Abstract: In general, in a first aspect, the invention features a system including an interferometer configured to direct test light to an overlay target and subsequently combine it with reference light to form an interference pattern, the test and reference light being derived from a common source, a multi-element detector, one or more optics to image the overlay target on the multi-element detector; and an electronic processor in communication with the multi-element detector. The overlay target includes a first pattern and a second pattern and the electronic processor is configured to determine information about the relative alignment between the first and second patterns.

Abstract: Systems are disclosed that include an interferometer configured to direct test light to an overlay test pad and subsequently combine it with reference light, the test and reference light being derived from a common source, one or more optics configured to direct at least a portion of the combined light to a multi-element detector so that different regions of the detector correspond to different illumination angles of the overlay test pad by the test light, the detector being configured to produce an interference signal based on the combined light, and an electronic processor in communication with the multi-element detector. The overlay test pad comprises a first patterned structure and a second patterned structure and the electronic processor is configured to determine information about the relative alignment between the first and second patterned structures based on the interference signal.

Abstract: While a wafer stage linearly moves in a Y-axis direction, a multipoint AF system detects surface position information of the wafer surface at a plurality of detection points that are set at a predetermined distance in an X-axis direction and also a plurality of alignment systems that are arrayed in a line along the X-axis direction detect each of marks at positions different from one another on the wafer. That is, detection of surface position information of the wafer surface at a plurality of detection points and detection of the marks at positions different from one another on the wafer are finished, only by the wafer stage (wafer) linearly passing through the array of the plurality of detection points of the multipoint AF system and the plurality of alignment systems, and therefore, the throughput can be improved.

Abstract: Through a first diffraction grating, two conical fluxes different in wavefront propagation angle relative to its optical axis are applied to a first surface. Through a second diffraction grating, two conical fluxes different in wavefront propagation angle relative to its optical axis are applied to a second surface. Two sets of interference fringes formed by the fluxes reflected from the first surface and a reference beam are analyzed to obtain surface misalignment and angular misalignment of the first surface relative to the optical axis. Similarly, two sets of interference fringes formed by the fluxes reflected from the second surface and the reference beam are analyzed to obtain surface misalignment and angular misalignment of the second surface relative to the optical axis. Surface misalignment and angular misalignment of a sample lens are obtained from the measurement results of the first and second surfaces.

Abstract: A display substrate includes a signal line, a thin-film transistor (“TFT”), a key pattern, a light-blocking pattern, a color filter, a pixel electrode and an alignment key. The signal line and the key pattern are formed on a substrate. The TFT is electrically connected to the signal line. The light-blocking pattern is formed on the substrate and covers the signal line, the TFT and the key pattern. The color filter is formed in a unit pixel area of the substrate. The pixel electrode is formed on the color filter and is electrically connected to the TFT. The alignment key is formed on the light-blocking pattern, and a position of the alignment key on the substrate corresponds to a position of the key pattern on the substrate.

Abstract: A method for machine measurement for an NC processing machine is provided. The processing machine has a machine head, for example, a fork head and an associated mechanical and electrical spindle changing interface for holding a motor spindle. A laser interferometer with a beam generator and a beam detector is also provided and at least one measurement optic which interacts with the laser interferometer, for example, in the form of a reflector, and laser interference measurements, which are directed at a measurement optic, in particular distance measurements, carried out for machine measurement. The laser interferometer has an interface which corresponds to the spindle changing interface, and the laser interferometer is substituted for the motor spindle via the spindle changing interface for machine measurement, and is aligned by means of the machine axes for the laser interference measurements.

Abstract: The present patent application provides an interference cavity for precisely controlling an optical path including a cavity formed by two equal distance arms, wherein a positive adjusting plate and a negative adjusting plate are disposed in the interference cavity for compensating the change of a cavity length with temperature and thereby ensuring that the interference cavity length is a constant. The present patent application utilizes the matching relationship between the change of the refractive index of the positive adjustment plate with the temperature and the change of the refractive index of the negative adjusting plates with the temperature to make the optical path difference OPL invariant with changes in the environment temperature and thereby to ensure the precision of the optical path.

Abstract: A multi-aperture interferometric optical system collects light propagating from a source of light and develops overlapping diffraction patterns on an optical detector that produces output signals for processing to automatically focus the optical system and form an image corresponding to the diffraction patterns. A preferred embodiment of the invention is a large aperture orbiting, earth-watching ring interferometric optical system configured such that there is no macro-structure pointing. Four mirror-ring structures direct incoming light to a multi-spectral primary optical detector that acquires light-pattern information to focus the optical system and derive an image.

Abstract: Device and method for acquiring position with a confocal Fabry-Perot interferometer. In a general aspect, the device for acquiring position may include an arrangement for acquiring position where the acquiring arrangement has a confocal Fabry-Perot interferometer. In another general aspect, a method for acquiring position may include generating an interference pattern dependent on a position of an object by a confocal Fabry-Perot interferometer; detecting the interference pattern to obtain a measuring signal; and evaluating the measuring signal.

Abstract: An assembly including a conditioning system and an object moveable into and/or out of an area to be conditioned is disclosed. The conditioning system has fluid outlet passages to supply conditioning fluid to the area to be conditioned and is configured to adjust outflow of the conditioning fluid from the fluid outlet passages depending on a position of the object.

Abstract: An optical telescope system, method of actively, adaptively providing optical control to an array of articulated mirrors in a sparse aperture in the optical telescope system and a computer program product therefor. Array apertures are selected sequentially for imaging. Each aperture is temporally modulating at a unique/different frequency and, simultaneously, focal plane images are detected for each array aperture with known and separable temporal dependencies. The images are processed for the current set of said focal plane images to detect an image wavefront. The feeding back wavefront errors are fed back to aperture actuators for controlling the array.

Abstract: An alignment interferometer telescope apparatus comprises a coherent laser source, a first beam splitter, a reference spherical mirror, a light source, first and second reticles, and a second beam splitter. At an interference location within the apparatus, a reference laser wave and a test laser wave are allowed to interfere to produce a combined laser wave.

Abstract: A method for calibrating an encoder in a lithographic apparatus, the encoder including a sensor and a grating, the encoder configured to measure a position of a moveable support of the lithographic apparatus, the method including measuring a position of the moveable support using an interferometer; and calibrating the encoder based on the position of the moveable support measured by the interferometer.

Abstract: A method of and system for forming two laser processing beams with controlled stability at a target specimen work surface includes first and second mutually coherent laser beams propagating along separate first and second beam paths that are combined to perform an optical property adjustment. The combined laser beams are separated into third and fourth laser beams propagating along separate beam paths and including respective third and fourth main beam components, and one of the third and fourth laser beams contributes a leakage component that copropagates in mutual temporal coherence with the main beam component of the other of the third and fourth laser beams. An effect of mutual temporal coherence of the leakage component and the other main beam component with which the leakage component copropagates is reduced through acousto-optic modulation frequency shifts or through incorporation of an optical path length difference in the two beams.

Abstract: A system for detecting piston diversity between mirror segments. The system includes a pupil plane mask, a transform optical element, and an image detector. The pupil plane mask includes two or more open mask areas and two or more polarizers. Each polarizer is disposed within a respective one of the open mask areas. A first one of the two or more polarizers has a first polarization orientation, and a second of the two or more polarizers has a second polarization orientation.

Abstract: Positional information of a movable body in a Y-axis direction is measured using an interferometer and an encoder whose short-term stability of measurement values excels when compared with the interferometer, and based on the measurement results, a predetermined calibration operation for obtaining correction information for correcting measurement values of the encoder is performed. Accordingly, by using measurement values of the interferometer, correction information for correcting the measurement values of the encoder whose short-term stability of the measurement values excels the interferometer is obtained. Then, based on the measurement values of the encoder and the correction information, the movable body is driven in the Y-axis direction with good precision.

Abstract: An alignment interferometer telescope apparatus comprises a coherent laser source, a first beam splitter, a reference spherical mirror, a light source, first and second reticles, and a second beam splitter. At an interference location within the apparatus, a reference laser wave and a test laser wave are allowed to interfere to produce a combined laser wave.

Abstract: A position detecting apparatus includes a light source which supplies a detecting light; a light-collecting optical system which collects the detecting light onto a diffracted light generating portion provided on the object; a light guiding optical system which guides, to a predetermined position, a diffracted measuring light generated from the diffracted light generating portion by receiving the detecting light and a reference light generated from a reference surface by receiving the detecting light; and a photodetector which is arranged at the predetermined position and which detects interference fringes generated by the diffracted measuring light and the reference light. Three-dimensional positional information of, for example, a mask pattern surface or an exposure surface of a photosensitive substrate can be highly accurately detected by a relatively simple construction.

Abstract: System for monitoring a position of one or more optical elements in a projection objective (PO) include a plurality of sensors each configured to receive input light and to form output light, each sensor including a first sensor optic and a second sensor optic, the first sensor optic of at least one of the sensors being affixed to a first PO optical element and the second sensor optic of the at least one sensor being affixed to a support element that positions the first PO optical element within the PO, the first and second sensor optics being configured introduce a first optical path length difference (OPD) between two components of the input light to form the output light, the first OPD being related to the position of the first PO optical element with respect to the support element.

Abstract: In an overlay key used for measuring overlay accuracy between first and second layers on a substrate, a first mark may be formed in the first layer, and a second mark may be formed on the second layer. The first mark may include first patterns having a first pitch and extending in a first direction. The second mark may include second patterns extending in substantially the same direction as the first direction and having a second pitch substantially equal to the first pitch. First and second images may be acquired from the first and second marks. The overlay accuracy may be produced from position information of first and second interference fringes formed by overlaying a test image having a third pitch onto the first and second images.

Abstract: A system for aligning a segmented mirror includes a source of radiation directed along a first axis to the segmented mirror and a beamsplitter removably inserted along the first axis for redirecting radiation from the first axis to a second axis, substantially perpendicular to the first axis. An imaging array is positioned along the second axis for imaging the redirected radiation, and a knife-edge configured for cutting the redirected radiation is serially positioned to occlude and not occlude the redirected radiation, effectively providing a variable radiation pattern detected by the imaging array for aligning the segmented mirror.

Abstract: A level sensor for determining a height of a substrate. In one configuration, the level sensor forms part of a lithographic apparatus that includes a projection lens system. The level sensor generates one or more measurement beams and directs the measurement beam to a measurement spot on a substrate having a first reflecting surface, and produces a reflected measurement beam. The level sensor also generates one or more reference beams. A detector detects both the reflected measurement beam and the reference beam, respectively, and produces a measurement signal and a reference signal, respectively, the measurement signal being indicative for the height at the measurement spot. A processor that receives these signals and corrects the measurement signal based on the reference signal.

Abstract: A part of a plate of a predetermined shape detachably mounted on a moving body is detected by an alignment system while the position of the moving body is measured by a measurement unit that sets a movement coordinate system of the movement body, and based on the detection results and the measurement results of the measurement unit corresponding to the detection results, position information of an outer periphery edge of the plate is obtained. Therefore, even if there are no alignment marks on the moving body for position measurement, the position of the plate, or in other words, the position of the moving body can be controlled on the movement coordinate system set by the measurement unit, based on the position information of the outer periphery edge of the plate.

Abstract: A system and method for active visual measurement and servo control using laterally sampled white light interferometry (L-SWLI) for real-time visual tracking of six-degree-of-freedom (6 DOF) rigid body motion with near-nanometer precision. The visual tracking system is integrated with a 6 DOF motion stage to realize an ultra precision six-axis visual servo control system. Use of L-SWLI obtains the complete pose of the target object from a single image frame to enable real-time tracking. Six-degree-of-freedom motions are obtained by measuring the fringe pattern on multiple surfaces of the object or from a single surface with additional information gained from conventional image processing techniques.

Abstract: System for monitoring a position of one or more optical elements in a projection objective (PO) include a plurality of sensors each configured to receive input light and to form output light, each sensor including a first sensor optic and a second sensor optic, the first sensor optic of at least one of the sensors being affixed to a first PO optical element and the second sensor optic of the at least one sensor being affixed to a support element that positions the first PO optical element within the PO, the first and second sensor optics being configured introduce a first optical path length difference (OPD) between two components of the input light to form the output light, the first OPD being related to the position of the first PO optical element with respect to the support element.

Abstract: A measuring member has a first face and a plurality of first marks arranged on the first face. The first marks have respective orientations corresponding to their positions in a first direction.

Abstract: A method of aligning an array of mirrors and computer program product therefor. The method may be used to align mirrors in a sparse aperture telescope system, e.g., a spaced based imaging interferometer. An image projected onto mirrors in an array of mirrors is reflected onto a sensor, where a point spread function (PSF) is collected from a pair of mirrors. A spatial image is extracted from PSF sidebands and a difference (e.g., piston difference) is determined for the pair of mirrors from the spatial image. Tip and tilt are determined for the pair of mirrors from spatial image characteristics.

Abstract: A method of manufacturing an optical system having plural optical elements mounted relative to each other on a mounting structure of the optical system comprises disposing the optical system in a beam path of an interferometer apparatus having an interferometer optics and a selectable hologram for shaping a beam of measuring light to be incident on surfaces of the optical elements of the optical system; selecting a first hologram of the interferometer apparatus and recording at least one first interference pattern generated by measuring light reflected from a surface of a first optical element; selecting a second hologram of the interferometer apparatus, wherein the second hologram is different from the first hologram, and recording at least one second interference pattern generated by measuring light reflected from a surface of a second optical element, which is different from the first optical element; and adjusting a position of the first optical element relative to the second optical element on the mounti

Abstract: A method of measuring an optical characteristic of an optical system using a measurement apparatus, comprises determining a position of each of object points by arranging, on a side of the object plane, an object point measurement device array, and sequentially inserting the object point measurement devices in an optical path, determining a position of each of image points by arranging, on a side of the image plane, an image point measurement device array, and sequentially inserting the image point measurement devices in the optical path, calculating an error attributed to the measurement apparatus based on the positions of object points and the positions of the image points, obtaining a measured value by measurement to obtain information representing the optical characteristic of the optical system using the measurement apparatus, and correcting the measured value based on the error.

Abstract: In general, in a first aspect, the invention features a system including an interferometer configured to direct test light to an overlay target and subsequently combine it with reference light to form an interference pattern, the test and reference light being derived from a common source, a multi-element detector, one or more optics to image the overlay target on the multi-element detector; and an electronic processor in communication with the multi-element detector. The overlay target includes a first pattern and a second pattern and the electronic processor is configured to determine information about the relative alignment between the first and second patterns.

Abstract: A measurement apparatus which measures a surface position of an object comprises a first measurement device configured to make measurement light from the object and reference light from a reference mirror interfere with each other on a light receiving surface of a photo-electric conversion device to form an interference pattern, and photo-electrically convert the interference pattern by the photo-electric conversion device to output an interference signal, a second measurement device configured to measure the surface position of the object, and an arithmetic processing unit configured to detect the surface position of the object based on a peak, of the interference signal, which is ensured to be a peak of a central fringe according to the measurement result obtained using the second measurement device.

Abstract: A resultant image of a grating target may be obtained by dividing an image of the target into first and second portions and optically modifying the first and/or second portion such that a final image formed from their combination is characterized by a Moiré pattern. The resultant image may be analyzed to determine a shift in the grating target from a shift in the Moiré pattern. Optical alignment apparatus may include a first beam splitter, an image transformation element optically coupled to the first beam splitter, and a second beam splitter. The first beam splitter divides an image of a grating target into first and second portions. The second beam splitter combines the first portion and the second portion. The image transformation element optically modifies the first and/or second portion such that a final image formed from their combination is characterized by a Moiré pattern.

Abstract: Demand is growing for affordable advanced sensor systems for use in counter-terrorism, criminal forensic analysis, and medical diagnosis. Next generation, million RPM class laser interferometry and spectrometry scanning systems are the ideal solution for this need due to their inherent ability to detect and identify microscopic quantities of evidence and resolve microscopic detail however a means to produce these systems with sufficient precision efficiently and inexpensively has been elusive. The scanning head is the heart of the system and in order for scanning heads of million RPM rotational speed class to be precisely aligned and balanced at operational speed they must be assembled while rotating. To facilitate this, a fully integrated feed-back based assembly system that measures and corrects optical alignment and balance of the scanning head during final assembly has been devised that subsequently enables economical high-precision, high production rate assembly.

Abstract: An apparatus using optical coherence tomography based on spectral interference and an ophthalmic apparatus, which can accurately obtain information on an object in a depth direction by correcting misalignment between an optical member of a spectral optical system and a photodetector, includes an interference optical system for irradiating measurement light being low coherent light onto the object and synthesizing the measurement light reflected from the object and reference light being low coherent light to interfere, a spectral optical system which disperses interference light for every frequency, a photodetector photo-receiving the dispersed interference light, means guiding calibration light for adjusting alignment between the spectral optical system and the photodetector to the spectral optical system, means storing reference spectral information, and means adjusting the alignment based on a comparison between spectral information on the calibration light guided to the spectral optical system and photo-re

Abstract: Two X encoder heads (X heads) and one Y head are mounted on one wafer stage, and an X scale and a Y scale corresponding to these heads are arranged on a surface facing the wafer stage so that the scales connect the exposure area and the alignment area. The wafer stage is made to move back and forth between the exposure area and the alignment area along a path where the X scale and the Y scale are set, while performing position measurement using three encoder heads. In this case, a switching process between XZ interferometer will not be necessary.

Abstract: An apparatus including a stage configured to be moved. A first laser interferometer measures a position of the stage in a first direction. A second laser interferometer measures a position of the stage in the first direction. A control unit (i) obtains a position of the stage based on an output of one of the first and second laser interferometers, (ii) controls a position of the stage based on the obtained position of the stage, (iii) performs switching of one of the first and second laser interferometers to the other of the first and second laser interferometers while the stage is moved at a constant velocity in the first direction, (iv) calculates a distance by which the stage is to be moved during a time interval, and (v) sets an initial value of the other of the first and second laser interferometers after the switching, based on a position measured by the one of the first and second laser interferometers at a start time of the time interval and the calculated distance.

Abstract: An interferometric-spatial-phase imaging (ISPI) system includes a substrate wafer. An alignment configuration is permanently embedded in the substrate wafer. The alignment configuration uses a global coordinate reference system by providing a plurality of global reference marks that encompass up to the entire substrate wafer. A plurality of alignment markings is provided on a surface in close proximity to the alignment configuration for obtaining continuous six-axis control to provide positional information of a scanning probe tip or an electron beam with respect to said global coordinate reference system.

Abstract: A structure for overlay measurement is provided in the present invention, using the diffraction characteristics on the boundary portion between two microstructures formed on each of two material layers. The optical intensity distribution on the boundary portion between microstructures formed on the two overlaid material layers respectively are measured by an optical microscope to obtain the overlay error between the two overlaid material layers. In addition, the present invention also provides a method for overlay measurement using the structure for overlay measurement, wherein a merit relation based on the optical intensity distribution on the boundary portion between different microstructures is determined. The merit relation can be used to analyze the overlay error to improve the efficiency and accuracy of on-line error measurement.

Abstract: In an exposure apparatus having a plurality of substrate stages moving between a plurality of stations, errors due to the combination of the stage and a position measuring unit, such as Abbe error and errors due to the surface configuration of a reflection mirror, are precisely corrected to reduce the position error of the substrate stage. The exposure apparatus includes a control device having a storage unit and a correction unit. The storage unit stores the correction information established every combination of the plurality of substrate stages and a plurality of position measuring units, and the correction unit corrects the result measured by the plurality of position measuring units on the basis of the correction information corresponding to the combination of the substrate stages and the position measuring units among pieces of correction information stored in the storage unit.

Abstract: A surface measuring apparatus for measuring a surface shape of an element includes a measurement frame having a mount for mounting the element to be measured, a stage including a rotatable device, the stage being movable in at least a first direction relative to the measurement frame, and a contactless distance measurement device for measuring in the first direction a distance between the measurement frame and a predetermined measurement surface provided on the rotatable device. The apparatus further comprises a second distance measurement device for measuring in a second direction a second distance between the device and a selected position on a surface of an element mounted relative to the measurement frame and a rotation measurement device for measuring an angle of rotation between the first and second direction. In this way, aspheric or free-form surfaces of optical elements can be measured easily in closed loop without introducing abbel-errors.

Abstract: In general, in one aspect, the invention features methods that include using an interferometer to produce an output beam having a phase related to an optical path difference between a path of a first beam and a path of a second beam, wherein the first beam contacts a measurement object and either the measurement object or the interferometer are coupled (e.g., directly attached) to a stage that is moveable within a reference frame. The methods further include monitoring variations in the phase while both varying an orientation of the stage with respect to at least one degree of freedom in the reference frame and keeping a reference mark on the stage in a common position with respect to the reference frame, and determining information based on the monitored variations, the information being related to a contribution to the optical path difference caused by a deviation of the path of the first or second beam from a nominal beam path.

Abstract: An apparatus including a stage configured to be moved. A first laser interferometer measures a position of the stage in a first direction. A second laser interferometer measures a position of the stage in the first direction. A control unit (i) obtains a position of the stage based on an output of one of the first and second laser interferometers, (ii) controls a position of the stage based on the obtained position of the stage, (iii) performs switching of one of the first and second laser interferometers to the other of the first and second laser interferometers while the stage is moved at a constant velocity in the first direction, (iv) calculates a distance by which the stage is to be moved during a time interval, and (v) sets an initial value of the other of the first and second laser interferometers after the switching, based on a position measured by the one of the first and second laser interferometers at a start time of the time interval and the calculated distance.

Abstract: A system for positioning an eye of a patient, for example, for laser ophthalmic surgery includes a reflectometer adapted to receive as input a reflected beam from an anterior surface of a cornea of an eye of a patient. The interferometer is calibratable to a desired position of the corneal anterior surface. A comparator is in signal communication with the interferometer and is adapted to calculate from the input a difference between an actual position and the desired position of the corneal anterior surface. A device is in signal communication with the comparator for moving the patient a distance in a direction for matching the actual position to the desired position of the corneal anterior surface.

Abstract: An alignment apparatus which drives to a target position a stage capable of moving at least in a two-dimensional direction. A first measurement device and a second measurement device have a function of measuring positions of the stage in one direction from different positions, a switching device performs a switching operation for switching the first measurement device to the second measurement device, and a controller sets an initial value for the second position measurement device, which is used after the switching operation, based on the position of the stage finally measured by the first position measurement device before the switching operation.

Abstract: Improved systems, apparatus, and methods for detecting positions of moving stages and accurately compensating position error during operation (in “real time”) are provided. For some embodiments, rather than rely on two dimensional position measurements, measurements in at least three dimensions may be taken allowing compensation for pitch and roll and, therefore, more accurate position measurements. Further, by including a measurement of a beam column, compensation for movement of the beam may be performed.

Abstract: An exposure apparatus which irradiates a photosensitive agent applied to a substrate to form a latent image pattern on the photosensitive agent. The exposure apparatus includes a substrate stage which drives the substrate, a focus measurement unit which obliquely irradiates the substrate with measurement light to measure the position of the substrate in the direction of the axis of the exposure beam on the basis of the light reflected by the substrate, and a controller which executes a calibration for correcting, on the basis of the measurement result obtained by the focus measurement unit, a track plane of the substrate stage with reference to the reference plane of the focus measurement unit so as to set the track plane parallel to the reference plane.

Abstract: Defects are prevented from occurring during an exposure process by detecting vibration of and measuring the relative position of components of the exposure apparatus. The exposure apparatus includes an external frame on which a reference mirror is disposed, a projection lens, a first mirror fixed relative to the projection lens, a wafer stage, a second mirror fixed relative to the wafer stage, and an interferometer system that detects vibration of the projection lens using the reference mirror and the first mirror and detects the position of the wafer stage relative to the projection lens using the first and second mirrors. A second interferometer system may be provided to detect vibration of the first interferometer system.

Abstract: Disclosed is a method of determining an overlay error between two layers of a multiple layer sample. For a plurality of periodic targets that each have a first structure formed from a first layer and a second structure formed from a second layer of the sample, an optical system is employed to thereby measure an optical signal from each of the periodic targets. There are predefined offsets between the first and second structures. An overlay error is determined between the first and second structures by analyzing the measured optical signals from the periodic targets using a scatterometry overlay technique based on the predefined offsets.

Abstract: In general, in one aspect, the invention features methods that include interferometrically monitoring a distance between an interferometry assembly and a measurement object along each of three different measurement axes while moving the measurement object relative to the interferometry assembly. The methods also include monitoring an orientation angle of the measurement object with respect to a rotation axis non-parallel to the three different measurement axes while the measurement object is moving, determining values of a parameter for different positions of the measurement object from the monitored distances, wherein for a given position the parameter is based on the distances of the measurement object along each of the three different measurement axes at the given position, and deriving information about a surface figure profile of the measurement object from a frequency transform of at least the parameter values.

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.