Abstract:
A method and apparatus for providing information associated with at least one portion of a sample can be provided. For example, at least one wavelength of electro-magnetic radiation provided on a sample can be encoded to determine at least one transverse location of the portion. A relative phase between at least one first electro-magnetic radiation electro-magnetic radiation being returned from a sample and at least one second electro-magnetic radiation returned from a reference can be obtained to determine at least one relative depth location of the portion. Further, the information of the portion can be provided based on the transverse location and the relative depth location. For example, the information can be depth information and/or three-dimensional information associated with the portion of the sample.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application claims the benefit under 35 U.S.C. §119(e) of Provisional Application No. 60/525,684 filed Nov. 28, 2003. 

   STATEMENTS REGARDING FEDERALLY SPONSORED RESEARCH 
   Not applicable. 
   FIELD OF THE INVENTION 
   This invention relates generally optical imaging and more particularly to a method and apparatus for performing three-dimensional surface measurements. 
   BACKGROUND OF THE INVENTION 
   As is known in the art, optical techniques for surface profilometry are commonly performed using interferometric measurements. Analyzing the interference fringe pattern formed by overlap of a reflected wave from an optically smooth surface with a reference wave, enables surface profile measurements with high accuracy. Projecting an interference fringe pattern on an object surface is effective for probing rough surfaces. High-resolution, point-by-point measurements of rough surfaces have been demonstrated using a long coherence length source with a Fizeau interferometer and with a broadband source. 
   White-light interferometry is capable of simultaneously imaging large field of views by scanning only the path length of a reference arm. In this approach, light reflected from the surface interferes with a reference wave to form a speckle pattern on a camera. When the reference optical path length is scanned, each individual speckle exhibits an intensity modulation. The surface height is determined at the maximum point of the modulation envelope. White-light interferometry is an extremely robust technique, allowing for high resolution imaging in three dimensions with a large field of view. 
   Depth resolved imaging with a large, three-dimensional field of view is more challenging when utilizing small diameter flexible imaging probes such as borescopes, laparoscopes, and endoscopes. Confocal imaging through a fiber-bundle using a lens with a high numerical aperture is one solution to this problem. The three-dimensional field of view for these devices, however, is limited to less than a few millimeters due to the small objective lens clear aperture and low f-number required for high-resolution optical sectioning. 
   Other methods, such as stereo imaging and structured illumination have been proposed. These methods all require additional hardware for the probe, increasing the size, cost, and complexity of these devices. 
   SUMMARY OF THE INVENTION 
   In accordance with the present invention, an imaging technique includes encoding a transverse location of an object by wavelength and encoding an axial or depth coordinate of each point on the object by phase. With this particular arrangement, a technique for generating two-dimensional images of an object as well as surface profile measurements of the object is provided. By combining the surface profile with the two dimensional image, a three-dimensional spectrally-encoded imaging technique is provided. Encoding the depth (or height) information is accomplished by changing a phase length of a reference path and detecting phase differences in signals reflected from the surface of the object each time the phase length of the reference path is changed. The phase length of the reference path establishes a coherence length (CL) at the surface being measured. Thus by changing the phase length of the reference path, a different coherent length is established. By detecting phase differences in signals reflected from the surface of the object each time the phase length of the reference path is changed, the height at different points along the surface can be detected. 
   In one embodiment, a surface profile of an object is measured by utilizing the technique of the present invention in conjunction with a probe of the type described in published PCT application number WO 02/038040 A2 (now pending in the U.S. Patent and Trademark Office as application Ser. No. 09/709,162 filed Nov. 10, 2000) said application being assigned to the assignee of the present invention. The techniques of the present invention can thus be used in conjunction with techniques for performing a miniature endoscopy with a high number of resolvable points as described in the aforementioned U.S. application Ser. No. 09/709,162. The aforementioned U.S. application Ser. No. 09/709,162 describes a technique in which a broadband light source and a diffraction grating are used to spectrally encode reflectance across a transverse line within a sample and a two-dimensional image is formed by scanning this spectrally encoded line. Since this method only requires a single optical fiber, it is capable of enabling two-dimensional imaging through a small diameter, flexible probe. By utilizing the techniques of the present invention, a three-dimensional spectrally-encoded image can be provided. In three-dimensional spectrally-encoded imaging, the transverse location of the image is encoded by wavelength and the axial or depth coordinate of each point is encoded by phase. 
   Using the phase-sensitive spectrally encoded imaging techniques of the present invention, volume data can be acquired through a single optical fiber. The present invention thus makes possible three-dimensional macroscopic imaging within the confines of a miniature, flexible probe. Data measured using techniques of the present invention has clearly demonstrated the potential of this technology for probe-based imaging for industrial applications. It should be appreciated, however, that the phase-sensitive spectrally encoded imaging technique of the present invention can also be used in medical and other applications. For example, phase-sensitive spectrally encoded imaging technique of the present invention can be used to visualize multiply scattering tissues in three-dimensions for biomedical applications. 
   In accordance with a further aspect of the present invention, a method for measuring a surface of a specimen includes operating a beam provided as spectrally-encoded points of a spectrum, focusing the beam onto a specimen disposed in a sample arm, scanning the beam in a first direction across the specimen to create a two dimensional image, changing a path length of a reference path and generating an interference pattern with a reflection from light from the sample and reference arms. The signals from the sample and reference arms are then directed to a detection arm where they are combined. With this particular arrangement, a method for detecting a height of a surface is provided. In order to obtain a surface profile of the specimen, the propagation path length of the reference path is changed and interference patterns at each changed path length are used to provide the height information. 
   In accordance with a still further aspect of the present invention, a system includes a source, a splitter/combiner having a first port coupled to the source, having a second port coupled to a reference path, having a third port coupled to a sample path and having a fourth port coupled to a detection path. The sample path includes a dispersive element which provides a spectrally encoded focal plane. The reference path includes a path length change device which is adapted to change a propagation path length of light propagating in the reference path. With this particular arrangement, system for three-dimensional imaging is provided. By changing the propagation path length of the reference path, a phase-sensitive spectrally encoded imaging system is provided. The phase information contained in signals reflected form the specimen in the sample path can be used to provide depth (height) information of a surface. Thus, both transverse and depth information can be transmitted through a single-mode optical fiber, allowing such a system to be incorporated into a miniature probe. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing features of this invention, as well as the invention itself, may be more fully understood from the following description of the drawings in which: 
       FIG. 1  is a block diagram of an apparatus for three-dimensional spectrally encoded imaging; 
       FIG. 2  is a schematic diagram of an exemplary embodiment of an apparatus for three-dimensional spectrally encoded imaging; 
       FIG. 2A  is an enlarged view of the sample in  FIG. 2  taken around lines  2 A- 2 A in  FIG. 2 ; 
       FIG. 2B  is a plot of an interference pattern provided from the system of  FIG. 2 ; 
       FIG. 2C  is a plot of a measured surface profile; 
       FIG. 3A  is an image of a doll&#39;s face obtained using white light illumination and a charge coupled device (CCD) camera; 
       FIG. 3B  is a conventional spectrally encoded-two-dimensional image of a doll&#39;s face obtained by blocking a reference arm in the system of  FIG. 2 ; 
       FIG. 3C  is a gray scale image which shows a surface height obtained by determining the location of a maximum speckle intensity difference along an axial (z) axis; 
       FIG. 3D . is a doll&#39;s face represented by surface 3-D rendering; 
       FIG. 4A  is plot of sagital (y-z) section from a data set; 
       FIG. 4B  is a plot of a doll&#39;s actual profile; and 
       FIG. 5  is a flow diagram which illustrates an exemplary technique for three-dimensional spectrally encoded imaging. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Referring now to  FIG. 1 , a three-dimensional spectrally encoded imaging system  10  includes a source  12  coupled to a beam splitter  14  at first port  14   a . It should be appreciated that beam splitter  14  may be implement using any techniques now known or later discovered. For example, splitter  14  may be provided as a fiber optic beam splitter, a free space splitter or a glass plate splitter. 
   The system  10  includes a reference path  16  coupled to a second port  14   b  of the beam splitter  14  and a sample path  18  coupled to a third port  14   c  of the beam splitter  14 . The reference path  16  includes a path-length change device  17 . Path-length change device  17  is adapted to change a propagation path length of light propagating in the reference path  16 . The device  17  allows the optical path length of the reference arm  17  to be changed in a controlled and known manner. In some embodiments, device  17  may be provided such that it can introduce a change in the group delay of optical signals propagating in path  16 . Such a change in group delay may or may not be accompanied by a physical change in the optical path length of the reference arm. Changes in group delay in optical signals may be desired to reduce speckle artifacts and possibly result in increased system sensitivity. It should be appreciated that in embodiments in which the reference arm does not include a path-length change device  17 , then the depth at a single spot along a scan line of a sample may be computed. 
   The sample path  18  has disposed therein a sample  19  (also referred to herein as a specimen  19 ). The sample path  18  may optionally include one or more of a dispersive elements  18   a , a beam focusing device  18   b  and a scanning element (or more simply, a scanner)  18   c  as described in co-pending application Ser. No. 09/709,162. The dispersive element may be provided, for example, as a diffraction grating and in response to a signal fed thereto from the beam splitter, the dispersive element disperses the signal into a spectrum in an image plane. The dispersive element may also be provided as a dispersive prism, a fiber grating, a blazed grating, a grism, a holographic lens grating or any other element which provides angular separation of light signals propagating at different wavelengths. That is, in response to light signals incident thereon, the dispersive element directs different wavelengths in different directions or, stated differently, the dispersive element disperses the spectrum of the light signal provided thereto to provide a spectrally encoded focal plane. 
   The beam focusing device  18   b  focuses individual spectrally-encoded points toward the sample  19  disposed in the sample path  18 . The beam focusing device may be provided, for example, from an optical system such as a lens system. 
   The scanning element  18   c , scans the spectrally-encoded beam across the specimen  19  to produce a two-dimensional image. It should be understood that the positions of the dispersive device  18   a  and beam focusing device  18   b  are selected in accordance with the requirements and needs of the particular application. 
   It should be appreciated that in some embodiments, it may be desirable to provide the dispersive element  18   a  the scanner  18   c  and the beam focusing device  18   b  as separate elements. For example, the dispersive element  18   a  may be provided as a diffraction grating, the beam focusing device  18   b  may be provided as a lens disposed to focus the beam on the specimen and the scanner  18   c  may be provided as a galvanometric scanner disposed to direct light to and from the diffraction grating. The dispersive element  18   a , scanner  18   c  and lens system  18   b  may be combined in a single housing. 
   In other embodiments, however, it may be desirable to provide the dispersive element  18   a , the scanner  18   c  and the lens system  18   b  as a single integrated element. Alternatively still, the functions performed by the dispersive element  18   a , scanner  18   c  and lens system  18   b  may be provided from a single device. 
   In order to obtain a surface profile of the specimen  19 , the propagation path length of the reference path  16  is changed. In one embodiment, the path length of the reference path  16  is changed by providing the device  17  as a movable reflective device disposed at the end of the reference arm. Movement of the reflective device changes the path length of the reference arm  16 . In one embodiment, the movable reflective device can be provided as a mirror disposed on a movable platform at the end of the reference arm  16 . Movement of the platform (and thus the mirror) changes the optical path length of the reference arm  16 . Other techniques for changing the path length of the reference path, may of course, also be used. 
   The source  12  emits a light signal to the beam splitter  14  which splits the light and provides a first portion of the light signal to the reference arm  16  and a second portion of the signal to the sample arm  18 . The light impinges upon device  17  and sample  19  in the reference and sample paths  16 ,  18  respectively and is reflected back toward ports  14   b ,  14   c  of splitter/combiner  14 . Ideally, the splitting ratio of the splitter/combiner  14  is selected such that an equal amount of reflected power is received at each of the splitter ports  14   b ,  14   c.    
   The reference line can also include an optical attenuator (not shown in  FIG. 1 ) having an attenuation setting selected to adjust the strength of a reference beam reflected from a reflective device to increase (and in some cases maximize) the contrast of an interference pattern generated from the reflected reference beam and the reflected beam from the sample arm. 
   Signals reflected from the reference and sample arms  16 ,  18  are coupled to a detector arm  20  via splitter/combiner circuit  14 . The detector arm  20  receives signals fed thereto and detects depth. As mentioned above, it is possible for detector arm  20  to analyze a pattern provided thereto without scanning the reference arm. Detector  21   b  can thus determine depth information at a single point in an image, along a line in an image or in an entire two-dimensional image (i.e. to provide a three-dimensional image). 
   In one embodiment, the detector receives time-domain measurements and provides depth information by using a Fourier transform (e.g. an FFT). In another embodiment, detector arm  20  includes a dispersive device  21   a  and a detector  21   b.  In this case, the dispersive element disperses the wavelengths of an optical signal provided thereto and the dispersed spectrum is detected by the detector  21   b . The dispersive device  21   a  may be provided from a number of devices including but not limited to a grating or a dispersive prism. Similarly, the detector  21   b  may be provided from a number of devices including but not limited to a charge coupled device (CDD) camera. 
   Referring now to  FIG. 2 , a system  30  for performing three-dimensional spectrally encoded imaging includes a source  32  having a relatively broad bandwidth coupled to a single mode fiberoptic interferometer  34  at first port  34   a.  A reference path  36  is coupled to a second port  34   b  of the interferometer  34 , a sample path  42  is coupled to a third port  34   c  of the interferometer  34  and a detection path  52  is coupled to a fourth port  34   d  of the interferometer  34 . 
   In one embodiment, the source  32  is provided as abroad-bandwidth titanium-sapphire source having a center wavelength of 860 nanometers (nm) and an FWHM bandwidth of 200 nm while the interferometer  34  is provided as a 50/50 Michelson interferometer and the sample arm  42  includes a diffraction grating (600 lines/mm) to disperse the spectrum in the horizontal image plane (x-axis). A lens  48  (f=75 mm, beam diameter=1 mm) focuses the individual spectrally-encoded points onto a specimen  50 . 
   The beam was scanned in the vertical dimension (y-axis) by a galvanometric scanner (60 Hz)  44  to create a two-dimensional image. These parameters resulted in a spatial transverse resolution of approximately 40 μm. The image was comprised of approximately 585×585 resolvable points; each transverse spot contained a bandwidth of 0.34 nm. The overall power on the sample was 10 mW. 
   In order to obtain surface profiles, the path length of the reference arm  36  was controlled by moving a mirror  40  mounted on a translation stage. The power of the reference beam was attenuated using a neutral density (ND) filter  308  to maximize the contrast of the interference pattern. 
   Referring now to  FIGS. 2 and 2A , by placing the mirror in a first location  41   a , the reference arm is provided having a first path length. This path length results in a first coherence length (CL)  41   a.  Reflections from the surface of the sample  50  at this coherence length represent a first depth. When the mirror is moved to a second location  41   b , the reference arm is provided having a second path length in this example, the second reference arm path length is longer than the first reference arm path length. This path length results in a second coherence length (CL)  41   b . Reflections from the surface of the sample  50  at this second coherence length represent a second depth. Similarly, when the mirror is moved to a third location  41   c , the reference arm is provided having a third path length in this example, the third reference arm path length is longer than the first and second reference arm path lengths. The third path length results in a third coherence length (CL)  41   c . Reflections from the surface of the sample  50  at this second coherence length represent a third depth. In this manner, the depth information of the surface sample is provided. 
   Although this example utilizes only three coherence lengths, it should be appreciated that the any desired number of coherence lengths can be used. The particular number of coherence lengths to use will depend upon the particular application. Its should also be appreciated that while the coherence lengths are changed by moving a mirror to adjust a phase length of the reference path, any technique which effectively changes the coherence length such that phase can be used to determine surface depth of a sample can also be used. 
   Referring again to  FIG. 2 , at the detection path  52 , the signals from the sample and reference arms are combined and detection is performed. In one embodiment, the fields from the sample and reference arms  36 ,  42  were combined and spatially dispersed by a diffraction grating  56  (600 lines/mm) and a lens  58  (f=60 mm) onto a charge-coupled device (CCD) array  60 . It should be appreciated that the focusing function provided by lens  58  could also be provided at the output of the combiner (i.e. output  34   d ) or at the input to the detector arm. For example, if a fiber optic cable were used to couple interferometer  34  to detector  52 , then the focusing function could be accomplished at the detector end the of fiber optic cable. Vertical scanning was performed by another galvanometric scanner  54  which was synchronized with the sample arm y-axis scanner. The resulting interference pattern was viewed on a display  62  (e.g. a monitor) in real time, digitized, and stored. 
   At each horizontal line on the CCD, the intensity is given by:
 
 I (ω)=| E (ω)+ E   0 (ω)| 2 =2 |A   0 (ω)| 2 ·{1−cos[φ(ω)−φ 0 (ω)]},  (1)
 
where E(ω)=A(ω) exp(iφ 0 (ω)) and E 0 (ω)=A 0 (ω)exp(iφ(ω) are the spectra reflected from the sample and the reference arms, respectively. For simplicity, it is assumed that the spectral amplitudes from the sample and reference arms are real and equal, A(ω)=A 0 (ω). Algorithms for extracting phase difference from a spectral interference signal between two waves with continuous and smooth phases are well known. Spectral phase measurements were performed mainly for dispersion measurements using broadband sources and white light. Using a Fourier-limited reference field (φ 0 (ω)=0) with a given delay τ between the reference and the signal fields, the interference term in Eq. (1) is simply cos[φ(ω)−ωτ]. With a straight forward algorithm, the spectral phase can be unambiguously extracted from the interference pattern I(ω). In one configuration, the depth or surface height h at each point is given by h=c·φ(ω)/(2ω), where c is the speed of light.
 
   To demonstrate the ability of this scheme to probe optically smooth surfaces, a plano-convex lens (Melles-Griot, f=1 m, BK7 glass) was placed in the sample arm (e.g. lens  48  was provided as a plano-convex lens), with its convex surface facing toward the grating. In order to match the optical path length over the entire field of view, an additional two lenses, in a confocal configuration, were placed at the sample arm between the scanner and the diffraction grating. A delay of 2.18 ps (654 μm) was introduced between the sample and the reference arms. The interference pattern for this setup is shown in  FIG. 2B . The surface profile was obtained using the algorithm described in “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467 (1995) L. Lepetit, G. Chériaux, and M. Joffre.  FIG. 2A  is a two-dimensional spectrally-encoded interferogram provided from the curved surface of a lens (f=1 m). 
   Referring Now to  FIG. 2C , a measured surface profile along a horizontal line is plotted as a solid line  66  in  FIG. 2C . For comparison, the spherical curve of the lens&#39;s radius, calculated according to R=f·(n−1), (n=1.5187), is plotted as a dashed line  68  ( FIG. 2C ).  FIG. 2C  thus illustrates that the profile of the lens (solid line  66 ) measured using the described system agrees with a calculated profile (dashed line  68 ). The differences between the measured and the calculated profiles can be attributed to the loss of fringe contrast on the right side of the frame and due to low fringe density on the left side. When the sample contains steep local slopes, the fringe pattern became too dense to be resolved by the imaging system. This limitation prevented the system from measuring optically smooth surfaces with slopes greater than λ/d, where λ is the wavelength and d is the transverse spot size. 
   In most industrial and medical applications, the specimen surface is not optically smooth, but contains many surface irregularities. When the surface is rough and the diffraction-limited point-spread function of the imaging system is broad in comparison to the microscopic surface variations, the interference between the sample and the reference is manifested by a granular speckle pattern. This pattern has a characteristic speckle size that matches the system&#39;s point-spread function. The depth of the speckle pattern along the z axis is defined by the coherence length,
 
 CL= ( c·N )/Δω  (2)
 
where N is the number of resolvable points along the x-axis (wavelength) and Δω is the total source bandwidth. Unlike white-light interferometry, where the coherence length is given by CL=c/Δω and can be as short as a few microns, here the coherence length is N times larger, since it is determined only by the spectral width of each spectrally encoded spot. Throughout this work, the coherence length (310 μm) was smaller than the confocal parameter (2.7 mm) and therefore determined the axial resolution. The large depth of focus allowed imaging over a range equivalent to the confocal parameter by scanning only the optical path length of the reference arm.
 
   To demonstrate the ability of a 3-D spectrally-encoded imaging apparatus to measure the profile of rough surfaces, the face of a small plastic doll was imaged. The doll&#39;s face is shown in  FIG. 3A . The image of the doll&#39;s face in  FIG. 3A  was obtained using white light illumination and a standard CCD camera. It should be noted that the scale bar in  FIG. 3A  represents 4 mm while the scale bars in  FIGS. 3B-3D  represent 1 mm. 
   In  FIG. 3B , the standard spectrally encoded-two-dimensional image is shown. The surface height, measured by 3D spectrally encoded imaging, is represented as a gray scale image, where z values closer to the probe have a higher pixel intensity. This image is obtained by blocking a reference arm in the system of  FIG. 2 . When the light returned from the reference arm was allowed to interfere with that of the sample arm, a speckle pattern was observed in portions of the image. A full three-dimensional data set was acquired by capturing 45 frames as the reference arm path length was scanned in steps of 100 μm. The natural logarithm of the absolute value of the difference between consecutive frames was calculated, followed by moderate volumetric smoothing (kernel=3×3×3 pixels). The surface height was obtained by determining the location of the maximum speckle intensity difference along the axial (z) axis (displayed as a gray scale image in  FIG. 3C ).  FIG. 3D  corresponds to a surface rendering of the dolls face using the data shown in  FIG. 3C . 
   Referring now to  FIGS. 4A and 4B , for estimating the experimental depth resolution a sagital (y-z) section was plotted ( FIG. 4A ) from the data. The sagital section was placed next to the actual doll&#39;s profile ( FIG. 4B ). The measurement revealed an axial resolution of approximately 330 μm (FWHM of the coherence envelope), which is in reasonable agreement with the predicted axial resolution of 310 μm. The scale bar (visible in  FIG. 4B ) is 1 mm. 
   Three dimensional (3-D) spectrally-encoded imaging can be used in many configurations to suit specific applications. For example, this method is capable of measuring a surface within a volume of 50×50×30 millimeters (x, y, z respectively) with, typically, 200×200×280 resolution points (250 μm transverse spot-size and 107 μm axial resolution). Using a CCD camera (10,000 frames per second) and a rapidly scanning optical delay line in the reference arm the three-dimensional data set could be captured and displayed in real time (30 frames per second). 
   Referring now to  FIG. 5 , a technique for producing a three-dimensional image begins by illuminating a line on a sample and then scanning a reference line as shown in processing blocks  70 ,  72 . Next, the depth information is determined as shown in block  74 . In one embodiment, this is achieved by measuring the number of fringes within a spot on the sample (e.g. analyzing the number of fringes using a fast Fourier Transform (FFT) or other technique) and translating this information to depth information. As shown in decision block  76 , if there are no more lines on the sample to detect, then processing ends. Otherwise a next line on the sample is selected and illuminated as shown in blocks  78 ,  80  and blocks  72 - 78  are repeated until the imaging process is complete. 
   In summary the techniques and apparatus described above can be used to provide three-dimensional macroscopic images using a phase-sensitive spectrally encoded imaging technique. Using the techniques of the present invention, volume data can be acquired through a single optical fiber without any additional modifications to the spectrally-encoded imaging device. These features make three-dimensional imaging within the confines of a miniature, flexible probe possible. 
   Although only a few exemplary embodiments of this invention have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of this invention. Accordingly, all such modifications are intended to be included within the scope of this invention as defined in the following claims. It should further be noted that any patents, patent applications and publications referred to herein are incorporated by reference in their entirety.