Systems, methods, apparatuses, and articles of manufacture are provided for recovering a digitized spectrum and may comprise: an optical system configured to transform rays, the optical system including a diffraction grating, a steering mirror, a stage, and an actuator configured to move one of the stage, diffraction grating, or steering mirror according to a movement regime to vary an incidence of the rays on the stage; a sensor array disposed on the stage configured to receive the rays incident from the optical system at a plurality of measurement locations to obtain a plurality of ray spectra; and a processor electrically connected to the sensor array configured to receive the ray spectra, interleave the ray spectra to yield an interleaved spectrum, and deconvolve a point spread function corresponding to the optical system from the interleaved spectrum to yield a recovered digitized spectrum.

Methodology of characterizing surface properties and determining refractive index and extinction coefficient of a prism shaped material, including simultaneously for a multiplicity of wavelengths, using an easy to practice technique.

Methods, devices and systems for estimating polarization characteristics of materials based on partial polarimetry are described. One example method for estimating polarization characteristics of a material includes illuminating the material with incident light, which can be unpolarized or have a particular polarization state. Two polarimetric measurements are conducted based on the interaction of the incident light with the material. The two polarimetric measurements detect light having orthogonal polarization states, and the interaction of the incident light with the material includes a depolarizing interaction. The method additionally includes determining an estimated coherency matrix eigenvalue and an estimated Mueller matrix throughput parameter using the first and the second polarimetric measurements, and determining an estimate of a full depolarizing Mueller matrix by extrapolating a reduced-rank Mueller matrix to obtain all sixteen elements of the depolarizing Mueller matrix that identifies the polarization characteristics of the material.

There is provided a polarization analysis apparatus that adjusts an angle of incidence or a numerical aperture by using an aperture. The apparatus includes: a first aperture that transmits a lighting beam reflected from a sample on a substrate; a second aperture that transmits a lighting beam having passed through the first aperture; and a detector that detects a lighting beam having passed through the second aperture and selects an angle of incidence of the lighting beam and numerical apertures of the first aperture and the second aperture.

According to examples, a system for implementing structured polarized illumination techniques to determine and reconstruct a shape and a material property of an object is described. The system may include a light source to transmit an original beam of light; a first grating to diffract the original beam of light into a first light beam and a second light beam, a second grating to emit overlapping light beams towards an object, a polarization camera to capture light reflected from the object, and a computer system, comprising a processor and a non-transitory computer-readable storage medium having an executable stored thereon. The processor, when executing the instructions, may cause the system to analyze the light reflected from the object to determine a fringe projection analysis associated with the object, determine a shape of the object; and determine a Mueller matrix to describe material properties of the object.

Methods and systems for performing simultaneous spectroscopic measurements of semiconductor structures over a broad range of angles of incidence (AOI), azimuth angles, or both, are presented herein. Spectra including two or more sub-ranges of angles of incidence, azimuth angles, or both, are simultaneously measured over different sensor areas at high throughput. Collected light is linearly dispersed across different photosensitive areas of one or more detectors according to wavelength for each subrange of AOIs, azimuth angles, or both. Each different photosensitive area is arranged on the one or more detectors to perform a separate spectroscopic measurement for each different range of AOIs, azimuth angles, or both. In this manner, a broad range of AOIs, azimuth angles, or both, are detected with high signal to noise ratio, simultaneously. This approach enables high throughput measurements of high aspect ratio structures with high throughput, precision, and accuracy.

Provided is a pupil ellipsometry measurement apparatus configured to measure an object, the pupil ellipsometry measurement apparatus including a stage configured to support the object to be measured, a light source unit configured to generate and output light, an irradiation optical system configured to focus the light from the light source unit on the object, a first detector configured to detect an image of reflected light from the object on an imaging plane, a self-interference generator (SIG) configured to generate self-interference with respect to the reflected light, a second detector configured to detect a hologram image of interference light of the SIG on a pupil plane, and a processor configured to reconstruct reflectance information based on the hologram image, and measure the object.

Embodiments of the present invention relate to an ellipsometer that includes a combination of a plurality of reflective devices to measure a Mueller matrix reflectance of a material in the VUV and EUV region. Ellipsometer in accordance with embodiments of the present invention relate to an ellipsometer that includes a multi-mirror polarization state generator combined with a multi-mirror polarization state analyzer and a detector to realize a Mueller matrix ellipsometer. Embodiments of the present invention utilize two rotating assemblies with each assembly including multiple mirrors that combine to act as amplitude and phase retarders.

Methods, devices and systems for estimating polarization characteristics of materials based on partial polarimetry are described. One example method for estimating polarization characteristics of a material includes illuminating the material with incident light, which can be unpolarized or have a particular polarization state. Two polarimetric measurements are conducted based on the interaction of the incident light with the material. The two polarimetric measurements detect light having orthogonal polarization states, and the interaction of the incident light with the material includes a depolarizing interaction. The method additionally includes determining an estimated coherency matrix eigenvalue and an estimated Mueller matrix throughput parameter using the first and the second polarimetric measurements, and determining an estimate of a full depolarizing Mueller matrix by extrapolating a reduced-rank Mueller matrix to obtain all sixteen elements of the depolarizing Mueller matrix that identifies the polarization characteristics of the material.

Variable-angle ellipsometry is performed using a high speed polarization state modulator, a photodetector, and a digital micromirror device or spinning disk to encode the angle of incidence of light with a high sampling rate in a time domain or frequency domain. A variable-angle ellipsometer uses a high speed, axially stationary polarization state modulator, such as a photoelastic modulator, and a high speed detector, such as a photodiode, for high speed data acquisition. To acquire data at a plurality of incident angles, a lens is used to generate a large incident angle distribution along an optical axis that is at an oblique angle of incidence and discrete or combinations of incident angles of light are selected in a sequence in the time domain or modulated over a plurality of incident angles in the frequency domain.