A first reflection member, when light is incident, reflects a part of the light by a first reflection surface, reflects light transmitted through the first reflection surface by a second reflection surface, and emits reflected light components in an opposite direction. The second reflection member, when light emitted from the first reflection member is incident, reflects a part of the light by a first reflection surface, reflects light transmitted through the first reflection surface by a second reflection surface, and emits reflected light components. Interference fringes are formed on a screen by light reflected on the first reflection surface of the first reflection member and the second reflection surface of the second reflection member and light reflected on the second reflection surface of the first reflection member and the first reflection surface of the second reflection member.

An interferometric tracking device including: an optical cascade comprising a plurality of image dividers, each of the image dividers splitting incident light into a plurality of non-parallel orthogonally polarized beams, the plurality of image dividers including: an incident image divider receiving light into the optical cascade; one or more intermediary image dividers optically coupled to the incident image divider; and one or more exit image dividers, each exit image divider optically coupled to one of the intermediary image dividers; a plurality of pairs of shearing interferometers, each pair of the shearing interferometers being optically coupled between optically adjacent image dividers in the optical cascade; and one or more focal plane arrays, the orthogonally polarized beams from the one or more exit image dividers being imaged onto the one or more focal plane arrays.

A wavefront analyzer is modified to simply determine the differences in amplitude and tilt which can exist between the different regions of an initial wavefront (S0). To achieve this, interference between two waves only is produced from beams (F1, F2) which come from neighboring regions on the initial wavefront. Such an analyzer can be used to coherently combine laser radiation produced by different sources arranged in parallel. Another use is for the determination of the differences in height and inclination which exist between the neighboring mirror segments of a Keck telescope.

A method for characterizing a light beam includes separating the light beam by a separator optic into first and second sub-beams; propagating the first and second sub-beams over first and second optics, respectively, said first and second optics being respectively arranged so that the sub-beams on leaving the optics are separated by a time delay ?; recombining the sub-beams so that they spatially interfere and form a two-dimensional interference pattern; measuring the frequency spectrum of at least part of the interference pattern; calculating the Fourier transform in the time domain of at least one spatial point of the frequency spectrum, the Fourier transform in the time domain having a time central peak and first and second time side peaks; calculating the Fourier transform in the frequency domain for one of the side peaks; calculating the spectral amplitude A.sub.R(?) and the spatial-spectral phase ?.sub.R(x,y,?) for the Fourier transform in the frequency domain.

A characterization method of a light beam includes separating the light beam into first and second sub-beams; propagating the first and second sub-beams over first and second optics respectively; the first sub-beam, which forms a reference beam, and the second sub-beam, which forms a characterized beam, being separated by a time delay ?; recombining the reference and characterized beams so that they spatially interfere and form a two-dimensional interference pattern; measuring the pattern to obtain a temporal interferogram; calculating the Fourier transform in the frequency domain of a spatial point of the interferogram, the Fourier transform having a frequency central peak and first and second frequency side peaks; calculating the Fourier transform in the frequency domain for the first or second time side peaks calculating the spectral amplitude and the spatial-spectral phase for the first or second frequency side peak of the Fourier transform in the frequency domain.

A method for performing optical wavefront sensing includes providing an amplitude transmission mask having a light input side, a light output side, and an optical transmission axis passing from the light input side to the light output side. The amplitude transmission mask is characterized by a checkerboard pattern having a square unit cell of size . The method also includes directing an incident light field having a wavelength to be incident on the light input side and propagating the incident light field through the amplitude transmission mask. The method further includes producing a plurality of diffracted light fields on the light output side and detecting, at a detector disposed a distance L from the amplitude transmission mask, an interferogram associated with the plurality of diffracted light fields. The relation

[00001]$0<L<\frac{1}{8}.Math.\frac{{}^2}{}.Math..Math.\mathrm{or}.Math..Math.\frac{1}{4}.Math.\frac{{}^2}{}.Math.\left(2.Math.n-1\right)<L<\frac{1}{4}.Math.\frac{{}^2}{}.Math.\left(2.Math.n+1\right)$

is satisfied, where n is an integer greater than zero.

An apparatus and method are provided. In particular, at least one first electro-magnetic radiation may be provided to a sample and at least one second electro-magnetic radiation can be provided to a non-reflective reference. A frequency of the first and/or second radiations varies over time. An interference is detected between at least one third radiation associated with the first radiation and at least one fourth radiation associated with the second radiation. Alternatively, the first electro-magnetic radiation and/or second electro-magnetic radiation have a spectrum which changes over time. The spectrum may contain multiple frequencies at a particular time. In addition, it is possible to detect the interference signal between the third radiation and the fourth radiation in a first polarization state. Further, it may be preferable to detect a further interference signal between the third and fourth radiations in a second polarization state which is different from the first polarization state. The first and/or second electro-magnetic radiations may have a spectrum whose mean frequency changes substantially continuously over time at a tuning speed that is greater than 100 Tera Hertz per millisecond.

According to a first aspect, there is provided a method of holographic wavefront sensing, the method including: receiving a light beam, which has a wavefront to be analyzed, on a transparent, flat substrate, which is provided with a lattice of opaque dots, wherein the substrate is arranged above an image sensor; detecting by the image sensor an interference pattern formed by diffracted light, being scattered by the opaque dots, and undiffracted light of the light beam received by the image sensor; processing the detected interference pattern to digitally reconstruct a representation of a displaced lattice of opaque dots, which would form the interference pattern on the image sensor upon receiving the light with a known wavefront; and comparing the representation of the displaced lattice to a known representation of the lattice of opaque dots on the substrate to determine a representation of the wavefront form of the received light beam.

Hybrid sensors comprising Shack-Hartmann Wavefront Sensor (S-HWFS) and Zernike Wavefront Sensor (Z-WFS) capabilities are presented. The hybrid sensor includes a Z-WFS optically arranged in-line with a S-HWFS such that the combined wavefront sensor operates across a wide dynamic range and noise conditions. The Z-WFS may include the ability to introduce a dynamic phase shift in both transmissive and reflective modes.

Spectral interferometric systems and methods to characterize lateral and angular spatial chirp to optimize intensity localization in spatio-temporally focused ultrafast beams are described. Interference between two spatially sheared beams in an interferometer leads to straight fringes if the wavefronts are curved. To produce reference fringes, one arm relative to another is delayed in order to measure fringe rotation in the spatially resolved spectral interferogram. Utilizing Fourier analysis, frequency-resolved divergence is obtained. In another arrangement, one beam relative to the other is spatially flipped, which allows the frequency-dependent beamlet direction (angular spatial chirp) to be measured. Blocking one beam shows the spatial variation of the beamlet position with frequency (i.e., the lateral spatial chirp).