WO2001025721A1

WO2001025721A1 - Methods and apparatus for splitting, imaging, and measuring wavefronts in interferometry

Info

Publication number: WO2001025721A1
Application number: PCT/US2000/027343
Authority: WO
Inventors: James E. Millerd; Neal J. Brock
Original assignee: Metrolaser, Inc.
Priority date: 1999-10-06
Filing date: 2000-10-04
Publication date: 2001-04-12
Also published as: US6304330B1; AU7752600A; US7298497B2; US20030053071A1; US20020003628A1; US20060132795A1; US7170611B2; US6552808B2

Abstract

Apparatus for splitting, imaging, and measuring wavefronts with a reference wavefront and an object wavefront. A wavefront-combining element receives and combines into a combined wavefront (66) an object wavefront (58) from an object and a reference wavefront (56). A wavefront-splitting element (80) splits the combined wavefront (66) into a plurality of sub-wavefronts (70a, 70b, 70c, 70d) in such a way that each of the sub-wavefronts (70a, 70b, 70c, 70d) is substantially contiguous with at least one other sub-wavefront. The wavefront-splitting element (80) may shift the relative phase between the reference wavefront and the object wavefront of the sub-wavefronts (70a, 70b, 70c, 70d) to yield a respective plurality of phase-shifted sub-wavefronts. The wavefront-splitting element (80) may then interfere the reference and object wavefronts of the phase-shifted sub-wavefronts to yield a respective plurality of phase-shifted interferograms (74a, 74b, 74c, 74d). An imaging element (76) receives and images the phase-shifted interferograms (74a-d). A computer connected to the imaging element (76) measures various parameters of the objects based on the phase-shifted interferograms (74a-d). Examples of measurements include flow parameters such as the concentrations of selected gaseous species, temperature distributions, particle and droplet distributions, density, and so on. In addition to flow parameters, the displacement (e.g., the vibration) and the profile of an object may be measured.

Description

METHODS AI D APPARATUS FOR SPLITTING. IMAGING, AND MEASURING WAVEFRONTS IN INTERFEROMETRY

STATEMENT REGARDING FEDERALLY SPONSORED

RESEARCH/DEVELOPMENT This invention was made with United States Government support under Contract

No DMI-9531391 awarded by the National Science Foundation The United States Government has certain πghts in this invention.

BACKGROUND OF THE INVENTION

Field of the Invention The present invention relates to interferometry More particularly, the present invention relates to methods and apparatus for imaging wavefronts. The methods and apparatus of the present invention may be implemented in measuπng systems that measure vaπous parameters of test objects by simultaneously generating a plurality of phase-shifted interferograms.

Descπption of the Related Art Phase-shift interferometry is an established method for measuπng a vaπety of physical parameters ranging from the density of gasses to the displacement of solid objects. Interferometπc wavefront sensors can employ phase-shift interferometers to measure the spatial distπbution of relative phase across an area and, thus, to measure a physical parameter across a two-dimensional region. An interferometπc wavefront sensor employing phase-shift interferometry typically consists of a spatially coherent light source that is split into two wavefronts. a reference wavefront and an object wavefront, which are later recombined after traveling different optical paths of different lengths. The relative phase difference between the two wavefronts is manifested as a two-dimensional intensity pattern known as an interferogram. Phase-shift interferometers typically have an element in the path of the reference wavefront which introduces three or more known phase steps or shifts By detecting the intensity pattern with a detector at each of the phase shifts, the phase distπbution of the object wavefront can be quantitatively calculated independent of any attenuation in either of the reference or object wavefronts. Both continuous phase gradients and discontinuous phase gradients (speckle waves) can be measured using this technique. Temporal phase shifting using methods such as piezo-electπc dπven mirrors have been widely used to obtain high-quality measurements under otherwise static conditions The measurement of transient or high-speed events requires either ultra high-speed temporal phase shifting (1 e , much faster than the event timescales), which is limited due to detector speed, or spatial phase shifting that can acquire essentially instantaneous measurements

Several methods of spatial phase shifting have been disclosed in the pπor art In 1983 ^•^ Smythe and Moore descnbed a spatial phase-shifting method in which a seπes of co entional beam splitters and polaπzation optics are used to produce three or four phase-shifted images onto as many cameras for simultaneous detection A number of United States patents, such as U S Patent Nos 4,575.248, 5,589,938, 5,663,793, 5,777,741 , and 5,883,717. disclose vaπations of the Smythe and Moore method where multiple cameras are used to detect multiple 10 interferograms One of the disadvantages of these methods is that multiple cameras are required and complicated optical aπangements are need to produce the phase-shifted images, resulting in expensive complex systems

Other methods of spatial phase shifting include the use of gratings to introduce a relative phase step between the incident and diffracted beams, an example of which is disclosed in U S 15 Patent No 4,624,569 However, one of the disadvantages of these grating methods is that careful adjustment of the position of the grating is required to control the phase step between the beams

Spatial phase shifting has also been accomplished by using a tilted reference wave to induce a spatial earner frequency to the pattern, an example of which is disclosed in U S Patent 20 No 5,155,363 This method requires the phase of the object field to vary slowly with respect to the detector pixels, therefore, using this method with speckle fields requires high magnification Yet another method for measuπng the relative phase between two beams is disclosed in U S. Patent No 5,392,116, m which a linear grating and four detector elements are used This method has a number of drawbacks, including the inability to measure of wavefronts u e , the ^~25 spatial phase distπbution across the profile of a beam) and to form contiguous images on a single pixelated detector such as a standard charge coupled device (CCD)

Finally, it is noted that wavefront sensing can be accomplished by non-interferometnc means, such as with Shack-Hartmann sensors which measure the spatially dependent angle of propagation across a wavefront These types of sensors are disadvantageous in that they 30 typically have much less sensitivity and spatial resolution than interferometπc wavefront sensors and are not capable of performing relative phase measurements such as two-wavelength interferometry BRIEF SUMMARY OF THE INVENTION

It is one object of the present invention to provide an mterferometπc wavefront sensor that incorporates spatial phase shifting but avoids the complexity of multi-camera systems by using a single two-dimensional pixelated detector, such as a standard charge coupled device (CCD) camera

It is another object of the present invention to provide methods and apparatus tor performing two-wavelength interferometry that utilize a compact spatial phase-shifting device to acquire data at high speeds and provide improved tolerance to vibration

It is yet another object of the invention to provide methods and apparatus for dividing an incoming wavefront into four sub-wavefronts that are imaged substantially contiguous to maximize the coverage of a pixelated area detector, while mimimizing the number of necessary optical components to provide a compact system

It is still another object of the invention to provide methods and apparatus for introducing a phase shift between orthogonally polaπzed reference and object wavefronts that is uniform across each sub-wavefront and not sensitive to the positiomng of a diffractive optical element

According to one aspect of the invention, apparatus for splitting a wavefront and producing four substantially contiguous images of the wavefront consists of an input plane, a first lens element, a diffractive optical element, a second lens element, and an output plane The lens elements are placed in a telescopic arrangement (separated by the sum of their focal lengths) and the diffractive optical element is placed at or near the mutual focal points The diffractive optical element produces four output wavefronts (or beams) from a single input wavefront In a preferred embodiment the diffractive element produces four diffracted orders of equal intensity and symmetπc to the incident axis so that it can be characteπzed by a single divergence angle α and a radial angular spacing of β The diffractive optic is constructed to suppress the zero order component to the greatest extent possible Alternatively, the diffractive optical element may produce three diffracted orders each of equal intensity with the transmitted zero order beam The diffractive optic may include a wedged substrate to provide a uniform angular tilt to all four beams so they propagate symmetπcally to the axis of the incident beam Again, the compound diffractive optical element is characteπzed by a single divergence angle α and a radial angular spacing β Any higher-order diffracted components from the diffractive optic should be at least twice the angular divergence The focal length of the second lens may be selected to be equal to the detector size divided by two times the tangent of the diffractive optic's divergence angle The front lens mav be chosen to produce an overall svstem magnification equivalent to the oπginal wavefront dimension divided by half the detector size

According to another aspect of the invention, apparatus for introducing a uniform phase- shift between orthogonally polaπzed reference and object wavefronts includes a polaπzation mask element made of discrete sections Each section includes a phase retardation plate or a blank and a linear polaπzer The relative angular oπentation of the phase retardation plate and linear polaπzer is selected to be different for each discrete section In one exemplary embodiment, the mask element includes four quadrants each providing a phase shift of π/2 relative to the clockwise adjacent quadrant According to still another aspect of the present invention, a system for providing an improved wavefront sensor includes a wavefront splitting element, a polaπzation mask element, a pixelated detector element, a polaπzation interferometer, and a computer The phase of an object beam can be measured with a single frame of data acquired from the pixelated detector

Yet another aspect of the invention provides a two-wavelength interferometer including a wavefront sensor with a tunable laser or multiple laser sources Multiple wavefronts are measured at each of several wavelengths with the relative phase values substracted to determine the contour of an object

Other objects, features, and advantages of the present invention will become apparent to those skilled in the an from a consideration of the following detailed descπption taken in conjunction with the accompanying drawings

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG 1 is a schematic view of measurement apparatus configured in accordance with the present invention, particularly illustrating the measurement apparatus with the use of functional blocks, FIG 2 is a schematic perspective view of an exemplary embodiment of apparatus for generating multiple phase-shifted images in accordance with the present invention,

FIG 3 is a schematic perspective view of an exemplary phase-retardant plate according to the invention, particularly illustrating a phase-retardant plate for shifting the phase of four wavefronts, FIG 4 is a plan view of the phase-retardant plate shown in FIG 3,

FIG 5 is a schematic view of an exemplary embodiment of measurement apparatus of the invention, particularly illustrating transmit and image portions thereof, FIG 6 is a schematic view of an exemplary embodiment of an image portion of the measurement apparatus of the invention,

FIG 7 is a schematic view of an active surface of a detector array of an image portion of the present invention, particularly illustrating an exemplary plurality of sub-wavefronts coaxially ^■^ along an optical axis of the image portion,

FIG 8 is a schematic view of another exemplary embodiment of an imaging portion of the present invention, particularly illustrating the inclusion of a polaπzer and a mask,

FIG 9 is a schematic view illustrating an exemplary imaging portion of the invention,

FIG 10 is a schematic view of another exemplary embodiment of measurement apparatus 0 of the invention, particularly illustrating apparatus for performing profilometry,

FIG 11 is a schematic view of the measurement apparatus of FIG 6, particularly illustrating an exemplary commercial embodiment of the profilometer of the invention,

FIG 12 is a schematic view of a yet another exemplary embodiment of measure apparatus of the invention, particularly illustrating apparatus for measunng displacement, 15 FIG 13 is a schematic view of still another exemplary embodiment of the measurement apparatus of the invention, particularly illustrating apparatus for performing wavefront sensing, and

FIG 14 is a schematic view of a graphical user interface illustrating mterferometπc data according to the present invention

0 DETAILED DESCRIPTION OF THE INVENTION

The present invention provides apparatus and methodology for measuπng vaπous parameters of test objects by simultaneously generating multiple phase-shifted images More particularly, the apparatus and methodology of the present invention enable multiple phase- shifted images (or interferograms) to be obtained with a single imaging device and by a single

25 pulse of a laser and at very high rates In doing so. the present invention splits, images, and measures a wavefront made up of a reference and an object wavefront from an object under test The apparatus of the present invention may be configured to measure — in situ and in real time — flow parameters in a multiphase environment Examples of such flow parameters include the concentrations of selected gaseous species, temperature distπbutions. particle and droplet

"0 distπbutions, density, and so on In addition to flow parameters, the apparatus of the present invention may be configured to measure the displacement (e g , the vibration) of an object Moreover, the apparatus of the invention may be configured to perform profilometry of an object, that is. to measure the absolute three-dimensional profiles of solid objects These and other utilizations and embodiments of the technology of the present invention are discussed in detail herein

Turning to the drawings, a measurement system 50 exemplifying the pπnciples of the present invention is illustrated in FIG. 1. Exemplary measurement system 50 generally includes a transmit portion 52 and an image portion 54 The transmit portion 52 transmits a reference wavefront 56 to the image portion 54 and an object wavefront 58 to an object 60 under measurement The reference and object wavefronts 56 and 58 are preferably generated by a spatially coherent light source such as a laser. The object wavefront 58 is received by the image portion 54 after acting upon the object 60, for example, by reflection or by transmission Data obtained by the image portion 54 from the object 60 may be provided to a computer 62 for processing The transmit portion 52 and the image portion 54 may be oπented with respect to the object 60 according to a plurality of measurement configurations, which are discussed in detail below With continued reference to FIG. 1, exemplary image portion generally includes a wavefront-combimng element 64 for receiving the reference wavefront 56 and the object wavefront 58 and for combimng the wavefronts into a combined wavefront 66 The reference and object wavefronts 56 and 58 are combined to be supeπmposed and orthogonally polaπzed, which is discussed below A wavefront-sphttmg element 68 receives the combined wavefront 66 and splits the wavefront into a plurality of sub-wavefronts 70 A phase-shifting interference element 72 receives the sub-wavefronts 70 and is configured to shift the relative phase between the reference and object wavefronts 56 and 58 and to interfere the reference and object wavefronts 56 and 58 by polaπzation. for each of the sub-wavefronts 70, to yield a plurality of phase-shifted interferograms 74 A sensing element 76 receives the phase-shifted interferograms 74 from the phase-shifting interference element 72 substantially simultaneously The sensing element 76 provides data 78 indicative of the interferograms 74 to the computer 62 for processing.

According to the present invention, the phase-shifting interference element 72 shifts the relative phase between the reference and object wavefronts 56 and 58 for each of the sub- wavefronts 70 discretely by a factor of a predetermined amount p The predetermined amount p may be determined by a number N of sub-wavefronts 70 in the plurality of sub-wavefronts generated by the wavefront-splitting element 68 from the combined wavefront 66 For example, the predetermined amount p mav be determined as the quotient of 360 degrees and the number N of sub-wavefronts 70, or

/? = 360° - N ( 1 )

Accordingly, the discrete phase shift Δφ of each of the plurality of sub-wavefronts 70 may be determined as

Δφ, = (z - l) x / (2) where i = 1 to N For example, if the wavefront-sphttmg element 68 provides four sub- wavefronts 70, then the discrete phase shifts Δφ of the four wavefronts are 0°, 90°, 180°, and 270° According to this embodiment, there is a 90° phase shift between each of the interferograms 74

An exemplary embodiment of the combination of the wavefront-sphttmg element 68, the phase-shifting interference element 72. and the sensing element 76 is illustrated in FIG 2 As shown, the combined wavefront 66 includes the reference wavefront 56 from the transmit portion 52 and the object wavefront 58 from the object 60. The wavefront-combimng element 64 is configured so that the reference wavefront 56 and the object wavefront 58 are orthogonally polaπzed, which is indicated m FIG. 2 by the scientific convention of an arrow and a dot Exemplary wavefront-sphttmg element 68 is preferably a two-dimensional diffractive optical element (DOE) such as a holographic optical element (HOE) 80. According to a preferred embodiment of the invention, exemplary DOE 80 splits the combined wavefront 66 into four sub-wavefronts 70a. 70b, 70c. 70d Each of the sub-wavefronts 70a-70d follows a spatially discrete path

With continued reference to FIG 2, exemplary phase-shifting interference element 72 includes a plurality of sections 82, the number of which preferably equals the number N of sub- wavefronts 70 provided by the wavefront-sp ttmg element 68 According to the prefeπed embodiment shown, exemplary phase-shifting interference element 72 includes four sections 82a, 82b, 82c, 82d. The phase-shifting interference element 72 is disposed with respect to the wavefront-splitting element 68 so that the plurality of sub-wavefronts 70 are respectively incident on the plurality of sections 82, that is, each section 82 receives one of the sub- wavefronts 70 As discussed above, each of the sections 82 shifts the relative phase between the reference and object wavefronts 56 and 58 and interferes the two wavefronts 56 and 58 for each of the sub-wavefronts 70 incident thereon by a discrete phase shift Δφ,. Each of the sections 82a, 82b, 82c, 82N of the phase-shifting interference element 72 accordingly provides a respective phase-shifted interferograms 74a. 74b, 74c. 74N The phase of each phase-shifted mterferogram 74 is out of phase with the phase of the other phase-shifted interferograms 74 by a factor of the predetermined amount /? of phase shift, which is discussed further below

Continuing to reference FIG 2, exemplary sensing element 76 is preferably an imaging sensor or a detector aπay 84 The detector array 84 may be a video-imaging sensor such as a charged coupled device (CCD) camera According to the present invention, the detector aπav 84 preferably has an active surface 86 The active surface 86 may be defined by a pixel aπay The detector aπay 84 may be made from a plurality of individual detector aπays configured to function as a single active sensing element For example, the active surface 86 may be defined by more than one CCDs collectively functioning as a single aπay For the purposes of this descπption, the active surface 86 has a surface area S

The detector aπay 84 is disposed with respect to the phase-shifting interference element 72 so that the plurality of phase-shifted interferograms 74 are substantially simultaneously incident on the active surface 86, thereby imaging on the active surface 86 a respective plurality of phase-shifted interferograms Based on the imaged interferograms, the spatially resolved phase of each of the phase-shifted interferograms 74 can be measured instantaneously In addition, the detector array 84 is disposed with respect to the phase-shifting interference element 72 so as to maximize the area of the active surface 86, which is discussed in more detail below With additional reference to FIG 3, an exemplary embodiment of the phase-shifting interference element 72 includes a plurality of plates 88 For the prefeπed four-component embodiment descπbed above, exemplary phase-shifting interference element 72 includes a first plate 88a and a second plate 88b For purposes of claπty and illustration, the plates 88 are shown m a spaced relationship, however, according to exemplary embodiments of the invention, the plates 88 are substantially planar, disposed m a parallel relationship, and abut each other The first plate 88a includes a quarter-wave plate 90 and a blank plate 92 As known in the art, a quarter waveplate shifts the relative phase of two orthogonally polaπzed incident wavefronts by 90°, and a blank plate shifts the relative phase of two orthogonally polaπzed incident w a\ etronts by 0° (l e , there is no relative phase shift) The plates 90 and 92 are preferably coplanar and divide the first plate 88a into respective halves The second plate 88b of exemplary phase-shifting interference element 72 includes a pair of polaπzmg plates 94a and 94b that are configured to polaπze an incident wavefront linearly so that electπc field vectors of the transmitted wavefront are perpendicular with each other Specific to the illustrated embodiment, one ot the polaπzing plates, e g , plate 94a. is configured to polaπze light at -τ-45°wιth respect to the vertical axis (as shown by aπow A in FIG 3), thereby interfeπng the in-phase components of the reference and object wavefronts 56 and 58 The other polaπzing plate, e g , plate 94b. is configured to polaπze light at -45° with respect to the vertical axis (as shown by aπow B in FIG 3), thereby mterfeπng the out-of-phase components of the reference and object wavefronts 56 and 58 The polaπzing plates 94a and 94b are preferably coplanar and divide the second plate 88b into respective halves

With continued reference to FIG 3 and additional reference to FIG 4, the first and second plates 88a and 88b are configured so that the respective halves thereof are perpendicular with each other, thus forming a phase-retardation mask or plate 96 In the four-component embodiment shown, the phase-retardation plate 96 includes four sections 82, each of which defines a quadrant Section 82a, or quadrant Q₀, is defined by the blank plate 92 and polaπzing plate 94a. thus interfeπng the in-phase (I e , 0°) component between the incident reference and object wavefronts 56 and 58 Section 82b, or quadrant Q,, is defined by the quarter-wave plate 90 and polaπzing plate 94a, thus interfeπng the in-phase quadrature (l e., 90°) component between the incident reference and object wavefronts 56 and 58. Section 82c, or quadrant Q₂, is defined by the blank plate 92 and polaπzmg plate 94b, thus interfeπng the out-of-phase (I e., 180°) component between the incident reference and object wavefronts 56 and 58 And section 82d, or quadrant Q₃, is defined by the quarter-wave plate 90 and polaπzing plate 94b, thus interfeπng the out-of-phase quadrature (I e , 270°) component between the incident reference and object wavefronts 56 and 58

The operation of the phase-shifting interference element 72 may be descπbed with respect to the reference and object wavefronts 56 and 58 which, as mentioned above, are orthogonally polaπzed The electπc field vectors for each of the wavefronts 56 and 58 may be wπtten as t_r - κe s _(3a)

E_s = Se'^ilσ-^w,+Aφ)p (3b)

where R and S are the amplitudes of each wavefront 56 and 58, respectively, ω is the optical frequency, t is time, k is the wavevector = 2π/λ, p and s are orthogonal unit polanzation vectors; and

ΔΦ is the phase difference between the wavefronts 56 and 58 The intensity (I) of each of the phase-shifted interferograms 74 incident on the active surface 86 of the detector aπay 84 is given by

I₀ ^ -(I_r + I_s + 2^1 cos(A )) (4a)

I₂ = ^(l_r + I_s + 2 j ;cos{Aφ + π)) (4c)

where L and I_s are the intensities of the reference and object wavefronts 56 and 58, respectively (which intensities are proportional to R² and S²). This set of phase-shifted intensities I₀, 1,, I,, and I₃ may be analyzed numeπcally using a number of algonthms to solve explicitly for the phase difference between the reference and object wavefronts 56 and 58, which is discussed in detail below

As it is preferable to maximize the imaging area of the detector aπay 84 (1 e , to maximize the portion of the surface area S of the active surface 86 that is illuminated by the interferograms 74). the phase-retardation plate 96 is preferably disposed adjacent to or substantially at the active surface 86 of the detector aπay 84. which is discussed in more detail below By detecting the plurality of phase-shifted interferograms 74 instantaneously with an imaging sensor exemplified by the detector array 84, the image portion 54 of the invention enables the measuπng system 50 to instantaneously measure the entire test object 60 In addition, the instantaneous detection of the phase-shifted interferograms 74 eliminates the need to scan individual beams spatially through or across the surface of the object 60

As mentioned above, exemplary measurement system 50 of the present invention may be configured m a plurality of prefeπed embodiments each designed to carry out a particular type of real-time measurement, including a profilometer, a displacement sensor, and a wavefront sensor In other words, exemplary embodiments of the measuπng system 50 include a common transmit portion 52 and a common image portion 54 that can be physically oπented in a plurality of configurations with a plurality of optical and imaging components to undertake a plurality of measurements, which is discussed in detail below

FIG 5 illustrates one such exemplary configuration of the measurement system 50 of the invention which may be used to perform real-time interferometry for measuπng transient events. The transmit portion 52 according to this embodiment includes a coherent light source such as a laser or laser diode 98 The laser 98 may include a half-wave plate 100 to provide a coherent light wavefront 102 which is split by a polaπzing beam splitter (PBS) 104 into the reference wavefront 56 and the object wavefront 58 The PBS 104 is configured to provide orthogonally polaπzed wavefronts as shown The object wavefront 58 is expanded by, for example, a combination of an expanding lens 106 and a colhmatmg lens 108. Upon expansion, the object wavefront 58 is transmitted to the test object 60 where the object wavefront 58 is incident upon the surface or boundary thereof and either reflected from or transmitted through the object 60

Exemplary image portion 54 receives the object wavefront 58 from the object 60 and may include optics for colhmatmg the received object wavefront 58, such as a combination of a collecting lens 110 and a collimatmg lens 112. Collimating lens 112 is preferably spaced from the collecting lens 100 by a distance equal to the sum of their respective focal lengths f and/. The object wavefront 58 is then supeπmposed with the reference wavefront 56 at the wavefront- combinmg element 64 which may be a polaπzing beam splitter (PBS) 114 to yield the combined wavefront 66 PBS 114 is preferably spaced from colhmatmg lens 112 by a focal length f₂ of the colhmatmg lens The combined wavefront 66 may be focused on the diffractive optical element 80 by means of a convex lens 116 In turn, the plurality of sub-wavefronts 70 may be focused on the phase-retardation/mterference plate 96 either directly or by means of a colhmatmg lens 118 as shown The placement of the vaπous elements with respect to each other is chosen to maximize the operabihty of the image portion 54 For example, PBS 114, the convex lens 116, and the diffractive optical element 80are preferably respectively spaced apart by focal length f₃, which is the focal length of the convex lens 116 In addition, the diffractive optical element 80, the colhmatmg lens 118. and the phase-retardation/interference plate 96 are preferably respectively spaced apart by a focal length f , which is the focal length of the colhmatmg lens 118 The placement of the diffractive optical element 80 at the focus of colhmatmg lens 118, which is defined as the input focal plane or the Fouπer transform plane, optimizes the area of the active surtace 86 of the detector aπav 84 illuminated by the plurality of phase-shifted interferograms 74

Referencing FIG 6, the optics of exemplary imaging portion 54 are shown in more detail The optical elements of the imaging portion 54 are aligned along an optical axis O As mentioned above, the diffractive optical element 80 splits the combined wavefront 66 into a plurality of (e g , four) sub-wavefronts 70 Each of the sub-wavefronts 70 follows an optical path defined by the distance each of the sub-wavefronts 70 follows from the diffractive optical element 80 to the active surface 86 of the detector array 84

The diffractive optical element 80 and lenses 116 and 118 are configured so that each of the imaged sub-wavefronts 70 incident at detector surface 86 are adjacent to or substantially contiguous with at least one other sub-wavefront, which is shown in FIG 7 For example, in the exemplary embodiment shown, sub-wavefront 70a is substantially contiguous with sub- wavefronts 70b and 70c, which is respectively indicated by reference alphas AB and AC, sub- wavefront 70b is substantially contiguous with sub-wavefronts 70a and 70d, which is respectively indicated by reference alphas AB and BD, sub-wavefront 70c is substantially contiguous with sub-wavefronts 70a and 70d, which is respectively indicated by reference alphas AC and CD, and sub-wavefront 70d ^ substantially contiguous with sub-wavefronts 70b and 70c, which is respectively indicated by reference alphas BD and CD. This substantially contiguous nature of the sub-wavefronts 70 is further enhanced m an embodiment in which the diffractive optical element 80 splits the combined wavefront 66 into a plurality of sub-wavefronts having a substantially rectangular cross section as shown in FIG 8

The exemplary diffractive optical element 80 preferably splits the combined wavefront 66 in such a manner that the sub-wavefronts 70 diverge from the optical axis O at substantially equal angles In a prefeπed embodiment, the diffractiv e optical element 80 may produce four diffracted orders that have equal intensity and are symmetπc to the incident axis so that the diffracted orders may be characteπzed by a single divergence angle α and a radial angular displacement β The diffractive optical element 80 may be constructed to suppress the zero order component to the greatest extent possible

In another exemplary embodiment, the diffractive optical element 80 may produce three diffracted orders each of equal intensity with the transmitted zero order beam The diffractive optical element 80 may include a wedged substrate to provide a uniform angular tilt to all four beams so that the beams propagate symmetπcally to the axis of the incident beam As mentioned above the diffractive optical element 80 is preferably characteπzed bv a single divergence angle α and a radial angular displacement β

Referring to FIG 7, the radial angular displacement β produced by exemplary diffractive optical element 80 is determined by the aspect ratio of the height h and the w idth u of the active surface 86 of the detector aπay 84 The desired radial angular displacement β is given by

where w and h are the width and the height of the active surface 86 of detector array 84 For a detector with a unity aspect ratio (I e , square), the radial angular displacement β becomes 90 degrees and all four images are radially symmetnc

10 Accordingly, each of the sub-wavefronts 70 follows an independent optical path from the diffractive optical element 80 to the active surface 86 that has a length substantially equal to each of the other optical paths As such, the plurality of sub-wavefronts 70 reach the active surface 86 substantially simultaneously By configuring the imaging portion 54 so that the sub-wavefronts 70 have substantially equal optical path lengths, the imaging portion 54 is less susceptible to l ^ eπors that may introduced by vibration to the system

With particular reference to FIG. 7, exemplary active surface 86 of the detector aπay 84 may have a plurality of sections 119 for respectively receiving the plurality of sub-wavefronts 70 Each of the sections 119 has a surface area on which the respective sub-wavefront 70 is incident According to the present invention, the portion or percentage of the surface area of

20 each section 119 on which a sub-wavefront is incident is preferably maximized, thereby maximizing the resolution of the detector aπay 84 For example, each of the sub-wavefronts 70a-70d is incident on at least half of the surface area of a respective section 119a-119d More preferably, the percentage is at least 75% In the embodiment shown in FIG 7 bv the circular cross-hatched regions, the incident percentage of each sub-wavefront 70 ma\ be determined by

2-> πr divided by (h/2 + w/i In the embodiment shown in FIG 7 by the rectangular cross hatched region, the incident percentage of each sub-wavefront is substantially 100%

Further referencing FIG 6 and with addition reference to FIG 8, an aperture 121 may be provided at an input focal plane of the convex lens 116 (I e , at a focal length /j), with the diffractive optical element 80 positioned at the output focal plane of the com ex lens 116 0 Alternatively, as shown in FIG 9, a pair of apertures 121a and 121b may be positioned upstream of PBS 114 through which the reference and object wavefronts 56 and 58 respectively travel According to a prefeπed embodiment of the invention, the aperture(s) 112 mav be rectangular with an aspect ratio substantially the same as the active surface 86 of the detector aπay 84 The presence of the aperture(s) 121 reduces the amount of ambient noise received in the image portion 54 and reduces crosstalk between the imaged sub-wavefronts.

An example of a design method that maximizes the surface area coverage follows With reference to FIGS. 6 and 7, the focal length of lens 118 is selected to be equal to one fourth of the diagonal length D of the active area of detector 84 divided by the tangent of the divergence angle α of the diffractive optical element 80. For illustrative clanty, the diagonal length D is shown as segment AB in FIG. 7 Thus:

The front lens 116 is chosen to produce an overall system magnification equivalent to the diagonal length d, of the input aperture 112 (shown in FIG. 6) divided by the diagonal length D of the detector aπay 84 Thus:

The overall length L of the imaging portion 54 is given by-

According to an exemplary embodiment of the invention, the aperture(s) 121 may be selected so that the diagonal length d, is substantially equal to the diagonal length D of the detector aπay 84 (i.e., d, = D). According to such an embodiment, focal length f₃ is equal to focal length , and the overall system length L is given by

_{= 2}(/_{3 +} /₄) = -°- (9) tanαr

It can be seen from Equations 7 and 8 that in many embodiments it is desirable to have a large diffractive optic divergence angle α to reduce the overall size of imaging portion 54 In practice, divergence angles α of 5 degrees to 10 degrees produce a relatively compact system

In addition to the real-time interferometer embodiment illustrated in FIG. 5. exemplary measurement system 50 of the present invention may be configured in a plurality of additional preferred embodiments each designed to carry out a particular type of real-time measurement, including a profilometer, a displacement sensor, and a wavefront sensor, each of which is descπbed in detail below.

Referencing FIG. 10, exemplary measurement system 50 of the present invention is configured to perform profilometry Exemplary profilometer 50 is configured to perform on-axis illumination and viewing, which is useful in obtaimng three-dimensional (3D) information of the object 60 Many mdustnes utilize profilometry in research and development, quality control, and manufactuπng, including the semiconductor and medical industπes

Exemplary transmit portion 52 includes the laser 98 which transmits the coherent light wavefront 102 A single polaπzing wavefront splitter (PBS) 120 is shared by both the transmit and image portions 52 and 54 for splitting the light wavefront 102 into the reference wavefront 56 and the object wavefront 58 and combining the reference wavefront 56 and the object wavefront 58 into the combined wavefront 66 In addition to PBS 120, exemplary image portion 54 of the profilometer includes the convex lens 116, the diffractive optical element 80, the colhmatmg lens 118 displaced from element 80 by its focal length, the phase-retardation/ - interference plate 96, and the CCD camera The computer 62 may be connected to both the transmit and image portions 52 and 54 to control the operation of the laser 98 and to receive imaging data 78 from the detector aπay 84

FIG 11 illustrates an exemplary commercial embodiment of the profilometer 50 of FIG 10 As shown, the laser 98 provides the light wavefront to an integrated measuπng unit 122 by means of an optical cable 124 The integrated measunng unit 122 includes a housing 126 in which the common PBS 120, as well as each of the elements of the image portion 54 shown in FIG 9, is received The integrated measuπng unit 122 transmits and receives the object wavefront 58, w h the detector aπay 84 providing image data to the computer 62 via a cable 128.

Referencing FIG 12, another exemplary commercial embodiment of the measurement system 50 of the present invention is shown and configured to function as a displacement sensor Displacement sensors are useful in measuπng, for example, the vibration or the strain of an object Exemplary transmit portion 52 of the displacement-sensor embodiment of the measuπng system 50 includes the laser 98 which transmits the coherent light wavefront to a fiber wavefront splitter 130 via an optical cable 132 The fiber wavefront splitter 130 splits the light wavefront into the reference wavefront 56, which is provided to the image portion 52 by an optical cable 134, and the object wavefront 58, which is provided to an optics unit 136 by an optical cable 138 The optical unit 136 of the transmit portion 52 includes the wavefront-expanding optics of the concave lens 106 and colhmatmg lens 108 (see FIG. 5) The operation of the displacement sensor illustrated in FIG 12 is analogous to that descπbed above

According to the displacement-sensor embodiment of the measurement unit 50, the separate and portable optics unit 136 mav be positioned relative to the test obiect 60 and the image portion 54 The object wavefront 58 can thus be directed to the object 60 from any angle or position

Referencing FIG 13, yet another exemplary commercial embodiment of the measurement svstem 50 of the present invention is shown and configured to function as a avefront sensor Wavefront sensors mav be used to measure, for example, pressure, temperature, or density gradients in transparent solids, liquids, or gases Exemplary transmit portion 52 may include an integrated transmit unit 140 with a housing 142, and exemplary image portion 54 may include an integrated receive unit 144 with a housing 146 Similar to the layout of the measurement system 50 shown in FIG 5, exemplary transmit unit 140 of the wavefront- sensor embodiment of the measuπng system 50 includes the laser which transmits the reference wavefront 56 to the integrated receive unit 144 via an optical cable 148 and the object wavefront 58 to the test object 60 The operation of the wavefront sensor illustrated in FIG 13 is analogous to that descπbed above For each of the foregoing embodiments of the measuπng system 50 of the present invention, a software application may be utilized by the computer 62 for data acquisition and processing The software application causes the computer 62 to acquire, process, analyze, and display data associated with the phase-shifted interferograms 74 Data acquisition may be accomplished by recording two interferograms for each measurement a reference mterferogram for the reference wavefront 56 and an object mterferogram for the object wavefront 58 Wrapped phase maps are calculated for each of the interferograms and then subtracted from each other The result is unwrapped to yield a map of the phase change between the reference and object interferograms Unwrapping is the procedure used to remove the modulo 2π ambiguity that is charactenstic of interferometπc data Phase may be calculated based on a single frame of data according to

Φ( , ) = tan ^l {[I₂(x,y ) - /,(x,y)] - [I₀(x,y) - I₂(x,y)], (10) where I₀, 1, , I₂, and /₃ are the respective intensities of each of the phase-shifted interferograms 74a-74d incident on the active surface 86 of the detector aπay 84 from the four sections 82a- 82d (I e , quadrants Q₀, Q,, Q,, and Q₃) as calculated m Equations 4a-4d abo\ e The vaπables x and v are the pixel coordinates To reduce noise in the image, spatial averaging mav be used to smooth the phase map while retaining a sharp transition at the 2π-0 phase step The spatially averages phase may be calculated using the following equations Φ(x.y) = tan^"1 {sum(x.veδ)[/₃(x.v) - 7,( ,v)l ÷ sum(x,veδ)[/₀( ,v) - I₂(x,y)]}, (11) where the sums are performed over the range of δ nearest neighbors. Increasing the number of averaged pixels improves smoothness of the phase map at the expense of spatial resolution; however, the sharpness of the phase discontinuity is retained, thereby permitting rapid phase unwrapping. The unwrapping of phase maps removes the discontinuous step and permits quantitative analysis of the images.

The number of pixels averaged may be selected by a user. For comparing two states of the system of to subtract background phase noise from the system, the phase difference mode can be used. Phase may be calculated according to: AΦ(x,y) = tan^l[X(x,y) ÷ Y(x,y)], (12) where:

X(x,y) = [Ib₃(x,y) - Ib,(x,y)} * [It_Q(x,y) - I ,y)} - [If(x,y) - It,(x,y)\ * [Ib₀(x,y) - Ib₂(x,y)],

Y(x,y) = [Ib_Q(x,y) - Ib₂(x,y)] * [It₀(x,y) - It₂(x,y)] + [Ib(x,y) - Ib,(x,y)} * [It₃{xy) - It_{(x,y)}, lb is the baseline image captured, and

It is the image captured for comparison. Spatial averaging can be accomplished using the formula:

ΔΦ(x,y) = tan^~'[sum(;,ye5)X(; >) ÷ sumQ,'eδ)y(.x:,j>)]. (13)

The three dimensional shape of an object can be determined by using two color interferometry. To do so, a first set of four phase-shifted interferograms is captured at a first wavelength λ, (i.e., Ib_n), and a second set of phase-shifted interferograms is captured at a second wavelength λ_: (i.e., It_n). The relative distance to the object (or range) is calculated by: , (i4,

where:

X(x,y) = [ _i(x,y) - Ib^x^^ilt^y - It₂(x,y))-[It₃(x,y) - It_](x,y)]*[Ib_Q(x,y) - Ib₂(x,y)] Y(x,y) = [Ib₀{x,y)-a₂(x,y)]*[It₀{x,y)-It₂(x,y)] + [n> {x,y)-Ibi(x,y)]*

Noise in the image can be significantly reduced using a weighted spatial average over neighboring pixels. This can be accomplished by:

where the sums are performed over the range of δ nearest neighbors. Because of the modelo 2π behavior of the arctangent function, the range is wrapped (ambiguous) beyond the so-called synthetic wavelength of

)}

( 16)

' Aπ Aλ

The well-known process of spatial phase unwrapping can be used to remove the discontinuous steps and to permit quantitative analysis of the images. Alternatively, it is possible to use multiple synthetic wavelengths and incrementally add the range distance as known in the art. The overall range is then given by:

R'(χ,y) = ∑ ^{RAλm iX}'^y) , (17) m rn where m is the number of wavelength steps used and R^_m is the range measured with a frequency tuning of Δλ/m Implied in this method is that no single measurement should have a phase value greater than 2π, which can place a restnction on the maximum size of the object that can be measured.

Referencing FIG. 14, a user interface 148 provided by the software of the invention is shown displaying a raw mterferogram 150 and wrapped phasemaps 152 from a central portion of the raw mterferogram 150. The raw interferogram 150 illustrates data 78 resulting from the measurement of a diffusion flame.

Those skilled in the art will understand that the preceding exemplary embodiments of the present invention provide the foundation for numerous alternatives and modifications thereto.

These other modifications are also within the scope of the present invention. Accordingly, the present invention is not limited to that precisely as shown and descnbed above

Claims

What is claimed is:

1. Apparatus for splitting a wavefront. said apparatus comprising: a wavefront-splitting element for: receiving a wavefront; splitting said wavefront into a plurality of sub-wavefronts such that each of said sub-wavefronts is substantially contiguous with at least one other said sub- wavefront; providing said plurality of sub-wavefronts; a sensing element for receiving said sub-wavefronts from said wavefront-splitting element.

2. Apparatus as claimed in claim 1 wherein said sensing element is a detector aπay.

3. Apparatus as claimed in claim 1 wherein said sensing element has a surface area, said plurality of sub-wavefronts being incident on a substantial portion of said surface area of said sensing element.

4. Apparatus as claimed in claim 1 wherein said wavefront-splitting element splits said wavefront into four sub-wavefronts.

5. Apparatus as claimed in claim 1 wherein said wavefront-splitting element includes a diffractive optical element.

6. Apparatus as claimed in claim 1 wherein said wavefront-splitting element and said sensing element are positioned with respect to each other so that an optical axis is defined between said elements and is substantially normal to said elements.

7. Apparatus as claimed in claim 6 wherein said wavefront-splitting element and said sensing element are positioned along said optical axis such that said sub-wavefronts are incident on said sensing element at substantially the same time. 8 Apparatus as claimed in claim 6 wherein said wavefront-splitting element splits said wavefront such that said sub-wavefronts diverge from said optical axis at about the same angle

9 Apparatus as claim 6 wherein each of said sub-wavefronts has an optical path defined between said wavefront-sphttmg element and said sensing element, said optical paths of said sub-wavefronts having substantially the same length

1 10 Apparatus as claimed in claim 6 further compπsing a colhmatmg lens positioned between said wavefront-splitting element and said sensing element, said colhmatmg lens for colhmatmg said sub-wavefronts

1 11 Apparatus as claimed in claim 10 wherein said colhmatmg lens has a focal length, said wavefront-splitting element and said sensing element are positioned from said colhmatmg lens by a distance substantially equal to said focal length

1 12. Apparatus as claimed in claim 10 further compπsing an input lens having a focal length and being positioned from said wavefront-sp ttmg element by a distance substantially

3 equal to said focal length

l 13 Apparatus as claimed m claim 12 further compπsing an aperture positioned from said

-> input lens by a distance substantially equal to said focal length

1 14 Apparatus as claimed in claim 1 wherein said wavefront includes a reference

2 wavefront and an object wavefront, said reference wavefront and said object wavefront being

3 orthogonally polanzed,

4 said wavefront-sphttmg element splitting said wavefront such that each of said sub-

5 wavefront includes said reference wavefront and said object wavefront

1 15 Apparatus as claimed in claim 14 further compπsing a phase-shifting interference

2 element positioned between said wavefront-sphttmg element and said sensing element, said phase-shifting interference element for

4 shifting the relative phase between said reference wavefront and said object wavefront of

5 said sub-wavefronts to yield a respective plurality of phase-shifted sub- wavefronts; interfering said reference and said object wavefronts of said phase-shifted sub-wavefronts to yield a respective plurality of phase-shifted interferograms; said phase-shifted interferograms being incident on said sensing element.

16. Apparatus as claimed in claim 14 wherein said phase-shifting interference element discretely shifts the relative phase between said reference wavefront and said object wavefront.

17. Apparatus as claimed in claim 14 wherein said phase-shifting interference element has a plurality of sections; each of said sections for receiving a respective one of said sub-wavefronts.

18. A method for splitting a wavefront. said method comprising the steps of: receiving a wavefront; and splitting said wavefront into a plurality of sub-wavefronts such that each of said sub- wavefronts is substantially contiguous with at least one other said sub-wavefront.

19. A method as claimed in claim 18 wherein said splitting step comprises the step of: splitting said wavefronts such that said sub-wavefronts are incident on a sensing element substantially simultaneously.

20. A method as claimed in claim 18 further comprising the step of: coUimating said sub-wavefronts.

21. A method as claimed in claim 20 further comprising the step of: sensing said sub-wavefronts after said coUimating step.

22. A method as claimed in claim 21 wherein said coUimating step comprises the step of: coUimating said sub-wavefronts such that said sub-wavefronts are incident on a substantial portion of a sensing element.

23. A method as claimed in claim 22 wherein said splitting step comprises the step of: splitting said wavefront such that said sub-wavefronts respectively have optical paths to said sensing element of substantially the same length.

24. A method as claimed in claim 18 wherein splitting step comprises the step of: splitting said wavefront into four sub-wavefronts.

25. A method as claimed in claim 24 further comprising the step of: sensing said sub-wavefronts with a single detector array.

26. A method as claimed in claim 25 wherein said splitting step comprises the step of: splitting said wavefront such that said sub-wavefronts are imaged with a single detector array.

27. A method as claimed in claim 18 wherein said splitting step comprises the step of: splitting said wavefront such that sub-wavefronts diverge from an optical axis of said wavefront at substantially the same angle.

28. A method as claimed in claim 18 further comprising the step of transmitting a first wavefront at a first wavelength to an object, wherein: said receiving step comprises the step of receiving said first wavefront from said object; and said splitting step comprises the step of splitting said first wavefront into a first set of sub-wavefronts such that each is substantially contiguous with at least one other said sub- wavefront; further comprising the step of sensing said first set of sub-wavefronts.

29. A method as claimed in claim 28 further comprising the step of: transmitting a second wavefront at a second wavelength to the object; receiving said second wavefront from the object; splitting said second wavefront into a second set of sub-wavefronts such that each is substantially contiguous with at least one other said sub-wavefront; and sensing said second set of sub-wavefronts.

30. A method as claimed in claim 29 further comprising the steps of: determining the distance to the object based on said first and second sets of sub- wavefronts.

31. Apparatus for measuring a spatial phase of wavefronts, said apparatus comprising: a wavefront-splitting element for: receiving a combined wavefront including a reference wavefront and an object wavefront, said reference wavefront and said object wavefront being orthogonally polarized; splitting said combined wavefront into a plurality of sub-wavefronts such that each of said sub-wavefronts is substantially contiguous with at least one other said sub-wavefront, each of said sub-wavefronts including said object wavefront and said reference wavefront, each of said sub- wavefronts having a phase; providing said plurality of sub-wavefronts; a phase-shifting interference element including a plurality of sections each for: receiving a respective one of said sub-wavefronts; shifting the relative phase between said reference and said object wavefronts of said sub-wavefront received thereby to yield a phase-shifted sub- wavefront; interfering said reference and said object wavefronts of said phase-shifted sub- wavefront to yield a phase-shifted mterferogram; providing said phase-shifted mterferogram; and a sensing element having a pixelated surface for receiving said phase-shifted mterferogram from each of said sections of said phase-shifting element.

32. Apparatus as claimed in claim 31 wherein each of said sections of said phase- interference shifting element shifts the relative phase of said sub-wavefront received thereby by a factor of a predetermined amount substantially equal to the quotient of 360 degrees and the number of sub-wavefronts in said plurality of sub-wavefronts.

33. Apparatus as claimed in claim 32 wherein said wavefront-splitting element splits said combined wavefront into four sub-wavefronts.

34. Apparatus as claimed in claim 31 wherein said sensing element is positioned at or near said phase-shifting interference element.

35. Apparatus as claimed in claim 31 wherein said combined wavefront is coherent light.

36. Apparatus as claimed in claim 31 wherein said wavefront-splitting element includes a diffractive optical element.

37. Apparatus as claimed in claim 31 wherein said sensing element includes a charged coupled device.

38. Apparatus as claimed in claim 31 wherein said phase-shifting interference element includes: a first plate including a quarter-wave plate and a blank plate, said quarter-wave plate for shifting said reference and object wavefronts by 90°, said blank plate for shifting said reference and object wavefronts by 0°; and a second plate including a first polarizing plate and a second polarizing plate, said first polarizing plate for interfering in-phase components of said reference and object wavefronts, said second polarizing plate for interfering out-of-phase components of said reference and object wavefronts.

39. Apparatus as claimed in claim 38 wherein: one of said sections is defined by said blank plate and said first polarizing plate; one of said sections is defined by said quarter-wave plate and said first polarizing plate: one of said sections is defined by said blank plate and said second polarizing plate; and one of said sections is defined by said quarter-wave plate and said second polarizing plate.

40. Apparatus as claimed in claim 39 wherein said first plate and said second plate are disposed in a parallel relationship.

41. Apparatus as claimed in claim 40 wherein said first plate and said second plate abut.

42. Apparatus for measuring spatial phase of wavefronts, said apparatus comprising: a transmit portion for providing a reference wavefront and an object wavefront, said object wavefront acting upon an object; an image portion including a combining element for receiving said reference wavefront from said transmit portion and said object wavefront from the object and for combining said reference and object wavefronts into a combined wavefront, said object wavefront and said reference wavefront being orthogonally polanzed with respect to each other, a wavefront-splitting element for splitting said combined wavefront into four sub- wavefronts such that each of said sub-wavefronts is substantially contiguous with at least one other said sub-wavefront, each of said sub- wavefronts having a phase, a phase-shifting interference element including four sections, said phase-shifting interference element being disposed with respect to said diffractive optical element so that said sub-wavefronts are respectively incident on said sections, each of said sections for shifting the relative phase of and for interfeπng said reference and object wavefronts of said sub-wavefront incident thereon to yield a phase-shifted mterferogram, and an imaging element for receiving said phase-shifted interferograms from said sections of said phase-shiftmg interference element, said imaging element being disposed with respect to said phase-retardant plate so that said phase-shifted interferograms are imaged substantially simultaneously

43 Apparatus as claimed in claim 42 wherein said transmit portion includes a laser for providing coherent light

44 Apparatus as claimed in claim 43 wherein said transmit portion further includes a beam splitting for splitting said coherent light into said reference wavefront and said object wavefront

45 Apparatus as claimed in claim 42 wherein said wavefront-sp ttmg element includes a diffractive optical element

46 Apparatus as claimed in claim 42 wherein said imaging element includes a charge coupled device 47 Apparatus as claimed in claim 42 further compπsing a computer connected to said imaging device for processing said phase-shifted interferograms

48 A method for measuπng spatial phase of wavefronts, said method compπsing the steps of splitting a combined wavefront into four sub-wavefronts such that each of said sub- wavefronts is substantially contiguous with at least one other said sub-wavefront, said combined wavefront including a reference wavefront and an object wavefront orthogonally polaπzed with respect to each other, each of said sub-wavefronts having a phase; shifting the relative phase of said reference and object wavefronts of each said sub- wavefront, interfeπng said reference and object wavefronts of each said sub-wavefront, and imaging each of said sub-wavefronts.

49 A method as claimed in claim 48 wherein said imaging step compπses the step of. imaging each of said sub-wavefronts substantially contiguously on a single sensing element

50 A method as claimed in claim 49 wherem said imaging step compπses the step of: imaging each of said sub-wavefronts on multiple imaging elements configured to function as a single element

51 A method as claimed in claim 48 further compπsing the step of generating coherent light, splitting said coherent light into said reference wavefront and said object wavefront; and transmitting said object wavefront to an object under measure

52 A method as claimed in claim 48 wherein said shifting step compπses the step of discretely shifting the relative phase of said reference and object wavefronts of each said sub-wavefront

53 A method for measuπng a profile of an object, said method compπsing the steps of generating a plurality of wavefronts each having a unique wavelength, each said wavefront includes a reference wavefront and an object wavefront. transmitting said object wavefront of each said wavefront to an object, combining each said object wavefront from the object with said reference wavefront of same wavelength to yield a respective plurality combined wavefronts, splitting said combined wavefronts into a respective sets of sub-wavefronts such that each said sub-wavefront is substantially contiguous with at least one other said sub-wavefront of the same set, each said sub-wavefront includes said reference wavefront and said object wavefront, imaging said sets of sub-wavefronts; and determining distance to the object based on said imaged sets of sub-wavefronts

54. A method as claimed in claim 53 wherein said splitting step compπses the steps of shifting the relative phase between said reference wavefront and said object wavefront of said sub-wavefronts to yield a respective plurality of phase-shifted sub-wavefronts, and interfeπng said reference and said object wavefronts of said phase-shifted sub-wavefronts to yield a respective plurality of phase-shifted interferograms, wherein said imaging step compπses the step of imagmg said phase-shifted interferograms; and said determining step compπses the step of determining distance to the object based on said phase-shifted interferograms.

55. Apparatus for measuπng a profile of an object, said apparatus compπsing a plurality of wavefronts each having a wavelength, each said wavefront includes a reference wavefront and an object wavefront, said object wavefront of each said wavefront being incident on an object, a wavefront-combinmg element for receiving said object wavefronts from the object and said reference wavefronts and for combimng each said object wavefront with said reference wavefront of same wavelength into a combined wavefront, a wavefront-sphttmg element for receiving each said combined wavefront; and splitting each said combined wavefront into a set of sub-wavefronts such that each of said sub-wavefronts is substantially contiguous with at least one other said sub-wavefront of the same set, an imaging element for receiving from said wavefront-splitting element and imaging said sets of sub-wavefronts; and l ^ a computer connected to said imaging element for determining distance to the object

16 based on said sets of sub-wavefronts

1 56 Apparatus for splitting a wavefront including orthogonally polaπzed reference and

2 object wavefronts. said apparatus compπsing

3 a wavefront-sp ttmg element for splitting the wavefront into a plurality of sub-

4 wavefronts such that each of said sub-wavefronts is substantially contiguous with at least one ^ other said sub-wavefront and that each of said sub-wavefront includes the reference wavefront

6 and the object wavefront, and

7 a phase-shifting interference element for discretely shifting the relative phase between the

8 reference wavefront and the object wavefront of each of said sub-wavefronts to yield a plurality

9 of phase-shifted sub-wavefronts

1 57 Apparatus as claimed in claim 56 further compπsing a sensing element for receiving

2 said plurality of phase-shifted sub-wavefronts from said phase-shifting interference element

1 58. A method for splitting a wavefront including orthogonally polaπzed reference and

2 object wavefronts, said method compπsing the steps of.

3 splitting the wavefront into a plurality of sub-wavefronts such that each of said sub-

4 wavefronts is substantially contiguous with at least one other said sub-wavefront, and

5 discretely shifting the relative phase between the reference wavefront and the object

6 wavefront of each of said sub-wavefronts to yield a plurality of phase-shifted sub-wavefronts