Cyclic Shearing Interferometer Research Articles

Spherical wavefront measurement on modified cyclic radial shearing interferometry.

We propose a radial shearing interferometric approach to measure spherical wavefronts as both of the reflective and transmissive optical configurations. The modified cyclic radial shearing interferometer uses a single lens in the optical layout, which can conveniently adjust the radial shearing ratio between two shearing spherical wavefronts, and the use of a polarization camera enables to reconstruct the wavefront by a single image. The wavefront mapped onto the camera plane can be identified and quantified throughout an optimized wavefront reconstruction algorithm. In the experiments, plano-convex lenses and concave mirrors were used to generate spherical wavefronts, and the proposed system was able to reconstruct the surface figures after system characterization and calibration. Further investigations were performed to evaluate the system measurement accuracy by the radius of curvature comparison with design value and a commercial Shack-Hartmann wavefront sensor.

Wire grid polarizer-based cyclic shearing interferometer with polarization phase shifting

Imaging of transparent phase samples using a wire grid polarizer (WGP)-based shearing interferometer is demonstrated. The proposed setup employs a WGP as a beam splitter in a triangular cyclic interferometer setup, so that the two counterpropagating beams are rendered linearly polarized in orthogonal directions as they emerge from the interferometer. These sheared waved fronts are made to pass through the phase sample. The magnitude of shear is affected by controlled angular shifts of one mirror about the reference X and Y axes. For each of these directional shears, the polarization phase shifting is implemented so as to generate a three-dimensional phase pattern, which is digitally combined and integrated to yield the sample phase. The proposed setup is robust, sufficiently tolerant to ambient vibrations, and shows very encouraging experimental results.

Diverging cyclic radial shearing interferometry for single-shot wavefront sensing.

In this investigation, we describe a simple cyclic radial shearing interferometer for single-shot wavefront sensing. Instead of using the telescope lens system used in typical radial shearing interferometry, a single lens is used to generate two diverging radial shearing beams. This simple modification leads to the advantages of conveniently adjusting the radial shearing ratio, compactness of the system, and practical ease of alignment. With the aid of a polarization pixelated CMOS camera, the spatial phase-shifting technique is used to extract the phase with a single image. The most important feature is the fringe contrast enhancement by reducing the aberrations caused by the complicated optical system even though an incoherent light is used. The experimental results show the fringe contrast enhancement is at least 0.1 better than that of the conventional method, and the wavefronts are properly reconstructed with less than 0.071λ root-mean-squared wavefront error regardless of the coherence of the light.

Measurement of flow density field by cyclic radial shearing interferometer

Transient measurements of high-speed airflow field are needed in the measurement of boundary layer. Digital interferometry can measure flow field quantitatively to obtain density information, which is very necessary in flow field measurement. In this paper, a common-path shearing interferometry method is introduced. It is insensitive to vibration and does not need a reference plane. It is suitable for flow field measurement. A fast algorithm based on spatial phase modulation, coupled with a pulse laser and a synchronous control system, is used to measure the disturbance density field quantitatively in real time. The acquisition resolution of the system is 200 pixels × 200 pixels, and the acquisition frequency can reach more than 1000 frames per second. The wavefront reconstruction method of the system has been simulated by computer, and the detection result is better than 1/20λ. The experimental results in a 0.6 m wind tunnel show that the system can restrain the vibration interference and distinguish the disturbance signal and the vibration noise remarkably. It has good application prospects.

Highly stable lens-less digital holography using cyclic lateral shearing interferometer and residual decollimated beam

Lens-less digital holography for quantitative phase contrast imaging is established with a cyclic lateral shearing interferometer and non-collimated light beam. In a self-reference type configuration, the object and reference beams are generated from the same spherical wavefront after the light beam has passed through the sample plane. The experimental configuration is implemented with simple optical components involving beam splitter and mirrors. This proposed architecture has the advantage that the system does not require any special optical element such as pinhole, gratings, and other customized optical components and hence can be easily realized with significantly simplified alignment procedure. Experimental results for both amplitude and phase objects are presented as a proof of concept.

Dynamic phase imaging of microscopic measurements using parallel interferograms generated from a cyclic shear interferometer.

We present a technique which allows us to generate two parallel interferograms with phase shifts of π/2 using a Cyclic Shear Interferometer (CSI) and a polarizing splitter. Because of the use of a CSI, we obtain the derivative phase data map directly, due to its configuration, it is immune to vibrations because the reference wavefront and the object wavefront have a common path; the shearing interferometer is insensitive to temperature and vibration. To obtain the optical phase data map, two interferograms are generated by collocating a polarizing device at the output of the CSI. The optical phase was processed using a Vargas-Quiroga algorithm. Related experimental results obtained for dynamic microscopic transparent samples are presented.

Parallel two-step phase shifting interferometry using a double cyclic shear interferometer

A parallel two-step polarizing phase shifting interferometer based on a Double Cyclic Shear Interferometer (DCSI) is proposed in this paper for quantitative phase imaging. The system has the advantage of retrieving the derivative phase data map directly. Due to its configuration, it presents better stability against external configurations than other types of interferometers. The DCSI generates two π-shifted interferograms, which are recorded by the CCD camera in a single-shot. The separation between parallel interferograms can be varied in the two axes for convenience. To obtain the optical phase data map, a parallel phase shift between interferograms is obtained by rotating a half wave plate retarder. We analyzed the cases of four patterns with shifts of π/2 captured in two shots; the optical phase was processed by a four-step algorithm. Related experimental results obtained for microscopic transparent samples are presented.

Analysis of the fringes visibility generated by a lateral cyclic shear interferometer in the retrieval of the three-dimensional surface information of an object

We report the evaluation of the topography of an object with projected fringes generated with a lateral cyclic shear interferometer (CSI) and we then compare the topography recovery obtained with the proposed method with the one obtained from a coordinate measuring machine (CMM). We also study how the fringes visibility along the z axis affects the retrieval. Finally, we discuss the advantages and drawbacks of this profilometry system.

Off-axis cyclic radial shearing interferometer for measurement of centrally blocked transient wavefront

An off-axis cyclic radial shearing interferometer (OCRSI) to test a centrally blocked transient wavefront is proposed. Based on the standard cyclic radial shearing interferometer (CRSI), the OCRSI consists of a beam splitter, two folding mirrors, and a Galilean telescope. With the same but reversal tilt introduced to the two mirrors in OCRSI, the shearing interferogram can be obtained even when the central part of the test aperture is blocked. An improved wavefront retrieval method for OCRSI is employed, and a method to obtain the laterally sheared amount between the contracted and expanded beams is proposed. Numerical simulation and comparison experiments with a ZYGO GPI interferometer demonstrate that the OCRSI exhibits high precision and nice repeatability.

First direct measurement of the spatial coherence of sunlight

Direct sunlight is often deemed incoherent, hence unsuitable for antenna power conversion. However, all radiation exhibits spatial coherence when detected on a sufficiently small scale. We report the first direct measurement of the spatial coherence of solar beam radiation, achieved with a customized tabletop cyclic-shearing interferometer. Good agreement is found between experiment and theory, with promising ramifications for solar aperture antennas.

Femtosecond laser-induced phase modulation based on KTP crystal

The femtosecond laser-induced phase modulation based on KTP crystal is demonstrated. The phase modulation in femtosecond laser irradiated area is deduced through Drude model and color centers model, and the phase shift was also measured by cyclic radial shearing interferometer. As a result, a phase modulator with 2π phase shift is achieved using a 2.5-mm-thick KTP crystal and femtosecond laser pulses, and the spatial distribution of phase shift was also given. Such approach will be of great potential values for optical cross-connect switching, laser beam steering, low-cost electro-optic sensor, adaptive optics, coherent beam combination.

Slope measurement of a phase object using a polarizing phase-shifting high-frequency Ronchi grating interferometer

An interferometric method to measure the slope of phase objects is presented. The analysis was performed by implementing a polarizing phase-shifting cyclic shear interferometer coupled to a 4-f Fourier imaging system with crossed high-frequency Ronchi gratings. This system can obtain nine interference patterns with adjustable phase shifts and variable lateral shear. In order to extract the slope of a phase object, it is only analyzed using four patterns obtained in a single shot, and applying the classical method of phase extraction.

Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer

Transient, high repetition pulse laser can be applied to test numerous physical parameters, where in situ, real time measurement and isolation of vibration is highly demanded. Because of its short half-width, high power, high repetition, and even large distortion, the laser presents unique challenges to conventional diagnosing methods. A system based on a novel cyclic radial shearing interferometer is proposed to diagnose the transient, high repetition pulse laser with common path, no reference plane, and high precision. With the spatial-carrier methods, the system needs only one interferogram to reconstruct amplitude and wavefront of the laser. The theories of amplitude and wavefront reconstruction have been validated by computer simulation, and errors less than 1/1000lambda are obtained for both. Comparing with the results of the ZYGO interferometer, an error less than 1/20lambda for both peak-valley and root-mean-square values is gained with good repeatability for the wavefront. The calibration process and real time diagnosis of a high repetition pulse laser are presented then. Finally, the error consideration and system optimization are discussed in detail.

Interferometric studies of optical inhomogeneities induced in glasses by intense light

This paper reports the development of an interferometric technique for studying the dynamics of the appearance and relaxation of the refractive-index variation of optical glasses, produced when intense light acts on them. The technique is based on the use of a cyclic shearing interferometer. The rationale for choosing this type of interferometer is given, and its basic characteristics are presented. The solution obtained in this paper for the problem of reconstructing the wavefront deformations caused by the action of light on the test objects is explained. Results are presented for the use of the technique to study photoinduced refractive-index variations in cerium-doped optical glasses. The mechanisms of the observed effects are discussed.

Cyclic plasma shearing interferometry for temporal characterization of a laser-produced plasma

A cyclic shearing interferometer has been employed to characterize a laser-produced plasma with 180 ps resolution. Counterpropagation maintains an equal path length for the probe and reference beams, and the shear is provided solely by the plasma, which appears within the circuit after the reference beam has passed the laser focal spot. The background is virtually fringe free because of the overlapping of the reference and probe beams so that analysis is simplified. The plasma, which is formed by a line focus, is seen to expand in a cylindrical manner away from the line focus with an exponential density profile. In addition, the interferometer shows evidence of a bow shock when an interaction beam is introduced into the plasma parallel to the direction of the line focus.

Simple algorithms of wavefront reconstruction for cyclic radial shearing interferometer

Two new iterative algorithms to be used to reconstruct a tested wavefront from its cyclic radial shearing (CRS) fringe pattern are proposed. First, the phase difference (PHD) in the common area of the contracted and expanded tested wavefront are determined directly from the CRS fringe pattern of the tested wavefront by the Fourier transform method. Then, according to the PHD, the tested wavefront is reconstructed precisely by the two iterative algorithms. The numerical simulation of the reconstruction of a tested wavefront with distortion is implemented, showing that the wavefront reconstruction can be performed precisely by these algorithms with root mean square (rms)??/20. A CRS interferometer is constructed with a radial shearing ratio of s51:1.4 and is used to test a distorted wavefront with a one-step phase jump successfully. The results of numerical simulation and optical testing show that with these algorithms, the CRS interferometric technique can be easily used to make the evaluation of the optical component quality as well as testing of the wavefront distortion of a high-power laser. Finally, the convergence of two algorithms is also analyzed.

Optical probing of fiber z-pinch plasmas

An experimental study of optical probing of a dense z-pinch plasma using the MAGPIE (mega-ampere generator for plasma implosion experiments) generator [I. H. Mitchell et al., Rev. Sci. Instrum. 67, 1533 (1996)] is reported. The generator was operated with a peak current of 1.1 MA rising in 150 ns (10%–90%). The loads were 33 μm diam carbon fibers. Faraday rotation was used to investigate the distribution of the current flowing in the plasma. A measurable Faraday rotation angle was observed only in a time window from 50 to 60 ns after the current start, due to the fact that this effect depends on a combination of the magnetic-field strength and electron number density. A new type of self-referencing cyclic radial shear interferometer was used to evaluate the plasma density profiles which are necessary for the reconstruction of the current distribution. It was calculated that ∼110 kA was flowing in the plasma at 52 ns after the current start. Shadowgraphy was used to study the dynamics of the plasma and to investigate the formation of instabilities. Plasma instabilities were observed at very early times (∼5 ns). These instabilities appeared to be not entirely axi-symmetric implying the existence of m=1 and maybe higher modes as well as m=0. The perturbations increased with time and evolved into density islands (isolated plasma fragments) distributed along the axis at late times (∼70 ns).

Self-referencing cyclic shearing interferometer for collimation testing

We present here a self-referencing dual-field cyclic shearing interferometer for collimation testing. To generate the two fields, one of the two mirrors of a cyclic shearing interferometer is replaced by a double mirror. Ray tracing is carried out to determine conditions for obtaining fringe patterns suitable for self-referencing. Actual fringe patterns obtained in a self-referencing cyclic shearing interferometer are shown and the setting sensitivity of the interferometer is determined.

Self-referencing cyclic shearing interferometer for collimation testing

Self-referencing cyclic shearing interferometer for collimation testing

Cyclic shearing interferometer for collimating short coherence-length laser beams

Until now there has not been an accurate method for measuring the radius of curvature, R, of a short coherence-length light source, such as a short-pulse or broadband laser. We show that the easily aligned cyclic shearing interferometer (CSI) solves this problem. The CSI produces a stable fringe pattern from which R can be determined and can be used on beams with short coherence times down to 300 fs because the two beams in the interferometer follow nearly the same path. Comparison with data from a broadband XeCl laser (30-ps coherence time) confirms that the CSI performs as theory predicts.