Patent Application
20190137932
The technical field generally relates to methods and devices for detecting birefringent crystals or birefringent materials in a sample. In one embodiment, the technical field relates to methods and devices for observing monosodium urate (MSU) crystals and calcium pyrophosphate (CPP) dihydrate crystals in synovial fluid aspirated from a subject's joint for the diagnosis of gout and pseudogout, respectively.
Gout is a type of inflammatory arthritis caused by the deposition of monosodium urate (MSU) crystals in the joints and periarticular structures such as the tendons and ligaments. During an acute gout attack, the patient experiences severe pain and swelling of the affected structures which can often be debilitating for the patient. The prevalence of gout has been gradually increasing by as much as fourfold for the past five decades, and is the most common type of inflammatory arthritis in the United States affecting over 8 million adults, 3.9% of the entire population. Gout is caused by a combination of factors including diet, medication, and genetics and it occurs more commonly in individuals who consume red meat, consume beer, and are overweight.
Pseudogout is clinically similar to gout but caused by the deposition of calcium pyrophosphate (CPP) crystals in and around joints including cartilage, menisci and synovial fluid. Diagnosis of pseudogout can be made by identification of CPP crystals from synovial fluid or other body tissue. CPP crystals are weakly and positively birefringent. Estimates of CPP disease (CPPD) are harder to specify given the greater difficulty identifying CPP crystals (in comparison to MSU crystals), but best estimates put the prevalence of CPPD at 10 million adult Americans.
The pathogenesis of gout is complex, involving abnormalities in both metabolism and immunity. The key components include hyperuricemia (high level of serum urate) and MSU crystallization. Uric acid is a byproduct of purine metabolism, degraded by the enzyme uricase by most mammals; however, humans lack this enzyme because of multiple evolutional mutations of its coding gene and hence have higher levels of serum urate than other mammals. Once serum urate rises above 6.8 mg/dL, urate can form MSU crystals under certain environmental factors, (typically in and around joints) which then act as a potent trigger of inflammation in the joints. As such, diseases that are caused by crystal deposition of the joints are defined as crystal arthropathy. The etiology of CPPD is less clear. Crystals typically form within cartilage or menisci and may take decades to form. Crystal formation is most commonly associated with concurrent osteoarthritis, but may also be prevalent in conditions affecting calcium metabolism.
Diagnosis of a rheumatic disorder such as crystal arthropathy can be established by identifying these birefringent crystals, namely MSU crystals for gout and calcium pyrophosphate (CPP) crystals for pseudogout, in the joints of a patient by examining synovial fluid samples with a compensated polarized light microscope (CPLM). Compared to a standard bright-field light microscope, a CPLM has a pair of linear polarizers using the cross-polarized configuration, and a full-wave retardation plate (red compensator) to convert birefringence of the objects into color variations. MSU crystals have strong negative birefringence and needle-like shape i.e., the fast axis is along the axial direction of the crystal, which, when observed under a CPLM, appear yellow (or blue) when the MSU crystal is aligned parallel (or perpendicular) with the slow axis of the full-wave retardation plate, upon a red/magenta background color. On the other hand, CPP crystals have weak positive birefringence and rhomboid or rod-like shape. Although polarized microscopy has been considered as the “gold standard” for diagnosis of crystal arthropathy since 1961, recent studies show that joint aspiration is not regularly performed in primary care clinics. In some observational studies, only about 10% of primary care physicians performed polarizing microscope examination in diagnosing gout or pseudogout patients.
Among other reasons, limitations of the conventional lens-based microscopes play an important role. Most critically, conventional lens-based microscopes have relatively small field-of-view (FOV), especially when high-numerical aperture (NA) and high-magnification objective lenses are used. For example, in the identification of MSU crystals, routinely a 40× (e.g., 0.75NA) objective lens is used to observe the morphology of the crystals, resulting in an extremely small FOV (˜0.2 mm2) which leads to long examination times by diagnosticians. In particular, when there is only a limited number of crystals present in a synovial fluid sample taken from the patient, the examination of the entire sample can be not only time-consuming but also can produce a non-reliable diagnostic result because of operator-dependent bias in detecting the crystals over a limited FOV. The concentration of crystals directly correlates with diagnosticians' ability to positively identify crystals. Furthermore, the reliability of CPLM for detection of MSU and CPP crystals can vary widely depending on the examiner's level of training. Moreover, polarized light microscopes are bulky, heavy and expensive (e.g., $10,000 to $20,000 or more). These drawbacks of current methods and microscope devices call for a newer methods and systems to detect to detect crystal arthropathy such as MSU and CPP with higher-throughput, easier to use; and ideally automated.
In one embodiment, to address the limitations of the conventional lens-based polarized light microscopes, a lens-free microscope device has been developed that uses holographic imaging to produce high-resolution images of the deposited crystals contained in synovial fluid. A source of illumination generates light that is first passed through a first circular polarizer prior to reaching a sample contained on an optically transparent substrate such as a microscope slide. The light passes through a second polarizer and retarder film that are both interposed between the opposing side of the optically transparent substrate and an image sensor that is used to capture the holographic images of the sample. The captured holographic images of the birefringent crystals are then subject to computational reconstruction such as pixel super-resolution and multi-height phase recovery to generate reconstructed phase and amplitude images of the crystals. Images are obtained at different orientations or positions of the first polarizer and amplitude subtraction is performed on the reconstructed images which are used to identify or characterize crystals in the sample.
With ˜2 orders of magnitude larger FOV than a CPLM, the microscopy technique described herein has the potential to largely improve the efficiency and accuracy of crystal arthropathy, while also reducing costs. Furthermore, as the lens-free imaging set-up can be extremely compact, cost-effective and field-portable, the presented method is especially promising for automated diagnosis of crystal arthropathy at the point of care or in resource-limited clinical settings.
Lens-free computational microscopy addresses the efficiency and reliability issues of conventional crystal arthropathy diagnosis using the CPLM. However, the adaptation of the current bright-field lens-free microscopy setup to polarized imaging is not straightforward: the cross-polarized configuration used in CPLM can totally extinguish the background light that is not modified by the birefringent sample, and therefore is not applicable to lens-free holography where a reference light is necessary to form interference. Moreover, the color contrast of birefringent objects as generated by a conventional CPLM is challenging to replicate by a lens-free microscope which inherently uses narrow-band illumination sources, unless multiple wavelengths are used.
In one embodiment, a method of imaging a sample having birefringent crystals or birefringent materials using a lens-free polarized microscopy device includes illuminating the sample contained on a sample holder with circularly polarized partially coherent or coherent light and capturing lower resolution holographic images of the birefringent crystals with an image sensor. A polarization analyzer unit made from a λ/4 retarder and a linear polarizer is positioned between the sample holder and the image sensor. The polarization analyzer unit can be moved or rotated into different positions or orientations. The lower resolution holographic images are obtained with the polarization analyzer unit in two different orientations (e.g. ˜90° orientations with respect to one another). Phase-retrieved, higher resolution images of the birefringent crystals at the two different orientations are obtained using the lower resolution holographic images. For example, pixel super-resolution (PSR) and multi-height phase recovery may be used to obtain the higher resolution image. A differential image is generated from the respective phase-retrieved, higher resolution images. An object support mask is applied to identify the birefringent crystals which can then be pseudo-colored.
In another embodiment, a lens-free polarized microscopy device includes a light source emitting coherent or partially coherent light and a circular polarizer that receives light from the light source. An optically transparent sample holder holds the sample that contains the birefringent crystals or birefringent material and is disposed along an optical path that is positioned to receive the circular polarized light. The output light from the circular polarizer is located a distance (z1) from the optically transparent sample holder. The device includes an image sensor disposed on an opposing side of the optically transparent sample holder and is positioned along the optical path, wherein an active imaging surface of the image sensor is located a distance (z2) from the sample holder and z2<<z1. The microscopy device includes a mechanical stage configured to move the image sensor in the x, y, and z directions. A polarization analyzer unit that is formed from a λ/4 retarder and a linear polarizer is positioned between the sample holder and the image sensor. The polarization analyzer unit is moveable or rotatable between two orientations.
The birefringent crystals 4 that may be present in the synovial fluid (or other bodily fluid or tissues) include, for example, monosodium urate (MSU) crystals or calcium pyrophosphate (CPP) dihydrate crystals. The presence of MSU crystals in a synovial fluid sample 12 is used to diagnose gout in the subject. MSU crystals appear as needle-shaped crystals. When analyzed using a polarizing filter and red compensator filter, the MSU crystals appear yellow when aligned parallel to the slow axis of the red compensator but turn blue when aligned perpendicular across the direction of polarization (i.e., MSU crystals exhibit negative birefringence). The presence of CPP crystals in a synovial fluid sample 12 is used to diagnose pseudogout. CPP crystals are generally shorter than MSU crystals and may be either rod-like or rhomboidal in shape. Under a polarizing filter, CPP crystals exhibit positive birefringence; appearing blue when aligned parallel with the slow axis of the red compensator and yellow when oriented perpendicular.
Other crystals that can be formed in the mammalian body fluid or tissue besides MSU and CPP that cause or contribute to crystal-associated diseases, including but not limited to, crystal arthropathy, ureteral, or kidney stones caused by crystals among others, and exhibit birefringence may also be imaged using the methods and devices described herein. For example, urine may be examined for calcium oxalate crystals in subjects with kidney or ureteral stones. While the methods described herein are largely described in the context of imaging birefringent crystals 4 of biological origin, it should be understood that the methods and devices may also have applicability to imaging birefringent crystals 4 that are of non-biological origin. For example, birefringent crystal or material analysis may be used for material, mineralogical, or geological examination. Asbestos fibers are, for example, an example of a birefringent material. In yet another alternative, the birefringent crystal 4 may be synthetic, such as those that are synthesized. Thus, the sample 12 may be organic or inorganic in some embodiments.
Still referring to
The lens-free microscope system 2 includes an image sensor 24 that is located adjacent to the underside of the sample holder 20. As explained below, a polarization analyzer unit 25 is positioned between the sample holder 20 and the image sensor 24. The image sensor 24 may be CMOS-based image sensor. The image sensor 24 may be a color sensor or a monochrome color sensor.
The distance between the output of the light from the circular polarizer 21 and the sample 12 referred to as the z1 distance is generally on the order of several centimeters (e.g., ˜10-15 cm). The active surface (i.e., imaging surface) of the image sensor 24 is located a distance z2 below the surface of the sample holder 20 that holds the sample 12 and is significantly smaller as compared to the z1 distance (i.e., z2<<z1). The typical distance for the z2 dimension is generally less than 1 mm and, in other embodiments, between about 100 μm to about 800 μm, and in other preferred embodiments within the range of about 600 μm to about 800 μm. The image sensor 24 in the lens-free microscope system 2 is used to capture holographic images of birefringent crystals 4.
With reference to
In still another alternative embodiment, rather than move the optical fiber 18 in the x and y directions, a plurality of spaced apart illumination sources (e.g., an array of light sources not shown) can be selectively actuated to achieve the same result without having to physically move the optical fiber 18, circular polarizer 21, or image sensor 24. The small discrete shifts (either by movement or actuation of spatially separated light sources) parallel to the image sensor 24 are used to generate a pixel super-resolution hologram image. In addition to movement in the x and y directions, the translation stage 30 may also move the sample holder 20 and/or image sensor 24 in the z direction (i.e., orthogonal to x, y plane) so that images may be obtain at multiple heights. This enables multi-height phase recovery as described in more detail below.
In the pixel super-resolution process, a plurality of lower resolution images are taken at different positions and are used to generate a computational image reconstruction that has a higher resolution. As seen in
Next, as seen in operation 1200, the distance between the sample 12 and the image sensor 24 is adjusted to a different distance (dn) (e.g., by adjusting z distance using translation stage 30). At this new distance (dn), as seen in operation 1300, a plurality of lower resolution images are obtained of the sample 12 containing the birefringent crystals 4 while the illumination source 14 (or optical fiber 18), sample holder 20, and/or the image sensor 24 are moved relative to another at a plurality of different locations (e.g., x, y locations) to create the sub-pixel image shifts. The plurality of lower resolution images are obtained while the sample 12 and the image sensor 24 are located at the new or different distance (dn). After the lower resolution images are obtained, as seen in operation 1400, a pixel super-resolved hologram (at the different distance (dn)) is synthesized based upon the plurality of lower resolution images obtained in operation 1300. As seen by arrow 1500, process is repeated for different sample-to-sensor differences. Generally, the process repeats such that a pixel super-resolved hologram is created at between 2-20 different distances although this number may vary.
Now referring to
Still referring to
To initiate the phase recovery process, a zero-phase is assigned to the object intensity measurement. One iteration during this phase-recovery process can be described as follows: Intensity measurement #1 (step 1700) is forward propagated (with zero initial phase) to the plane of intensity measurement #2 (step 1800). Then, the amplitude constraint in measurement #2 (step 1800) is enforced while the calculated phase resulting from forward propagation remains unchanged. The resulting complex field is then forward propagated to the plane of intensity measurement #3 (step 1900), where once again the amplitude constraint in measurement #3 is enforced while the calculated phase resulting from forward propagation remains unchanged. This process continues until reaching the plane of intensity measurement #M (step 2000). Then instead of forward propagating the fields of the previous stages, back propagation is used as seen by respective arrows A, B, and C. The complex field of plane #M (step 2000) is back propagated to the plane of intensity measurement #M−1. Then, the amplitude constraint in measurement #M−1 is enforced while the resulting phase remains unchanged. The same iteration continues until one reaches the plane of intensity measurement #1 (step 1700). When one complete iteration is achieved (by reaching back to the plane of intensity measurement #1), the complex field that is derived in the last step will serve as the input to the next iteration. Typically, between 1-1,000 iterations and more typically between 1-70 iterations are required for satisfactory results. After the phase recovery iterations are complete, as seen in operation 2100, the acquired complex field of any one of the measurement planes is selected and is back propagated to the object plane to retrieve both phase image 2200 and amplitude image 2300 of the sample 12.
Referring back to
The computer 32 may be associated with or contain a display 38 or the like that can be used to display images that are generated in accordance with the methods described herein. These may be greyscale images or pseudo-color images of the birefringent crystals 4. The user may, for example, interface with the computer 32 via an input device 40 such as a keyboard or mouse to select different software functions using a graphical user interface (GUI) or the like. It should be noted that the method described herein may also be executed in a cloud-based processing operations. Image data could be sent to a remote computer 32 (e.g., remote server) for processing with a final image being generated remotely and sent back to the user on a separate computer 32 or other electronic device (e.g., mobile phone display) for ultimate display and viewing. Image and other data may be transferred over a wide area network such as the Internet or a proprietary communication network (like those used for mobile devices).
Referring back to
Importantly, the angle at which the λ/4 retarder 42 and a linear polarizer 44 are bonded to one another is optimized for the particular birefringent crystals 4. For example, it was found that, for MSU birefringent crystals 4, the linear polarizer film 44 should be optimally angled relative to the λ/4 retarder film 42 with a linear polarizer 44 orientation of around +65°. That is to say, if the λ/4 retarder film 42 has its long side parallel to the x axis, the linear polarizer film of the 44 is angled at around 65° with respect to the x axis. For CPP birefringent crystals 4, it was found that the linear polarizer film 44 should be optimally angled relative to the λ/4 retarder film 42 with a linear polarizer 44 orientation of around +50°. Thus, in one embodiment of the invention, the linear polarizer film 44 should be angled relative to the λ/4 retarder film 42 with a linear polarizer 44 orientation within the range of about +40° to about +60°. While CPP birefringent crystals 4 are visible where the polarizer analyzer angle-mismatch is +65° (i.e., MSU optimization), by setting the angle-mismatch to +50°, enhancement of the weaker CPP birefringent crystals 4 is improved. However, at 50° MSU birefringent crystals 4 lose some of their birefringent intensity. For viewing MSU birefringent crystals 4 the angle-mismatch should be in the range of about 55° to about 75° with 65° being preferred as described herein.
In one embodiment, different polarization analyzer units 25 may be provided for different birefringent crystals 4. For example, a polarization analyzer unit 25MSU may be created that is optimized for identifying MSU birefringent crystals 4. Another polarization analyzer unit 25CPP may be created that is optimized for identifying CPP birefringent crystals 4. These different polarization analyzer units 25MSU, 25CPP can be swapped in and out of the microscopic imaging system 2 to look for specific birefringent crystals 4. In another embodiment, a single polarization analyzer unit 25 may be used. In this embodiment, the angle-mismatch may be provided somewhere in between the optimal angle for MSU and CPP crystals (e.g., ˜58°).
Operation 115 illustrates the lens-free reconstructed image of a FOV of a sample containing birefringent crystals 4 after rotation of the polarization analyzer unit 25. Because differential imaging is used to subtract image amplitudes, image registration is performed to match to high resolution lens-free reconstructed images in the 0° orientation and the 90° orientation. Image registration is seen in
While reference is made to rotating the polarization analyzer unit 25 by approximately 90° it should be understood that the amplitude subtraction process works even if the rotation is somewhat off of 90°. For example, without limiting the scope of the invention, a rotation within the range of 90°±15° will still remove or reduce absorptive objects. Useful results may even be obtained for angle orientations that fall outside the above-noted range. In addition, while the experiments described herein describe the polarization analyzer unit 25 being rotated the same result could be achieved by bonding or adhering the analyzer unit 25 to the image sensor 24 and rotating the sample holder 20 between the two imaging runs.
The holographic microscope system 2 illustrated in
A broad band source (WhiteLase-Micro, Fianium Ltd, Southampton, UK) was used to provide illumination at a wavelength of 532 nm, with a spectral bandwidth of ˜2.5 nm and an optical power of ˜20 μW. Note that, as explained herein, in other embodiments, the light source could be a narrow band light source such as LEDs or laser diodes or the like. The source is coupled to a single-mode optical fiber and the light is emitted at the end of this fiber without any collimation, as shown in
Before image acquisition, the orientation of the circular polarizer is rotated manually to maximize the total illumination power on the sample by observing the histogram of the live readout from the image sensor. This alignment step does not need to be repeated for further imaging experiments if the illumination part remains unchanged, and for an unpolarized light source, no such alignment is necessary.
At the first stage of the image acquisition, the long side of the polarization analyzer unit is aligned with the long side (i.e., horizontal direction) of the image sensor chip. After PSR and multi-height hologram acquisition, the polarization analyzer unit is rotated by 90° and the same PSR and multi-height hologram acquisition process is repeated. As noted herein, rotation does not need to be exactly 90° because good subtraction results may be obtained with other angled orientations. Since the rotation of the analyzer is equivalent to the rotation of the sample, in an alternative design, one can permanently bond the polarization analyzer unit to the image sensor and rotate the sample between the two imaging runs.
A 1.8 cm-by-1.5 cm piece of λ/4 retarder film (75 μm thickness, Edmund Optics, Inc., Barrington, N.J.) is cut out from a larger sheet, with the long side parallel to the slow axis. A piece of linear polarizing film (180 μm thickness, Edmund Optics, Inc., Barrington, N.J.) of the same dimensions is cut, with the long side at 65° with respect to the polarization direction (for MSU crystals). Then the two pieces are aligned and bonded together using ultraviolet (UV)-curable adhesive (NOA 68, Norland Products, Cranbury, N.J.) with the λ/4 retarder on top (i.e., closer to the sample), and cured under a UV lamp.
In general, for an unpolarized light source, a piece of circular polarizer placed in front of the light source is sufficient to generate circularly polarized light, without the need for alignment. However, in the experimental set-up the light generated by the tunable illumination source is close to linearly polarized light. Therefore, the orientation of the circular polarizer in the set-up translates into output light intensity variations. To better utilize the power of the illumination source, a 3D-printed rotatable holder was designed for the circular polarizer to achieve free manual rotation with a range of 180°. First, a circular polarizer piece is cut from a larger sheet (left-handed plastic circular polarizer, Edmund Optics, Inc., Stock #88-087), and is glued to a 3D-printed rotary piece with a handle. Then the rotary piece is placed inside a 3D-printed outer shell with openings on the top and at the bottom, and with tick marks for 10° increments. Finally an optical fiber holder is embedded inside the same outer shell, on top of the rotary piece.
As depicted in
(1) Image registration. The automated feature-matching algorithm in the Computer Vision System Toolbox™ of MATLAB® was used to calculate a geometric transform between the two sets of complex images assuming a similarity relationship, based on which the 90° image is aligned to the 0° image. Note that this feature matching requires that the inputs are real-valued images. Therefore, the absolute-background-subtracted versions of the two complex images was used for feature extraction purposes:
O
j
3
=|O
j
−Ō
j| (1)
where Oj(j={0°, 90°}) denotes the two complex images to be aligned, Ōj denotes the mean value of Oj.
(2) Image normalization. Both the 0° and 90° complex images after image registration in step (1) are divided by their respective mean values, such that the discrepancy between their brightness is minimized. This step results in two normalized complex images
A
j(j={0°, 90°}).
(3) Subtraction of image amplitudes. Next, one calculates As=|A0°|−|A90°|, resulting in a differential image As whose values are centered around 0.
(4) Birefringent object support calculation. To further exploit the information about the object support, i.e., the specific positions and maps of birefringent objects within the sample FOV, the complementary brightness property of this optical design is advantageously leveraged, where the brighter-than-background pixels caused by birefringence in the 0° image will roughly correspond to darker-than-background pixels in the 90° image, and vice versa. Based on this, the object support mask (M) for birefringent objects in the imaging FOV can be calculated using the following binary operation:
M=(|A0°|−1>thr AND |A90°|−1<-thr)
OR
(|A0°|−1>-thr AND |A90°|−1<thr) (2)
where thr is a predefined threshold value, e.g., 0.1, AND and OR refer to pixel-wise logical operators. The object support mask is then softened using a Gaussian function with σ=0.56 μm, resulting in a new mask:
where * denotes two-dimensional convolution operation.
(5) Application of object support. After the calculation of the birefringent object support mask Mb, a grayscale differential image is then created, AM=As ∘Mb, where ∘ denotes pixel-wise multiplication of two images.
(6) Pseudo-coloring of the lens-free image. In this final step, the grayscale differential image AM is mapped into a color image C to create a similar color contrast compared to a conventional CPLM image for the ease of a rheumatologist to inspect the lens-free images. This color map is statistically learned using a sample lens-free grayscale differential image from step (5) and a corresponding CPLM image (40×0.75NA) of the same sample. First these two images (lens-free and CPLM) are aligned with respect to each other using image registration. Then, a set of 128 bins are created for the sample lens-free grayscale differential image, spanning the entire range of its values:
bink=[a+(k−1)w, a+kw) (4)
where k=1, . . . , 128, a is the minimum value of the sample lens-free grayscale differential image (AM), and a+128w is equal to the maximum value of AM. For each one of these bins, the following is then performed:
a) Find the set of pixels in the sample lens-free grayscale differential image that fall into the kth bin.
b) For this set of pixels found in step (a), find the corresponding pixels in the sample CPLM image, and calculate the mean R, G and B values for these pixels.
After steps (a) and (b), the mapping between the pixel values of the sample lens-free differential image with respect to the R, G and B components of the corresponding CPLM image is created. Finally, a piecewise linear function is used to approximate these three mapping functions (for R, G and B channels) to avoid rapid fluctuations due to insufficient sampling. For values that can potentially occur outside the range of these bins, linear extrapolation method is used.
The pixel size of the image sensor imposes a physical limit on the resolution of a lens-free on-chip microscope, according to the Nyquist sampling theorem. The PSR technique is applied to break this undersampling related resolution limit by capturing multiple subpixel-shifted low-resolution holograms and synthesizing them into a single high-resolution hologram. During the lens-free hologram acquisition, a positioning stage is used to shift the image sensor chip on an 8-by-8 orthogonal grid (x and y directions) with a grid size of 0.28 μm. Note that these subpixel shifts do not need to be precise or known a priori, as a digital shift estimation algorithm can be used to accurately estimate these sub-pixel shifts after image capture. Details regarding the estimation algorithm may be found in Bishara et al., discussed herein, which is incorporated herein by reference. Then a conjugate-gradient-descent method is used to find the optimal high-resolution hologram that is statistically consistent with all the low-resolution pixelated holograms that are undersampled at the sensor array.
If the complex wavefront of an optical field is known, which includes its amplitude and phase information, one can digitally calculate its propagation for a given distance using the angular spectrum method. The complex field is first Fourier-transformed to the angular spectrum domain using a fast Fourier transform (FFT) algorithm. Then an optical phase function is calculated, parameterized by the wavelength, index of refraction of the medium, and the distance of the digital propagation. The multiplication of the angular spectrum of the original optical field and the calculated phase function is inverse Fourier transformed to the spatial domain, yielding the digitally propagated complex optical field.
An autofocus algorithm is used to automatically find the z2 distance (i.e., the sample-to-sensor distance) for a PSR hologram by solving a maximization problem, with the objective function being a focus criterion, and the variable being the propagation distance. The focus criterion used herein is the negative of the Tamura coefficient calculated for the amplitude of the complex image, which is found to give a distinct peak at the correct z2 distance. The hologram is digitally propagated to a range of z2 distances with the focus criterion evaluated at each height, and the corresponding maximum is found. Next, a smaller range of z2 distances are evaluated around this maximum point, with the scanning resolution also refined. These steps are repeated until the scanning resolution falls below a predefined threshold (e.g., 0.01 μm).
A multi-height iterative phase recovery algorithm with ten heights (z direction) is used to retrieve the optical phase of the holograms, in order to mitigate the twin image artifact caused by the loss of phase information at the sensor array. These heights are separated by ˜15 μm. An initial guess of the complex optical wave is calculated using the back-propagation of the hologram at the first measurement height, assuming that the heights are ordered in ascending order (i.e., the closest z2 corresponds to the first height). Then, this initial guess is propagated to the second height, where its amplitude is averaged with the square root of the measured hologram at the second height, and the phase is kept unchanged. Next, this updating process is repeated at the subsequent heights and then backwards after it reaches the last height. Each one of these digital round-trips among these different heights counts as one iteration, and after ˜10-20 iterations the optical phase converges, yielding a unique complex wave for each one of the measurement heights. The converged complex wave of any one of these heights is finally propagated to the plane of the sample to obtain the complex image of the sample. Note that the transport of intensity equation (TIE) is not used here as it is known that TIE is more sensitive to low-frequency components, whereas the multi-height based iterative phase recovery is more sensitive to high-frequency components. Because the birefringent crystals of interest in synovial fluid are relatively small and sharp, the multi-height iterative phase recovery converges rather quickly without the need for using a solution of TIE.
The reference slides containing MSU or CPP crystals were anonymously prepared from a surgically resected large tophus without a link to any subject related information. The tophus was obtained when a patient with confirmed gout or CPP disease received resection surgery of the tophus located in the olecranon bursa. The surgery was routine elective surgery to alleviate the symptom, as part of standard clinical care and unrelated to this study. The tophus was cut in half, revealing a soft semi-liquid center. A smear sample was prepared (touch-prep method), and a small amount of adhesive mounting medium (Cytoseal™, Richard Allan Scientific, Kalamazoo, Mich.) was applied onto the sample. Finally, the slide was cover-slipped.
For the slides of steroid crystals (used as negative control sample), a mixture of methylprednisolone acetate suspension (Depo-Medrol® 40 mg/ml, Pfizer, New York) and 1 cc of 1% lidocaine was made. Twenty microliters of this mixture was placed onto a slide and smeared, and then air-dried. Adhesive mounting medium was not used for the steroid crystals slides, because applying the medium to steroid crystals had a tendency of creating bubbles next to the crystals, which was not observed in the MSU or CPP sample preparation.
All biologic samples were obtained after de-identifying the patients' information. The methodology for obtaining these samples was reviewed by UCLA Institutional Review Board (IRB) and deemed exempt.
In order to model the optical design described herein, one can effectively decompose the presented lens-free polarized imaging system into two sections that deal with polarization and diffraction. In the polarization related part, the circular polarizer, birefringent sample and the analyzer are assumed to be thin and the vertical gaps between these components are assumed to be negligible. In the diffraction part, the light that exits the analyzer diffracts to be sampled by the image sensor, after a propagation distance of z2. The polarization part of this lens-free on-chip imaging system was modeled using Jones calculus and simulated it in MATLAB®. The Jones representation of the respective elements of the imaging system can be written as:
a) Input left-hand circularly polarized (LHCP) light:
where i=√{square root over (−1)}.
Particular attention should be paid to the convention of handedness: the LHCP used in herein is defined from the point of view of the source, i.e., if one looks away from the source, along the direction of light propagation, the temporal rotation of the field at a given point in space is counterclockwise.
b) Birefringent sample:
where φ is the relative phase retardation induced by the object birefringence after the sample plane, and α is the orientation of the fast axis of the birefringent sample with respect to the x-axis.
c) λ/4 retarder:
where β is the orientation of the fast axis of the λ/4 retarder with respect to the x-axis.
d) Linear polarizer:
L=[cos γ sin γ] (8)
where γ is the polarization orientation of the linear polarizer with respect to the x-axis. Note that one can write L as a row vector instead of a 2-by-2 matrix, such that p=LQSW can be a scalar complex output.
Based on these definitions, the variables of interest in the lens-free optical design for polarization imaging are α, β, γ, and φ. In simulations, the shape of the MSU was approximated crystals as a cylinder. It was further assumed that the lower bound on the diameter of the MSU crystal is 0.5 μm, and the lower bound on the birefringence is |Δn|=0.1 with the fast axis being the axis of the cylinder; therefore the relative birefringence induced phase retardation at the center of the cylinder at a wavelength of 532 nm can be approximated as φ˜0.19π. As the incident wave is circularly polarized, without loss of generality, β was selected to be equal to 90°. In order to detect birefringence as well as its sign (+/−) similar to a CPLM image, ideally the brightness in the output image should vary when the MSU crystal takes different orientations in the sample FOV. More specifically, when the MSU crystals are aligned with a certain direction, the output should appear brighter than the background; when perpendicular to the same direction, the output should appear darker than the background. In this way, if the sign of the birefringence changes, the brightness variation will invert, helping to determine the sign of the birefringence of the sample.
With these in mind, the remaining two parameters α and γ were scanned, and calculated the normalized output ({circumflex over (p)}) against a while varying γ, i.e.:
where in the calculation of p0, the Jones matrix of the birefringent sample is replaced by the identity matrix I representing no sample being present. As can be seen in
Next, simulations were run on the behavior of four different types of objects with the same cylindrical morphology with a diameter of 0.5 μm: (1) Transparent and negatively birefringent (φ=0.19π, fast axis is along the cylinder axis); (2) Transparent and positively birefringent (φ=0.19π, fast axis is perpendicular to the cylinder axis); (3) Transparent and non-birefringent (φ=0); (4) Absorptive and non-birefringent (φ=0 and transmission light intensity is attenuated by 36% per micron).
These numerical simulations were performed to better understand how different target objects would appear in the imaging design as compared to potential false positive objects, and the results are summarized in
A close observation of
For this differential lens-free imaging design, it is also important to understand and quantify the linearity of the differential output signal {circumflex over (p)}s with respect to the relative birefringent phase retardation φ. Here, the crystals are assumed to be aligned at 45° (α=45°). Since {circumflex over (p)}s is a periodic function of φ with a period of 2π, one only need to investigate {circumflex over (p)}s with respect to φ varying between −π and π, where 0<φ<π implies that the fast axis is along 45°, and −90 <φ<0 implies that the slow axis is along 45°. As shown in 9A, for small φ(|φ|<0.22g), the differential output {circumflex over (p)}s is almost perfectly linear as a function of φ. However this linearity does not hold for larger φ. In fact, beyond the turning points |φ|≈0.22π, the curve moves backwards and reaches zero at |φ|=π. This is an interesting observation that is revealed by the numerical simulations and analysis, and it should not affect the sensitivity of the imaging platform. The thickness of the needle-shaped MSU crystal gradually increases from its edge (approximately zero thickness) to the middle (largest thickness), so that the relative phase retardation φ also gradually increases from 0 to its maximum value. Therefore, it is guaranteed that even for a thick MSU crystal with a large maximum φ value, there will be a strong linear birefringence signal toward the edges of the crystal for its detection and identification. This is also verified by the simulation results shown in
To demonstrate the imaging capabilities of the lens-free polarized on-chip microscopy platform to be used in gout diagnosis, MSU crystal samples were imaged made from the tophus of a de-identified patient using the lens-free microscope. These images were then compared against the gold standard images captured using a benchtop CPLM (Olympus BX51 with additional polarization components: drop-in polarizer U-POT and gout analyzer U-GAN) with a 40×0.75NA objective lens.
In panel image (h) of
Next, in order to test the performance of the lens-free holographic imaging method to differentiate other types of birefringent crystals from MSU crystals, steroid crystal samples were imaged as a negative control sample. Corticosteroid crystals are birefringent crystals that can be found in some patients' joint fluids following a corticosteroid injection and sometimes can lead to false positives in gout diagnosis. Their irregular shape provides a means to differentiate them from MSU crystals. As shown in
Synovial aspirates from de-identified discarded clinical samples were imaged with the lens-free polarized microscopy device. One different with the experimental setup was that a different angle mismatch was used for the polarization analyzer unit. Specifically, the angle mismatch between the λ/4 retarder and the linear polarizer was +50° which was optimized for the more weakly birefringent CPP crystals. While CPP crystals are visible where the polarizer analyzer angle-mismatch is +65° (i.e., optimized for MSU), by setting the angle-mismatch to +50°, enhancement of the weaker birefringent crystals is improved. However, at +50° MSU crystals lose some of their birefringent intensity.
While embodiments of the present invention have been shown and described, various modifications may be made without departing from the scope of the present invention. The invention, therefore, should not be limited, except to the following claims, and their equivalents.
This Application claims priority to U.S. Provisional Patent Application No. 62/341,540 filed on May 25, 2016, which is hereby incorporated by reference in its entirety. Priority is claimed pursuant to 35 U.S.C. § 119 and any other applicable statute.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US2017/034311 | 5/24/2017 | WO | 00 |
| Number | Date | Country | |
|---|---|---|---|
| 62341540 | May 2016 | US |
