion of temperature and wind velocity. In this paper, we present the principle of static wind imaging interferometer and derivate the variation of OPD caused by the two-dimensional tilt of arm glass in detail. By considering a rectangle incident beam, we analyze the effect of arm glass tilt on wind speed and temperature inversion. The results show that in order to realize the wind velocity error less than 3 m/s, the temperature error less than 3 K, and the instrument visibility greater than 0.8, the two-dimensional tilted angle of arm glass should be less than 1”. The tolerance of tilted angle can expand by adjusting the refractive index of the medium on both two sides of the arm glass or by adjusting the reflector mirror of the interferometer precisely. The results would be helpful for the cement of arm glass, beam splitter of SWIMI, and provide a reference for the design of a field-widened wind imaging interferometer.

Ultrahigh-sensitive optical coherence elastography

The phase stability of an optical coherence elastography (OCE) system is the key determining factor for achieving a precise elasticity measurement, and it can be affected by the signal-to-noise ratio (SNR), timing jitters in the signal acquisition process, and fluctuations in the optical path difference (OPD) between the sample and reference arms. In this study, we developed an OCE system based on swept-source optical coherence tomography (SS-OCT) with a common-path configuration (SS-OCECP). Our system has a phase stability of 4.2 mrad without external stabilization or extensive post-processing, such as averaging. This phase stability allows us to detect a displacement as small as ~300 pm. A common-path interferometer was incorporated by integrating a 3-mm wedged window into the SS-OCT system to provide intrinsic compensation for polarization and dispersion mismatch, as well as to minimize phase fluctuations caused by the OPD variation. The wedged window generates two reference signals that produce two OCT images, allowing for averaging to improve the SNR. Furthermore, the electrical components are optimized to minimize the timing jitters and prevent edge collisions by adjusting the delays between the trigger, k-clock, and signal, utilizing a high-speed waveform digitizer, and incorporating a high-bandwidth balanced photodetector. We validated the SS-OCECP performance in a tissue-mimicking phantom and an in vivo rabbit model, and the results demonstrated a significantly improved phase stability compared to that of the conventional SS-OCE. To the best of our knowledge, we demonstrated the first SS-OCECP system, which possesses high-phase stability and can be utilized to significantly improve the sensitivity of elastography.

A Fiber-Optic Displacement Sensor Using the Spectral Demodulation Method

This paper reports a fiber-optic displacement sensor based on a Michelson interferometer using the spectral demodulation method. The displacement information is sensed through the length variation of the sensing fiber following the deformation of the measured object. By deploying the relaxed reference arm along the sensing arm, the optical path difference variation introduced by temperature can be eliminated. A spectral demodulation method is employed to obtain the displacement from the interference spectrum by using the fast Fourier transform and the Buneman frequency estimation. The experimental results show that the proposed displacement sensor has a high resolution of 90 nm over a long span of 15.7 m and a large displacement measurement range of 7.5 mm. The theoretical displacement measurement range of the proposed sensor can be up to 10 cm. The proposed displacement sensor will be very useful and promising in large-scale civil infrastructure monitoring applications.

FSI-based non-cooperative target absolute distance measurement method using PLL correction for the influence of a nonlinear clock.

We propose a frequency swept interferometry (FSI)-based absolute distance measurement method that can be used to measure a noncooperative target located at a distance of 10s of m. In this method, an external cavity laser serves as the frequency tuning laser, and a single frequency laser and two acoustic optical modulators (AOMs) are used to measure the optical path difference (OPD) variation during the frequency tuning, which can correct the Doppler effect. A phase-locked loop (PLL) is introduced to synchronize the nonlinearities between the OPD variation measurement signal and the absolute distance measurement signal, improving the signal-to-noise ratio (SNR) of the OPD variation measurement signal. The distance to a noncooperative target located at 15m is experimentally measured using this method, and a precision of 3.43μm is obtained.

Research and implementation of OPD algorithm for spatial gravitational wave telescope based on ZEMAX and Python sof twares

The optical design softwares ZEMAX and Python were used to realize the precision solution of optical path difference (OPD) for spatial gravitational wave telescope.The dynamic data exchange(DDE) closed-loop communication between ZEMAX and Python was realized. First, the Python software processed the data of telescope mirror after the finite element analysis, and transmitted the analysis results to the ZEMAX with DDE for tracing ray.Secondly, the ZEMAX software transferred the ray coordinate value to the Python software through the DDE. Lastly, the Python software calculated the OPD and wavefront changes caused by rigid body translation through the global coordinate system. Through simulating the deformation of the gravitational wave telescope with the temperature change of 1 mK, the OPD and wavefront variation of the spatial gravitational wave telescope was solved by means of ZEMAX software and Python software. The results show that the OPD precision reaches the order of 1e-13 meter, which can satisfy the requirements of telescope for pico-level stability.It is concluded that the method is feasible to calculate the OPD, and it provides a technical reference for the OPD analysis for the further mechanism design of the gravitational wave telescope.

Full-field interferometry using infinity corrected optics

In this paper the construction of full-field (imaging) interferometers using infinity corrected optics commonly used in microscopy is discussed, with an emphasis on self-mixing interferometry configurations where the imaged light field is mixed with itself rather than a reference wave. Such configurations are used in speckle shearing interferometry, flow visualisation and quantitative flow measurement. The critical considerations for constructing path-length imbalanced full-field interferometers for these and similar applications are discussed, expressions are derived for key calculations and interferograms from example interferometers are presented. These include the concept of balancing the infinity-spaces of the two arms via the use of a glass block to minimise the optical path difference variation across the interferogram and ensure adequate sampling of the fringes on the detector. Further, the use of tilted glass blocks in single-pass and double-pass arrangements is detailed for the generation and control of spatial carrier fringes without extensive realignment of the interferometer, and for phase shifting.

Measurement of displacement and distance with a polarization phase shifting folded Twyman Green interferometer.

A Sagnac interferometer (SI), consisting of a polarization beam splitter (PBS), along with two equally spaced plane mirrors that are inclined at 45° to each other, is transformed into a folded Twyman Green interferometer (TGI) by placing a mirrored parallel plate (MPP) into the hypotenuse arm of the SI. The converging input beam produced by a telescope objective (TO) is split into reflected (s-polarized) and transmitted (p-polarized) components by the PBS. The p- and s-polarized focal spots are made to fall on the mirrored end surfaces of the parallel plate (PP). The retroreflected p- and s-polarized beams become collimated after passing through the TO. A linear shift of the PP in either (longitudinal) direction alters the positions of the p- and s-polarized focal spots and results in a set of converging and diverging spherical wavefronts that interfere to form concentric circular fringes. We applied polarization phase-shifting interferometry to obtain the optical path difference (OPD) variation of the interference field. The displacement is calculated from the OPD variation. A validation experiment has been carried out by introducing known shifts to the PP. The setup can be used for displacement as well as distance measurement.

Determination of surface roughness of plane optical components using quasimonochromatic light source and phase shifting interferometry

A differential interferometric technique for the measurement of surface roughness of plane optical surfaces is proposed. A polarization Sagnac interferometer, placed in the image space of a reflection microscope system with linearly polarized, spatially coherent, quasimonochromatic incident beam illumination, splits the image-forming beam from a plane test surface (TS) into laterally sheared (LS) linear orthogonal components. The LS components interfere when brought to the same state of polarization. The optical path difference (OPD) variation along the direction of lateral shear is a measure of the slope variation on the TS. Polarization phase shifting interferometry has been applied to extract the OPD variation and thus the slope distribution, slope errors, and, subsequently, height errors. System error contribution is eliminated by combining height error data obtained for parallel sections of the TS that lie along a section of the image field parallel to the direction of lateral shear, as the TS is shifted in a direction normal to the lateral shear direction between the data capture. Results obtained for an aluminized plane polished TS are presented.

Determination of the index inhomogeneity of transparent isotropic optical material with a dual Sagnac interferometer

A technique for the measurement of inhomogeneity of optical glass, fused silica, etc., using a Sagnac interferometer (SI) has been presented. An SI produces a pair of laterally separated, mutually parallel, collimated beams with orthogonal planes of polarization, i.e., p and s polarizations from an expanded, linearly polarized (45°) collimated He-Ne (632.8 nm) input laser beam. The p and s beams pass through a liquid-filled cell with plane parallel glass windows. The test glass with plane parallel end surfaces is kept in the path of the p beam in the index matching liquid, while the s beam traverses a parallel path through the liquid. Another SI recombines the emergent p and s beams by removing the lateral shear. A quarter-wave plate transforms the state of polarization of the beams to opposite circular polarizations of which the components selected by a linear polarizer interfere to form Fizeau fringes. Polarization phase shifting interferometery has been applied to determine the optical path difference (OPD) variations. The OPD variation without the test glass is subtracted from that with test glass to eliminate the effect of system aberration. The results for a phosphate laser glass sample have been presented.

Self-referenced technique for the determination of meridional figure errors of a toroidal mirror with a Sagnac interferometer

A simple, self-referenced technique for the determination of meridional surface slope errors of toroidal mirrors (TMs) used in synchrotron radiation is presented. An expanded, collimated, linearly polarized laser beam is allowed to fall on a TM, and the reflected toric wavefront from the TM is allowed to enter a Sagnac interferometer based lateral shearing interferometer setup, which duplicates the beam into identical wavefront components having orthogonal linear polarizations, i.e., p and s polarizations, and introduces appropriate lateral shear between the identical pair of wavefronts along the meridional direction. The laterally sheared identical wavefronts interfere when brought to the same state of polarization. The optical path difference (OPD) variation along the direction of the lateral shear in the interference field is a map of the slope variation. Polarization phase shifting interferometery has been applied to find the OPD variation and thus the slope distribution and errors. Results obtained for a TM of moderately long average radius of curvature along the central meridional section and a relatively shorter radius of curvature along the sagittal section are presented and compared with that obtained with a long trace profiler.

Label-free characterization of living human induced pluripotent stem cells by subcellular topographic imaging technique using full-field quantitative phase microscopy coupled with interference reflection microscopy

There is a need for a noninvasive technique to monitor living pluripotent stem cell condition without any labeling. We present an optical imaging technique that is able to capture information about optical path difference through the cell and cell adhesion properties simultaneously using a combination of quantitative phase microscopy (QPM) and interference reflection microscopy (IRM) techniques. As a novel application of QPM and IRM, this multimodal imaging technique demonstrated its ability to distinguish the undifferentiated status of human induced pluripotent stem (hiPS) cells quantitatively based on the variation of optical path difference between the nucleus and cytoplasm as well as hiPS cell-specific cell adhesion properties.

Simple technique for the accurate internal measurement of a right angle with a polarization phase-shifting, lateral-shearing, cyclic path optical configuration

A simple, new, self-referenced technique for the internal measurement of a right angle is presented. A polarization cyclic path optical configuration (CPOC) receives as the input beam a pair of laterally separated plane wave components, having angular separation of ψw = (π±4nδ), produced due to internal reflection of a linearly polarized plane wave on the surfaces enclosing the 90-deg (±δ) angle of a right-angled prism (where δ is the error in 90-deg angle and n is the index of refraction of the material of the prism). The CPOC is used to superpose the mutually inclined plane wave components by duplicating the input pair of plane wave fronts and introducing appropriate lateral shear between the identical pairs. The superposed inclined plane wave components interfere to produce two beam Fizeau fringes (FF), when brought to the same state of polarization. The error in the right angle can be calculated simply from the spacing of the resulting FFs or, more accurately, from the slope of the optical path difference variation obtained by applying polarization phase-shifting interferometry. Results obtained for a right-angled prism are presented.

Analyzing wavelength behavior of a cubic phase mask imaging system based on modulation transfer function

The wavefront coding technology is an effectively method for extending the depth of field. However, the phase delayed by the phase mask changes with light wavelength, and the chromatic aberration is caused by chromatic dispersion of the optical elements. The modulation transfer function (MTF) of the cubic phase mask (CPM) system is derived with considering the axial chromatic aberration and optical path difference variation with wavelength, and the wavelength behavior of CPM system is analyzed in details. We yield that the MTF is approximately wavelength invariant within a certain frequency bandwidth, and the bandwidth is nearly inverse proportional to wavelength and varies with axial chromatic aberration. The effect induced by dispersion of the CPM material is very weak. If the CPM system is illuminated by wideband spectral light and the ACA exists, then the frequency bandwidth may become narrower than the monochromatic case, and the position of image sensor can be relocated to balance frequency bandwidth among all wavelengths.

Study on the wide-angle Michelson interferometer with large air gap

A wide-angle Michelson interferometer with large air gap is proposed to effectively reduce the size of the glass arms and constraint on material. It provides a novel and practical instrument for ground based wind measurement of the upper atmosphere. The field widening conditions for the large air gap are calculated in theory. For the five spectral lines of 557.7 nm, 630.0 nm, 732.0 nm, 834.6 nm, and 865.7 nm, the optimal results under ideal condition are obtained with air gaps of 1.0 cm, 1.5 cm, and 2.0 cm, respectively. With the fixed optical path difference (OPD) of 7.495 cm, three pairs of glass arms are optimized. The pair with length of 1.5 cm for air gap, 5.765 cm for H-ZF12, and 2.956 cm for H-ZLaF54, has better effect of field widening than the other two pairs and its OPD variation is only within 0.30 wavelengths at incident angle of 3°. For developing a more practical wide-angle Michelson interferometer, the H-K9L glass with size of 4.445 cm is employed as the arm material of solid interferometer. The experiment for field of view of 3° is designed and the data processing and analysis for 60 images show the agreement between experimental results and theoretical simulation. The OPD variations are only within 0.27 wavelengths for image edge. The feasibility and practicality of the wide-angle Michelson interferometer with large air gap is proved by means of theory and experiment.

Measurement of longitudinal displacement using lateral shearing cyclic path optical configuration setup and phase shifting interferometry

We present a technique for the measurement of longitudinal displacement using a lateral shearing cyclic path optical configuration (CPOC) setup and phase shifting interferometry. In the technique, a plane mirror mounted on a linear translation stage, placed slightly away from the focal plane of a lens, introduces a longitudinal focal shift to the incident focusing beam. The resulting spherical wavefront emerging from the lens is sheared into two orthogonally polarized beams using the CPOC setup. By applying polarization phase shifting interferometry (PPSI), the longitudinal focal shift of the beam focus is calculated by determining the slope of the optical path difference variation between the sheared beams. Similarly, the additional focal shift introduced due to longitudinal translation of the mirror, by an unknown amount, is determined using PPSI. Half of the difference between the two longitudinal focal shifts measured gives the longitudinal displacement of the mirror. The technique can be used for an extended range of distance measurement. The novelty of the technique is the introduction of CPOC for the distance measurement. The advantages of the technique compared to other related methods are discussed.

Thickness measurement of transparent glass plates using a lateral shearing cyclic path optical configuration setup and polarization phase shifting interferometry

We present a measurement technique to determine the thickness of a transparent glass plate (GP) by using a lateral shearing cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI). In the technique, the GP introduces a longitudinal shift in the focus of the beam and, as a result, a spherical wavefront emerges from the lens, which is otherwise set for producing a collimated beam. Using CPOC, two laterally sheared orthogonally polarized beams are generated from the incident spherical wavefront. By applying PPSI, the slope of the optical path difference variation between the laterally sheared interfering beams is evaluated, and the radius of the spherical wavefront and the longitudinal shift of the beam focus are calculated. The thickness of the GP is determined from the standard relation between the longitudinal shift of the focus introduced by the GP and the thickness of the GP. Results obtained for a GP of 9.810mm thickness are presented.

One-wavelength tuning method for a tunable optical filter based on a cascaded polarization interference filter.

A one-wavelength tuning method is proposed to solve the tuning difficulty in a tunable optical filter based on cascaded cells. This method ensures that the optical path difference variation of all of the cells for the tuning is less than one wavelength and lowers the relative tuning accuracy requirement. Simulations show that different cells have different cross talk and loss deterioration when they undergo an error in optical path difference between the O-ray and the E-ray. An optimal error ratio in each cell is obtained. Under the error ratio, the deterioration from the random error in every cell is further simulated.