Vectorial shearing interferometer

High-resolution phase-shifting Ronchi test

A method adding phase-shifting capacity in two mutually perpendicular axes to the Ronchi test is presented in this work. The phase of the object with the position of the reflected ray on the grating was identified and used to solve the equation of reflection in two orthogonal directions. In this manner, the test-surface figure was obtained. The procedure was demonstrated with an inverse qualitative test and a direct, quantitative test. Both tests give results comparable to Fizeau interferometry, with the precision of the order of 25 nm peak to valley. This technique is a good alternative to interferometry because, in addition to its inherent high-resolution, it is possible to obtain the radius of curvature and conic constant, which interferometers, requiring auxiliary optics, cannot provide. This method also has a high dynamic range and is not as susceptible to vibrations or turbulence. The setup can be built with low-cost, readily available components, is easily aligned, uses a white light source, and can be made very lightweight and compact, which makes it ideal for mounting onto existing polishing machines in any optical fabrication workshop, to perform in situ surface metrology.

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.

Complete characterization of ultrashort optical pulses with a phase-shifting wedged reversal shearing interferometer

The ability of an interferometer to characterize the spatial information of a light beam is often limited by the temporal profile of the beam, with femtosecond pulse characterization being particularly challenging. In this study, we developed a simple, stable, controllable shearing and vectorial phase-shifting wedged reversal shearing interferometer that is able to characterize all types of coherent and partially coherent light beams. The proposed interferometer consists of only a single beam splitter cube with one wedged entrance face and is insensitive to environmental vibration due to its common path configuration. A near zero-path length difference of the proposed interferometer ensures its operation for ultrashort pulses, providing, for the first time, a simple and stable interferometric tool to fully characterize sub-100  fs laser pulses. All common beam characterization can be carried out with the interferometer, such as the amplitude, phase, polarization, wavelength, and pulse duration. Furthermore, this technique is sensitive to the wavefront tilt and can be used for precise beam alignment. Therefore, this interferometer can be an essential tool for beam characterization, optical imaging, and the testing required for a wide range of applications, including astronomy, biomedicine, ophthalmology, optical testing and imaging systems, and adaptive optics.

Error compensation in a pointing system based on Risley prisms

Risley prisms are widely used for beam pointing in several optical systems. The exact solution for the inverse problem does not exist, except using numerical methods. However, the errors introduced by misalignment are usually greater than the approximation errors. We present a novel method to compensate alignment errors in pointing systems based on Risley prisms. The prism model that we used is based on paraxial approximation with an additional vector to compensate typical alignment errors. Simulation and experimental results show that the improvement in pointing accuracy is achievable even in comparison with exact ray tracing methods.

Neutral density filters with Risley prisms: analysis and design

We achieve the analysis and design of optical attenuators with double-prism neutral density filters. A comparative study is performed on three possible device configurations; only two are presented in the literature but without their design calculus. The characteristic parameters of this optical attenuator with Risley translating prisms for each of the three setups are defined and their analytical expressions are derived: adjustment scale (attenuation range) and interval, minimum transmission coefficient and sensitivity. The setups are compared to select the optimal device, and, from this study, the best solution for double-prism neutral density filters, both from a mechanical and an optical point of view, is determined with two identical, symmetrically movable, no mechanical contact prisms. The design calculus of this optimal device is developed in essential steps. The parameters of the prisms, particularly their angles, are studied to improve the design, and we demonstrate the maximum attenuation range that this type of attenuator can provide.

Integrated diffractive shearing interferometry for adaptive wavefront sensing

We present theory, design, and preliminary experimental studies for a compact wavefront sensor based on lateral shearing interferometry using a binary phase grating, image sensor, and Fourier-based processing. The integrated system places a diffractive element directly onto an image sensor to generate interference fringes within overlapping diffraction orders. The shearing ratio and the interferogram signal-to-noise ratio directly affect the reconstruction accuracy of wavefronts with differing spatial variations. Optimal shearing parameters associated with the autocorrelation of the input encourage placing a spatial light modulator as the diffractive element allowing adaptive wavefront sensing. Experimental results from a fixed-grating system are presented as well as requirements for next-generation adaptive systems.

Phase recovery from a single undersampled interferogram

A new method of phase determination from a single undersampled interferogram is described. Two low-fringe-density synthetic interferograms corresponding to the phase differences along orthogonal directions are obtained from neighboring pixels of the aliased measured data. The only assumption is that the illumination background, the modulation intensity, and the searched phase are smooth and continuous functions. The synthetic interferograms are demodulated by use of either standard frequency or spatial-domain procedures to obtain the phase differences. The phase is then recovered by integration of the phase differences with a least-squares method. The proposed method is demonstrated to be noise tolerant.

Phase-shifting lateral shearing interferometer with two pairs of wedge plates

We present a compact and robust phase-shifting lateral shearing interferometer that produces shearing fringes in orthogonal directions without any mechanical rotation or precise alignment. It consists of two pairs of wedge plates, a beam splitter, and a single CCD camera. Both phase-shifting and tilt for lateral shearing are achieved with two pairs of wedge plates, which can reduce systematic errors caused by external vibration and atmospheric disturbance.

Improved Saunders method for the analysis of lateral shearing interferograms

An interferogram obtained by use of ordinary interferometers, such as Fizeau and Twyman-Green interferometers, will show a contour map of the wave front under test. A lateral-shearing interferogram, however, will show a contour map of the difference between the wave front under test and a sheared wave front, that is, a contour map of the derivative of the wave front under test. Therefore one can reconstruct the shape of the wave front under test by analyzing that difference. Many methods for reconstructing a wave front have been proposed. The Saunders method reconstructs a wave front; rapidly however the wave-front data are reconstructed only at intervals of the amount of shear along the direction of the shear. Therefore the method has low spatial resolution. A method for reconstructing a wave front that is based on the Saunders method and has high spatial resolution is proposed. The method analyzes the differences that are produced by shearing of the wave front under test in many directions. This method requires a large number of interferograms for reconstructing the wave front. Here the method is described, and its validity is confirmed by simulation.

Risley prisms to control wave-front tilt and displacement in a vectorial shearing interferometer

A pair of thin prisms is used to deviate a light beam without changing the image orientation in a vectorial shearing interferometer. The relative angle between prisms determines the displacement of the wave front and its tilt. The direction of the beam displacement is controlled by means of changing the relative angle between prisms. This system is employed to control the displacement of a sheared wave front as a vector quantity and to introduce a controlled amount of tilt in what we believe is a novel interferometric shearing system. The predicted performance of this wave-front director is confirmed experimentally.

Reflective grating interferometer: a folded reversal and shearing wave-front interferometer

The reflecting grating interferometer (RGI) is a folded and reversal wave-front interferometer sensitive only to asymmetrical aberrations such as third-order coma. The RGI can isolate and evaluate coma both in nearly collimated and in noncollimated beams. We propose a RGI with a different optical configuration that includes a lateral shearing in addition to folding and reversal operations. With lateral shear, the RGI also becomes sensitive to other terms of third-order aberrations such as defocusing, astigmatism, and spherical aberration. Optical path difference equations for interpreting interferograms and numerical simulations are presented to show how the interferometer works in the shearing configuration. Its potential applications are described and discussed.