Patent Publication Number: US-8525091-B2

Title: Wavefront imaging devices comprising a film with one or more structured two dimensional apertures and their applications in microscopy and photography

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This is a continuation application of co-pending U.S. patent application Ser. No. 12/435,165, filed on May 4, 2009, which is a non-provisional of, and claims priority to, U.S. Provisional Patent Application No. 61/126,441, filed on May 5, 2008, entitled “QUANTITATIVE DIFFERENTIAL INTERFERENCE CONTRAST (DIC) MICROSCOPY BASED ON WAVEFRONT SENSORS.” These applications are hereby incorporated by reference in their entirety for all purposes. 
     This application is related to the following commonly-assigned patent applications, which are hereby incorporated by reference in their entirety for all purposes: 
     U.S. patent application Ser. No. 11/743,581, filed on May 2, 2007, by Xiquan Cui, Xin Heng, Demetri Psaltis, Axel Scherer, and Changhuei Yang, entitled “ON-CHIP PHASE MICROSCOPE/BEAM PROFILER BASED ON DIFFERENTIAL INTERFERENCE CONTRAST AND/OR SURFACE PLASMON ASSISTED INTERFERENCE,” now U.S. Pat. No. 7,768,654, which application claims priority to the following applications: U.S. Provisional Patent Application No. 60/796,997, filed on May 2, 2006, by Xiquan Cui, Xin Heng, and Changhuei Yang, entitled “DIFFERENTIAL INTERFERENCE CONTRAST (DIC) MICROSCOPE BASED ON YOUNG&#39;S INTERFERENCE,” and U.S. Provisional Patent Application No. 60/796,996, filed on May 2, 2006, by Xin Heng, Xiquan Cui, Axel Scherer, Demetri Psaltis, and Changhuei Yang, entitled “SURFACE PLASMON ASSISTED OPTOFLUIDIC MICROSCOPE;” and 
     U.S. patent application Ser. No. 11/686,095, filed on Mar. 14, 2007, by Changhuei Yang and Demetri Psaltis, entitled “OPTOFLUIDIC MICROSCOPE DEVICE,” now U.S. Pat. No. 7,751,048, which application is a continuation-in-part application of U.S. patent application Ser. No. 11/125,718, filed on May 9, 2005, now U.S. Pat. No. 7,773,227, which is a non-provisional of and claims priority to U.S. Provisional Patent Application Nos. 60/590,768, filed on Jul. 23, 2004, and 60/577,433, filed on Jun. 4, 2004. U.S. Patent Application No. 11/686,095 is also a non-provisional of, and claims the benefit of the filing date of U.S. Provisional Patent Application No. 60/783,920, filed on Mar. 20, 2006. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to microscopy and photography, and in particular, to differential interference contrast (DIC) microscopy and photography based on wavefront sensors. 
     2. Description of the Related Art 
     (Note: This application references a number of different publications as indicated throughout the specification by reference numbers enclosed in brackets, e.g., [x]. A list of these different publications ordered according to these reference numbers can be found below in the section entitled “References.” Each of these publications is incorporated by reference herein.) 
     Differential interference contrast (DIC) microscopy renders excellent contrast for optically transparent biological samples without the need to introduce any exogenous contrast agents into the samples. Due to this noninvasive nature, DIC microscopes are widely used in biology laboratories. However, the conventional DIC technique has several limitations. One major disadvantage is that the conventional DIC microscope translates phase variations into amplitude (intensity) variations, and therefore phase variations cannot be easily disentangled from amplitude variations that arise from sample absorption and/or scattering [1]. In other words, conventional DIC microscopes are inherently qualitative as a consequence of nonlinear phase gradient response and entanglement of amplitude and phase information. In addition, conventional DIC images of birefringent samples can have significant artifacts as the conventional DIC microscope depends on polarized light and uses polarization in its phase imaging strategy. 
     SUMMARY OF THE INVENTION 
     One or more embodiments of the invention provide a quantitative DIC microscopy or photography method based on a wavefront sensor. Such a sensor may be either a structured-aperture (SA) wavefront sensor or a microlens aperture based sensor (i.e., a Shack-Hartmann sensor). Benefiting from the unique features of such a wavefront sensor, a DIC microscopy or photography system separates the amplitude and the phase gradient information of the image wavefront, and forms quantitative intensity and DIC images of the sample with good resolution (˜2 μm or less). Furthermore, since embodiments of the invention utilize unpolarized light and contain no polarization-dependent components, birefringent samples can be imaged (e.g., potato starch storage granules) without artifacts. Finally, unlike most of the recently developed quantitative phase microscopy techniques, embodiments of the invention can be used with a standard microscope light-source [11][12]. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Referring now to the drawings in which like reference numbers represent corresponding parts throughout: 
         FIG. 1  illustrates a conventional DIC microscope system that operates by interfering slightly displaced duplicate image light fields; 
         FIG. 2  illustrates a structured aperture differential contrast microscope that operates by interfering light from two adjacent points on the image light field in accordance with one or more embodiments of the invention; 
         FIG. 3  illustrates a configuration for DIC microscopy based on wavefront sensors using a single pixel wavefront sensor scheme in accordance with one or more embodiments of the invention; 
         FIG. 4  illustrates a configuration for a DIC microscopy based on wavefront sensors using a wavefront sensor array scheme in accordance with one or more embodiments of the invention; 
         FIG. 5  illustrates a configuration of a wavefront sensor used in accordance with one or more embodiments of the invention; 
         FIG. 6(   a ) illustrates a configuration of a structured aperture wavefront sensor in accordance with one or more embodiments of the invention; 
         FIGS. 6(   b ),  6 ( d ), and  6 ( f ) illustrate different patterned structured apertures used in the configuration of  FIG. 6(   a ) while  FIGS. 6(   c ),  6 ( e ), and  6 ( g ) illustrate resulting images from the patterned structured apertures of  FIGS. 6(   b ),  6 ( d ), and  6 ( f ) respectively, and  FIG. 6(   h ) illustrates a Fresnel-Zone plate structured aperture with a circular frame; 
         FIG. 7  illustrates an example of a side-view of a DIC microscope system constructed by an SA wavefront sensor array in accordance with one or more embodiments of the invention; 
         FIG. 8  illustrates a Shack-Hartmann wavefront sensor in a DIC microscope system in accordance with one or more embodiments of the invention; 
         FIG. 9  is a flowchart illustrating the processing of data received in a photodetector array in accordance with one or more embodiments of the invention; 
         FIG. 10A  illustrates a side view of a wavefront sensor in accordance with one or more embodiments of the invention; 
         FIG. 10B  illustrates a top down view of a photodetector array of  FIG. 10A  with signals received thereon in accordance with one or more embodiments of the invention; 
         FIG. 11  is an exemplary hardware and software environment used to implement one or more embodiments of the invention; 
         FIG. 12(   a ) illustrates a configuration of a structured aperture differential contrast microscope used in accordance with one or more embodiments of the invention; 
         FIG. 12(   b ) illustrates a graph of an offset of a zero-order interference spot of the structured aperture of  FIG. 12(   c ) and wavefront gradient in accordance with one or more embodiments of the invention; 
         FIG. 12(   c ) illustrates a scanning electron microscope image of a structured aperture defined on silver film in accordance with one or more embodiments of the invention; 
         FIG. 12(   d ) illustrates a resulting interference pattern of the structured aperture recorded by a CMOS (complementary metal-oxide-semiconductor) image sensor in accordance with one or more embodiments of the invention; 
         FIGS. 13(   a )- 13 ( e ) illustrates images of starfish embryo.  FIG. 13(   a ) illustrates a conventional transmission microscope image;  FIG. 13(   b ) illustrates a conventional DIC microscope image;  FIG. 13(   c ) illustrates intensity,  FIG. 13(   d ) illustrates X DIC phase images from a structured aperture DIC microscope, and  FIG. 13(   e ) illustrates Y DIC phase images from a structured aperture DIC microscope; 
         FIGS. 14(   a )-( e ) illustrates images of potato starch storage granules in microscope immersion oil;  FIG. 14(   a ) illustrates a conventional microscope image;  FIG. 14(   b ) illustrates maltese-cross artifacts in a conventional DIC image;  FIG. 14(   c ) illustrates intensity and is artifact free;  FIG. 14(   d ) illustrates X DIC phase images from a structured aperture DIC microscope, and  FIG. 14(   e ) illustrates Y DIC phase images from a structured aperture DIC microscope; 
         FIG. 15  illustrates a completed wavefront-sensing sensor chip (top left), a camera port housing for the chip (top right), and the use of the entire unit plugged into a camera port of a microscope in accordance with one or more embodiments of the invention; 
         FIG. 16  illustrates the approach for the propagation of light in accordance with one or more embodiments of the invention; and 
         FIG. 17  illustrates an approach for the propagation of light using a computer ( 17 ( a )) and using a microscope ( 17 ( b ) and  17 ( c )) in accordance with one or more embodiments of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the following description, reference is made to the accompanying drawings which form a part hereof, and which is shown, by way of illustration, several embodiments of the present invention. It is understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention. 
     Overview 
     One or more embodiments of the invention provide a mechanism to create a simple, quantitative and birefringent-artifact-free DIC microscopy or photography method with wavefront sensors. 
     Configuration of the Quantitative Differential Interference Contrast (DIC) Microscopy Based on Wavefront Sensors 
     Using conventional microscopy, a sample may be illuminated and a photodetector may be used to receive the diffracted light. Two types of information are desirable based on the illumination—(1) the number/distribution of photons; and (2) the direction/wavefront slope/phase gradient of the photons. Conventional microscopy fails to provide the phase gradient of the photons diffracted by a sample. Further, as described above, due to the dependency on polarized light, conventional techniques further fail to provide accurate results with birefringent samples (i.e., samples that have double refraction where the direction of light diffracted through the sample will depend on the polarization of the light). Accordingly, what is needed is a mechanism that is not dependent on polarized light that is further able to provide the phase gradient of the light after interacting with the sample. 
     Embodiments of the invention provide the ability to measure both (1) the number/distribution of photons, and (2) the phase gradient of the photons on birefringent and homogeneous samples. A DIC microscopy-based system of embodiments of the invention may utilize wavefront sensors in two different configurations: (1) a single pixel wavefront sensor scheme; or (2) a wavefront sensor array scheme. To better understand these two configurations, a close examination of convention DIC microscopy is useful. 
     In essence, a conventional DIC microscope operates by first creating two identical illumination light fields through polarization selection.  FIG. 1  illustrates a conventional DIC microscope system that operates by interfering slightly displaced duplicate image light fields. As illustrated, the light fields  100  are laterally displaced (displacement=a) with respect to each other (along the x-direction) and are transmitted through the sample  102 . A net phase lag  104  (typically π/2) is then introduced on one of the transmitted image light fields. The two light fields  100  are allowed to interfere with each other at the image plane  106 . More simply, the process is equivalent to simply duplicating the transmitted image light field, laterally displacing the copy slightly (i.e., at  104 ) and interfering the two light fields (at image plane  106 ). 
     Mathematically, this implies that the observed conventional DIC intensity image from a microscope with a magnification factor of M is given by: 
                             I   DIC     ⁡     (     x   ,   y     )       =       ⁢              ψ   DIC     ⁡     (     x   ,   y     )            2                 =       ⁢       B   ⁡     (     x   ,   y     )       +       C   ⁡     (     x   ,   y     )       *                       ⁢     sin   ⁡     (       arg   ⁡     (     ψ   ⁡     (       x   -     Δ   /   2       ,   y     )       )       -     arg   ⁡     (     ψ   ⁡     (       x   +     Δ   /   2       ,   y     )       )         )                   ≈       ⁢       B   ⁡     (     x   ,   y     )       +       C   ⁡     (     x   ,   y     )       *                       ⁢     (       arg   ⁢     (     ψ   ⁡     (       x   -     Δ   /   2       ,   y     )       )       -     arg   ⁡     (     ψ   ⁡     (       x   +     Δ   /   2       ,   y     )       )         )                   (   1   )               
where B(x,y)=|(ψ(x−Δ/2,y))| 2 +|(ψ(x+Δ/2,y)) 2 , C(x,y)=2|(ψ(x−Δ/2,y))∥(ψ(x+Δ/2,y))|, and ψ(x,y), is the image wavefront as relayed by the microscope for each light field, ψ DIC  (x,y), is the DIC image wavefront, and Δ=Ma is the relative displacement of the images associated with the light fields. The last expression in Eq. (1) is valid only in situations where the phase difference is small.
 
     A similar phase comparison can also be performed by acquiring a simple microscope image of the object and selectively combining-and-interfering the light fields at two adjacent points of the image (separation=a′) as illustrated in  FIG. 2 . Such a phase comparison is employed in a DIC imaging method of one or more embodiments of the invention. 
     Single Pixel Wavefront Sensor Scheme 
     A first configuration for a DIC microscopy-based on wavefront sensors is that of a single pixel wavefront sensor scheme as illustrated in  FIG. 3 . The light source  300  illuminates a sample  302  which diffracts/refracts the light into a shaped wavefront  304 . 
     A wavefront relay system  308  is used to project the wavefront  304  generated by the sample  302  onto a single pixel wavefront sensor  310 . The sensor  310  measures the local intensity (i.e., number/distribution of the photons) and phase gradient of the wavefront  304  induced by the sample  302  which conjugates with the sensor pixel  310 . By raster-scanning  306  the sample  302  or the sensor pixel  310 , two-dimensional (2D) maps of the local intensity/distribution and phase gradient of the wavefront  304  modulated by the sample  302  can be achieved at the same time. 
     Wavefront Sensor Array Scheme 
     A second configuration for a DIC microscopy based on wavefront sensors is that of a wavefront sensor array scheme as illustrated in  FIG. 4 . Similar to  FIG. 3 , the light source  400  illuminates the sample  402  which diffracts/refracts the light into a shaped wavefront  404 . 
     The relay system  408  is used to project the wavefront  404  generated by the sample  402  onto a wavefront sensor array  410 . Each pixel of the wavefront sensor array  410  measures the local intensity/distribution and phase gradient of the wavefront  404  induced by the sample point  402  which conjugates with the sensor pixel. In this case, 2D maps of the local intensity/distribution and phase gradient of the wavefront  404  modulated by the sample  402  are obtained naturally at the same time. In addition, the sample  402  or the sensor array  410  can be raster-scanned to form more densely sampled images. 
     Configuration Benefits and Alternatives 
     Since embodiments of the invention do not depend on the polarization of the illumination, artifact-free DIC images can be obtained (using unpolarized illumination), for both birefringent and homogenous samples. In addition, the imaging scan  306  may be performed in many other ways. For example, a 2D raster scan  306  can be replaced by a one-dimensional (1D) OFM (opto-fluidic microscope) scanning scheme as described in U.S. patent application Ser. Nos. 11/686,095 and 11/743,581, which are incorporated by reference herein. Further, sample scanning can be replaced by wavefront sensor  310 / 410  scanning. Lastly, embodiments of the invention can be used to target transparent samples, cell level or larger. In this regard, there is no constraint with respect to the size of the sample. 
     In view of the above described configurations, embodiments of the invention provide a new DIC microscopy method where the DIC functionality of a microscope is integrated onto the detector. Such integration is advantageous over conventional DIC microscopy methods which use bulky optical elements in the microscope. Accordingly, embodiments of the present invention are more compact, less expensive, less tedious in training and preparation, and more convenient to operate by users than conventional DIC methods. 
     Use in a microscope can involve a wavefront-sensing sensor chip that is placed into a camera-port compatible housing for the chip. The entire unit can be plugged into the camera port of a microscope and used to capture simultaneous amplitude and phase images. 
     Nonetheless, embodiments of the invention can be utilized in adaptive optics as part of a wavefront sensing component. The term adaptive optics refers to systems that operate by measuring distortions in a wavefront and compensating for them with a spatial phase modulator such as a deformable minor or liquid crystal array. 
     Wavefront Sensors 
     Multiple types of wavefront sensors  310 / 410  may be used in accordance with one or more embodiments of the invention. The wavefront sensor, which can measure the local intensity/distribution and phase gradient of the wavefront modulated by the sample at the same time, can be implemented in several ways. Two different cases are presented: (1) structured aperture interference and (2) Shack-Hartmann schemes. Both sensors can be used as either a single pixel  310  or an arrayed wavefront sensor  410 , and form quantitative DIC microscopes of the configurations described above. 
     Structured Aperture (SA) Wavefront Sensor 
     The basic concept of the SA sensor is similar to the Young&#39;s double-slit phase decoding scheme described in U.S. patent application Ser. Nos. 11/743,581 and 11/686,095, which are fully incorporated by reference herein. 
       FIG. 5  illustrates a configuration of a wavefront sensor  310 / 410  used in accordance with one or more embodiments of the invention. A light source  500  is used to illuminate a sample/specimen  502 . A metal film  504  has apertures  506  (i.e.,  506 A and  506 B) which are used to focus the diffracted/refracted light from the sample (i.e., in accordance with Young&#39;s interference  508 ) onto a photodetector array such as a charge coupled device (CCD)  510 . The photodetector array  510  can be used to determine the light intensity distribution  512 . The local phase gradient of the wavefront  304 / 404  (that is focused via apertures  506 ) is determined by examining the offset of the zero diffraction order on the back photodetector array  510 . The local intensity  512  of the wavefront is determined by integrating the diffracted signal on the photodetector array  510 . 
     One or more embodiments of the invention utilize varieties of 2D structured apertures including four holes, petal-shaped, a single hole, a ring or Fresnel zone plate (some are illustrated in  FIG. 6 ). As illustrated in  FIG. 6(   a ), the incident light field  300 / 400 / 500  (e.g., received from the wavefront relay system  308 / 408 ) passes through apertures in the metal (e.g., silver) film where the light is projected (e.g., through a transparent polymer such as SU-8 resin) onto an image sensor (e.g., CMOS image sensor). The light may be projected at different angles (e.g., left side of  FIG. 6(   a ) v. right side of  FIG. 6(   a )) resulting in a different projection onto the image sensor  510 . 
       FIGS. 6(   b ),  6 ( d ), and  6 ( f ) illustrate the different structured aperture patterns (via scanning electron microscope images) while  FIGS. 6(   c ),  6 ( e ), and  6 ( g ) illustrate the resulting interference pattern of the respective aperture patterns recorded by the photodetector/image sensor  510 .  FIGS. 6(   b ) and  6 ( c ) illustrate a petal-shaped aperture and resulting interference pattern;  FIGS. 6(   d ) and  6 ( e ) illustrate a four (4) structured aperture and resulting interference pattern; and  FIGS. 6(   f ) and  6 ( g ) illustrate a 4-hole structured aperture (with round holes) and resulting interference pattern.  FIG. 6(   h ) illustrates a Fresnel-zone plate structured aperture with a circular frame. Using a Fresnel zone plate or ring based structured aperture, one can shrink a projected sport FWHM (full width half maximum) by appropriate design. 
     With these 2D structured apertures (i.e., illustrated in  FIGS. 6(   b ),  6 ( d ), and  6 ( f ) as examples), one can measure the local phase gradient of the wavefront  304 / 404  along both orthogonal directions X and Y at the same time. As used herein, such an aperture-based phase decoding scheme is referred to as SA wavefront sensing. 
     As illustrated in  FIG. 6 , the sensor of the invention  310 / 410  includes the metal film based apertures  504  and photodetector/image sensor  510 . The sensor  510  is used to receive the wavefront shaped by the sample. Wherever the projection is received onto the sensor  510 , the resulting image may be used to represent a single pixel. As in  FIG. 3 , raster scanning may be used to capture an image of the entire sample. Alternatively, as in  FIG. 4 , multiple sensors  310 / 410  may be arranged in a 2D array to capture the entire sample in a single snapshot. 
     The 4-hole aperture and single hole aperture sensor measure the spatial phase gradient of the light field. Mathematically, one measures:
 
 G   x ( x,y )= k   x ( x,y )/ k   0 ≈( d φ( x,y )/ dx )/ k   0  
 
 G   y ( x,y )= k   y ( x,y )/ k   0 ≈( d φ( x,y/dy )/ k   0  
 
A(x,y)
 
with an aperture sensor.
 
     As such, one can mathematically reconstruct the observed wavefront at the sensor by combining the information appropriately. One approach is: 
                 ψ   measured     ⁡     (     x   ,   y   ,   z     )       =         A   measured     ⁡     (     x   ,   y   ,   z     )       ⁢     exp   (     ⅈ   ⁢           ⁢         k   0     ⁡     (       ∫   0   x     ⁢       G   x     (         (     x   ,     y   =   0       )     ⁢     ⅆ   x       +       ∫   0   y     ⁢         G   y     ⁡     (       x   =   x     ,   y     )       ⁢     ⅆ   y           )       )       .                 
Numerous approaches for reconstructing a field distribution exist (unwrapping). The methods should all return the same answer if the SNR (signal to noise ratio) of the measurement approaches infinity. The methods vary in their performance based on the quantity and type of noise present in the measurements.
 
       FIG. 7  illustrates an example of a side-view of a DIC microscope system (and wavefront camera system as described below) constructed by an SA wavefront sensor array in accordance with one or more embodiments of the invention. The light source  700  illuminates  700 A the sample  702  causing a wavefront  704  to pass through a relay system such as lens  706 . The wavefront passes through the SA array  708  which causes the light to project onto the photodetector array  710 . As illustrated,  FIG. 7  depicts a 3-aperture SA array  708 . 
     Shack-Hartmann Wavefront Sensor 
     One or more embodiments of the invention utilize a Shack-Hartmann wavefront sensor in a DIC microscope system (and wavefront camera system described below) as illustrated in  FIG. 8 . As with the SA wavefront sensor implementation, a light source  800  illuminates  800 A a sample  802  to generate a wavefront  804  which passes through a wavefront relay system such as lens  806 . The Shack-Hartmann sensor consists of an array  808  of microlenses of the same focal length. Each microlens in the array  808  focuses the local wavefront  804  across each lens and forms a spot onto a photodetector array  810 . The local phase gradient of the wavefront  804  can then be calculated from the position of the focal spot on the sensor  810 . The history and principles of Shack-Hartmann wavefront sensing is further described in [3] and [4]. However, prior art Shack-Hartmann sensors have been limited in their use and have not been used in microscopy or DIC/phase based microscopy. 
     It is also worth noting that the diffraction spot size in SA wavefront sensors and the focal spot size in the Shack-Hartmann wavefront sensors can be used to determine the spread of wave vector k at any given image point. It is useful for rendering images where the extent of scattering is plotted (amongst other things). 
     Wavefront Detection 
     SA wavefront sensors can be used in a variety of wavefront sensing applications including adaptive optics [3], optical testing [3], adaptive microscopy [5], retina imaging [6], etc. In a SA wavefront sensor of the invention, structured apertures are used on a metal film to convert the phase gradient of a wavefront into a measurable form—the offset of the projection of the aperture. Shack-Hartmann wavefront sensors utilize a microlens array to perform the conversion. The simplicity of the structured apertures provides the ability to build the SA wavefront sensor in an easier and more cost-effective way than Shack-Hartmann sensors. In addition, the spacing between structured apertures can be much smaller than that between the microlenses of a Shack-Hartmann sensor which are usually spaced more than 100 μm apart to sense invarying wavefronts. Further, the SA wavefront sensor provides for high spatial resolution and much denser wavefront sampling for use in detecting complicated wavefronts generated by many biological samples. 
     One may note that wavefront sensing using SA and Shack-Hartmann wavefront sensors does not only apply to monochromatic illumination, but also applies to broad band light illumination. The feasibility of such broad band light illumination is described in [13] which is fully incorporated by reference herein. In this regard, wavefront sensing applies to a monochromatic light field distribution in which k is well defined at each point on the image plane. However, wavefront sensing may also be used for a broadband light source and with situations where k at any given point may be a mix of different wave vectors. In this regard, wavefront sensors can be used with broadband light illumination, monochromatic illumination with mixed k, and broadband light illumination with mixed k. Such capabilities may be better understood with a description of computed depth sectioning ability. 
     For purposes of the following discussion, assume that a light field is linearly polarized and that no interaction of the light field will depoloarize or in any other way disrupt polarization. Under a first concept, the light field at any given plane can be fully described by a complete set of spatially varying amplitude and phase information. In other words, a light field at plane z can be described by:
 
ψ( x,y,z )= A ( x,y,z )exp( i φ( x,y,z )),
 
     Under a second concept, Huygen&#39;s Principle states that the light field at a earlier or later (higher or lower z value) can be calculated from the light field at plane z. In other words, a known function (f) connects:
 
ψ( x,y,z+Δz )= f (ψ( x,y,z ),Δ z )
 
The function f is well known and studied in EM (electromagnetic) theory (see [14]). This computation assumes that the absence of unknown scattering objects between plane z and plane (z+Δz).
 
     These two concepts are powerful when applied to phase imaging in the context of embodiments of the present invention. It implies that if we can measure the phase and amplitude distribution at the plane of the sensor (optofluidic microscope [OFM] floor—see details described herein), one can calculate and render the light field distributions at different heights above the sensor. These light field distributions are, in effect, images at those chosen planes. 
       FIG. 16  illustrates the approach for the propagation of light in accordance with one or more embodiments of the invention. The propagation of the light field is governed by Maxwell&#39;s equations entirely. If one measures the phase and amplitude distribution of the light field  1600  at the sensor  1602 , such information can be used to calculate the light field distribution at any given plane above the sensor (or below the sensor). The amplitude distribution of the computed light field is equivalent to the traditional microscope image taken at the focal plane  1604  set at z+Δz. This treatment is strictly true if no unknown object (e.g., sample) is present between the plane z (i.e., at the sensor  1602 ) and z+Δz ( 1604 ). 
       FIG. 17  illustrates an approach for the propagation of light using a computer ( 17 ( a )) and using a microscope ( 17 ( b ) and  17 ( c )). The imaging of an unknown but weak scatterer can be performed computationally (e.g., as illustrated in  FIG. 17(   a )) by using the same mathematical frame work as described above—by ignoring the presence of the scatterer during the calculation and back-computing the light field at z+Δz. 
     The amplitude distribution of the computed light field is equivalent to the traditional microscope image (e.g., as illustrated in  FIG. 17(   b )) taken at the focal plane set at z+Δz. In fact, the amplitude distribution is identical. In the traditional microscope (i.e.,  FIGS. 17(   b ) and  17 ( c )), the calculation is performed optically by the optical elements. By adjusting the optics, you can bring different planes into focus but effectively, one is making slight adjustments to the optical computing process. As an example,  FIG. 17(   b ) illustrates a microscope based approach where the optics are tuned to focus on the plane z+Δz  1702 . The resulting distribution of such a focal plane  1702  is apparent at the sensor  1704 . Similarly, in  FIG. 17(   c ), the optics are tuned to focus on plane z+Δz′  1706  which is also apparent at sensor  1704 . 
     The process may not be perfect because one may fail to achieve a good image if the sample is thick and/or highly scattering because the assumption that scattering is negligible in the computation process is violated in this case. However, this problem affects computation-based depth sectioning and optical-based sectioning equally. 
     The axiom of ‘no free lunch’ applies equally in both situations. For thin tissue sections or cell samples, the distortion is nominally tolerable. In practical situations, one can typically deal with a 100 μm thick tissue sample before distortion starts becoming significant. 
     One may also note that with computation based sectioning, a sensor capable of spatially measuring amplitude and phase may be needed. Further, the signal to noise ratio (SNR) of the sensor movements may have to be high. Otherwise, the computed images may be poor in quality. 
     Wavefront Camera 
     Embodiments of the invention can also be implemented by insertion of a SA wavefront sensor ( FIG. 7 ) or a Shack-Hartmann wavefront sensor ( FIG. 8 ) into a camera system instead of microscope. Such an embodiment in camera imaging provides similar advantages and benefits to that of a microscopy based embodiment. For example, one can not only capture the intensity information of the projected object wavefront onto the image sensor, but the phase gradient of the projected object wavefront can also be detected. In  FIG. 7  the light source  700  illuminates  700 B an object  702  wherein the remaining elements are similar to the microscopy based device described above. Similarly, in  FIG. 8 , the light source  800  illuminates  800 B the object  802  (which could be a person, or other object that is being captured via the wavefront camera) with the remaining elements similar to the microscopy based device described above. As illustrated in  FIGS. 7 and 8 , the illumination  700 B and  800 B reflects off of the object  802  to generate a wavefront  704 / 804  that is passed to the lens and eventually reaches the photodetector array  710 / 810 . 
     Data Analysis 
     Once a wavefront has been received at the photodetector array, embodiments of the invention provide the ability to analyze the received data and output an image or information based on such data analysis.  FIG. 9  is a flowchart illustrating the processing of the data received at the photodetector array in accordance with one or more embodiments of the invention.  FIG. 9  will be described in relation to  FIG. 10A  which illustrates a side view of a wavefront sensor and  FIG. 10B  which illustrates a top down view of the photodetector array  1010  with signals received thereon. 
     In  FIG. 10A , a wavefront  1004  (e.g., from a wavefront relay system) is received at the SA array  1008 . The SA array  1008  causes the wavefront  1004  to project onto the photodetector array  1010 . The distribution/intensity of the wavefront signals  1004  received on the photodetector array  1010  is illustrated in  FIG. 10A  as wave  1012  and in  FIG. 10B  by the circles  1012 . In this regard, at step  900 , a snapshot (via the illumination via wavefront  1004 ) is taken at the photodetector array  1010 . At step  900 , the projection of every hole is also recorded. It may be noted that while there are multiple photosensors in the photodetector array  1010 , the different photosensors may be cumulatively used or a single photosensor may be used to provide a single data point that is used in accordance with embodiments of the invention. 
     At step  902 , the projection of the hole/aperture is separated from all other projections. Such a separation may be performed by suppressing the crosstalk from neighboring hole projections iteratively. Any variety of methods may be used to separate the projections of the wavefront  1004  through the SA array  1008 . For example, in one embodiment, a maximum intensity value (e.g., in  FIG. 10A ) is found and a determination is made regarding when the intensity value decreases. The wave projection is followed to determine when the intensity value begins to rise again (i.e., signaling the wavefront from an adjacent aperture). The midpoint between two maximum intensity values can be used to suppress cross talk and separate the projections. Alternatively, the height  1014  (i.e., between the SA array  1008  and the photodetector array  1010 ) can be established and the distribution  1012  can be examined to determine the peak/maximum pixel. A defined number of pixels can be used on each side of the peak signal (e.g., from the center of the projection) to define the projections from individual apertures. However, any variety of techniques can be used to separate out the pixels/projections. Such a separation is useful to map the different regions of the photodetector array  1010  to the appropriate aperture in the SA array  1008 . 
     At step  904 , the center of the projection of the hole/aperture is predicted. Any methodology can be used for this prediction including the examination of the intensity values (e.g., as described above with respect to the separation of the projection of the holes). Step  904  may also include the summing of all signals of the hole projections. 
     Steps  900 - 904  are performed twice. The first time steps  900 - 904  are performed, no sample is used. Such a performance serves to initialize the system and determine base measurements to be used to determine the phase gradient. The second time steps  900 - 904  are performed, a sample is utilized such that the projections will be diffracted differently (compared to the projections without the sample). 
     At step  906 , the center position change of the hole projection (i.e., the offset  1016 ) is determined. Such an offset may be determined in both the X and Y directions. This center position change/offset  1016  is directly related to the phase gradient of the wavefront at the hole (i.e., the offset divided by the height may provide the phase gradient). In addition, at step  906 , the total signal of the hole projection is determined which is proportional to the intensity of the wavefront at the hole. 
     The phase gradient of the wavefront along any direction can be calculated based on the phase gradient of the wavefront along 
               X   ⁡     (       ∂   ϕ       ∂   x       )       ⁢           ⁢   and   ⁢           ⁢     Y   ⁡     (       ∂   ϕ       ∂   y       )             
directions acquired as described above. It is because the phase of a wavefront is a fixed scalar potential function, and the phase gradient of the wavefront along any direction
 
                    ∂   ϕ       ∂     n   →                  
can be represented as the inner product of the unit direction vector {right arrow over (n)} and the gradient vector of the phase {right arrow over (Δ)}φ
 
     
       
         
           
             
                
               
                 
                   ∂ 
                   ϕ 
                 
                 
                   ∂ 
                   
                     n 
                     → 
                   
                 
               
                
             
             = 
             
               
                 
                   n 
                   → 
                 
                 · 
                 
                   
                     ∇ 
                     → 
                   
                   ⁢ 
                   ϕ 
                 
               
               = 
               
                 
                   n 
                   → 
                 
                 · 
                 
                   ( 
                   
                     
                       
                         
                           ∂ 
                           ϕ 
                         
                         
                           ∂ 
                           x 
                         
                       
                       ⁢ 
                       
                         i 
                         → 
                       
                     
                     + 
                     
                       
                         
                           ∂ 
                           ϕ 
                         
                         
                           ∂ 
                           y 
                         
                       
                       ⁢ 
                       
                         j 
                         → 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     At step  906 , the data can be output. For example, the angles of the projections (i.e., the direction of the light at a particular point) can be plot into a 2D image that reflects how the light is diffracted by the sample. The structure of the sample can therefore be displayed in an image using the phase gradient. 
     Such processing of  FIG. 9  may be performed by the computer illustrated in  FIG. 11 . In this regard,  FIG. 11  is an exemplary hardware and software environment  1100  used to implement one or more embodiments of the invention. Computer  1102  may be a user computer, server computer, or may be a database computer. The computer  1102  comprises a general purpose hardware processor  1104 A and/or a special purpose hardware processor  1104 B (hereinafter alternatively collectively referred to as processor  1104 ) and a memory  1106 , such as random access memory (RAM). The computer  1102  may be coupled to other devices, including input/output (I/O) devices such as a keyboard  1114 , a mouse device  1116  and a printer  1128 . 
     In one embodiment, the computer  1102  operates by the general purpose processor  1104 A performing instructions defined by the computer program  1110  under control of an operating system  1108 . The computer program  1110  and/or the operating system  1108  may be stored in the memory  1106  and may interface with the user and/or other devices to accept input and commands and, based on such input and commands and the instructions defined by the computer program  1110  and operating system  1108  to provide output and results. 
     Output/results may be presented on the display  1122  or provided to another device for presentation or further processing or action. In one embodiment, the display  1122  comprises a liquid crystal display (LCD) having a plurality of separately addressable liquid crystals. Each liquid crystal of the display  1122  changes to an opaque or translucent state to form a part of the image on the display in response to the data or information generated by the processor  1104  from the application of the instructions of the computer program  1110  and/or operating system  1108  to the input and commands. The image may be provided through a graphical user interface (GUI) module  1118 B. Although the GUI module  1118 B is depicted as a separate module, the instructions performing the GUI functions can be resident or distributed in the operating system  1108 , the computer program  1110 , or implemented with special purpose memory and processors. 
     Some or all of the operations performed by the computer  1102  according to the computer program  1110  instructions may be implemented in a special purpose processor  1104 B. In this embodiment, the some or all of the computer program  1110  instructions may be implemented via firmware instructions stored in a read only memory (ROM), a programmable read only memory (PROM) or flash memory within the special purpose processor  1104 B or in memory  1106 . The special purpose processor  1104 B may also be hardwired through circuit design to perform some or all of the operations to implement the present invention. Further, the special purpose processor  1104 B may be a hybrid processor, which includes dedicated circuitry for performing a subset of functions, and other circuits for performing more general functions such as responding to computer program instructions. In one embodiment, the special purpose processor is an application specific integrated circuit (ASIC). 
     The computer  1102  may also implement a compiler  1112  which allows an application program  1110  written in a programming language such as COBOL, Pascal, C++, FORTRAN, or other language to be translated into processor  1104  readable code. After completion, the application or computer program  1110  accesses and manipulates data accepted from I/O devices and stored in the memory  1106  of the computer  1102  using the relationships and logic that was generated using the compiler  1112 . 
     The computer  1102  also optionally comprises an external communication device such as a modem, satellite link, Ethernet card, or other device for accepting input from and providing output to other computers or from the photodetector array device of the invention. 
     In one embodiment, instructions implementing the operating system  1108 , the computer program  1110 , and the compiler  1112  are tangibly embodied in a computer-readable medium, e.g., data storage device  1120 , which could include one or more fixed or removable data storage devices, such as a zip drive, floppy disc drive  1124 , hard drive, CD-ROM drive, tape drive, etc. Further, the operating system  1108  and the computer program  1110  are comprised of computer program instructions which, when accessed, read and executed by the computer  1102 , causes the computer  1102  to perform the steps necessary to implement and/or use the present invention or to load the program of instructions into a memory, thus creating a special purpose data structure causing the computer to operate as a specially programmed computer executing the method steps described herein. Computer program  1110  and/or operating instructions may also be tangibly embodied in memory  1106  and/or data communications devices  1130 , thereby making a computer program product or article of manufacture according to the invention. As such, the terms “article of manufacture,” “program storage device” and “computer program product” as used herein are intended to encompass a computer program accessible from any computer readable device or media. 
     Of course, those skilled in the art will recognize that any combination of the above components, or any number of different components, peripherals, and other devices, may be used with the computer  1102 . 
     Although the term “user computer” is referred to herein, it is understood that a user computer  1102  may include portable devices such as cellphones, notebook computers, pocket computers, or any other device with suitable processing, communication, and input/output capability. 
     Implementation Details 
     As described above, the SA wavefront sensor may be used in a DIC microscope system in accordance with one or more embodiments of the invention. In one or more embodiments, the structured-apertures consist of four holes (1 μm diameter, 1 μm center-to-center spacing, with the two long axes in the orthogonal x-and y-directions respectively) defined in a sliver film (100 nm thick) above a CMOS image sensor (e.g., the image sensor offered by Micron MT9V403™) ( FIG. 12(   c )). The holes and the CMOS sensor are separated by a 80 μm thick layer of SU-8 resin (depicted as “d” in  FIG. 12(   b ) (measured by a Thorlabs™ optical coherence tomography system [e.g., OCMP1300SS™]). By placing the SA wavefront sensor in the image plane of a standard microscope system, the four holes will selectively transmit and combine the light fields from four adjacent points on the image to create an interference pattern on the CMOS sensor. The total transmission of the interference is proportional to the average image intensity at the aperture. In addition to the spacer thickness “d,” the offsets offset x (x,y) and offset y (x,y) of the zero-order interference spot are related to the net wavefront gradient G x (x,y) and G y (x,y) at the aperture respectively [7]: 
     
       
         
           
             
               
                 
                   
                     
                       
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     The relative simplicity and absence of image intensity-related terms makes this a particularly appealing way to measure the wavefront gradient. In addition, this approach provides the ability to measure the wavefront gradient in both image-plane spatial dimensions simultaneously. 
     The exact proportionality of a device may be experimentally determined by measuring the interference pattern as illustrated in  FIG. 12(   d ). Referring to  FIG. 12(   a ), the SA wavefront sensor is illuminated with a collimated He—Ne laser beam (632.8 nm wavelength, 25 mm beam diameter and 4 mW power) from a range of incident angles. A least-square 2D Gaussian fit is used to compute the total transmission and the offsets (offset x  and offset y ) of the zero-order spot in both x-and y-directions. 
       FIG. 12(   b ) shows the relationship between offset x  (offset y ) of the zero-order spot and the wavefront gradient G x (G y ). Both curves are approximately linear in the measurement ranges. This is consistent with the geometric optics prediction: offset x =d tan(θ)≈dG x , offset y , where θ is the incident angle of the laser beam and when the angle is small. The experimentally measured proportionality from  FIG. 12(   b ) was 70 μm while the predicted value from thickness “d” measurement was 80 μm. Finally, it may be noted that this SA wavefront sensor works with broadband light sources and the zero-order interference spots coincide spatially for all wavelengths. As can be seen in  FIG. 12(   b ), the offset of x of the zero-order interference spot of the structured aperture is linearly proportional to the wavefront gradient G x (G y ) along the x-(y-)direction in a defined measurement range. 
       FIG. 12(   a ) illustrates an experimental scheme of an SA-DIC microscope used in accordance with one or more embodiments of the invention. Two 20× objective lenses (Newport M-20X™) are aligned such that their rear conjugate planes (160 mm behind the objective lens) overlap. The sample is placed at the front conjugate plane of the top objective (L 1 ), and illuminated with a collimated white light (halogen lamp, 200 mW/cm 2 ). Since the microscope system is symmetric, a 1:1 image of the sample is formed at the front conjugate plane of the bottom objective (L 2 ). This image is equivalent to the convolution of the input sample light field with the PSF (point spread function) of the microscope system. 
     The SA wavefront sensor may be placed at the center of the image plane. Once placed, the sample may be raster-scanned (e.g., by two Newport CMH-25CCCL™ actuators) in the x-y plane to complete the mapping of the intensity and wavefront gradient of the image. During the imaging process, the illumination, the optical system and the sensor may be fixed with respect to each other. Such positioning/fixation provides stable and precise measurement with a simple optical system. 
     To demonstrate the quantitative DIC sensing capability and its application in biological imaging, a starfish embryo (Carolina Scientific™) may be used as a test sample.  FIG. 13(   a ) shows a microscope (e.g., Olympus BX41™) image of the sample acquired with a 10× objective.  FIG. 13(   b ) is the corresponding image under a standard DIC microscope (Zeiss Axioplan™, 40× objective).  FIG. 13(   c - e ) show the intensity, X and Y DIC phase images acquired by a microscope with a single scan in accordance with one or more embodiments of the invention. The spatial sampling step size was 0.5 μm in both x- and y-directions, and the exposure time associated with each sampling point was 8 ms. 
     The conventional transmission microscope image and the SA-DIC intensity image are consistent with each other. However, the SA-DIC phase images (i.e.,  FIG. 13(   c )- 13 ( e ) appear to be different from the conventional DIC image. Such differences result because the SA-DIC phase images purely maps the wavefront gradients while the conventional DIC image contains some intensity image variations. This distinction is particularly apparent when one compares the embryo&#39;s gastrocoel for all of the images. The image intensity associated with the gastrocoel region was low and the region appeared darker in the conventional DIC image. In comparison, the corresponding areas of the SA-DIC phase images do not appear darker because they are pure phase maps. Finally, it may be noted that the SA-DIC phase and amplitude images are also an improvement over conventional DIC images in that they are quantitative maps. The wavefront gradient sensitivity of operating in the above described experimental conditions is approximately 4 mrad; the sensitivity can be improved by using a better sensor platform, increasing measurement time and/or increasing the illumination intensity. [7] 
     The ability to image birefringent samples properly is yet another advantage of embodiments of the present invention. Birefringent objects, such as the potato starch storage granules, can alter the polarization of the two displaced light fields in a conventional DIC microscope, such that the subsequent combination of the two fields is no longer describable by Eq. (1). This can give rise to Maltese-cross pattern artifacts in the resulting conventional DIC images (as illustrated in  FIG. 14(   b )). Since the SA-DIC microscope uses unpolarized illumination and does not rely on polarization for image processing, it can image birefringent samples without artifacts, as shown in  FIGS. 14(   d ) and ( e ). It is also worth noting that the dark absorption spots of the starch granules in the center of the intensity images ( FIG. 14(   c )) do not appear in SA-DIC phase images ( FIGS. 14(   d ) and ( e )). This is another clear indication that the SA-DIC microscope can separate the intensity variations of the image wavefront from the phase variations. 
       FIG. 15  illustrates a completed wavefront-sensing sensor chip (top left), a camera port housing for the chip (top right), and the use of the entire unit plugged into a camera port of a microscope in accordance with one or more embodiments of the invention. Such a use provides for the integration of the DIC functionality of the microscope onto the detector whereas conventional DIC microscopy methods use bulky optical elements in the microscope itself. 
     The aperture size may impact several aspects of the system performance. The SA-DIC microscope resolution may be limited by the numerical aperture of the collection optics or the aperture size divided by the system&#39;s magnification (M). By limiting the system magnification, a resolution equal to the aperture size (2 μm) may result (e.g., an imaging system with M=1). A system can be created that is limited by the numerical aperture of the collection optics by either increasing M or decreasing the aperture size. 
     A smaller aperture can lead to a decreased sensitivity of the wavefront gradient measurement for two reasons. Firstly, a smaller aperture will lead to a broader interference pattern which can negatively impact the ability to determine the offsets of the zero order interference spot [8]. Secondly, a smaller aperture will transmit less light and therefore lead to an overall decrease in the detected signal. 
     In conclusion, one can demonstrate a high-resolution and artifact-free quantitative DIC microscopy method based on the SA wavefront sensor. The method can simultaneously generate one intensity and two orthogonal wavefront gradient images. Unlike a conventional DIC microscope, SA-DIC is capable of imaging birefringent samples without artifactual image errors. Further, imaging speed can be increased by using more sensitive detectors, e.g. avalanche photodiode (APD) array, employing faster scanning system, and/or parallelizing the imaging process [9][10]. 
     Conclusion 
     As described above, one or more embodiments of the invention provide various different types of and methods for utilizing a wavefront sensor. A wavefront microscope or camera may include a light source, a wavefront relay system, a wavefront sensor, and an output mechanism. DIC functionality of the microscope or camera may be integrated into the wavefront sensor. 
     The light source of the microscope or camera is configured to illuminate a sample. 
     The wavefront relay system is configured to relay a wavefront generated by the sample. 
     The wavefront sensor is configured to receive the wavefront from the relay system, measure a local intensity of the wavefront, and measure a phase gradient of the wavefront. The wavefront sensor may be a single pixel wavefront sensor where the different measurements and image maps are obtained via raster scanning. Alternatively, the sensor may be a wavefront sensor array where the measurements and images consist of a snapshot of the entire sample. 
     The wavefront sensor may be configured as a Shack-Hartmann type device that consists of a microlens array that focuses the wavefront across each lens of the array and forms a spot onto a photodetector array. The photodetector array outputs a measurement of the phase gradient of the wavefront and the local intensity of the wavefront. 
     Whether used in the wavefront microscope or in any other type of imaging device, embodiments of the invention may provide a specific type of wavefront sensor using structured apertures. In such a device, a metal film has one or more patterned structured 2D apertures configured to convert a phase gradient of the wavefront into a measurable form. A photodetector array receives the wavefront projected through the apertures and outputs a measurement of the phase gradient and local intensity of the wavefront. 
     The output mechanism outputs a local intensity 2D image map and a phase gradient 2D image map (e.g., onto a display device). In addition, the output mechanism may further analyze the data. Such an analysis may receive a recording of signals of the wavefront projected onto the photodetector array. A computer (e.g., computer processor) may be used to separate the signals from the projection of one patterned structured aperture from the other apertures. Such a separation may be performed by suppressing the crosstalk from neighbor hole projections iteratively. All signals of the projections for each aperture are summed together and is proportional to an intensity of the wavefront. A center of the projection from each aperture is predicted. A center position change from the predicted center (based on snapshots taken with and without the sample in place) is determined and is directly related to the phase gradient of the wavefront (i.e., of the sample). 
     The foregoing description of the preferred embodiment of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto. 
     References 
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     [3] Ben C. Platt and Roland Shack, History and Principles of Shack-Hartmann Wavefront Sensing, Journal of Refractive Surgery 17, S573-S577 (September/October 2001). 
     [4] Shack-Hartmann, Wikipedia (Mar. 30, 2009). 
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     [6] J. Z. Liang, D. R. Williams, D. T. Miller, Journal of the Optical Society of America a-Optics Image Science and Vision 14, 2884 (November 1997). 
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