Abstract: Various embodiments of the present invention relate to oblivious transfer protocols and to system for performing oblivious transfer. Embodiments of the present invention include a private data sampling protocol that is designed to balance the competing privacy interest of a database user and a database owner. Protocol embodiments enable the database user to obtain a fixed size random sample of the available data held by the database owner without the database owner learning which bits of data were accessed.

Abstract: A differential-phase polarization-sensitive optical coherence tomography system includes a polarized heterodyne interferometer for generating a reference beam to be reflected by a movable mirror unit, and a signal beam to be reflected by an imaging plane in a specimen. The interferometer further generates a first electrical signal output corresponding to first linear polarized waves of the reference and signal beams, and a second electrical signal output corresponding to second linear polarized waves of the reference and signal beams. A differential amplifier receives the first and second electrical signal outputs, and generates a differential signal output therefrom. A data acquisition unit is used to measure amplitudes of the first and second electrical signal outputs and the differential signal output. A computing unit computes the amplitudes measured by the data acquisition unit to determine a reflectivity, a phase retardation, and a fast axis angle of the imaging plane in the specimen.

Abstract: A multi-beam interferometer displacement measuring system has a light source module, a resonator module and a detecting device. The light source module has an emitter and a polaroid sheet. The emitter emits a non-polarizing beam. The polaroid sheet receives and transforms the non-polarizing beam into a polarizing beam. The resonator module receives the polarizing beam and has a coated glass panel, a corner cube prism and a wave-delay plate. The coated glass panel receives and reflects the polarizing beam. The corner cube prism receives and reflects the polarizing beam to the coated glass panel to form a resonant cavity. The wave-delay plate is mounted between the coated glass panel and the corner cube prism to receive the polarizing beam. The detecting device faces the coated glass panel to receive the interferential stripes formed in the resonator module and has a polarizing beam splitter, two power detectors and a signal processor.

Abstract: Methods are disclosed wherein the structural health of a civil structure, such as, but not limited to, a bridge or the like is measured by electronic distance measurement from a plurality of stable locations to a plurality of cardinal points on the structure in a methodical manner. By measuring the coordinates of the cardinal points, the dynamic and long-term static behavior of the structure provide an indication of the health of the structure. Analysis includes; comparison to a Finite Element Model (FEM), comparison to historical data, linearity, hysteresis, symmetry, creep, damping coefficient, and harmonic terms.

Abstract: A differential-phase interferometric system includes a polarized heterodyne interferometer for generating reference and signal beam that travel along reference and signal channels, respectively. The signal beam is directed to a specimen and contains measured information of the specimen. The interferometer further generates a first electrical signal output corresponding to first linear polarized waves of the reference and signal beams, and a second electrical signal output corresponding to second linear polarized waves of the reference and signal beams. A differential amplifier receives the first and second electrical signal outputs, and generates a differential signal output therefrom. A data acquisition unit is used to measure amplitudes of the first and second electrical signal outputs and the differential signal output.

Abstract: A method is disclosed whereby a laser-based spherical coordinate measurement system is dynamically calibrated. A mechanical oscillator, such as, but not limited to, a Foucault pendulum is used to generate periodic motions which can be fitted to Fourier series models. The residuals between the experimental measurements and the model can provide information which can be used to calibrate the instrument. The calibration information is used to augment the ASME B89.4.19-2006 standard to improve sensitivity to cyclic errors and include the servo systems.

Abstract: A polarimeter based on a modified Fizeau interferometer and a method for measuring the optical rotation of a polarized light beam by an optically active substance using the polarimeter, are provided.

Abstract: An optical interference measuring apparatus comprises a first multiple-wavelength light source 200a emitting a light beam having a plurality of spectra, a second multiple-wavelength light source 200b emitting a light beam having a wavelength different from that of the light beam from the first multiple-wavelength light source, a polarizing beam splitter 6 separating the light beams, a reference surface 7 reflecting the light beam from the second multiple-wavelength light source 200b, a test surface 8 reflecting the light beam from the first multiple-wavelength light source 200a, spectral optical elements 9a, 9b dividing interference signals of the light beams, detecting devices 10a, 10b which detect interference signals having single wavelengths of the light beams for a plurality of frequencies, and an analyzer 11 processing the signals from the detecting devices 10a, 10b to calculate an optical path difference between the reference surface 7 and the test surface 8.

Abstract: A laser interferometer system for measuring roll angle around the direction of linear displacement comprises a light source of a frequency stabilized input beam (15) with two linear orthogonally polarized components which may or may not be of the same frequency, a polarizing beam splitting prism, two quarter-wave retardation plates, a corner cube retroreflector, a prism assembly, attached to the mechanical apparatus whose roll angle of travel is to be measured, a wedge mirror assembly, a polarizer, a photoelectric detector, and a phase meter; the light source emits a frequency-stable incident beam and generates a stable electric reference signal; under the actions of the polarizing beam splitting prism, quarter-wave plate and corner cube retroreflector, the incident beam travels twice through and then reflected twice by the wedge mirror assembly, and finally exits from the polarizing beam splitting prism.

Abstract: An interferometer and corresponding system are provided having several aspects. In a first aspect, there is provided an interferometer adapted to receive separate first and second beams f1 and f2 therein, the interferometer comprising substantially equivalent and separate first and second optical pathways for the first and second beams f1 and f2. In a second aspect, there is provided an interferometer adapted to receive as separate inputs therein first and second beams f1 and f2, where such beams are not mixed or combined until just prior to being output by the interferometer. In a third aspect, an interferometer is provided having one or more beam blockers for intercepting extraneous or undesired light, and keeping such light from contaminating or interfering with separate beams f1 and f2.

Abstract: An optical characteristic measuring apparatus includes: a light source section which sweeps wavelengths of a first input light and a second input light respectively, frequencies of the first and second input lights being different from each other and polarized states of the first and second input lights being perpendicular to each other, and outputs the first and second input light; an interference section which inputs one branched light of the first and second input lights to a measuring object, makes output light from the measuring object interfere with other branched light of the first and second input lights, and outputs a plurality of interference lights; a plurality of light receiving sections which are respectively provided for the interference lights, receives the interference lights respectively, and outputs signals in accordance with optical powers of the interference lights respectively; and a low-pass filter for filtering the outputted signals.

Abstract: A differential-phase polarization-sensitive optical coherence tomography system includes a polarized heterodyne interferometer for generating a reference beam to be reflected by a movable mirror unit, and a signal beam to be reflected by an imaging plane in a specimen. The interferometer further generates a first electrical signal output corresponding to first linear polarized waves of the reference and signal beams, and a second electrical signal output corresponding to second linear polarized waves of the reference and signal beams. A differential amplifier receives the first and second electrical signal outputs, and generates a differential signal output therefrom. A data acquisition unit is used to measure amplitudes of the first and second electrical signal outputs and the differential signal output. A computing unit computes the amplitudes measured by the data acquisition unit to determine a reflectivity, a phase retardation, and a fast axis angle of the imaging plane in the specimen.

Abstract: In a displacement measurement apparatus using light interference, a probe light path is spatially separated from a reference light path. Therefore, when a temperature or refractive index distribution by a fluctuation of air or the like, or a mechanical vibration is generated, an optical path difference fluctuates between both of the optical paths, and a measurement error is generated. In the solution, an optical axis of probe light is brought close to that of reference light by a distance which is not influenced by any disturbance, a sample is irradiated with the probe light, a reference surface is irradiated with the reference light, reflected light beams are allowed to interfere with each other, and a displacement of the sample is obtained from the resultant interference light to thereby prevent the measurement error from being generated by the fluctuation of the optical path difference.

Abstract: A measuring device for the optic measuring of an object 13a is provided, in particular for measuring a motion of the object. The device includes an interferometer 20 with a measuring beam exit 12, a reflection beam entry 14, an interfering beam exit 15, and a light source 1 for creating a light beam 8, an optic detector 16, which is arranged at the interfering beam exit 15 of the interferometer 20 such that a light beam exiting the interfering beam exit 15 impinges the detector and a signal processing unit 17 connected to the detector 16 being embodied such that they can measure measuring signals of the detector 16.

Abstract: A laser interferometric measuring instrument includes: a light source that emits a laser beam of 1064 nm and another laser beam of 532 nm; a polarizing beam splitter; a dichroic mirror that splits a long-wavelength laser beam provided in a measurement optical path; a long-wavelength corner cube that reflects the split laser beam; a measurement corner cube that is displaceable along the measurement optical path; a reference corner cube that is displaceable along a reference optical path; a optical path changing unit that changes an optical path length of the long-wavelength laser beam; a phase detector that outputs interference signals; a sum signal computer that calculates a sum signal; a displacement controller that displaces the reference corner cube so as not to change a phase of the sum signal; a reference displacement detector that detects a displacement of the reference corner cube; and a measurement displacement computer that calculates a displacement of the measurement corner cube.

Abstract: A two-wavelength laser interferometer includes: a two-wavelength laser light source that emits two laser beams having different wavelengths; a two-wavelength polarizing beam splitter that includes a beam splitter and a beam superposer, the beam splitter splitting each of the two laser beams having the different wavelengths into a reference beam and a measurement beam, the beam superposer superposing the reference beam and the measurement beam reflected by a reference surface and a target measurement surface together; and a calculator that obtains a displacement amount of the target measurement surface per wavelength from the beams superposed together and obtains a displacement amount of the target measurement surface applied with atmospheric refractive index correction through a calculation in which the displacement amount obtained per wavelength is used. In the two-wavelength laser interferometer, an optical-axis superposer is provided between the two-wavelength laser light source and the beam splitter.

Abstract: A double pass apparatus for detecting defects on a disk surface includes a light source that generates a light beam and a beamsplitter that splits the light beam into a first light beam portion and a second light beam portion. A modulator is provided that modulates the second light beam portion into a frequency shifted modulated light beam for illuminating the surface of the disk. The frequency shifted modulated light beam is twice reflected from the surface of the disk, thus doubling the frequency shift of the reflected light beam. A polarizing beamsplitter combines the first light beam portion with the reflected light beam portion providing an interference signal.

Abstract: A method is disclosed including conditioning a measurement signal from an interferometer, said conditioning characterized by one or more conditioning parameters; measuring a plurality of values for the conditioned measurement signal; providing one or more values indicative of the conditioning parameters; determining an adjustment value at each measured value of the conditioned measurement signal based on the one or more of the measured values indicative of the conditioning parameters; and adjusting a measured value of the measurement signal according to the adjustment value.

Abstract: A system for measuring electromagnetic interference, the system comprising: a plane mirror interferometer receiving a first electromagnetic beam and a second electromagnetic beam having a same linear polarization, each of the first and second electromagnetic beams transmitted on separate paths such that the beams are non-overlapping until immediately before detection of the beams, wherein the interferometer includes: a reference surface and a measurement surface, the reference surface reflecting the first beam, and the measurement surface reflecting the second beam; and a polarization beam splitter, wherein the first and second beams enter the polarization beam splitter at a same facet of the polarization beam splitter.

Abstract: In general, in a first aspect, the invention features a method that includes using an interferometry assembly to provide three different output beams, each output beam including an interferometric phase related to an optical path difference between a corresponding first beam and a corresponding second beam, each first beam contacting a measurement object at least once, monitoring the interferometric phases for each of the three different output beams, and deriving information about variations in the optical properties of a gas in the first beam paths from the three monitored phases.

Abstract: In certain aspects, the invention features interferometry systems that include an input assembly positioned to receive a beam emitted from a light source comprising a first component beam and a second component beam, the input assembly being configured to change a dimension of one of the component beams relative to the dimension of the other component beam, an interferometer positioned to receive the component beams propagating from the input assembly, the interferometer being configured to direct the component beams along different paths and to produce an output beam by directing the component beams along a common path, wherein the output beam comprises information about an optical path difference between the different component beam paths, and an output assembly positioned in the path of the output beam and configured to change a dimension of the component beam that contacts the measurement object.

Abstract: A differential-phase interferometric system includes a polarized heterodyne interferometer for generating reference and signal beam that travel along reference and signal channels, respectively. The signal beam is directed to a specimen and contains measured information of the specimen. The interferometer further generates a first electrical signal output corresponding to first linear polarized waves of the reference and signal beams, and a second electrical signal output corresponding to second linear polarized waves of the reference and signal beams. A differential amplifier receives the first and second electrical signal outputs, and generates a differential signal output therefrom. A data acquisition unit is used to measure amplitudes of the first and second electrical signal outputs and the differential signal output.

Abstract: In the method and a device for detecting the phase of a moving object using a heterodyne interferometer, a heterogeneous mode helium-neon laser is used as a direct light source to increase a measuring speed, a measuring resolution, and minimize the loss of the light source. Signals, which have only a frequency difference between reference signals or measured signals and arbitrary signals, are extracted from signals which are obtained by multiplying the arbitrary frequency signals by the reference or measured signals. After frequencies of the reference and measured signals are converted, a phase difference of the extracted signals and displacement of the moving object is measured. The system includes a laser light source, an optical interferometer, a frequency converter, and a phase measurer. The light source uses output light, emitted from the laser generator, which is stabilized in frequency, and has two frequencies which are at right angles to each other and linearly polarized.

Abstract: A light source system includes a beam source generating a first input beam of light. An anisotropic acousto-optic modulator (AOM) is positioned to receive the first input beam. The AOM includes a plurality of transducers for receiving control signals and generating corresponding acoustic waves that operate on the first input beam to generate first and second output beams with different frequencies and orthogonal linear polarizations. The first and second output beams have a combined optical power that is substantially the same as an optical power of the first input beam for a first input beam with one polarization and for a first input beam with two polarizations.

Abstract: A light source system includes a beam source generating a first input beam of light with first and second beam components. The first component has a first linear polarization and a first frequency. The second component has a second linear polarization and a second frequency. The first and second linear polarizations are orthogonal. An anisotropic acousto-optic modulator (AOM) is positioned to receive the first input beam. The AOM is operable to change the polarization and frequency of the first and the second beam components in response to a control signal, and thereby generate first and second output beams corresponding to the first and second components, respectively.

Abstract: Apparatus and methods for adjusting the polarizations of the components of an input beam to reduce leakage caused by imperfections in an interferometer are disclosed. The apparatus includes an interferometer positioned to receive an input beam that includes two components having different frequencies and different polarizations, the interferometer including a polarizing beam splitter positioned to spatially separate the input beam into two intermediate beams, the first intermediate beam corresponding to the first component and the second intermediate beam corresponding to the second component, where imperfections in the interferometer cause leakage of one of the components into the intermediate beam corresponding to the other of the components. The apparatus further includes a polarization compensator that includes at least one retardation plate positioned to adjust the polarizations of the components of the input beam to reduce the leakage caused by the imperfections in the interferometer.

Abstract: An exposure apparatus includes a projection optical system for projecting an exposure pattern, onto an object to be exposed, and a measuring apparatus for measuring, as an interference fringe, optical performance of the projection optical system, wherein the measuring apparatus includes an optical element having opposing first and second surfaces, wherein the first surface has a first measurement pattern, and the second surface has a second measurement pattern and is closer to the projection optical system than the first measurement pattern, and wherein the measuring apparatus introduces light into the projection optical system via first and second measurement patterns.

Abstract: At least two discrete quarter wave plates are provided for use as plane mirrors or reflectors in a displacement measuring interferometer, where the plates share common or substantially common reflecting surface geometries. A plurality of geometrically matched discrete matched quarter wave plates reduces the amount of tilt between an input beam provided to, and an output measurement beam provided by, an interferometer, resulting in increased interferometer dynamic range.

Abstract: An optical image measuring apparatus capable of measuring an object to be measured which includes a birefringent layer in a short time is provided. The optical image measuring apparatus includes a broad-band light source, lenses for increasing a diameter of the light beam, a polarizing plate, a half mirror, a wavelength plate for converting the reference light to circularly polarized light, a wavelength plate for converting the signal light to circularly polarized light and converting the signal light to linearly polarized light, a frequency shifter, a polarization beam splitter for separating an S-polarized light component and a P-polarized light component from interference light, CCDs for receiving the respective polarized light components and outputting detection signals each including intensity change information, and a signal processing portion for forming an image reflecting a birefringent property, of an object to be measured based on the intensity change information.

Abstract: A system and method for analyzing the characteristics of a thin film is provided whereby the in-plane birefringence of thin films is determined by measuring the interference fringes in the transmission or reflection spectra using unpolarized light and light linearly polarized along the MD and CD directions. The three spectra can be measured simultaneously or sequentially. The in-plane birefringence data can be used to characterize clear polymer films, which are principally made of biaxial oriented polymer, as the film is being continuously fabricated on a production line.

Abstract: A method including: (i) directing a beam to an interferometer head using an optical connection, the beam including a first beam component having a first polarization and a first frequency and a second beam component having a second polarization different from the first polarization and a second frequency; (ii) rotating the polarization of the first beam component to the second polarization; (iii) rotating the polarization of the second beam component to the first polarization; and (iv) returning the beam with the rotated polarizations from the interferometer head using the optical connection. For example, the step of directing may include: directing the first beam component into a first fiber of the optical connection; and directing the second beam component into a second fiber of the optical connection. The first beam component may be returned using the second fiber, and the second beam component may be returned using the first fiber.

Abstract: An interferometer is provided that minimizes the introduction of non-linear errors into displacement measurements. In one embodiment, non-linear errors are reduced by isolating reference and measurement beams over most of their respective optical paths leading to the detector, and by employing a separate amplitude-splitting non-polarizing optical beam splitter for each beam input into the interferometer. Additionally, the interferometer is scalable to an arbitrary number of optical axes or inputs.

Abstract: An optical system provides information about tangential vibration components of a surface at remote location. The optical system includes a light source assembly that emits first and second beams, each having one or more wavelengths and one or two polarizations. The first and second beams are directed to the interrogated surface. A detector system is positioned to detect a third beam formed by at least a portion of the first and second beams being reflected from the interrogated surface. The first, second and third beams having incident and reflection angles relative to the interrogated surface that do not lay in a same plane. The detector system positioned remotely from the interrogated surface, and providing information on a phase change in the third beam relative to the first and second beam. The phase change is indicative of at least one surface vibration vector component of the interrogated surface. The detector system is a 90 degree optical hybrid balanced detector with four photodiodes.

Abstract: A light modulator incorporates a polarization sensitive prism and a novel MEMS ribbon device to impart a relative phase shift to polarization components of an incident light beam. A linear array of phase shifting elements in the MEMS device creates a linear image which is scanned to form a two dimensional scene. Alternatively the deflection of each cantilever in a linear array of atomic force microscope cantilevers may be measured simultaneously.

Abstract: A heterodyne interferometer, adaptive optics system, method of measuring movement of a target and/or variations in a beam propagation medium, and method of controlling an adaptive optics system are provided. The heterodyne interferometer includes an acoustic-optical modulator that can superimpose a RF signal on a source signal, and output a zero order beam and a higher order beam. One of the beams comprises a target beam and the other beam comprises a local oscillator beam. A telescope can receive the target beam, and direct the target beam through the beam propagation medium to the target. A beam splitter can receive the local oscillator beam and the reflected beam from the target, and coherently combine the local oscillator beam and the reflected beam to produce a fringe pattern. A detector can receive the fringe pattern and generate an electrical beat signal, which can be demodulated based upon the RF signal.

Abstract: A frequency splitting laser micrometer for measuring a displacement of an object. The laser micrometer includes a frequency splitting laser directing a first frequency splitting laser beam to the object via a laser output mirror at one end of the laser. The first laser beam is reflected thus outputting a second frequency splitting laser beam, such that a feedback cavity is created, wherein a frequency of the second laser beam is decided by a cavity length of said feedback cavity and accordingly the displacement of the object. A detecting and signal processing unit receives said first and second frequency splitting laser beams and measures the displacement of the object according to interference effects of said first and second laser beams.

Abstract: Multidirectional retroreflectors and methods of reflecting light beams from multiple directions are provided. The multidirectional retroreflectors utilize a four-mirror retroreflector with a common virtual reflection point.

Abstract: A microlithography method includes: interferometrically measuring information about a position of a microlithography stage with respect to each of multiple metrology axes during a photolithographic exposure cycle; analyzing the position information to determine correction factors indicative of a local slope on a side of the stage used to reflect an interferometric measurement beam and optical gradients caused by environmental effects produced by the photolithographic exposure cycle; and applying the correction factors to subsequent interferometric measurements of the stage.

Abstract: Bright and dark field imaging operations in an optical inspection system occur along substantially the same optical path using the same light source by producing either a circular or an annular laser beam. Multiple beam splitting is achieved through the use of a diffractive optical element having uniform diffraction efficiency. A confocal arrangement for bright field and dark field imaging can be applied with multiple beam scanning for suppressing the signal from under-layers. A scan direction not perpendicular to the direction of movement of a target provides for improved die-to-die comparisons.

Abstract: The invention is directed to the provision of a device and method for measurement of angle of rotation for measuring in a non-contacting fashion the concentration of an optically active substance such as a sugar, amino acid, vitamin, or the like dissolved in a sample. According to the invention, A coherent beam is split into two beams, one being an object beam and the other being a reference beam, the object beam passed through the sample is converted by a quarter wave plate into mutually perpendicular polarization components having therebetween a phase difference proportional to the angle of rotation produced by the sample, and the angle of rotation produced by the sample is obtained from the phase difference occurring between beat signals produced by causing the object beam with the reference beam.

Abstract: An interferometer includes a source of a heterodyne beam including frequency components having frequency components with orthogonal linear polarizations. A beam splitter separates frequency components of the heterodyne beams, and one or more AOMs increase the frequency separation between the separated beams. The separated beams can be sent via optical fibers to a beam-combining unit, which combines the beams for use in interferometer optics.

Abstract: A laser-based measuring apparatus divides a light beam from a laser light source into at least two light beams, passes the light beams through different optical paths from each other, recombines the light beams, has the light beams interfere with each other to generate interfered light, opto-electrically transduces the interfered light to an optical frequency, and measures the amount of travel of an object which changes an optical path length of a portion of an optical path based on the optical frequency. The measuring apparatus has a portion for generating at least two measuring light beams from the laser light source, two reflection planes included in an object moving on a measuring axis, arranged back-to-back to each other on the measuring axis, and an opposing incident optical system for directing the measuring light beams into the reflection planes, respectively, such that the measuring light beams oppose to each other on the measuring axis.

Abstract: A laser distance measuring system has a simple optical structure with which abnormal return light can be removed. The laser distance measuring system includes a laser light source that generates at least two interferable light beams with different frequencies on a same optical axis, a parallel reflecting portion that includes a reflecting surface, which is included in an object that moves along a measurement axis and that is arranged on the measurement axis, and returns an incident light beam in a direction opposite that at which it is incident and at a certain spacing from and parallel to the incident light beam, and an interferometer that is positioned between the laser light source and the parallel reflecting portion and that is arranged on the measurement axis. The optical axes of the light beams are displaced parallel to one another from the measurement axis and one of the light beams is passed through the interferometer and guided to the parallel reflecting portion.

Abstract: An interferometer includes a two-frequency laser and a polarizing beam splitter (PBS) that separates a heterodyne beam from the laser into separate beams having different the frequencies and orthogonal polarizations. Optical fibers conduct the separate beams to a beam combiner for interferometer optics. The PBS and/or the beam combiner can use a coating to reflect one linear polarization and transmit an orthogonal linear polarization. To improve extinction ratios in the PBS or the beam combiner, a yaw angle for an input beam is non-zero and corresponds to a peak in the extinction ratio of a reflected beam.

Abstract: An interferometer returns parallel beams that are subject to walk-off caused by reflector misalignment for an additional pass through the interferometer optics and thereby eliminates beam walk-off. A return reflector can be a plane mirror that directs returning beams to retrace paths through the interferometer optics to combine and exit along the axis of the input beam. Separation optics can separate the combined beam from the input beam. Alternatively, a return reflector such as an isosceles prism or a trapezoidal prism reflects and offsets returning beams so that the combined beam is offset from the input beam. The return reflector more generally responds to a shift in incident beam position with a matching shift of the reflected beam in contrast to a retroreflector, which shifts a reflected beam in a direction opposite to the shift in the incident beam.

Abstract: An interferometry system includes: i) a first polarizing beam splitter which during operation separates an input beam into a measurement beam and a reference beam; ii) a beam steering element positioned to direct the measurement beam, and not the reference beam, the measurement beam contacting the beam steering element; iii) an interferometer positioned to receive at least a portion of the measurement beam and direct it to a measurement object, which reflects it to define a return measurement beam, and wherein the interferometer is further positioned to receive at least a portion of the reference beam and direct it to a reference object, which reflects it to define a return reference beam; and (iv) an electronic control circuit coupled to the beam steering element. During operation the control circuit adjusts the orientation of the beam steering element in response to changes in the angular orientation of the measurement object.

Abstract: An interferometric measuring device for measuring the shape of a surface of an object has a radiation source which emits a short-coherent radiation, a beam splitter for forming an object beam which is directed via an object light path to the object and a reference beam which is directed via a reference light path to a reflective reference plane. The interferometric measuring device also has an image converter which picks up the radiation that has been brought to interference and reflected back from the surface and the reference plane and sends it to an analyzing device for determining a measurement result pertaining to the surface. To analyze the interference peak by scanning, the optical length of the object light path is altered relative to the optical length of the reference light path, or an intermediate image of the surface produced in the object light path is scanned.

Abstract: A multi-axis interferometer uses a combined beam for a first pass through the interferometer optics. Measurement and reference components of the combined beam that exit the interferometer optics are subject to walk-off that measurement or reference reflector misalignment can cause. A return reflector and non-polarizing beam splitter system split the combined beam into separated input beams for the various axes of the interferometer and return the separated beams for respective second passes through the interferometer optics. Walk-off for the separated beams in the interferometer optics cancels the walk-off for the combined beam to eliminate beam walk-off in separated output beams. Sharing a combined beam for a first pass through the interferometer optics reduces the sizes required for the interferometer optics and reference and measurement mirrors. The multi-axis interferometer may have a single return reflector.

Abstract: The invention comprises methods and apparatus for reducing sub-harmonic cyclic errors by rotating by a small angle an interferometer or elements thereof. The rotation of the interferometer or selective elements thereof introduces a corresponding small angle between a sub-harmonic type spurious beam that subsequently interferes with either the reference or measurement beam so that the fringe contrast of the interference terms between the subharmonic spurious beam and either the reference or measurement beam is reduced by a required factor for a given use application thereby reducing nonlinearities in the phase signal.

Abstract: Multidirectional retroreflectors and methods of reflecting light beams from multiple directions are provided. The multidirectional retroreflectors utilize a four-mirror retroreflector with a common virtual reflection point.