Abstract: Disclosed is a system including: (i) an interferometer configured to direct test electromagnetic radiation to a test surface and reference electromagnetic radiation to a reference surface and subsequently combine the electromagnetic radiation to form an interference pattern, the electromagnetic radiation being derived from a common source; (ii) a multi-element detector; and (iii) one or more optics configured to image the interference pattern onto the detector so that different elements of the detector correspond to different illumination angles of the test surface by the test electromagnetic radiation.

Abstract: Disclosed is an interferometry analysis method that includes comparing information derivable from multiple interferometry signals corresponding to different surface locations of a test object to information corresponding to multiple models of the test object, wherein the multiple models are parametrized by a series of characteristics that relate to one or more under-resolved lateral features of the test object; and outputting information about the under-resolved surface feature based on the comparison.

Abstract: A interferometer apparatus for studying the surface of an object, the apparatus comprising a source producing an object beam of coherent light, a source producing a reference beam which is coherent with the object beam, and a detector or a plurality of detectors arranged in a line or array, wherein the apparatus is arranged such that the object beam is diverging or substantially collimated, and wherein, in use the diverging or substantially collimated object beam is directed towards the surface of the object to produce a reflected object beam reflected from the surface of the object, the detector(s) is/are focused to a point beneath the surface of the object, and the reflected object beam is combined with the reference beam and detected by the detector(s). Also provided is a corresponding method for conducting an interferometric study of the surface of an object.

Abstract: The invention relates to a method and an apparatus for determining the height of a number of spatial positions on the sample, defining a height map of a surface through interferometry with a broadband light source. The method can involve for each spatial position: obtaining a correlogram during scanning of the surface plane of the objective and estimating the point of the correlogram where an amplitude of the correlogram is at its maximum, thus determining an approximation of the height of the spatial position on the sample. The estimation of the value where the correlogram has its maximum can involve subjecting the correlogram to a Fourier transform, subjecting the Fourier transformed signal to a filter, subjecting the filtered signal to an inverse Fourier transform, and calculating the location of the centre of mass of the inversed filtered Fourier transformed signal.

Abstract: A method utilizes an optical resonator that includes a reflective element and a spatial mode filter positioned relative to the reflective element such that light emitted from the spatial mode filter is reflected by the reflective element. The optical resonator has an optical resonance with a resonance lineshape that is asymmetric as a function of wavelength.

Abstract: An interferometer that measures a shape of a surface of an inspection object includes an interference optical system that splits light from a light source into inspection light and reference light and causes the inspection light reflected by the surface of the inspection object and the reference light to interfere with each other, and a photoelectric conversion element that detects interference fringes produced by interference between the inspection light and the reference light. The interference optical system includes a first optical element that transmits and reflects the inspection light, a second optical element that reflects the inspection light, and a moving unit configured to move the second optical element. The inspection light passes through the first optical element, is reflected by the second optical element, is reflected by the first optical element, and is then incident on the surface of the inspection object.

Abstract: A method and associated apparatus for capturing an image of a 3D object (100) which encodes the surface geometry of at least a portion of the object, comprising: 1. projecting (304) a plurality of fringe patterns (312A, 314A) onto the object; 2. capturing (306) phase alterations in reflections of the fringe patterns (312B, 314B) from the object; 3. projecting a uniform image (310A) onto the object; 4. capturing a reflection of the uniform image (310B) from the object; and 5. combining (310) captured phase alterations and captured uniform image reflection on a pixel-by-pixel basis, thereby forming a holoimage representation of the object.

Abstract: A shape measuring apparatus for measuring the shape of a measurement target surface includes an interferometer and computer. The interferometer senses interference light formed by measurement light from the measurement target surface and reference light by a photoelectric converter, while changing the light path length of the measurement light or the reference light. The computer Fourier-transforms a first interference signal sensed by the photoelectric converter to obtain a phase distribution and an amplitude distribution, shapes the amplitude distribution, inversely Fourier-transforms the phase distribution and the shaped amplitude distribution to obtain a second interference signal, and determines the shape of the measurement target surface based on the second interference signal.

Abstract: Systems configured to generate output corresponding to defects on a specimen and systems configured to generate phase information about defects on a specimen are provided. One system includes an optical subsystem that is configured to create interference between a test beam and a reference beam. The test beam and the reference beam are reflected from the specimen. The system also includes a detector that is configured to generate output representative of the interference between the test and reference beams. The interference increases contrast between the output corresponding to the defects and output corresponding to non-defective portions of the specimen.

Abstract: An apparatus is disclosed which includes an interferometry system configured to operate in a first mode to produce a first set of multiple interferometry signals corresponding to different illumination angles of a test object by test light and in a second mode produce a second set of multiple interferometry signals corresponding to different surface locations of a test object. An electronic processor coupled to the interferometry system is configured to receive the first set of interferometry signals and programmed to compare information derivable from the first set of multiple interferometry signals to information corresponding to multiple models of the test object to determine information related to one or features of the test object, and output the information. In some embodiments, the features include an under-resolved feature.

Abstract: An optical image measuring device 1 splits low-coherence light L0 into signal light LS and reference light LR, and splits an optical path of the reference light LR into two optical paths having different optical path lengths to split the reference light LR into two reference lights LRa, LRb. Furthermore, the optical image measuring device 1 makes the reference lights LRa, LRb interfere with the signal light LS propagated through an eye E, generates an interference light LC reflecting a morphology in each of two depth positions (fundus oculi Ef and cornea Ec) of an eye E, and detects the interference light LC to generate a detection signal. Then, the optical image measuring device 1 forms a fundus oculi tomographic image and a cornea tomographic image based on the detection signals, and analyzes the tomographic images to obtain a distance between the cornea and retina of the eye E.

Abstract: An apparatus for measuring a shape of a surface, comprises a measurement head which measures a distance between a reference point and the surface by detecting interference between test light obtained when light that passes through the reference point is emitted, is reflected by the surface, and returns to the reference point, and reference light, a scanning mechanism which scans the measurement head, and a processor which calculates the shape of the surface based on the distance measured using the measurement head and coordinates of the reference point.

Abstract: A system and method for measuring interferences are disclosed. The system is based on the concept of a composite interferometer. The sample is measured while a simultaneous compensation of the phase deviation due to the relative displacement of the optical delay component between the measurements at different pixels of the sample is performed. In the application of profilometry, the information of the surface profile of a material is obtained from the phase shift of the interference signal. By using the proposed compensation mechanism, an axial resolution at nanometer scale can be achieved. For the measurement of a thin film, a polarized probe beam is oblique incident on the sample. The system can perform a simultaneous measurement of the refractive index and the thickness of the thin film. From the ratio of the intensities of the interferograms of TE and TM waves as well as the phase shifts of the interferograms, the refractive index and the thickness of the thin film can then be obtained simultaneously.

Abstract: A measurement apparatus disclosed that has a radiation source configured to provide a measurement beam of radiation such that an individually controllable element of an array of individually controllable elements capable of modulating a beam of radiation, is illuminated by the measurement beam and redirects the measurement beam, and a detector arranged to receive the redirected measurement beam and determine the position at which the redirected measurement beam is incident upon the detector, the position at which the redirected measurement beam is incident upon the detector being indicative of a characteristic of the individually controllable element.

Abstract: A method is disclosed which includes: using a scanning interferometry system, generating a sequence of phase-shifted interferometry images at different scan positions of an object comprising a buried surface, identifying a scan position corresponding to a position of best focus for the buried surface based on the sequence of phase-shifted interferometry images of the object, and generating a final image based on the phase-shifted interferometry images and the scan position, where the interferometric fringes in the final image are reduced relative to the interferometric fringes in the phase-shifted interferometry images.

Abstract: The present invention provides a measurement apparatus which measures a height of a test surface, the apparatus including an image sensing device including a plurality of detection units configured to detect interfering light formed by measurement light from the test surface and reference light from a reference surface, and an optical system configured to guide measurement light beams, reflected at a plurality of measurement points on the test surface, and reference light beams, reflected at a plurality of reference points on the reference surface, to the plurality of detection units, respectively, wherein the reference surface generates differences among optical path differences between the measurement light beams and the reference light beams which enter the plurality of detection units, respectively.

Abstract: The present invention provides a measurement apparatus which measures a height of a test surface, the apparatus including an image sensing device including a plurality of detection units configured to detect interfering light formed by measurement light from the test surface and reference light from a reference surface, and an optical system configured to guide the measurement light and the reference light to the plurality of detection units, wherein the reference surface is placed such that differences are generated among optical path differences between measurement light beams and reference light beams which enter the plurality of detection units, respectively.

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: Disclosed is an apparatus which includes: an interferometer configured to direct broadband spatially coherent test light to a test surface of a test object over a range of illumination angles and subsequently combine it with reference light to form an interference pattern, the test and reference light being derived from a common source; and multi-element detector; and one or more optics configured to direct at least a portion of the combined light to the detector so that different elements of the detector correspond to different illumination angles of a region of the test surface illuminated by the test light.

Abstract: A phase-shifting interferometry (PSI) method and corresponding system including: (i) recording an interferogram for each phase in a sequence of phases between test light reflected from a test surface and reference light reflected from a reference surface, the test and reference light being derived from a common source, each interferogram corresponding to an intensity pattern produced by interfering the reflected test light with the reflected reference light, the interferograms defining an interferometry signal for each of different transverse locations of a cavity defined by the test and reference surfaces, each interferometry signal including a series of intensity values corresponding to the sequence of phases, with the difference between each pair of phases in the sequence defining a corresponding phase shift increment; (ii) calculating an initial phase map for the cavity based on at least some of the recorded interferograms; (iii) calculating an estimate for each of at least some of the phase shift increme

Abstract: A method is disclosed including: generating a scanning interferometry signal at each of multiple wavelengths for each of at least one location on a test object; obtaining the scanning interferometry signals at each of the multiple wavelengths for each of at least one location on the test object; analyzing the scanning interferometry signals to determine information about the test object; and outputting the information about the test object. Each scanning interferometry signal corresponds to interference between test light and reference light as an optical path length difference between the test and reference light is varied. The test and reference light are derived from a common source, and the test light emerges from the test object over a range of angles corresponding to a numerical aperture of greater than 0.7.

Abstract: To measure a hollow three-dimensional object without contact, this object being translucent or transparent vis-á-vis a visible light, an image of the object is acquired by single-view backlit shadowgraphy, along a viewing axis, by observing this object with visible light, this image comprising at least one luminous line, an equation is established that connects at least one optogeometric parameter of the object to at least one geometric parameter of the luminous line, this geometric parameter is determined, and the optogeometric parameter is determined by means of the equation and the geometric parameter thus determined.

Abstract: A vibration-resistant interferometric scanning system and method are provided in the present invention. In the present invention, the brightness distribution in a high-coherence interference pattern is analyzed so as to perform a compensation action to lock the brightness distribution of a high-coherence interference pattern and consequently locking the fringe distribution of a low-coherence interference pattern or to perform a scanning operation composed of plural shifting actions with specified scanning distances in sequence and plural compensation actions to lock the fringe distribution in a low-coherence interference pattern corresponding to the surface profile of a measured object. Consequently, with the system and method of the present invention, the surface profile of a measured object disturbed by external or internal vibrations can be measured accurately and precisely.

Abstract: A reference plane is arranged in a posture obliquely tilted at an optional angle relative to a traveling direction of a light-beam, so that an interference fringe is generated from the reflected light-beams which are reflected from a target plane and the reference plane and, then, return on a single optical path. An image of the interference fringe is taken by a CCD camera to acquire intensity value data of each pixel. A phase of an interference fringe waveform is obtained for each pixel by a CPU by fitting the intensity value data to a model equation expressing the interference fringe waveform, where the intensity value data contain that of each pixel and those of the pixels in the vicinity of the relevant pixel, on assumption that DC components, AC amplitudes and phases of the interference fringe waveforms are respectively constant in the vicinity of the relevant pixel. The obtained phase is converted into a height to measure a surface profile.

Abstract: A method of manufacturing an optical element (5) comprises testing an optical surface (3) of the optical element, using an interferometer 1a directing measuring light (23a) onto the optical surface wherein the measuring light traverses two successive holograms (44, 48) disposed in the beam path of the measuring light upstream of the optical surface.

Abstract: A system for measuring a shape of a target object includes a photonic integrated circuit and a light detector. The photonic integrated circuit includes a phase shifter configured to change a phase difference between a first portion of light and a second portion of light within the phase shifter, and an output element configured to output the light from the phase shifter directly toward the target object. The output element includes a first output waveguide configured to act as a first point source; and a second output waveguide configured to act as a second point source. The light detector is positioned to receive reflected light from the target object.

Abstract: The present invention relates to a scanning microscope using an I/Q-interferometer. The scanning microscope includes an I/Q-interferometer which demodulates the phase change and amplitude change induced on the probe beam to provide the I- and Q-signals, an XY scanner, a scanner driver, a precision motion stage controlling the displacement of the sample along the direction parallel to the direction of the probe beam, a motion stage driver, a focusing/collimating device, and a computer. The computer transfers control commends to the scanner driver for scanning the XY scanner, receives I- and Q-signal provided from the I/Q-interferometer, processes the I- and Q-signal to obtain the corresponding phase and amplitude values at each scanning point, calculates error signal for maintaining constant phase during the scanning, and transfers commends to the motion stage driver for the precision motion stage to compensate for phase changes caused by surface morphology during the scanning.

Abstract: A device for measuring the shape of freeform surfaces of objects includes a point-measuring optical and or interferometric scanning arm which is displaceable along a predefined path line, which device generates a measurement beam focused on the freeform surface to be measured. With reference to the scanning point, the scanning arm is able to rotate in at least one plane, in such a way that the measuring beam impinges upon the freeform surface to be measured in a perpendicular manner or within an acceptance angle of the scanning arm.

Abstract: A pulsed laser system includes a modulator module configured to provide pulsed electrical signals and a plurality of solid-state seed sources coupled to the modulator module and configured to operate, responsive to the pulsed electrical signals, in a pulse mode. Each of the plurality of solid-state seed sources is tuned to a different frequency channel separated from any adjacent frequency channel by a frequency offset. The pulsed laser system also includes a combiner that combines outputs from each of the solid state seed sources into a single optical path and an optical doubler and demultiplexer coupled to the single optical path and providing each doubled seed frequency on a separate output path.

Abstract: An apparatus for measuring surface topography of an object includes an optical arrangement capable of directing a first light beam at a surface of the object, providing a second light beam coherent with and spatially phase-shifted relative to the first light beam, and generating an interference beam from the second light beam and a reflection of the first light beam from the surface of the object. The apparatus further includes at least one line scan sensor for detecting and measuring the interference beam.

Abstract: Disclosed is an interferometry analysis method that includes comparing information derivable from multiple interferometry signals corresponding to different surface locations of a test object to information corresponding to multiple models of the test object, wherein the multiple models are parametrized by a series of characteristics that relate to one or more under-resolved lateral features of the test object; and outputting information about the under-resolved surface feature based on the comparison.

Abstract: The three-dimensional shape measuring apparatus includes a light source; a beam splitter to split illumination light from the light source; a target object to be measured, having a height difference between the highest point and the lowest point; a reference mirror, on which another beam emitted from the beam splitter is irradiated; a light detecting element to detect an interference pattern generated by the interference of an object beam reflected by the surface of the target object and a reference beam reflected by the surface of the reference mirror; and a control computer to process an image detected by the light detecting element, wherein a subsidiary reference beam generating unit to change the optical path of the beam from the beam splitter to generate a subsidiary reference beam is provided between the beam splitter and the reference mirror.

Abstract: The present invention relates to a vibration-insensitive interferometer using a high-speed camera and a continuous phase scanning method. The interferometer measures a measurement target by completely isolating influences of externally occurring vibrations from a frequency domain. The interferometer includes a light source unit for emitting light. A light transmission unit radiates the light emitted from the light source unit to the measurement target, splits light reflected from the measurement target into reference light and measurement light, and allows the reference light and the measurement light to interfere with each other, thus generating an interference fringe. A continuous phase scanning unit for radiates the reference light split by the light transmission unit through continuous phase scanning.

Abstract: A probe is presented that includes a light source, a coherent fiber bundle, and a pattern selector. The pattern selector is disposed between the light source and the proximal end of the coherent fiber bundle. The pattern selector includes at least one patterned zone through which light from the light source passes to project at least one fringe set onto a surface. Each of the at least one fringe sets has a structured-light pattern. The probe further includes an imager for obtaining at least one image of the surface and a processing unit that is configured to perform phase-shift analysis on the at least one image. A method for projecting a plurality of fringe sets suitable for phase-shift analysis on a surface using a probe is presented.

Abstract: An explicit relationship is developed between the ratio of average interferometric modulation produced by diamond-like carbon (DLC)-coated magnetic-head surfaces and the thickness of the DLC layer. Accordingly, the thickness of the DLC layer is calculated in various manners from modulation data acquired for the system using object surfaces of known optical parameters.

Abstract: A method and device for optical determination of physical properties of features, not much larger than the optical wavelength used, on a test sample are described. A beam is split into reference and illuminating beams having known polarization. The test sample is exposed to the illuminating beam and recombined to form an image. The image is detected using at least one sensor, which may be cameras. A point-to-point map of polarization, phase and power is extracted from data representing the image. Optionally, the sensor may be a camera. The sensor may detect at least three optical parameters, such as a Stokes vector, a Jones vector, a Jones matrix, a Mueller matrix or a coherency matrix.

Abstract: A measurement apparatus disclosed that has a radiation source configured to provide a measurement beam of radiation such that an individually controllable element of an array of individually controllable elements capable of modulating a beam of radiation, is illuminated by the measurement beam and redirects the measurement beam, and a detector arranged to receive the redirected measurement beam and determine the position at which the redirected measurement beam is incident upon the detector, the position at which the redirected measurement beam is incident upon the detector being indicative of a characteristic of the individually controllable element.

Abstract: An image processing apparatus is made up of a processing target area specification section for specifying a processing target area; a circumferential direction specification section for specifying the circumferential direction of a contour circle in the processing target area; an edge detection region specification section for specifying three or more regions made different in position in the circumferential direction in the processing target area as edge detection regions based on the processing target area and the circumferential direction; an edge position identification section for identifying edge positions with respect to the radial direction based on the intensity distribution in the edge detection regions; and a contour circle determination section for determining a contour circle based on the edge positions identified relative to the edge detection regions.

Abstract: A process of measuring a shape while changing the relative posture of an microscopic interferometer to a sample lens which is rotated about a rotation axis is divided into a process of measuring a top surface in a state where the sample lens is supported from a back surface and a process of measuring a back surface in a state where the sample lens is supported from the top surface. By combining first shape information of a flange side surface acquired by the process of measuring the top surface and second shape information of the flange side surface acquired by the process of measuring the back surface, the relative positional relation between the sample top surface and the sample back surface is calculated.

Abstract: A phase-shifting interferometry (PSI) method and corresponding system including: (i) recording an interferogram for each phase in a sequence of phases between test light reflected from a test surface and reference light reflected from a reference surface, the test and reference light being derived from a common source, each interferogram corresponding to an intensity pattern produced by interfering the reflected test light with the reflected reference light, the interferograms defining an interferometry signal for each of different transverse locations of a cavity defined by the test and reference surfaces, each interferometry signal including a series of intensity values corresponding to the sequence of phases, with the difference between each pair of phases in the sequence defining a corresponding phase shift increment; (ii) calculating an initial phase map for the cavity based on at least some of the recorded interferograms; (iii) calculating an estimate for each of at least some of the phase shift increme

Abstract: Described are an imaging device and method for determining three-dimensional position information of a surface of an object. The device includes a pair of optical fibers, a phase shifter, a detector array and a processor. The phase shifter is coupled to one of the optical fibers and is used to change a phase of optical radiation emitted from the optical fiber relative to a phase of optical radiation emitted from the other optical fiber. The detector array receives optical radiation scattered by the surface of the object. The processor communicates with the detector array and the phase shifter. Signals generated by the detector array are received by the processor and three-dimensional position information for the surface is calculated in response to the received optical radiation scattered by the surface of the object and the change in the relative phase of optical radiation emitted by the optical fibers.

Abstract: In a optical sensor (30) for measuring object surfaces (2) with high precision, measuring errors due to tilt of an object surface can be corrected by using a pupil monitor (72), which senses the intensity distribution of the reflected measuring beam (b?) in combination with a correction/calibration table (76) and use the monitor signal to correct the primary measuring signal (FES) of the sensor. Especially for a differential confocal sensor, a further order of correction can be obtained by determining optimum position and diameter of the pinholes. The measurement beam is directed to an object via a beams splitter cube and an objective that focuses the beam on an object surface. Light is received back from the object surface through the objective and split off by the splitter, from where it is directed to a sensor. In order to increase the measurement range the objective is mounted on an actuator. An interferometer is used to measure the position of the objective.

Abstract: There is disclosed an interferometer for measuring a surface shape of an examined object or a transmitted wavefront through the examined object. The interferometer includes an area light source having a low spatial coherence property, and a light-guiding optical system configured to arrange the area light source and the examined object in an optically conjugate relation with each other.

Abstract: An orthogonal-polarization Mirau interferometric system is provided, wherein an incident light is split into a reference light and an inspection light with the polarizations thereof being orthogonal to each other by using a beam-splitting module, while projecting the inspection light on a measured object to form an object light, and then the object light and the reference light are combined to form a combined light, and thereafter, an analyzer is utilized to modulate the polarizations and the intensities of the two lights for making the two lights interfere with each other and thus create an interference pattern. The polarization of the object light and that of the reference light can be adjusted by using an analyzer to become orthogonal to each other, and the intensities of the object light and the reference light can be adjusted to about the same for producing an interference pattern with high contrast.

Abstract: A method of measuring a volume in a fluid flow micromechanical device includes: a) providing and positioning an optical apparatus for measuring the profile of a surface; b) providing a device for acquiring and processing the images coming from the optical apparatus for measuring a profile; c) placing the moving member in a first position and then in a second position, and activating the optical apparatus for measuring the profile of the surface to direct a light beam on the reference face, and activating the image acquisition and processor device to obtain a first image in the first position of the moving member and a second image in the second position; and d) comparing the second image with the first image of the reference face to determine the variation in the volume of the cavity generated by the deformation of the moving member.

Abstract: A method for measuring the heights of patterns of an object, including: a light emission, the light includes a propagation mode of interest for at least one wavelength of interest, an illumination of the surface of the object by the light, a reflection of the light by the surface of the object, a collection of the reflected light, a division of the wavefront of the reflected light into division components, by at least one pattern of the illuminated surface, a filtering of the collected light, including a modal filtering removing all modes other than the propagation mode of interest, for the wavelengths of interest, and from the filtered light, and for the wavelengths of interest, an extraction of information about phase differences between the division components.

Abstract: The present invention provides a measurement apparatus which measures a surface shape of a measurement target surface, the apparatus including an optical system configured to split light from a light source into measurement light and reference light, guide the measurement light onto the measurement target surface, and guide the reference light onto a reference surface, a detection unit configured to detect an intensity of the measurement light reflected by the measurement target surface, an intensity of the reference light reflected by the reference surface, and an interference pattern formed between the measurement light reflected by the measurement target surface and the reference light reflected by the reference surface, and a processing unit configured to obtain a surface shape of the measurement target surface based on an interference signal of the interference pattern detected by the detection unit.

Abstract: A test surface is rotatable around a rotation axis and an interferometer main unit is movable with respect to a test surface so that an observation area is moved on the test surface which is rotating. While the observation area is moved within the test surface, an interfering light beam is successively captured by a one-dimensional image sensor, straight belt form observation-position-specific interference fringes formed by the interfering light beam are successively imaged, and the shape information of the test surface is obtained based on the imaged observation-position-specific interference fringes.

Abstract: Structure profiles from optical interferometric data can be identified by obtaining a plurality of broadband interferometric optical profiles of a structure as a function of structure depth in an axial direction. Each of the plurality of interferometric optical profiles include a reference signal propagated through a reference path and a sample signal reflected from a sample reflector in the axial direction. An axial position corresponding to at least a portion of the structure is selected. Phase variations of the plurality of interferometric optical profiles are determined at the selected axial position. A physical displacement of the structure is identified based on the phase variations at the selected axial position.

Abstract: A frequency scanning interferometer is arranged for simultaneously measuring multiple surfaces of a test object through a wide range of expected offsets. Knowledge of the expected locations of the test surfaces is compared with a sequence of ambiguity intervals based on a synthetic measurement wavelength to center the test surfaces within the ambiguity intervals.