Achromatic Phase Shifter Research Articles

Customized retarders based on waveplates.

Phase control is a critical parameter in polarization measurements. It is well known that a proper combination of wave plates allows to obtain achromatic phase shift, i.e., a constant retardation in certain spectral ranges. This paper is focused on a different, but more useful, goal, as it is to achieve customized variable retarders in broad spectral ranges. To do that, a merit function was used to measure the similarity between the overall phase shift of the wave plate combinations and the desired target. The control variables are the thicknesses and orientations of the wave plates. All possible combinations with four and five wave plates of quartz and MgF2 were analyzed, but our approach can be perfectly extended to deal with more wave plates. The result of an optimization process determines the thicknesses and orientations of the wave plates, which results in the closest retarder to the desired one. Numerical results show deviations below 10% between the target and the obtained retardation. These systems are of special interest in those fields and instruments in which polarization control plays a fundamental role.

Large Interferometer For Exoplanets (LIFE)

Aims. Optical interferometry from space for the purpose of detecting and characterising exoplanets is seeing a revival, specifically from missions such as the proposed Large Interferometer For Exoplanets (LIFE). A default assumption since the design studies of Darwin and TPF-I has been that the Emma X-array configuration is the optimal architecture for this goal. Here, we examine whether new advances in the field of nulling interferometry, such as the concept of kernel-nulling, challenge this assumption. Methods. We develop a tool designed to derive the photon-limited signal-to-noise ratio of a large sample of simulated planets for different architecture configurations and beam combination schemes. We simulate four basic configurations: the double Bracewell/X-array, and three kernel-nullers with three, four, and five telescopes respectively. Results. We find that a configuration of five telescopes in a pentagonal shape, using a five-aperture kernel-nulling scheme, outperforms the X-array design in both search (finding more planets) and characterisation (obtaining better signal, faster) when the total collecting area is conserved. This is especially the case when trying to detect Earth twins (temperate, rocky planets in the habitable zone), showing a 23% yield increase over the X-array. On average, we find that a five-telescope design receives 1.2 times more signal than the X-array design. Conclusions. With the results of this simulation, we conclude that the Emma X-array configuration may not be the best choice of architecture for the upcoming LIFE mission, and that a five-telescope design utilising kernel-nulling concepts will likely provide better scientific return for the same collecting area, provided that technical solutions for the required achromatic phase shifts can be implemented.

Two-harmonic complex spectral-domain optical coherence tomography using achromatic sinusoidal phase modulation

We resolve the complex conjugate ambiguity in spectral-domain optical coherence tomography (SD-OCT) by using achromatic two-harmonic method. Unlike previous researches, the optical phase of the fiber interferometer is modulated by an achromatic phase shifter based on an optical delay line. The achromatic phase modulation leads to a wavelength-independent scaling coefficient for the two harmonics. Dividing the mean absolute value of the first harmonic by that of the second harmonic in a B-scan interferogram directly gives the scaling coefficient. It greatly simplifies the determination of the magnitude ratio between the two harmonics without the need of third harmonic and cumbersome iterative calculations. The inverse fast Fourier transform of the complex-valued interferogram constructed with the scaling coefficient, first and second harmonics yields a full-range OCT image. Experimental results confirm the effectiveness of the proposed achromatic two-harmonic technique for suppressing the mirror artifacts in SD-OCT images.

Achromatic-phase-shifting low-coherence digital holography: theoretical analyses of zero-phase-shifting error condition and linear and nonlinear calibrations

Some methods for decreasing a measurement error derived from a phase-shifting error for broadband light in phase-shifting low-coherence digital holography are proposed based on theoretical analysis and numerical calculations. It is well-known that an achromatic-phase shifter based on a rotating polarizer drastically decreases the error, but it is found that a small error remains according to the imperfection of the achromatic-phase shifter. It is also found that an ideal achromatic-phase shifter perfectly eliminates the error only when the light source has a symmetrical spectrum. Furthermore, it is demonstrated that a simple linear calibration method decreases the error in a narrow range of optical path differences if a light source with an asymmetrical spectrum is used. Finally, a nonlinear calibration method that can further decrease the error in a wide range of optical path differences is discussed.

Spatially and spectrally engineered spin-orbit interaction for achromatic virtual shaping.

The geometries of objects are deterministic in electromagnetic phenomena in all aspects of our world, ranging from imaging with spherical eyes to stealth aircraft with bizarre shapes. Nevertheless, shaping the physical geometry is often undesired owing to other physical constraints such as aero- and hydro-dynamics in the stealth technology. Here we demonstrate that it is possible to change the traditional law of reflection as well as the electromagnetic characters without altering the physical shape, by utilizing the achromatic phase shift stemming from spin-orbit interaction in ultrathin space-variant and spectrally engineered metasurfaces. The proposal is validated by full-wave simulations and experimental characterization in optical wavelengths ranging from 600 nm to 2800 nm and microwave frequencies in 8-16 GHz, with echo reflectance less than 10% in the whole range. The virtual shaping as well as the revised law of reflection may serve as a versatile tool in many realms, including broadband and conformal camouflage and Kinoform holography, to name just a few.

High-axial-resolution, full-field optical coherence microscopy using tungsten halogen lamp and liquid-crystal-based achromatic phase shifter.

A high-axial-resolution, full-field optical coherence microscope (FFOCM) for topography and tomography applications is presented. The FFOCM is based on a polarization Linnik interference microscope equipped with a tungsten halogen lamp. The phase difference between the reference and test beams in the microscope is precisely and quickly shifted by using an achromatic liquid-crystal phase shifter (LCPS). The cross-sectional amplitude and phase maps of an interferogram are retrieved by using a three-step phase-shifting technique. The LCPS consists of three identical nematic liquid-crystal (NLC) cells sandwiched between two quarter-wave plates so that it functions as a typical quarter-half-quarter phase shifter. Instead of using high-cost NLC cells with precise thickness of half-wave retardation, a method is proposed to operate thicker NLC cells without scarifying the axial resolution. Experimental results reveal that the FFOCM is able to perform three-dimensional micrometer-resolution imaging.

Full-field optical coherence tomography using nematic liquid-crystal phase shifter

We present a polarization Linnik interference microscope with a nematic liquid-crystal (NLC) phase shifter for full-field optical coherence tomography of high-quality images. The rotating half-wave plate in conventional achromatic phase shifters was replaced by three liquid-crystal (LC) half-wave plates for implementing three-step phase-shifting interferometry. Thus, the NLC device generates phase shifts quickly and has no vibrations. In addition, the phase shift can be set to an arbitrary value between 0 and 2π by altering the azimuth angles of the LC cells. A tomographic image is retrieved from three sequential phase-shifted interferograms by using a three-step algorithm. The experimental results confirm the feasibility of the proposed technology.

Stellar coronagraph using the principle of achromatic null-interferometer

In order to observe exoplanets we propose a space-based achromatic stellar coronagraph combined with a 0.8–1.5 m telescope. We develop an achromatic common path interferometer for observing an exoplanet (a faint off-axis source) on the background of a hoste star (bright axial source). An image of the star and its copy acquire an achromatic phase shift by 180° and interfere in antiphase. The achromatic phase shift is caused by geometric phase in the scheme of a three-dimensional interferometer. The interference process divides spatially the dark and light fields of the star image redirecting them to the opposite sides of a beam splitter. The interference process does not weaken the image of a planet, with equal intensities it is redirected to both sides of a beam splitter. The suggested scheme of common path interferometer ensures mechanical stability. The background signal is experimentally demonstrated to be reduced by six orders of magnitude.

Achromatic phase shifter with eight times magnification of rotation angle in low coherence interference microscopy

An achromatic phase shifter with a rotating half-wave plate (HWP) used at the input and output of the low coherence interference microscopy is presented. This novel achromatic phase-shifter configuration is first investigated, and then its performances are compared with those of traditional phase shifters theoretically by means of Jones matrices. It is evident that the achromatism and the variation of the amplitude ratio of the proposed achromatic phase-shifter configuration is much better than other traditional phase-shifter configurations, and it can provide a phase shift of eight times the rotation angle of the HWP, which is the largest magnification achieved by far. A low coherence interference microscopy system based on the proposed achromatic phase-shifter configuration is also established to confirm the eight times relation between phase-shift and rotation angle of the HWP experimentally. At last, the three-dimensional profile and the groove depth of a step height calibration standard are obtained by using the traditional four-step algorithm to illustrate the capability and the accuracy of the low coherence interference microscopy system based on the proposed achromatic phase-shifter configuration.

The achromatic chessboard, a new concept of a phase shifter for nulling interferometry

Context. Nulling interferometry in the mid-IR using two telescopes (commonly referred to a Bracewell interferometer) is one possible way of directly detecting exoplanets in the habitable zone and their characterisation in terms of possible life signatures. A large wavelength domain is needed to simultaneously detect the infrared spectral features of a set of a bio-tracers. An achromatic phase shift of π is then required, and we previously presented a new concept for such a function that allows a simple design with only one device per beam. It is based on two cellular mirrors, called the chessboards, where each cell has a thickness that introduces, for any given central wavelength, a phase shift of (2k + 1)π or of 2kπ on the fraction of the wave it reflects. Aims. We explore a more rigorous way to establish the optimum cell pattern design to attain the best theoretical performances for planet detection over a broad wavelength range. Two possible types of interferometres are now considered: on-axis and multi-axis. Methods. We derived a rather simple iterative scheme for both designs, determining the thickness and XY position of the cells. The method confers to the chessboards a high degree of internal symmetry. Each design can be described as an iterative Bracewell interferometer characterised by an integer order. We demonstrate that their efficiencies increases with the power of that order. Results. The device acts both spatially and versus wavelengths as an optical differential operator on the 3D light distribution. Its power is best understood in the on-axis case since its effect is to push away the stellar light from the centre over a very broad range of wavelengths, leaving space for an out of phase object to appear in the cleaned central region. We explore the theoretical performances for on-axis and multi-axis designs in the parameter space, and we especially compute the rejection factor for starlight and the attenuation factor for planet light and introduce the relative nulling efficiency metric. We show that, even with some realistic piston error added, the performances could meet the Darwin space project specifications for both designs, i.e., cancellation of the starlight by a factor of 10 5 over a wavelength range of 6–17 μm.

Achromatic nulling interferometer for stellar coronography

A common-path interferometer that is intended for observation of a faint off-axis light source against the background of an intense on-axis source is suggested. The on-axis source and its replicated image acquire an achromatic phase shift of 180° and interfere in antiphase. The achromatic phase shift is due to the geometrical phase in the configuration of a 3D interferometer. Interference spatially separates the dark and bright fields of the on-axis source by directing them to different sides of a beam splitter. At the same time, interference does not attenuate the field of the off-axis source, directing it to different sides of the beam splitter with equal intensities. Such a configuration of the common-path interferometer provides mechanical stability.

Full-field optical coherence tomography by achromatic phase shifting with a rotatinghalf-wave plate

An achromatic phase shifter with a rotating half-wave plate (HWP) and a full-field opticalcoherence tomography (FF-OCT) system based on it are presented. The novelconfiguration of this phase shifter in the FF-OCT system can achromaticallyprovide a phase shift of eight times the rotation angle of the HWP. The theoreticalcalculation of the phase shift and numerical analysis of the phase shift error,as well as the amplitude ratio, are conducted by means of Jones matrices. Theactual phase shift has also been measured to confirm the validity of the ‘8θ phase shift—HWProtation angle θ’ relation. The coherent image of a mirror has been obtained by using the Hariharanalgorithm to verify the phase shifter’s feasibility. Using traditional phase shiftingalgorithms, en-face images of a coin have been measured at different depths to illustrate thetomographic capability of this FF-OCT system. In comparison with other current systems,our design has several advantages, and high-resolution high-speed FF-OCT imaging can beenvisioned. The phase shifter can be used for common path setups and is verysuitable for implementing the phase shifting of a broad-spectrum light source.

Achromatic deep nulling with a three-dimensional Sagnac interferometer

A 3-D Sagnac interferometer can null out light from an on-axis source achromatically. The 3-D Sagnac interferometer can make stable and achromatic pi phase shifts, because it has a common path structure. The achromaticity of the interferometer is theoretically proved by Jones calculus. The experimental setup is constructed, and its nulling characteristics are measured to be about 10(-6) at 5 lambda/d for green (lambda=532 nm) and red (lambda=633 nm) laser light simultaneously. This interferometer would be very useful for the direct detection of faint extrasolar planets.

Experimental evaluation of achromatic phase shifters for mid-infrared starlight suppression

Phase shifters are a key component of nulling interferometry, one of the potential routes to enabling the measurement of faint exoplanet spectra. Here, three different achromatic phase shifters are evaluated experimentally in the mid-infrared, where such nulling interferometers may someday operate. The methods evaluated include the use of dispersive glasses, a through-focus field inversion, and field reversals on reflection from antisymmetric flat-mirror periscopes. All three approaches yielded deep, broadband, mid-infrared nulls, but the deepest broadband nulls were obtained with the periscope architecture. In the periscope system, average null depths of 4x10(-5) were obtained with a 25% bandwidth, and 2x10(-5) with a 20% bandwidth, at a central wavelength of 9.5 mum. The best short term nulls at 20% bandwidth were approximately 9x10(-6), in line with error budget predictions and the limits of the current generation of hardware.

Development of full-field optical coherence tomography system

A full-field optical coherence tomography system using an achromatic phase shifter based on a rotating half-wave plate to implement phase shifting is developed. The phase shifter can achromatically introduce phase shift of eight times the rotating angle of the half-wave plate, and can rapidly provide various phase shifts for various algorithms. Real phase shift is measured and the result demonstrates that the system gives a phase shift of eight times the rotating angle of the half-wave plate, showing the achromatic phase shifter model is correct. Imaging experiment results of a mirror using Hariharan algorithm show that the system has high phase shift precision. A coin as the sample is imaged to demonstrate the performance of the system.

Dispersion in nulling interferometry for exoplanet detection: experimental validation

It is well known that dispersion affects the performance of a wide-band nulling interferometer, since it induces wavelength-dependent phase differences between the arms of the interferometer. This property is used to create achromatic phase shift by combining several dielectric plates. In this paper, we experimentally validate the use of a single glass plate in order to optimize the rejection ratio of a nulling interferometer.

Physical foundations of achromatic nulling interferometry for stellar coronagraphy

We propose an achromatic interferometer for the observation of a faint off-axis light source against the background of a bright on-axis light source. The on-axis source and its copy acquire an achromatic phase shift by 180° and interfere with a phase difference of π. The achromatic phase shift is attributable to the geometric phase in the three-dimensional interferometer scheme. Interference spatially separates the nulled and bright fields of the on-axis source, redirecting them on opposite sides of the beamsplitter. Interference does not attenuate the field of the off-axis source and redirects it with an equal intensity on both sides of the beamsplitter. We consider the principle of operation of the nulling interferometer and constraints on the attenuation of an extended source due to the decrease in coherence. The laboratory breadboard and experiment are briefly described.

The achromatic chessboard, a new concept of a phase shifter for nulling interferometry

Context. Direct detection of a planet around a star and its characterisation for identification of bio-tracers in the mid-IR requires a nulling interferometer. Such an instrument must be efficient in a large wavelength domain in order to have the capability of simultaneously detecting the infrared spectral features of several bio-tracers: CO2 ,O 3 ,a nd H 2O. Aims. A broad wavelength range can be effective provided that an achromatic phase shift of π can be implemented, with good enough accuracy to achieve a deep nulling at all considered wavelengths. A new design concept for such an achromatic phase shifter is presented here. The major interest of this solution is that it allows a simple design with only one device per beam. Methods. The heart of the system consists in two cellular mirrors where each cell has a thickness that introduces, for a given central wavelength, a phase shift of (2k + 1)π or of 2kπ on the fraction of the wave it reflects. Each mirror is put in one of the collimated beams of the interferometer. Because of the odd/even distribution, a destructive interference is produced on axis for the central wavelength when recombining the two beams. If the number of cells of a given thickness follows a rather simple law based on the Pascal’s triangle, we then show that the nulling is also efficient for a wavelength that is not too far from the central wavelength. Results. The effect of achromatization is more efficient the more cells there are. For instance, with two mirrors of 64 × 64 cells, where the cells’ phase shift ranges between −6π and +6π, one reaches a nulling of 10 −6 on a wavelength range [0.6λ0, 1.25λ0], i.e. on more than one complete octave. This is why we claim that this device produces a quasi-achromatic phase shift ; especially, it could satisfy the specifications of a space mission as DARWIN. In a second step, we study the optimum way to distribute the cells in the plane of the pupil. The most important criterion is the isolation of the planet image from the residual image of the star. Several algorithms and their nulling performances are presented.

Computing extinction maps of star nulling interferometers

Herein is discussed the performance of spaceborne nulling interferometers searching for extra-solar planets, in terms of their extinction maps projected on-sky. In particular, it is shown that the designs of Spatial Filtering (SF) and Achromatic Phase Shifter (APS) subsystems, both required to achieve planet detection and characterization, can sensibly affect the nulling maps produced by a simple Bracewell interferometer. Analytical relationships involving cross correlation products are provided and numerical simulations are performed, demonstrating marked differences in the aspect of extinction maps and the values of attained fringes contrasts. It is concluded that depending on their basic principles and designs, FS and APS will result in variable capacities for serendipitous discoveries of planets orbiting around their parent star. The mathematical relationships presented in this paper are assumed to be general, i.e. they should apply to other types of multi-apertures nulling interferometers.

In vivo video-rate cellular-level full-field optical coherence tomography

Full-field optical coherence tomography (FF-OCT) capable of in vivo cellular-level imaging is demonstrated for nonscanning horizontal cross-sectional imaging. The system is based on a white light interference microscope illuminated by a thermal light source. A dual-channel two-dimensional (2-D) detection technique incorporated with a pair of CCD cameras has been developed, where a pair of interferometric images with phase difference of pi/2 are simultaneously captured using an achromatic phase shifter. By acquiring an additional pair of images with a conventional phase shift method, a horizontal cross section is derived from every two consecutive CCD frames, enabling OCT imaging at the video rate. Using an ultrabroad bandwidth illumination incorporated with relatively high NA (0.8 NA) water immersion objectives, an axial resolution of 0.8 microm and a transverse resolution of 0.7 microm are experimentally confirmed. A field of view of 215 microm x 215 microm is covered by the 500 x 500 pixel CCD cameras. We demonstrate, for what is believed to be the first time, in vivo cellular-level blood flow imaging of a Xenopus laevis tadpole by FF-OCT.