An interferometer wherein an incident beam from a radiation source hits a beam splitter at a first oblique angle of incidence and is split into a first, reflected partial beam, and a second, transmitted partial beam, that subsequently travel along separate arms of the interferometer. The first and second partial beams are respectively intercepted, reflected, and re-split to form returning beam portions and reflected and transmitted exit beam portions. A second terminal mirror and a folding mirror, which intercepts the second partial beam at a second oblique angle of incidence, are associated with the second interferometer arm and positioned orthogonal to the reference plane and on opposite sides of the exit path, so that a section of the second partial beam from the folding mirror to the terminal mirror and back to the folding mirror crosses the exit beam twice.

A pair of light rays spatially-sheared with a controllable beam-shear distance is generated by a module having a beamsplitter (BS) and two mirrors. The BS splits an input light ray into first and second split light rays respectively propagated on first and second light paths. The two mirrors are respectively located at distal ends of the two light paths, and cause each split light ray to undergo a two-stage reflection, thereby generating first and second reflected light rays directed to the BS. The BS processes the two reflected light rays to generate the pair of spatially-sheared light rays. Orientations of the two mirrors in yaw angle, pitch angle, or both, are jointly adjustable to realize and control the beam-shear distance without using any birefringent crystal-based prism. The module is used to form differential interference contrast (DIC) microscopes providing variable shear distances, advantages of orientation independence, etc.

A method of determining a physical quantity is disclosed. The method uses a sensor system configured to sample a plurality of positions in parallel, wherein sampling each position uses radiation incident on an object plane patterning device (mark) and an image plane sensor. Each mark comprises a first portion and a second portion, the first portion being different to the second portion, and wherein the first and second portions of at least one of the marks is transposed relative to the first and second portions of the other marks. Each mark corresponds to a different sampling position. The method comprises, for each portion of each mark: performing a first measurement in a first direction; and performing a second measurement in a second direction different to the first direction. Four data sets are determined and subsequently combined to determine the physical parameter.

Systems and methods for a non-invasive determination of the characteristics of a light source include placing a non-redundant aperture mask in a path of light emanating from the light source, capturing an image of the interference pattern caused by the light passing through the non-redundant aperture mask, generating visibilities of the light distribution from the image, and determining the characteristics of the light source based on the visibilities of the light distribution, including a process of self-calibration in which the phase-solutions provide a sub-nanometer precision wavefront sensor, and through the use of closure amplitudes without requiring the process of self-calibration.

A to-be-measured partially coherent fractional vortex beam passes through a scattering object, an error between measurable information and to-be-measured information is minimized by using an optimization algorithm, and a main electric field mode and a weight of a to-be-measured fractional vortex beam are reconstructed by using a multimode stacked diffraction algorithm. A cross-spectral density function of the partially coherent fractional vortex beam is calculated, a cross-spectral density of a partially coherent fractional vortex optical field is reconstructed, and complete information including light intensity, a light intensity association, an electric field association, a phase, and the like of the partially coherent fractional vortex optical field is obtained. After the complete information of the partially coherent fractional vortex optical field is obtained, reverse transmission calculation is performed to obtain a source field vortex phase distribution, thereby implementing accurate topological charge measurement of the fractional vortex beam under low coherence conditions.

A method for reconstructing the wavefront of a light beam by analyzing wavefront-gradient data of said light beam, the light beam containing at least one optical vortex, considering the contribution of the optical vortices to the wavefront. The method including providing a phase-gradient map g of the wavefront of the light beam, generating a Laplacian of a vector potential based on the phase gradient map g, the resulting Laplacian of the vector potential map, called Laplacian map, exhibiting peaks, the location of each peak corresponding to the location of an optical vortex and the integral of the peak being proportional to a topological charge n of said optical vortex, computing a singular phase map .sub.s based on the topological charge n and location of each optical vortex, the singular phase .sub.s map being representative of the contribution of the optical vortex.

Methods, and corresponding systems for, determining one or more aberrations of a projection system (for example a projection system of a lithographic apparatus) are disclosed. One method includes performing a phase stepping or phase scanning process using a first patterning device (at object level) that includes a specular diffraction grating. Also disclosed is a calibration method for determining calibration data which characterizes any differences between: aberrations of a projection system determined using a diffusive grating at object level and aberrations of a projection system determined using a specular grating at object level.