Abstract:
The present invention relates to a full-field reflection phase microscope. In a preferred embodiment, the invention can combine low-coherence interferometry and off-axis digital holographic microscopy (DHM). The reflection-based DHM provides highly sensitive and a single-shot imaging of cellular dynamics while the use of low coherence source provides a depth-selective measurement. A preferred embodiment of the system uses a diffraction grating in the reference arm to generate an interference image of uniform contrast over the entire field-of-view albeit low-coherence light source. With improved path-length sensitivity, the present invention is suitable for full-field measurement of membrane dynamics in live cells with sub-nanometer-scale sensitivity.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims the priority to U.S. Application No. 61/436,026, filed Jan. 25, 2011. The entire contents of the above application being incorporated herein by reference. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    This work was funded by the National Center for Research Resources of the National Institutes of Health (P41-RR02594-18), the National Science Foundation (DBI-0754339). 
     
    
     BACKGROUND OF THE INVENTION 
       [0003]    Bio-microrheology is the quantitative study of mechanical properties of live cells. Variations in mechanical properties are intrinsic indicators of ongoing cellular processes such as increase in elasticity of certain cancer cells, change of membrane stiffness in malaria-infected red blood cells, and changes in cellular adhesion, for example. The measurement of rheological properties of cell membranes is advantageous since it may also indirectly provide information on the internal structures of cell. A number of different techniques exist to assess membrane rheological properties of live cells. These include atomic force microscopy (AFM), optical and magnetic tweezers, pipette aspiration, electric field deformation, and full-field transmission phase microscopy. Many of these methods use large deformations that can lead to a non-linear response. For point-measurement techniques such as AFM, the time scales to probe large surface areas of a cell membrane are in minutes, preventing the study of high-speed cell membrane dynamics over a wider surface area. Transmission phase microscopy has been successfully utilized to measure membrane rheological properties of red blood cells that have 2-D bilayer cytoskeleton. However, most types of cells have complicated 3-D internal cellular structures, rendering most of the above techniques unsuitable as they probe a combination of membrane as well as bulk properties of cells that are difficult to decouple. 
         [0004]    Thus further improvements are needed in the field of phase microscopy for measuring complex biological systems as well as other applications in scientific and industrial metrology. 
       SUMMARY OF THE INVENTION 
       [0005]    The present invention relates to full-field reflection-based phase microscopy. Preferred embodiments of systems and methods of the present invention involve the measurement of structures having small features, such as the plasma and/or nuclear membrane dynamics, in general cell types. Due to the 3-D cytoskeleton, these cells are much stiffer than red blood cells, for example, indicating that corresponding membrane fluctuations are much smaller than can be detected with transmission phase microscopy. In this respect, reflection-based optical methods can provide a 2n/Δn advantage in measurement sensitivity over the transmission-based optical techniques. Preferred systems and methods utilize a portion of light from a light source to interfere with light that is also used to illuminate the material to be measured. A selected diffraction order of the light from the light source is coupled to a two dimensional detector array along with an image of a selected field of view, or image field, of the material. This provides a full field interferogram of the material. 
         [0006]    Low-coherence interferometry is used to sample the reflection signal within a material at a selected depth of interest. In the past, both spectral domain as well as time domain optical coherence tomography (OCT) based implementations of reflection phase microscopy have had limitations that limit their usefulness. Previously, a quantitative phase microscope based on spectral domain OCT and line-field illumination have been used, for example. The line-field reflection phase microscope used low-coherent illumination and confocal gating to successfully obtain the surface profile of a cell membrane with sub-nanometer axial resolution. Using the line-field approach, a 1 kHz frame rate with more than hundred data points along the line illumination was demonstrated. The first full-field phase sensitive OCT was reported using swept-source OCT configuration, which required 1024 wavelength encoded images to make a volume image. However, the acquisition rate (25 ms integration time per wavelength) was not sufficient to observe cellular dynamics. 
         [0007]    Prior attempts using a time-domain reflection phase microscope based on phase shifting interferometry limited time resolution (1.25 sec) due to the need for taking multiple images. There was an attempt to use off-axis digital holography with a low-coherence source to take a full-field phase image in a single shot, but the tilting of the reference mirror caused uneven interference contrast and thereby impeded full-field imaging. 
         [0008]    Thus, the present invention provides the first single-shot full-field reflection phase microscope based on a low-coherence light source and off-axis interferometry. The low coherence source can be a pulsed laser, a superluminescent diode or a temporally and/or spatially low coherent source, such as a metal halide lamp (incoherent). The system provides the wavefront tilt in the reference beam such that it interferes with the sample beam across the whole field-of-view (or imaging field). The single-shot interferograms are processed to determine the optical phase of the beam reflected back from the sample being measured, providing a surface profile without the need for raster or 1-D scanning. Since single-shot interferograms are required to retrieve sample phase, the amount of light returning from the cell and camera frame rate define the speed of the surface imaging. Thus, the present invention provides 1 kHz full-field imaging to observe the membrane motion related to the thermal fluctuations in HeLa cells, for example. 
         [0009]    A preferred embodiment of the invention provides a quantitative reflection phase microscope based on en-face optical coherence tomography and off-axis digital holography. The system can utilize a diffraction grating in the reference arm to provide the desired angular tilt to the reference beam for off-axis interferometry. The full-field illumination allows single-shot phase measurement of multiple points on the surface of interest and enables the use of a self phase-referencing method to reject common-mode noise occurring in interferometric systems using a separate reference arm. In this full-field reflection phase microscope, the self-phase referencing suppressed phase noise down to as low as 21(pm/√{square root over (HZ)}). With such high phase sensitivity, the system can resolve thermal motion of the cell surface in the field of view, which can be on the order of 100 picometers to 150 nanometers, for example. An application of the full-field reflection phase microscope is to use plasma or membrane fluctuations to estimate the mechanical properties of cell membranes or the bulk visco-elastic properties of the cell cytoskeleton or nucleoskeleton. These variations in cell&#39;s mechanical properties can serve as non-invasive biomarker to measure the pathophysiology of general cell types. The system can also provide full-field and multi-cell imaging of cellular electromotility, including cell membrane motion driven by the action potential in single mammalian cells. 
         [0010]    Preferred embodiments of the invention can be used for applications relating to industrial metrology, such as the fabrication of small devices, such as integrated circuits. 
     
    
     
       DESCRIPTION OF THE DRAWINGS 
         [0011]      FIGS. 1A-1B  include a schematic of full-field single-shot reflection phase microscope using a grating, spatial filter, and Ti:sapphire light source where SMF: single mode fiber, Li: i th  spherical lens, BSi: i th  beam splitter, G: diffraction grating, Si: i th  spatial filter; and where  FIG. 1B  shows an interferogram with a flat surface as the sample. 
           [0012]      FIGS. 2A-2E  include a surface profile of a 40 micron diameter polystyrene microsphere measured using the single-shot full-field reflection phase microscope;  FIG. 2A  shows a raw interferogram,  FIG. 2B  shows amplitude component of the 2-dimensional Fourier transform of  FIG. 2A ;  FIG. 2C  shows a spatially filtered image of  FIG. 2B ;  FIG. 2D  is the phase component of the inverse Fourier transform of  FIG. 2C ; and  FIG. 2E  is the unwrapped phase image derived from  FIG. 2D . 
           [0013]      FIG. 3A  illustrates a system configuration to determine the sensitivity of FF-RPM. 
           [0014]      FIG. 3B  shows a measured phase fluctuation (radian) as a function of applied voltage, where M i : i th  mirror, and PZT: Lead Zirconate Titanate. 
           [0015]      FIGS. 4A-4B  show the location of a coherence gate for double-pass transmission and reflection phase imaging, respectively. 
           [0016]      FIG. 4C  shows a double-pass transmission phase image of a HeLa cell. 
           [0017]      FIG. 4D  shows a single-shot reflection phase image of the region inside square box in  FIG. 4C . 
           [0018]      FIGS. 5A-5B  show the system and results of the cell membrane fluctuation measurement; where  FIG. 5A  shows the location of coherence gate in which the sample is tilted at an angle, allowing to simultaneously acquire membrane fluctuations as well as background phase from the coverslip; and where  FIG. 5B  shows the power spectral density of membrane fluctuations as a function of frequency for three different populations: blue, formalin fixed; green, normal; and red, CytoD-treated HeLa cells. 
           [0019]      FIG. 5C  illustrates a method of performing full frame reflection and/or transmission microscopy in accordance with preferred embodiments of the invention. 
           [0020]      FIG. 6A  shows a phase microscopy system using a spatially low-coherence light source such as a metal halide lamp, for example. 
           [0021]      FIG. 6B  shows the interferogram detected by the system of  FIG. 6A . 
           [0022]      FIGS. 7A-7C  show a reflection phase microscopy system with a metal halide lamp as a spatially low coherent light source using a grating and spatial filter in the reference light path, and images obtained therefrom, respectively. 
           [0023]      FIGS. 8A-8C  show a noise substration method in accordance with preferred embodiments of the invention. 
           [0024]      FIGS. 9A-9C  illustrate phase images of a bead surface using a spatially low-coherence light source. 
           [0025]      FIGS. 10A and 10B  illustrate the measurement of system stability. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0026]      FIG. 1A  shows the schematic of a preferred embodiment of the invention providing single-shot full-field reflection phase microscope (FF-RPM). Light from a mode-locked Ti:Sapphire laser (center wavelength, λ c =800 nm) is coupled into a single-mode fiber  15  for delivery as well as for spectrum broadening. The full-width-half-maximum spectral width, AA at the fiber output measures 50 nm, which yields a round trip coherence length of 4 μm in a typical culture medium with refractive index, n, equal to 1.33. The sample beam that travels along the first beam path  16  through lenses L 2 , L 3 , L 4 , and a water immersion 60× objective lens L 5  (NA=1.2), reflects off the sample surface  24  and makes an image of the sample on a high-speed complementary metal oxide semiconductor (CMOS) camera via lenses L 6  and L 15 . The camera can be a pixelated imaging detector  20  that is connected to a data processor or computer  22  which can process images, provide the images to a display  26  or to a memory  28  for further processing and storage of the images. The computer can be connected to translation stages  25  and  40  that can control the position of the sample and the reference mirror in three orthogonal directions as well as the angular orientation relative to direction of incident light from the light source. The reference beam, which passes through lenses L 7 , L 8 , L 9  and L 10  on a second optical path  18 , is diverted on its way back using a beam splitter BS 2  onto a third beam path  12 . Portion of the reference beam that goes back through BS 2  is blocked using a spatial filter S 1 . On the other hand, the deflected beam passes through lenses L 11 -L 14  and combines with the returning sample beam on a fourth beam path  27  at the 3 rd  beam splitter BS 3 . For off-axis interferometry, a diffraction grating G ( 50 ) is introduced in one of the conjugate planes. Out of multiple diffracted orders, only the +1 st  order can be selected by placing a spatial filter S 2  ( 60 ) in the Fourier plane of lens L 12 . As a result, the diffracted reference beam interferes with the sample beam along path  29  in the image plane at an angle. Note that the period of the diffraction grating and the magnification between the grating and the camera provide the desired angular shift to the reference beam for off-axis interferometry. Moreover, this approach provides equal path length across the whole reference beam wavefront, unlike prior systems that simply used reference mirror tilt for off-axis interferometry. 
         [0027]    In other words, since the grating and the camera suffice the imaging condition, the optical path length measured from any point on the grating to the corresponding pixel on the camera is constant. As a result, this condition provides homogeneous fringe visibility across the whole field-of-view. Note that the system is capable of taking quantitative phase images in double-pass transmission mode as well as reflection mode, which is achieved by placing the coherence gate (see  400  in  FIG. 4A ) on the glass slide or the cell membrane, respectively. 
         [0028]      FIG. 1B  shows a measured interferogram with a flat surface as the sample. The spatial fringes are straight as well as equally spaced when the sample is flat. The total measured intensity at the CMOS camera can be written as 
         [0000]        I ( x,y )= I   R   +I   g ( x,y )+2√{square root over ( I   R   I   S ( x,y ))} cos [ ux+vy +φ( x,y )]  (1)
 
         [0000]    where I R  and I S (x,y) are the reference and sample beam intensity distributions, respectively. u and v represent the frequency of spatial fringes along the x- and y-axes, and is the spatially varying phase associated with the sample under study. A no-fringe image is also acquired that represents the DC component in Eq. (1) by shifting the coherence gate out of the sample using a translation stage  25 . By subtracting the no-fringe image from the original interferogram, generates only the interference term. 
         [0029]      FIG. 2A  shows an interference portion of the 2-D interferogram recorded by the full-field reflection phase microscope, using a 40 micron microsphere as a sample. The fringes, which are straight and equally-spaced for a flat sample, are changed by the modified wavefront of the sample beam reflected off the microsphere. In order to extract the profile of the sample under investigation, take the Hilbert transform of the interference portion of the 2-D interferogram, which yields both amplitude and phase of the returning sample beam. For more details on the use of a Hilbert transform for phase imaging, see U.S. application Ser. No. 11/389,670 filed Mar. 24, 2006, the entire contents of which is incorporated herein by reference. In the past, this approach has been used to retrieve sample amplitude and phase information in a transmission type quantitative phase microscope. For additional details on transmission phase microscopy, see U.S. application Ser. No. 12/218,029 filed Jul. 10, 2008, the entire contents of which is incorporated herein by reference. 
         [0030]      FIG. 2B  shows the amplitude of the 2-D Fourier transform of the interferogram in  FIG. 2A . More specifically, the 1 st  and −1 st  order components are shown in the first and third quadrants, respectively. First, crop or select the 1 st  order component in the Fourier image, shift it to the center of the Fourier plane (see  FIG. 2C ), and then take the inverse Fourier transform. The phase of the inverse Fourier transformed image ( FIG. 2D ) provides the optical phase of the sample beam wavefront. By applying 2-D spatial phase unwrapping, the surface profile of the sample without 2π phase ambiguity is obtained as shown in the  FIG. 2E . 
         [0031]    Intrinsic membrane fluctuations in living cells are typically on the order of a nanometer or less; the measurement of these small membrane fluctuations requires the development of quantitative phase microscopes with high signal-to-noise ratio (SNR). The measurement sensitivity of the full-field RPM can be illustrated in terms of the least detectable axial motion; the configuration to measure the measurement sensitivity is shown in  FIG. 3A . The full-field illumination shines on both the surfaces; mirror or reflector M 1  mounted on a translation stage  200  and mirror or reflector M 2  attached to a Lead Zirconate Titanate (PZT) actuator  202 . 
         [0032]    In order to suppress the common mode noise due to independent mechanical or thermal fluctuations of the reference beam path with respect to the sample beam path, a self-phase referencing method can be utilized. Since the phase of all the points in the full-field illumination is acquired at the same time, every point in the field of view shares the same interferometric noise as any other point. This method uses the phase measured from a portion of the beam illuminating the reflector M 1  as the reference phase, representing the common-mode noise. By subtracting this reference phase from the phase of the subsequent points on M 2 , the common-mode noise is removed to obtain actual fluctuation of the surface M 2 . 
         [0033]    To demonstrate common-mode phase noise rejection, the PZT actuator was driven at the frequency of 400 Hz whereas the amplitude of the PZT driving voltage was varied from 0.02-5 Volts. Single-shot phase images of the M 1  and M 2  were acquired simultaneously for duration of 1 second at 1 millisecond intervals. The temporal power spectral density (PSD) was calculated from the temporal fluctuation of the phase measured from M 2 , and the square-root of the PSD at 400 Hz was selected to determine the axial motion signal.  FIG. 3B  shows the measured axial motion at 400 Hz versus PZT driving voltage; the plot is well fit by the line 14.5 mrad/Volt.  FIG. 3B  also shows the noise floor estimated by taking the average of the square-root of the PSD from 395-405 Hz excluding the 400 Hz frequency. The maximum noise was only 0.44 (mrad/√{square root over (HZ)}). This corresponds to 21(pm/√{square root over (HZ)}), since the change in phase Δφ is linearly related to the change in the axial position Δ 1  as 
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         [0000]    where n is the refractive index of the medium (typically n=1.33). 
         [0034]    To demonstrate high-speed quantitative imaging of live cells, HeLa cells are sub-cultured on glass slides 2 days before the measurement and immersed in standard culture medium (Dulbecco&#39;s Modified Eagle Medium). As mentioned earlier, the setup is capable of taking transmission phase images as well as reflection phase images.  FIGS. 4A and 4B  show the location of the coherence gate  400 ,  402  for double-pass transmission phase imaging and the full-field reflection phase imaging, respectively. In double-pass transmission phase imaging, the illumination light passes through the cell, reflects off the glass surface reflector  404  and then passes through the cell again. The measured transmission phase difference Δφ T  is related to the optical thickness (OT) as 
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         [0000]    where Δ  n  is the mean of the refractive index difference between culture medium and cytoplasm and h is the height of the cell.  FIG. 4C  shows the corresponding transmission phase image of a live HeLa cell. The height of the cell was roughly estimated to be 8.5 μm by substituting Δ  n =0.03 and Δφ=4 in Eq. (2). 
         [0035]    For full-field reflection phase imaging, the focal plane as well as the coherence gate are placed on the cell surface  406  with gate  402 . Since the backscattered light from out-of-coherence gate region does not contribute to the interference, the full-field phase information [see  FIG. 4D ] of cell surface within the coherence gate is collected as depicted in  FIG. 4B . In this case, the reflection phase difference Δφ R  is directly related to the height difference Δh(x,y) . . . as 
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         [0000]    where n m  is the refractive index of the culture medium and is typically 1.335. 
         [0036]    The advantage of the reflection-mode imaging is clear when comparing Eqs. (3) and (4). For instance, 10 milli-radian of the phase change in reflection phase image corresponds to 0.5 nanometers, whereas the same phase change in transmission corresponds to 20 nanometers. In other words, supposing that the phase sensitivity of the transmission and reflection-mode measurements is same, the height resolution (or measurement sensitivity) of the reflection phase imaging is 40 times 
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         [0000]    better than that of transmission measurement. Moreover, the reflection phase image can reveal the shape of the cell surface independent of the distribution of intracellular refractive index since it depends only on the refractive index of the medium which can be accurately measured by a conventional refractometer. 
         [0037]    As discussed above, membrane fluctuations are intrinsic indicator of overall cellular condition and are used to estimate membrane mechanical properties in relation to different stages of malaria infection in human red blood cells. But for eukaryotic cells having complex internal structures, the present full-field reflection phase microscope can selectively measure membrane fluctuations by effectively choosing to reject contributions from the internal cellular structures. The membrane fluctuations in HeLa cells can be measured under different cell conditions. More specifically, consider (i) a sample of living normal HeLa cells, (ii) a fixed HeLa cell sample after treatment with 2% paraformaldehyde and (iii) a sample of HeLa cells treated with 8 nM Cytochalasin-D which inhibits actin polymerization. The frame rate of the image acquisition was set to 1 kHz and the data was recorded for duration of 1 sec for each cell. 
         [0038]    As shown in  FIG. 5A , the sample under test was tilted or rotated through an angle  502  with the translation stage to simultaneously acquire membrane fluctuations as well as background phase from the coverslip. By subtracting the background phase change observed on the coverslip, the common-mode mechanical noise was eliminated. The temporal fluctuations on the cell surface were measured and calculated the PSD of membrane motion for each cell. The translation stage can also move the sample in any of three orthogonal directions  504 .  FIG. 5B  shows the mean PSD for each cell population. The number of normal, fixed, and Cytochalasin-D treated cells used in this study were N=22, 20, and 33, respectively. The PSD of the fixed cells was measured and found to be smaller and flatter than the normal ones indicating that the cell membrane became stiffer after chemical fixation. On the other hand, the PSD of the Cytochalasin-D treated cells was measured larger than the normal ones indicating that the cell membrane became softer due to the inhibition of actin polymerization. 
         [0039]    A process sequence  500  for measuring a sample in accordance with the invention is illustrated in  FIG. 5C . The source, such as laser  14 , generates a signal (single shot)  510  which is coupled  520  onto the sample and the reference  42 . The stage  40  can position  530  the sample  24  relative to the coherence gate. The image is detected  540  and recorded  550  at a selected frame rate, preferably at least at 20 frames per second, or for faster dynamic processes at least at 30 frames per second or more. The image is processed  560  including the placement of image data in the Fourier plane  570 . The image can be unwrapped  580 , and noise components removed 590 for display and recording of quantitative data for the sample. 
         [0040]    A full-field reflection-phase-microscopy (FF-RPM) with spatially low-coherent light-source, and without a grating, is shown in  FIG. 6A . A broadband source, such as a metal halide lamp  600 , can be used.  FIG. 6B  shows an interference image obtained by the camera using the system of  FIG. 6A  with a circular pattern. 
         [0041]    A preferred embodiment of the invention is shown in  FIG. 7A  with a FF-RPM with grating  705  and spatial filter  707 .  FIG. 7B  shows an interference image obtained by the camera using the system of  FIG. 7A  and  FIG. 7C  shows an enlarged view of the indicated region of  FIG. 7B  where L 1 ˜L 6  are Lenses, OL 1  and OL 2  are objective lenses, BS 1 ˜BS 3  are beamsplitters IP: Image Plane, and FP: Fourier Plane. A broadband light source such as a metal halide lamp  700  provides the imaging light source, an X-Cite  120  (mfr. EXFO, Canada) with the center wavelength of 600 nm and the laser source  702  is a diode laser (Edmund optics) with an emission wavelength of 632 nm. 
         [0042]    The light emitted from the spatially incoherent light source  700  (metal halide lamp) is split into two beams; the sample light  750  reflects off the sample and is directed through beamsplitters  752  and  754  to camera  20 . The reference light  760  is directed using beamsplitters  762  and mirrors  764 ,  766  to the camera  20 . The spatially and temporally incoherent light for imaging (e.g. the metal halide lamp) comprises the imaging light source. The light reflected by the sample is focused onto the imaging plane (IP) between the L 1  and the L 3 . The image of the sample on the IP is focused onto the camera. 
         [0043]    The light reflected by the reference mirror is focused onto the grating  705  between the L 2  and the L 4 . The image of the grating is focused onto the camera but only the 1 st  order of the diffracted beam is delivered. 
         [0044]    If the grating is removed between L 2  and L 4  (See.  FIG. 6A ), the bulls-eye pattern of the interference fringe is obtained by the camera (See  FIG. 6B ). By inserting the grating  705  and the spatial filter  707  in  FIG. 7A , the diffracted reference beam is incident on the camera with an angle  710  so that the interference image with multiple fringes is obtained by the camera  20  (See  FIG. 7B ).  FIG. 7C  is the enlarged view of the indicated region  720  of  FIG. 7B . 
         [0045]    The laser  702  (spatially and temporally coherent light source) shown in  FIG. 7A  is for monitoring the mechanical noise of the system. The function of the laser  702  is described in reference to  FIGS. 8A-8C . The transform used (Hilbert Transform) to retrieve the phase information out of the interference image with multiple fringes can use the same process as described in connection with the spatially coherent light source. 
         [0046]      FIGS. 8A-8C  illustrate a system for common-mode noise subtraction.  FIG. 8A  shows detail of the configuration of the imaging light and the laser light for monitoring the mechanical (common-mode) noise.  FIG. 8B  shows schematic illustration of the interference image.  FIG. 8C  shows side view of the sample configuration. Due to the mechanical instability of the system, the fringe of the interference image moves over time. To compensate for the mechanical noise, the laser light is used to monitor the mechanical noise. 
         [0047]    The laser light shares the same optical path with the imaging light (see  FIG. 8A ). However, the beam is slightly shifted to the lateral direction by about 50 μm. The laser light hits the glass (substrate) surface while the imaging light is reflected from the surface of the sample; e.g. cells. Therefore, the detector can see both the interference fringes from the sample surface and the interference fringes from the glass substrate in the same image (see  FIG. 8B ).  FIG. 8C  shows the side view of the sample. By the coherence gating of the low-coherent imaging light source, only the reflected imaging light from a limited depth makes the interference fringe, while the laser light reflected from the glass substrate makes the interference fringe regardless of the optical path difference. 
         [0048]      FIGS. 9A-9C  illustrate a phase image of 10 μm polystyrene beads.  FIG. 9A  shows a one-shot interference image where  FIG. 9 . ( a - 1 ) and  FIG. 9  ( a - 2 ) is the zoom-in of the region indicated by rectangles.  FIG. 9B  shows a phase image where the pseudo-color shows the phase in radian.  FIG. 9C  shows the surface profile of the bead. 
         [0049]      FIG. 9A  shows the one-shot interference image. The coherence gating is adjusted to the surface of the beads. The interference fringes by the reflection of the imaging light from the bead surface are obtained (see.  FIG. 9  ( a - 2 )) as well as the interference fringes by the reflection of the laser light from the glass substrate (see.  FIG. 9  ( a - 1 )). By the Hilbert Transform, the full-field phase image is obtained as shown in the  FIG. 9B . The image of a bead can be cropped and processed to provide a two-dimensional phase unwrapping and thereby retrieve the surface profile of the bead. 
         [0050]    The result of the common-mode noise subtraction is illustrated with  FIG. 10A , where the phase fluctuation observed on the bead surface  950 , at the glass substrate  960  by the laser, and the true phase fluctuation of the bead surface observed by the system after subtration  970  are shown. 
         [0051]      FIG. 10B  shows a zoom-in of the true phase fluctuation of the bead. This is the same plot of the line  970  in  FIG. 10A  with a detailed scale. 
         [0052]    These show the result of the common-mode noise subtraction. In this example, the interference images were recorded within 12 seconds in 33 millisecond intervals (30 Hz) to obtain the time-series data of the phase image. The raw data of the phase fluctuated over 3 radians on both the bead surface and the glass surface. However, the trend of the fluctuation of the bead surface and the glass surface is similar because the source of this fluctuation is the overall fluctuation of the path length of the sample arm and the reference arm. By subtracting the fluctuation of the glass from the fluctuation of the bead, a very stable time-series of the phase on the bead was obtained. The remaining instability was 52 milliradians (standard deviation) which corresponds to 1.8 nanometer of the height resolution. Note that when the surface motion of the glass is subtracted from the one of the bead, the ratio of the wavelength between the imaging light and the laser light is taken into consideration. The ratio was 1.05 and the phase fluctuation of the glass multiplied by the factor of 1.05 was subtracted from the phase fluctuation of the beads. 
         [0053]    Hence, a preferred embodiment of the present invention has implemented a FF-RPM with a spatially incoherent light source so that the surface shape of the sample is obtained in nanometer z-resolution. The advantage of the system with a spatially incoherent light source to the one with a spatially coherent light source is that the image is free of speckle noise. 
         [0054]    While the invention has been described in connection with specific methods and apparatus, it is to be understood that the description is by way of example of equivalent devices and methods not as a limitation to the scope of the invention as set forth in the claims.