High-resolution, highly polarized sensitive imaging and polarimetry apparatus and method

Abstract

The lens has an optical center and an optical axis passing through the optical center, and at least a first lens portion positioned at a distance away from the optical center that refracts light rays of a given polarization state that impinge on the first lens portion at right angles from the first side towards the optical axis at the second side at a constant bending angle, thereby defining a focal line at the second side along the optical axis.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to and the benefit of U.S. patent application Ser. No. 63 / 320,589, filed March 16, 2022, the entire contents of which are incorporated herein by reference.

[0002] Field of Disclosure The present disclosure relates generally to imaging devices, and more particularly to Bijection Illumination Collection Ellipsometry (BICE) devices and methods for high resolution imaging and polarimetry. [Background technology]

[0003] Lenses are widely used in the field of imaging. Generally, a converging lens is associated with a focal point defined along the optical axis of the lens, which determines the position of a light sensor or photodetector (hereinafter referred to as a "focused sensor position" that defines an image plane) to capture a focused or sharp image of an object at a particular distance (hereinafter referred to as a "focused object position"). Examples of light sensors may be the eye, a light-sensitive material (e.g., a film in a camera), a photoelectron sensor, etc.

[0004] If the light sensor is displaced from the focused sensor position or the object is displaced from the focused object position, the captured image is blurred. In the prior art, the depth of focus (DOF) of a lens refers to the range (which may be characterized by a corresponding range around the focal point) around the focused sensor position where the captured image may be blurred (if the light sensor is displaced from the focused sensor position) while still providing acceptable sharpness (e.g., blurred, but perceptually clear), within a tolerance range. Extended depth of focus (EDOF) allows objects to be positioned within an extended object range around the focused object position while still obtaining an acceptable image.

[0005] High-resolution microscopic imaging of tissue microstructure is useful in biology and enables many clinical applications. Microscopic imaging in three dimensions enables many biological and clinical applications. However, high-resolution optical imaging sustained over a relatively large depth range is hindered by the rapid spreading of light, which is strongly confined due to diffraction.

[0006] As is known in the art, optical microscopy with tightly focused light cannot be sustained over a relatively large depth range due to the rapid spreading of light determined by diffraction. Imaging modalities (e.g., confocal (see ref. 1) and two-photon (see ref. 2) microscopy) achieve high-resolution imaging only from a small region around the focal point. Therefore, an additional scanning mechanism is required to axially translate the focal point relative to the target for depth-determined imaging (see ref. 3). This prevents rapid imaging, and the imaging depth, which is often limited to a few hundred microns (see ref. 4), is not feasible for many applications.

[0007] Using coherence gating, optical coherence tomography (OCT) captures real-time depth-resolved images of millimeter-long structures deep within scattering tissues (see refs. 5-9). Though addressing axial resolution, OCT still faces competing challenges of lateral resolution and depth of focus due to diffraction, which prevents high-resolution imaging in three dimensions over large depth ranges (see refs. 10-12).

[0008] The core problem is how to distribute the light intensity to obtain high-resolution imaging in three dimensions within a large depth range. The focusing of light to a single depth point, widely used in existing imaging systems, brings about an arbitrary advantage to that point that contradicts the objective of depth imaging. Instead, a more even distribution of light intensity along the axial direction would necessarily impair the lateral resolution due to diffraction.

[0009] Ellipsometry is the measurement of the optical polarization-altering properties of a material or system (see Reference 60). An optically linear material or system is characterized by the Stokes vector S inThe incident light has the Stokes vector S out (S out =M×S in ) to (reflected, transmitted, or scattered) light. If a material or system does not depolarize light, then a 2×2 Jones matrix (J) can fully describe the polarization-altering properties of the material or system. Determination of M and J requires at least four and three measurements, respectively.

[0010] Traditionally, ellipsometry is performed by recording multiple measurements and post-processing the measured values. However, this method is slow due to the sequential nature of the measurements. Real-time imaging of biological materials or in vivo tissues requires high-speed methods for ellipsometry. Rotating compensator ellipsometry (see reference 61) has been reported for high-speed ellipsometry, but in principle it is still a sequential method and requires moving parts that complicate the design. Summary of the Invention [Means for solving the problem]

[0011] According to one aspect of the disclosure, there is provided a lens including an optical center, an optical axis passing through the optical center, and one or more lens portions, the one or more lens portions including at least a first lens portion configured to refract light rays of a predetermined polarization state impinging on the lens portion from a first side toward the optical axis at a second side at a constant bending angle, thereby defining a focal line at the second side along the optical axis.

[0012] In some embodiments, at least the first lens portion is positioned a distance away from the optical center.

[0013] In some embodiments, the at least first lens portion includes a first lens portion and a second lens portion, the centers of the first and second lens portions being diagonally opposite each other from the optical center, and the first and second lens portions being configured to pass light rays of orthogonal polarization states.

[0014] In some embodiments, the one or more lens portions further include at least a third lens portion that refracts light rays hitting the lens portion at a constant bending angle from the focal line on the second side in a direction parallel to the optical axis to the first side.

[0015] In some embodiments, the at least third lens portion includes a third lens portion and a fourth lens portion, the centers of the third and fourth lens portions being diagonally opposite each other from the optical center, and the third and fourth lens portions being configured to pass light rays of orthogonal polarization states.

[0016] In some embodiments, in the case of a two-dimensional (2D) coordinate system defined by the lens with the origin of the two-dimensional coordinate system at the optical center, each of the one or more lens portions is positioned in a respective quadrant of the 2D coordinate system.

[0017] In some embodiments, the centers of each circumferentially adjacent pair of one or more lenticular portions are perpendicular to the optical center.

[0018] In some embodiments, the bend angle is 21 degrees.

[0019] In some embodiments, each of the one or more lenticules has a circular shape.

[0020] In some embodiments, each of the one or more lens portions has a diameter of 1.1 millimeters (mm).

[0021] In some embodiments, each of the one or more lens portions includes a metasurface coupled to the substrate.

[0022] In some embodiments, each metasurface includes a number of nanopillars in a pattern of arcs, which are part of a number of concentric circles centered around the optical center.

[0023] In some embodiments, the nanopillars have a cubic shape with a square cross-section, and the nanopillars have the same height and varying widths.

[0024] In some embodiments, the width of the nanopillars is between 80 nanometers (nm) and 300 nm.

[0025] In some embodiments, the height of the nanopillars is 750 nm.

[0026] In some embodiments, adjacent pairs of the nanopillars have a center-to-center distance of 370 nm.

[0027] In some embodiments, the lens further comprises an axicon, the apex of the lens being the optical center, and the one or more lens portions are defined by the axicon.

[0028] In some embodiments, the lens is opaque except for one or more lens portions.

[0029] According to one aspect of the disclosure, there is provided an imaging device including a polarizing beam splitter that splits a beam into a first polarized beam and a second polarized beam of orthogonal polarization states, a beam condition adjustment module that receives the first and second polarized beams and outputs the first and second polarized beams to a lens described in any one of claims 1 to 17, and an adjustment module that introduces a time delay into at least one of the first and second polarized beams and / or adjusts a frequency of at least one of the first and second polarized beams before inputting the first and second polarized beams into the beam condition adjustment module.

[0030] In some embodiments, the lens is the lens described above, and the beam conditioning module includes a primary knife-edge prism, a first knife-edge prism that directs the first polarized light beam to the primary knife-edge prism, and a second knife-edge prism that directs the second polarized light beam to the primary knife-edge prism, the primary knife-edge prism configured to output the first and second polarized light beams to the lens, receive the third light beam and the fourth light beam from the lens, and direct the third light beam to the first knife-edge prism and the fourth light beam to the second knife-edge prism.

[0031] According to one aspect of the disclosure, there is provided a method of manufacturing the above-mentioned lens, comprising depositing an amorphous silicon (a-Si) layer on a substrate using plasma enhanced chemical vapor deposition, applying a layer of negative photoresist to the a-Si layer, generating an etching pattern in the layer of negative photoresist using electron beam lithography (EBL), and generating a-Si nanopillars using deep reactive ion etching that form the metasurface of one or more lens portions.

[0032] In some embodiments, the etch pattern corresponds to a pattern of arcs.

[0033] In some embodiments, the etch pattern corresponds to a plurality of concentric circles.

[0034] In some embodiments, the method further includes opaquely masking one or more unusable regions.

[0035] According to one aspect of the disclosure, there is provided a method of using a lens as described in claim 5 or any one of claims 6 to 17, comprising at least one of directing a first light beam to a first lens portion and collecting a third light beam and a fourth light beam from a third lens portion and a fourth lens portion, respectively, wherein the first light beam has a cross-sectional size that matches the size of the first lens portion.

[0036] According to one aspect of the disclosure, a lens includes an optical center and an optical axis passing through the optical center, and a plurality of lens portions including first and second lens portions on diagonally opposite first and second quadrants of a plane perpendicular to the optical axis for refracting light rays from the first side to the second side, and a third lens portion on a third quadrant of the plane for refracting light rays from the second side to the first side, the first and second lens portions being configured to refract light rays that strike the lens portions perpendicularly from the first side towards the optical axis at the second side at a constant bending angle, thereby defining a focal line at the second side along the optical axis. and a third lens portion configured to refract light rays impinging on the lens portion from a focal line on the second side at a constant bending angle to a first side parallel to the optical axis, or the third lens portion configured to refract light rays impinging on the lens portion perpendicularly from the second side towards the optical axis on the first side at a constant bending angle, thereby defining a focal line on the first side along the optical axis, and the first and second lens portions configured to refract light rays impinging on the lens portion from the focal line on the first side at a constant bending angle to a second side parallel to the optical axis.

[0037] In some embodiments, the lens portions are spaced apart from the optical center.

[0038] In some embodiments, the centers of the first and third lens portions, or the centers of the second and third lens portions, are perpendicular to the optical center.

[0039] In some embodiments, the plurality of lens portions further comprises a fourth lens portion on a fourth quadrant of the plane for refracting light rays impinging on the lens portion from the focal line on the second side at a constant bending angle to the first side parallel to the optical axis, or for refracting light rays impinging on the lens portion perpendicularly from the second side towards the optical axis on the first side at a constant bending angle, thereby towards the focal line on the first side.

[0040] In some embodiments, the bend angle is 21 degrees.

[0041] In some embodiments, each of the one or more lenticules has a circular shape.

[0042] In some embodiments, each of the one or more lenticular portions has a diameter of 1.1 mm.

[0043] In some embodiments, each of the one or more lens portions includes a metasurface coupled to the substrate.

[0044] In some embodiments, each metasurface includes a number of nanopillars in a pattern of arcs, which are part of a number of concentric circles centered around the optical center.

[0045] In some embodiments, the nanopillars have a cubic shape with a square cross-section, and the nanopillars have the same height and varying widths.

[0046] In some embodiments, the width of the nanopillars is between 80 nm and 300 nm.

[0047] In some embodiments, the height of the nanopillars is 750 nm.

[0048] In some embodiments, adjacent pairs of the nanopillars have a center-to-center distance of 370 nm.

[0049] In some embodiments, the lens comprises an axicon, the apex of the lens being the optical center, and one or more lens portions are defined by the axicon.

[0050] In some embodiments, the lens is opaque except for one or more lens portions. [Brief description of the drawings]

[0051] [Figure 1A]FIG. 1 is a schematic plan view of a bijective illumination-collection-imaging (BICI) lens according to some embodiments of the present disclosure, in which the BICI lens includes an illumination lens portion and a collection lens portion, and the centers of the illumination and collection lens portions of the BICI lens are at a 90 degree angle with respect to the optical center of the BICI lens. [Figure 1B] 1B illustrates details of an illumination lens portion of the BICI lens shown in FIG. 1A in accordance with some embodiments of the present disclosure, where the illumination lens portion includes a metasurface. [Figure 1C] 1B is a schematic diagram of the BICI lens shown in FIG. 1A illustrating the metasurface patterns of the illumination and collection lenses. [Figure 2A] 1B illustrates the interaction of the BICI lens shown in FIG 1A with illumination and collection light. FIG 1C illustrates a simplified perspective view of the BICI lens shown in FIG 1A showing illumination light rays impinging orthogonally on the illumination lens portion of the BICI lens shown in FIG 1A at the point of the imaging optical axis, which bends or refracts the illumination light rays by an angle β to form a focal point on the z-axis. [Figure 2B] 1B illustrates the interaction of the BICI lens of FIG. 1A with illumination and collection light. FIG. 1C illustrates a simplified perspective view of the BICI lens of FIG. 1A showing a group or sheet of rays impinging on the illumination lens portion of the BICI lens of FIG. 1A at an arc of radius r, which bends or refracts the sheet of rays by an angle β to form a focal point on the z-axis. [Figure 2C] 2C is a schematic perspective view of the BICI lens shown in FIG 1A showing the interaction of illumination light and collection light with the BICI lens shown in FIG 1A, in which a ray sheet subjected to the same bending paradigm impinging on a location on the illumination lens portion of the BICI lens shown in FIG 1A constitutes a focal line along the z-axis, and although a finite number of focal points are illustrated in FIG 2C for clarity, the focal line is continuous. [Figure 2D] 1B illustrates the interaction of the BICI lens shown in FIG. 1A with illumination light and collection light. FIG. 1C illustrates a schematic perspective view of the BICI lens shown in FIG. 1A showing the collection lens portion of the BICI lens shown in FIG. 1A establishing the trajectory of the collected light in the light sheet, and imaging the illumination path onto the xz plane, thereby enabling a one-to-one correspondence (i.e., a bijective relationship) between the foci of the illumination and collection paths and eliminating out-of-focus signals. [Figure 2E] 2D illustrates the interaction of the BICI lens shown in FIG. 1A with illumination light and collection light. FIG. 2D illustrates an enlarged schematic perspective view of portion A of FIG. 2D demonstrating the bijective relationship. [Figure 2F] 1B illustrates the interaction of the BICI lens shown in FIG. 1A with illumination and collection light. FIG. [Figure 2G] 1B illustrates the interaction of the BICI lens shown in FIG. 1A with illumination and collection light. FIG. 1C illustrates a schematic diagram of an experimental setup to verify the optical properties of the BICI lens shown in FIG. [Figure 2H] 2C shows the interaction of the BICI lens shown in FIG. 1A with illumination and collection light. 2D shows a snapshot captured by the camera at a side intersecting the focal line shown in FIG. 2G illustrating an arrangement of illumination and collection paths that allows collection of photons only originating from the corresponding illumination focal point. [Figure 2I] 1B illustrates the interaction of the BICI lens shown in FIG 1A with illumination light and collection light;FIG 1C illustrates a schematic diagram of the BICI lens shown in FIG 1A showing the focal line length and the distance between the focal line and the BICI lens; [Figure 3A] 1 shows a metasurface for an illumination and collection lens portion; [Figure 3B] 3A shows the metasurface of the illumination and collection lens portion. FIG. 3B shows a schematic side view of the nanopillar shown in FIG. [Figure 3C] 3A shows the metasurface of the illumination and collection lens portion. [Figure 3D] 1 shows a metasurface for an illumination and collection lens portion, and a schematic top view of the nanopillars of the metasurface showing nanopillars with periodically varying sizes in a lattice pattern forming a pattern of arcs or circles. [Figure 3E] 1 shows the metasurfaces of the illumination and collection lenses. FIGURE 1 shows wide-field optical images of the fabricated metasurfaces of the illumination and collection lenses, each with a diameter of 1.1 millimeters (mm). [Figure 3F]1 shows the metasurface of the illumination and collection lens section. 2 shows a scanning electron micrograph of the fabricated metasurface of the illumination and collection lens section comprising square amorphous silicon (a-Si) nanopillars. [Figure 4] 1B shows an analytical point spread function (PSF) of the BICI lens shown in FIG. 1A, indicating that the BICI lens has a lateral resolution of about 3.2 micrometers (μm) and a focal line or depth of focus of about 1.25 mm. [Figure 5A] Analytical PSFs of the prior art using common-path Gaussian and Bessel beams. It can be seen that the PSF of a tightly focused Gaussian beam (approximately 3.2 μm full width at half maximum (FWHM)) falls off rapidly away from the focus. [Figure 5B] 1 shows the analytical PSFs of the prior art using common-path Gaussian and Bessel beams. It is shown that the PSF of the Gaussian beam with a relatively large focal depth (about 1.25 mm) suffers from significantly reduced lateral resolution. [Figure 5C] 1 shows the analytical PSF of the prior art using common-path Gaussian and Bessel beams. The PSF of the Bessel beam with 3.2 μm FWHM of the central lobe shows that there is power spreading into several side lobes that is detrimental to imaging quality. [Figure 6] 1B is a schematic diagram of an interferometer incorporating the BICI lens shown in FIG. 1A in one arm, according to some embodiments of the present disclosure. [Figure 7A] Test results are shown using the interferometer shown in Figure 6. Intensity distribution measurements of an illumination beam with a wavelength of 1300 nm in the xz plane are shown. [Figure 7B] Test results are shown using the interferometer shown in Figure 6. Intensity distribution measurements of a collected beam at a wavelength of 1300 nm in the xy plane are shown. [Figure 7C] 7 shows test results using the interferometer shown in Figure 6. The imaging PSF, which is the product of the illumination and collection intensity profiles, shows the maintenance of a sharp PSF over a large axial range. [Figure 8A] 2 shows measurements of the resolution and depth of focus of the BICI lens shown in Fig. 1. FIGURE 3 is a schematic of the measurement setup imaging a sub-wavelength gold line scanned across a focal line at various depth points. [Figure 8B] Figure 2 shows measurements of the resolution and depth of focus of the BICI lens shown in Figure 1. The measured imaging PSF at three depth points is shown. [Figure 8C] We show measurements of the resolution and depth of focus of the BICI lens shown in Figure 1. We show the measured resolution of the BICI lens shown in Figure 1 compared to the theoretical resolution obtained from a Gaussian beam (in a common path illumination-collection scheme) of the same lateral resolution, highlighting the ability of the BICI lens shown in Figure 1 to maintain high resolution over a large depth range. [Figure 9A] 1 is a schematic plan view of a BICI lens according to some embodiments of the present disclosure, in which the centers of the illumination and collection lens portions of the BICI lens are at angles less than 90 degrees to the optical center of the BICI lens. [Figure 9B] 1 is a schematic plan view of a BICI lens according to some embodiments of the present disclosure, in which the centers of the illumination and collection lens portions of the BICI lens are at angles greater than 90 degrees to the optical center of the BICI lens. [Figure 10A] 1 illustrates a schematic plan view of a BICI lens according to some embodiments of the present disclosure, where the illumination and collection lens portions of the BICI lens are at the diagonal anti-symmetric limits of the BICI lens. [Figure 10B] 10A illustrates a BICI lens according to some embodiments of the present disclosure.FIG. 10B illustrates a schematic top view of the BICI lens shown in FIG. [Figure 10C] 10A illustrates a BICI lens according to some embodiments of the present disclosure.FIG. 10B illustrates a simplified perspective view of the BICI lens shown in FIG. [Figure 10D] 10D, which illustrates a BICI lens according to some embodiments of the present disclosure. [Figure 11A] 1 is a schematic plan view of a BICI lens according to some embodiments of the present disclosure, in which the BICI lens includes two illumination lens portions and one collection lens portion. [Figure 11B]1 is a schematic plan view of a BICI lens according to some embodiments of the present disclosure, in which the BICI lens includes one illumination lens portion and two collection lens portions. [Figure 12] 1 is a schematic plan view of a BICI lens according to some embodiments of the present disclosure, in which the BICI lens includes two illumination lens portions and two collection lens portions. [Figure 13A] A comparison is shown between the resolution of the BICI lens shown in FIG. 1A (see FIG. 13A) and the resolution of the BICI lens shown in FIG. 12 (see FIG. 13B). [Figure 13B] A comparison is shown between the resolution of the BICI lens shown in FIG. 1A (see FIG. 13A) and the resolution of the BICI lens shown in FIG. 12 (see FIG. 13B). [Figure 14A] 1B illustrates a manufacturing process for the BICI lens shown in FIG. 1A according to some embodiments of the present disclosure. [Figure 14B] 1B illustrates a manufacturing process for the BICI lens shown in FIG. 1A according to some embodiments of the present disclosure. [Figure 15] FIG. 1 is a schematic plan view of a BICI lens according to some embodiments of the present disclosure, in which the BICI lens includes a metasurface having a pattern of multiple concentric circles centered on an optical center, and in use, may direct an illumination beam to a first region, which may be used as an illumination lens portion, and may direct a light collector to a second region, which may be used as a collection lens portion. [Figure 16] 1 is a schematic plan view of a BICI lens according to some embodiments of the present disclosure, in which the BICI lens has a square shape. [Figure 17] 1 is a schematic plan view of a BICI lens according to some embodiments of the present disclosure, in which the optical center of the BICI lens does not overlap with the geometric center of the BICI lens. [Figure 18] 1 is a schematic plan view of a BICI lens according to some embodiments of the present disclosure, the BICI lens including four circular lens portions each having a maximum size in a corresponding quadrant. [Figure 19A] 1 is a schematic perspective view of a BICI lens according to some embodiments of the present disclosure, in which the BICI lens includes an axicon. [Figure 19B]FIG. 19B is a schematic plan view of the BICI lens shown in FIG. 19A. [Figure 20A] 1 is a schematic plan view of a BICI lens according to some embodiments of the present disclosure, in which the BICI lens includes a collecting lens portion. [Figure 20B] FIG. 20B is a schematic perspective view of the BICI lens shown in FIG. 20A and a line camera that collects light rays from various focal points within the focal line of the BICI lens. [Figure 21] 1 is a schematic diagram illustrating a fully incident illumination and collection ellipsometry (BICE) lens for high speed, high resolution ellipsometry according to some embodiments of this disclosure. [Figure 22] FIG. 22 is a schematic perspective view of the BICE lens shown in FIG. 21 , which focuses a pair of illumination light beams toward the focal line of the BICE lens according to some embodiments of the disclosure. [Figure 23] FIG. 22 is a schematic perspective view of the BICE lens shown in FIG. 21, which focuses a pair of illumination light beams toward the focal line of the BICE lens and collects light beams from the focal line of the BICE lens, according to some other embodiments of this disclosure. [Figure 24] FIG. 22 is a schematic perspective view of the BICE lens shown in FIG. 21, which focuses illumination light rays toward the focal line of the BICE lens according to some other embodiments of the disclosure. [Diagram 25] FIG. 22 is a schematic perspective view of the BICE lens shown in FIG. 21, which focuses illumination light rays toward the focal line of the BICE lens and collects light rays from the focal line of the BICE lens, according to some other embodiments of this disclosure. [Figure 26] FIG. 22 is a schematic perspective view of the BICE lens shown in FIG. 21, which focuses illumination light rays toward the focal line of the BICE lens according to some other embodiments of the disclosure. [Figure 27] FIG. 22 is a schematic perspective view of the BICE lens shown in FIG. 21, which focuses illumination light rays toward the focal line of the BICE lens and collects light rays from the focal line of the BICE lens according to further embodiments of the disclosure. [Figure 28] FIG. 22 is a schematic diagram showing an ellipsometry system using the BICE lens shown in FIG. 21 with the introduction of a time delay into the light beam. [Figure 29]22 is a schematic diagram showing an ellipsometry system using the BICE lens shown in FIG. 21 with beam frequency tuning. [Diagram 30] FIG. 30 is a schematic perspective view of a beam conditioning module of the ellipsometry system shown in FIG. 28 or FIG. 29. [Figure 31A] FIG. 30 is a simplified perspective view of the beam conditioning module of the ellipsometry system shown in FIG. 28 or FIG. 29, showing the path of the illumination light beam. [Figure 31B] FIG. 30 is a simplified perspective view of the beam conditioning module of the ellipsometry system shown in FIG. 28 or FIG. 29, showing the path of the collected light beam. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0052] DETAILED DESCRIPTION OF THE DRAWINGS The presently disclosed embodiments relate to a Bijective Illumination Collection Imaging (BICI) apparatus and method for high resolution imaging in three dimensions within a relatively large depth range.

[0053] According to one aspect of the disclosure, a lens is provided having a focal line defined along the optical axis of the lens. Light rays that strike various positions of the lens at angles parallel to the optical axis are focused by the lens to various positions within the focal line. Thus, such a lens with a focal line provides an improved depth of focus (DOF) such that a photosensor positioned anywhere within the DOF of the lens can capture a sharp image (i.e., a high-resolution image). In comparison, images captured using a conventional extended depth of focus (EDOF) may still be blurred or have reduced resolution.

[0054] According to one aspect of this disclosure, high-resolution imaging is achieved by a specific arrangement of illumination and collection paths that allows a one-to-one spatial correspondence (bijection) between illumination and collection light defined along a focal line, thereby freeing optical imaging from the limitations imposed by diffraction. The impact on imaging is shown by applying BICI to overcome the limitations of high-resolution optical coherence tomography (OCT).

[0055] The boundaries of lateral resolution and depth of focus are bounded by diffraction. A class of so-called diffraction-free (see refs. 18-23) solutions of the Helmholtz equation exist. However, these modes in their exact mathematical form have a spatially unbounded profile (plane waves are a common example), giving rise to side lobes carrying a significant fraction of the optical power (even in physical realizations limited by a finite aperture). When used for imaging, the out-of-focus scattering from the side lobes impairs the imaging resolution and sensitivity.

[0056] Revisiting lateral resolution and depth of focus in the context of the imaging point spread function (PSF) offers an opportunity to circumvent the limitations imposed by diffraction. The PSF at any point is the fraction of illumination photons (P ill ) and collected photons (P coll ) probability product (PSF=P ill ×P coll (See References 24-25). Based on this idea, it is possible to separate the lateral resolution from the depth of focus using uniquely crafted illumination and collection paths, where the illumination path refers to the path of the light rays that strike the object from the light-emitting source, and the collection path refers to the path of the light rays that are scattered from the object or that otherwise originate from the object.

[0057] In some embodiments, metasurfaces with tailored stepping capabilities (see References 13-17) are used to realize the illumination and collection paths required for BICI implementations. In some embodiments, a lateral resolution of about 3.2 micrometers (μm) is maintained almost natively beyond an imaging depth of 1.25 mm without additional acquisition or computational burden, resulting in an imaging focal depth that is about 12 times larger than the focal depth obtained using an ideal Gaussian beam with the same lateral resolution. Imaging of a porcine tracheobronchial tissue specimen illustrates the promise of BICI for high-resolution imaging maintained within a large depth range. The methods disclosed herein may be adapted across a variety of existing imaging modalities.

[0058] 1A-1C. A BICI lens according to some embodiments of this disclosure is shown and generally identified with the reference numeral 100. For ease of explanation, a three-dimensional (3D) coordinate system is defined using an xy plane on the BICI lens 100 and a z-axis (see FIG. 2A) that is the optical axis of the BICI lens 100 and passes through the optical center 108 of the BICI lens 100 (i.e., the origin of the three-dimensional coordinate system is at the optical center 108). In these embodiments, the optical center 108 is also the centroid or geometric center of the BICI lens 100.

[0059] 1A-1C, the BICI lens 100 includes an illumination lens portion 102 and a collection portion 104 on the xy plane of the BICI lens 100 through which light rays can pass. Preferably, the illumination and collection lens portions 102 and 104 have the same size and circular shape.

[0060] Each of the illumination and collection lens sections 102 and 104 is positioned at a distance away from the optical axis. More specifically, in a two-dimensional (2D) xy coordinate system, the illumination and collection lens sections 102 and 104 are positioned in adjacent quadrants of the xy plane and are symmetrical about one of the axes (e.g., the x-axis on the BICI lens 100) such that the center 112 of each of the illumination or collection lens sections 102 and 104 relative to the optical center 108 is at φ=45 degrees relative to the x-axis. In other words, the center 112 of the illumination and collection lens sections 102 and 104 is at 90 degrees relative to the optical center 108. For noise reduction purposes, other areas of the BICI lens 100 (shown in FIGS. 1A-1C as area 106) except for the illumination and collection lens sections 102 and 104 are opaque, thus making it preferable to disable the area.

[0061] In these embodiments, each lens portion 102, 104 includes a metasurface formed by an array of nanoscale sub-wavelength spaced optical elements (denoted as "nanopillars") as shown in FIG. 1B. The two metasurfaces 102, 104 have a mirror profile (i.e., the mirror shape of the nanopillars) around the x-axis. In other words, the metasurface of the collection lens portion 104 has a flip profile of the metasurface of the illumination lens portion 102 with respect to the x-axis. More specifically, each of the metasurfaces of the lens portions 102 and 104 has a pattern of arcs 110 that are part of a number of concentric circles 114 centered on the optical center 108 (see FIG. 1C).

[0062] As shown in FIG. 2A, a collimated light source (not shown) emits an illumination ray 116 that strikes the illumination lens portion 102 at a point 118 of the illumination lens portion 102 having coordinates (r, θ), where r is the radius of the point 118 (relative to the optical center 108) and θ is the angle of the point 118 relative to the y-axis. The metasurface of the illumination lens portion 102 bends or refracts the light ray 116 incident at the point 118 by a certain angle β in the rz-plane towards the optical axis (i.e., the z-axis). A focal point 120 may be defined as the intersection of the refracted ray 116′ and the optical axis.

[0063] The ray bending angle β is constant with respect to r and θ. Thus, as shown in FIG. 2B, a group of rays of light 122 incident on an arc 110 of radius r (denoted as a "ray sheet of radius r") intersects (i.e., focuses at) a focal point 120 on the z-axis. Thus, as shown in FIG. 2C, a light beam or group of rays 132 that strike the illumination metasurface 102 orthogonally at arcs 110 of constant different radii collectively focuses into a continuous focal line 134 along the optical axis.

[0064] Since the collection metasurface 104 has the flip profile of the illumination metasurface 102 with respect to the x-axis, the illumination metasurface 102 has similar optical properties as the illumination metasurface 102. As shown in FIG. 2D and FIG. 2E, the light sheet 142 originating from the focal line 134 at a certain angle β in the rz-plane with respect to the optical axis hits the illumination metasurface 102 with an arc 110 of a certain radius, and is then refracted to form a light beam 142' parallel to the optical axis. A snapshot of the illumination and collection beams at one of the sides intersecting the focal line 134 is illustrated in FIG. 2F. Obviously, with the above-mentioned structure of the BICI lens 100, the BICI lens 100 provides separate illumination paths 132-132' and collection paths 142-142' that overlap only with the focal point along the focal line 134.

[0065] Although light beams 132 and 142 having any suitable cross-sectional size may be used, preferably, for highest optical efficiency, light beams 132 and 142 have a size similar to that of illumination and collection optics portions 102 and 104. Accordingly, the size of illumination and collection optics portions 102 and 104 will also be referred to hereinafter as beam size.

[0066] As an example, Figure 2G is a schematic diagram showing an experimental setup to verify the optical properties of the BICI lens 100, where two light beams 132 and 142' are directed at right angles to the illumination and collection lens assemblies 102 and 104, respectively. As described above, the light beams 132 and 142' are focused by the BICI lens 100 to a focal line 134. An image sensor (e.g., a camera (not shown)) placed on the side 144 intersecting the focal line 134 captures an image 152 of the light sheets 132' and 142. The light sheets 132' and 142 are focused to a point or dot 154 in the captured image 152, as shown in Figure 2H.

[0067] Remarkably, the BICI lens 100 produces an invariant lateral resolution (dependent on β) along the focal line 134. The lateral resolution is determined solely by the bending angle β (regardless of the beam size) based on waveform analysis using the Fresnel-Kirchhoff integral (see Reference 26). However, the focal depth or focal line 134 depends on both the bending angle β and the beam size due to the simple geometry shown in FIG. 2I, where the distance between the BICI lens 100 and the focal line 134 is approximately R(√2-1) / tan(β) and the length of the focal line 134 is approximately 2R / tan(β).

[0068] Thus, the desired depth of focus (set from the desired resolution) and bend angle β result in a beam size (e.g., radius R). In some embodiments, the calculation shown in FIG. 2I, which is based on ray optics, may be combined with waveform analysis to determine a more accurate quantity of depth of focus 134.

[0069] The BICI lens 100 establishes a one-to-one correspondence or bijective relationship between the illumination points and the collection points, defined exclusively at the focal line 134, and eliminates out-of-focus and back-reflected signals. Separate illumination paths 132-132' and collection paths 142-142' ensure that the illumination beams for the illumination points on the focal line 134 and the collection beams collected from the illumination points on the focal line 134 do not overlap.

[0070] As mentioned above, the illumination and collection lens units 102 and 104 may include metasurfaces. The distribution and shape of pillars on the metasurfaces are designed to realize illumination and collection beams with BICI. Based on the generalized Snell's law (see Reference 13), the phase φ required to bend the ray sheet with angle β in the rz plane (as defined in FIG. 2B, i.e., the set of rays hitting the illumination lens unit 102 at the same radius r) satisfies the following equation:

number

[0071] For example, in some embodiments, the a-Si nanopillars have the same height of H=750 nm. The a-Si nanopillars may have a square cross section with a width S between 80 nm and 300 nm (determining the base size of the a-Si nanopillars) that provides high transmittance (greater than 78%) at a wavelength of 1300 nm over the entire phase range [0-2π]. The a-Si nanopillars are distributed in a lattice pattern with unit cells 166 of P=370 nm (i.e., the center-to-center distance between adjacent a-Si nanopillars is P=370 nm).

[0072] 3D, square a-Si nanopillars 162 are distributed in a square lattice pattern on a glass (SiO2) substrate 164. The base size of the nanopillars 162 is periodically changed to form an arc or circular pattern 110 or 114.

[0073] Nanopillars of various basal sizes across the lattice provide the required local phase. Due to the high refractive index and low absorption of nanopillars in the near-infrared range (see refs. 29-31), a-Si is a suitable material to achieve an efficient metasurface (>70% of the incident power concentrated at the focal line 134) for this application. The metasurface may be fabricated on a glass substrate using electron beam lithography.

[0074] In particular, the metasurfaces of the illumination and collection lens portions 102 and 104 may be fabricated using top-down lithography techniques (see References 30 and 32). An a-Si layer (e.g., a 750 nm thick a-Si layer) is deposited on a glass substrate using plasma enhanced chemical vapor deposition. A negative photoresist (microresist technology, ma-N 2403) is then applied to the a-Si layer, and a desired pattern (e.g., the pattern of the illumination and collection lens portions 102 and 104 shown in Figures 1A-1C) is generated in the negative photoresist using electron beam lithography (EBL). Then, a-Si nanopillars are generated using deep reactive ion etching. The BICI lens 100 with the illumination and collection lens portions 102 and 104 is then fabricated.

[0075] FIG. 3E shows a wide-field optical image of the fabricated metasurface of the illumination and collection lens portions 102 and 104, and FIG. 3F shows a scanning electron micrograph of the fabricated metasurface containing square amorphous silicon (a-Si) nanopillars. A suitable distribution of a-Si nanopillars with various base sizes is used to achieve the phase profile of the metasurface.

[0076] The BICI lens 100 uses uniquely crafted illumination and collection paths 132-132' and 142-142' to eliminate out-of-focus signals without compromising the depth range, which is essential for high resolution imaging. Thus, the BICI lens 100 provides high lateral resolution within a large depth range. Furthermore, the BICI lens 100 may capture images of the full depth range due to the focal line 134 generated by the illumination and detection beams.

[0077] On the other hand, existing high-resolution imaging systems typically use tightly focused light to reduce the effect of out-of-focus signals and relatively increase the signal from the focus (using confocal geometry or nonlinear effects at the focus), but this approach necessarily limits the depth range due to the strong diffraction of tightly focused light.

[0078] Metasurfaces often exhibit strong chromatic dispersion unless corrected using special techniques (see refs. 33-37). The application of BICI to OCT operating in a wide wavelength range (1240 nm-1350 nm) solves the problems related to chromatic dispersion. The bending angle β imparted by the metasurface to the ray path (see Fig. 2B) is clearly wavelength dependent (Eq. (1)). For correct operation of BICI, the focal line 134 needs to remain on the optical axis in the entire spectrum to maintain the bijection between the foci. The azimuthally symmetric phase profile of the metasurface with respect to the optical axis together with the infinity-corrected configuration of the optical system guarantees the displacement of the focal point only along the optical axis (z-axis) due to chromatic dispersion. This in turn guarantees the preservation of the bijective relationship between the illumination and collection light over the entire spectrum.

[0079] To demonstrate the impact on imaging, the BICI lens 100 is used in a Fourier domain OCT system in the near infrared region. The illumination / collection beams have a Gaussian distribution (350 μm 1 / e 2 The illumination and collection lens sections 102 and 104 have a wavelength λ=1300 nanometers (nm) ±50 nm with a radius of curvature (intensity fall-off radius). The centers of the illumination and collection lens sections 102 and 104 are positioned at (x, y)=(550 μm, 550 μm) and (x, y)=(550 μm, +550 μm), respectively, according to the coordinates set forth in FIG. 1A. Each of the illumination and collection lens sections 102 and 104 has a metasurface with a diameter of 1.1 millimeters (mm) and a bending angle β=21 degrees (numerical aperture NA=0.36).

[0080] To design the imaging PSF required for the desired resolution and depth of focus, a waveform analysis using the Fresnel-Kirchhoff integral (see ref. 26) was performed. The design parameters are selected to achieve microscopic resolution imaging over a relatively large depth range (greater than 1 mm) where scattering becomes the primary limitation. Given the design parameters (collimated beam size of approximately 1.1 mm, β = 21 degrees), the waveform analysis results in a sharp PSF with a full width at half maximum (FWHM) of 3.2 μm, and negligible contribution from out-of-focus signals (1 / e in the axial direction), as shown in Figure 4. 2This results in a relatively large axial range of focal depth of 1.25 mm (defined as the PSF intensity falloff).

[0081] 5A-5C present the results of the conventional approach in terms of lateral resolution and depth of focus.

[0082] In particular, Figures 5A and 5B show the results of an imaging system with a conventional common path for illumination and collection using an ideal Gaussian beam. As shown, the PSF of a tightly focused Gaussian beam (FWHM of about 3.2 μm) falls off sharply away from the focus (Figure 5A), and the PSF of a Gaussian beam with a relatively large depth of focus (about 1.25 mm) shows a significantly reduced lateral resolution (Figure 5B). Clearly, such a conventional imaging system with a lateral resolution comparable to that of the BICI lens 100 has a significantly reduced depth of focus of 100 μm (see Figure 5A). Meanwhile, such a conventional imaging system with a lateral resolution comparable to that of the BICI lens 100 has a significantly reduced lateral resolution of 12 μm (see Figure 5B).

[0083] 5C shows a Bessel beam with the same FWHM of the central lobe (3.2 μm) as the FWHM of the BICI lens 100. Although providing an extended depth of focus, such a Bessel beam suffers from side lobes carrying a significant fraction of the optical power (see References 27 and 28).

[0084] FIG. 6 illustrates an interferometer 200 using the BICI metasurface lens 100. As illustrated, the interferometer 200 includes a light source 202 that emits a light beam 204. The light beam 204 is split into two that pass through a first path 206 toward a photodetector 212 and a second path 208 toward an illumination path via a collimating lens assembly 214. The collimating lens assembly 214 forms the second path light 208 into an illumination beam 132 toward the illumination lens portion 102 of the BICI lens 100. As described above, the illumination lens portion 102 of the BICI lens 100 refracts the illumination beam 132 such that the refracted illumination beam 132′ intersects the imaging optical axis at a focal line 134.

[0085] A target 216 (e.g., a sample) is positioned axially to overlap the focal line 134 that refracts the illumination beam 132'. The refracted light forms a collection beam 142' that is directed to the collection lens portion 104 of the BICI lens 100. The collection lens portion 104 refracts the collection beam 142' and launches the refracted collection beam 142 into the receiving lens assembly 218. The receiving lens assembly 218 passes the received light via a receiving light path 222 that is combined with the first path light 206. The combined light 224 is launched into the photodetector 212.

[0086] The intensity profiles of the illumination and collection beams 132 and 142 were measured. The measured illumination (see FIG. 7A) and collection (FIG. 7B) beams 132 / 132' and 142 / 142' form a coincident focal line 134 along the z-axis. FIG. 7C shows the imaging PSF (which is the product of the illumination and collection intensity profiles) that shows a sharp PSF with a small FWHM (about 3.7 μm at z=0) that is maintained over a relatively large depth range (about 1.22 mm), with the position z=0 being about 2 mm away from the BICI lens 100. These measurements are consistent with the waveform analysis shown in FIG. 4 (3.2 μm FWHM, 1.25 mm depth of focus), although slight deviations are likely to exist due to the nonlinear response of the camera, imperfect alignment of the optics, and / or manufacturing errors. Despite the chromatic dispersion of the metasurface (see references 33-37), the focal lines 134 of the illumination and collection beams 132 / 132′ and 142 / 142′ remain aligned across the entire spectrum of the light source without significant changes in the imaging PSF.

[0087] The BICI lens 100 was characterized in terms of lateral resolution and depth of focus by imaging a resolution target formed of a subwavelength gold line (200 nm wide and 50 nm high) fabricated on a glass substrate. The BICI lens 100 was coupled to an in-house Fourier domain OCT system. The lateral resolution and depth of focus were measured by scanning the gold line 242 across the focal line 134 (not shown) at various target-metasurface distances, as illustrated in FIG. 8A. FIG. 8B shows the imaging PSF measured at three selected depth points.

[0088] FIG. 8C shows the measured resolution of the BICI lens 100 compared to the theoretical resolution obtained from a Gaussian beam (in a common-path illumination-collection scheme) of the same lateral resolution by highlighting the ability of the BICI lens 100 to maintain high resolution over a large depth range, with position z=0 located about 2 mm away from the metasurface. Summarized in FIG. 8C, the results show high lateral resolution (about 3.28 μm) maintained over a depth range of more than 1.25 mm, consistent with the waveform analysis. To demonstrate the improvement, FIG. 8C further includes an analytical imaging PSF with an ideal Gaussian beam of the same lateral resolution that demonstrates a reduction in the imaging focal depth (about 12 times) compared to the focal depth of the BICI lens 100.

[0089] Furthermore, there are techniques to mathematically optimize phase profiles using free metasurfaces to obtain maximum depth of focus (see refs. 40–43). Although these techniques can somewhat mitigate the problem of a modest increase in depth of focus (approximately 1.5–2 times), these techniques cannot be considered as a strategy to fundamentally reconsider the limitations of maintaining high-resolution imaging over a relatively large depth range.

[0090] The BICI lens 100 may be implemented across a range of wavelengths since it does not require the burden of additional processing (see Reference 44) or acquisition (see Reference 10) and the operating principle remains unchanged as the wavelength changes. For example, the BICI lens 100 may be implemented in broadband OCT systems operating at shorter wavelengths with improved axial resolution. The wavelength ranges described herein are selected to avoid increased scattering at shorter wavelengths, which primarily limits imaging depth (see References 10, 45 and 46).

[0091] Various configurations of illumination and collection beams have already been reported in OCT (for speckle reduction (see refs. 47 and 48) and deep tissue imaging (see ref. 49)), two-photon microscopy (for improving signal-to-background ratio (see refs. 50–52)), theta confocal (see refs. 25 and 53), 4pi (see ref. 54), and light sheet (see ref. 55) microscopy (for improving resolution), and dark-field microscopy (see ref. 56) (for improving sensitivity). These systems are designed to capture signal from regions adjacent to a single focal point. As a result, imaging within a moderate depth range involves the use of very small (see refs. 47–49) (impairing lateral resolution) or physical translation (see refs. 25, and 50–56) (impairing imaging speed) of the target relative to the imaging system.

[0092] An optical arrangement for depth imaging with reasonable and maintained lateral resolution should 1) focus light evenly along the depth range (to a focal line), and 2) eliminate out-of-focus signals originating from points outside the focal line. Unlike previous works, the optical arrangement of BICI lens 100 meets both criteria and can image a relatively large depth range that maintains lateral resolution.

[0093] OCT, being a coherence imaging technique, involves speckle, which is a carrier of information, together with noise sources (see Reference 57). Signal-degrading speckle is mainly due to the effects of many backscattering, while signal-carrying speckle is the result of a single backscattering component whose spatial frequency content extends up to the diffraction limit of the imaging optics (see Reference 57). Zoomed in proportion to the spot size, signal-carrying speckle originates from the focal zone, while signal-degrading speckle is generated by multiple out-of-focus scattered light. The BICI lens 100 suffers less from the effects of speckle due to 1) significantly smaller speckle size as a result of the higher lateral resolution maintained along the depth range, 2) ability to eliminate out-of-focus signals as a result of the effects of multiple scattering, and 3) ability to eliminate back reflections from the imaging optics.

[0094] Pathological changes in the early stages of diseases such as cancer are often very subtle and can easily be overlooked. In-vivo high-resolution imaging maintained over a large depth range has the potential to enable early and accurate detection and diagnosis. When implemented with metasurfaces, the BICI lens 100 can be feasibly miniaturized into endoscopic devices (see references 58 and 59) for in-vivo high-resolution imaging of internal organs.

[0095] The emergence of high-resolution optical imaging techniques is impacting fundamental medical research and clinical applications. However, expanding the scope of applications requires overcoming major limitations of current techniques. Bijective illumination-collective imaging avoids the diffraction-forced trade-off between lateral resolution and focal depth, enabling high-resolution imaging in three dimensions. Although in this disclosure we apply the BICI metasurface lens 100 to OCT, the basic concept is general and the BICI metasurface lens 100 is suitable across a variety of imaging modalities (e.g., confocal and two-photon microscopy).

[0096] Those skilled in the art will appreciate that various alternative embodiments are readily available. For example, although the metasurface in the embodiment described above includes square nanopillars 162, in various embodiments the metasurface may include other suitable nanostructures (e.g., nanopillars having circular or elliptical cross sections).

[0097] In the above embodiment, the arcs 110 or circles 114 are concentric (see FIG. 1C). In some embodiments, the arcs 110 or circles 114 may not be concentric.

[0098] Although in the embodiment described above, the illumination and collection optics portions 102 and 104 have circular shapes of the same size, in alternative embodiments, the illumination and collection optics portions 102 and 104 may have any suitable shape and size.

[0099] In some embodiments, the area 106 of the BICI lens 100 may be transparent or translucent, but is prohibited or otherwise disallowed from use.

[0100] In the embodiments described above, the centers 112 of the illumination and collection optics sections 102 and 104 are at an angle φ=90 degrees with respect to the optical center 108. In some embodiments, such as shown in Figure 9A, the centers 112 of the illumination and collection optics sections 102 and 104 are at an angle φ less than 90 degrees with respect to the optical center 108. In some embodiments, such as shown in Figure 9B, the centers 112 of the illumination and collection optics sections 102 and 104 are at an angle φ greater than 90 degrees with respect to the optical center 108. However, the lateral resolution in the embodiments shown in Figures 9A and 9B may be degraded in the vertical and horizontal directions, respectively.

[0101] In the embodiment described above, the illumination and collection lens sections 102 and 104 are in adjacent quadrants with respect to the optical center 108, which allows the illumination and collection paths to each span diagonal anti-symmetry quadrants and ensures that the illumination and collection paths do not overlap except for the focal line 134.

[0102] In some alternative embodiments, such as those shown in Figures 10A-10D, the illumination and collection lens assemblies 102 and 104 may be placed anti-symmetrically and symmetric about the optical center 108. However, in these embodiments, the illumination and collection paths 132' and 142 overlap outside the focal line 134, as shown in Figures 9C and 9D. Waveform analysis shows that such overlap can cause PSF degradation due to the presence of out-of-focus signals.

[0103] 11A shows a BICI lens 100 according to some embodiments of the disclosure. In these embodiments, the BICI lens 100 may include two illumination lens sections 102 located in diagonal anti-symmetry quadrants (or diagonally opposite sides of the optical center 108) and symmetric about the optical center 108, and one collection lens section 104 in a quadrant adjacent to the two illumination lens sections 102 and symmetric about each axis to the illumination lens section 102. In other words, the centers of each circumferentially adjacent pair of lens sections 102 and / or 104 are perpendicular to the optical center 108. In these embodiments, the two illumination paths may overlap outside the focal line 134, but the collection path does not overlap with the illumination path.

[0104] 11B illustrates a BICI lens 100 according to some embodiments of the disclosure. In these embodiments, the BICI lens 100 is similar to the BICI lens illustrated in FIG. 11A, except that the two diagonally opposed lens portions are collection lens portions 104, and the third lens portion adjacent to the two collection lens portions 104 is an illumination lens portion 102.

[0105] In some embodiments in which the BICI lens 100 includes three lens portions (similar to the lens portions shown in Figures 11A and 11B), any circumferentially adjacent pair of the three lens portions may be illumination lens portions 102 and the other lens portions may be collection lens portions 104.

[0106] In some embodiments in which the BICI lens 100 includes three lens portions (similar to the lens portions shown in Figures 11A and 11B), any circumferentially adjacent pair of the three lens portions may be collection lens portions 104 and the other lens portions may be illumination lens portions 102.

[0107] The arrangement of the illumination and collection beams in BICI requires the use of a higher bending angle (β) to achieve a resolution comparable to that obtained by imaging the focal spot with an ideal diffraction-limited lens (with a NA that matches the bending angle β). However, in some embodiments, this can be corrected by using a BICI lens 100 with two illumination lens sections 102 and two collection lens sections 104. As shown in FIG. 12, two illumination lens sections 102 are placed in two oblique anti-symmetric regions, and two collection lens sections 104 are placed in the other two oblique anti-symmetric regions. The illumination and collection lens sections 102 and 104 are symmetric with respect to each axis.

[0108] In these embodiments, the two illumination paths overlap outside of the focal line 134, and the two collection paths also overlap outside of the focal line 134. However, the collection paths do not overlap with the illumination paths.

[0109] In these embodiments, the BICI lens 100 maintains the necessary bijective relationship with the resolution improvement. Figures 13A and 13B show a comparison of the resolution of the BICI lens shown in Figure 1A (see Figure 13A) with that of the BICI lens shown in Figure 12 (see Figure 13B). Clearly, the BICI lens shown in Figure 12 shows a resolution improvement approaching the diffraction limit (approximately 2 μm at NA=0.36, bending angle β=21 degrees at 1300 nm).

[0110] In some embodiments in which the BICI lens 100 includes four lens portions (similar to the lens portions shown in FIG. 12 ), any circumferentially adjacent pair of the four lens portions may be illumination lens portions 102 and the other two lens portions may be collection lens portions 104.

[0111] In some embodiments, the BICI lens 100 may be fabricated by fabricating a lens 100' with a metasurface having a pattern of multiple concentric circles 114 centered around an optical center 108, as shown in Figure 14A. The lens 100' is then masked opaque except for the areas of the illumination and collection lens portions 102 and 104. The BICI lens 100 is then formed, as shown in Figure 14B.

[0112] In some embodiments, the illumination and collection lens portions 102 and 104 may be manufactured first, and then the illumination and collection lens portions 102 and 104 may be assembled or otherwise coupled to the BICI lens 100 .

[0113] 15, in some embodiments, the BICI lens 100 may include a metasurface having a pattern of multiple concentric circles 114 centered about an optical center 108. In use, an illumination beam (not shown) may be directed toward region 102, using region 102 of the BICI lens 100 as the illumination lens portion 102, and a light collector (not shown) may be directed toward region 104, using region 104 as the collection lens portion.

[0114] In some embodiments, portions of the illumination and collection lens portions 102 and 104 may not be symmetrical.

[0115] In the embodiments described above, the BICI lens 100 is shown as having a circular shape. In some embodiments, the BICI lens 100 may have any suitable shape (e.g., a square as shown in FIG. 16).

[0116] In the embodiments described above, the optical center 108 of the BICI lens 100 is also the center of mass of the BICI lens 100. In some embodiments (e.g., the embodiment shown in FIG. 17 ), the optical center 108 of the BICI lens 100 may be offset from the center of mass 302 of the BICI lens 100. Each metasurface of the lens portions 102 and 104 has a pattern of arcs 110 that are part of multiple concentric circles 114 centered about the optical center 108.

[0117] 18, the BICI lens 100 may include multiple illumination and collection lens portions 102 and 104 in a circular lens body 312. Each lens portion 102, 104 has a maximum size that fits in each quadrant, and the BICI lens 100 has multiple unusable portions 106 distributed around the illumination and collection lens portions 102 and 104.

[0118] Those skilled in the art will appreciate that other suitable optical structures may be used to implement the illumination and collection lens portions 102 and 104. For example, in some embodiments, an axicon, which is a lens with a conical surface, may be used to implement the illumination and collection lens portions 102 and 104 and the linear phase profile in equation (1).

[0119] As shown in Figures 19A and 19B, the BICI lens 100 has a conical shape with an optical axis (i.e., z-axis) passing through the apex 108 of the BICI lens. The illumination lens section 102 and the collection lens section 104 are positioned in adjacent quadrants of the xy plane at a distance from the optical axis, e.g., symmetrical with respect to the x-axis (i.e., positioned similarly to the illumination and collection lens sections 102 and 104 described above). Preferably, the center 112 of each of the illumination and collection lens sections 102 and 104 relative to the optical center 108 is at φ=45 degrees with respect to the x-axis. As will be appreciated by those skilled in the art, in the same manner as above, the illumination and collection lens sections 102 and 104 can be obtained in these embodiments by making the remainder of the first face 322 opaque and the remainder of the transmission face 324 opaque, or by directing the illumination beam and a light collector (not shown) to the location of the illumination and collection lens sections 102 and 104.

[0120] BICI lenses implemented with axicons may not offer the same advantages as BICI lenses with metasurfaces. For example, BICI lenses with axicons may have a shorter focal depth than BICI lenses with metasurfaces for the same lateral resolution. Since the resolution achieved by a BICI lens is mainly determined by the bending angle β, given a desired resolution, the required bending angle can be accurately realized using metasurfaces. On the other hand, it may be more difficult to design a BICI lens with axicons to obtain the same bending angle β and subsequently the same resolution. Furthermore, BICI lenses with axicons may achieve different performances and it may be more difficult to achieve miniaturization for endoscopic applications.

[0121] In the above-described embodiments, the BICI lens 100 includes one or more illumination lens sections 102 and one or more collection lens sections 104 that are offset from the optical axis, and the illumination and collection lens sections 102 and 104 form a focal line 134 along the optical axis. In some embodiments, the illumination and collection lens sections 102 and 104 may be conventional lenses that do not form a focal line 134 but have sufficient depth of focus (although the lateral resolution may be reduced compared to the illumination and collection lens sections 102 and 104 described above). For spatially separated illumination and collection paths, in these embodiments, the BICI lens may still provide better performance than conventional lenses.

[0122] In the embodiments described above, the BICI lens 100 includes one or more off-axis illumination lens portions 102 and one or more collection lens portions 104. In some embodiments, the BICI lens 100 may include only one or more off-axis illumination lens portions 102. In these embodiments, other suitable means may be used to perform light collection and imaging of the sample or target object.

[0123] In some embodiments, the BICI lens 100 may include only one or more off-axis collection lens portions 104. In these embodiments, illumination of the sample or target object may be accomplished using other suitable means.

[0124] In some embodiments, such as those shown in Figures 20A and 20B, the BICI lens 100 is similar to the BICI lens shown in Figure 1A, except that in these embodiments, the BICI lens 100 includes a collection lens portion 104 that is away from or offset from the optical center 108 and does not include an illumination lens portion.

[0125] In these embodiments, the focal points along the focal line 134 (e.g., focal points 402-412) are mapped to arcs 422-432, which are then mapped to various pixels 442-452 of a photodetector 462, such as a camera having a line photosensor (i.e., a photosensor having multiple light-detecting pixels arranged in an array). This is achieved when the phase of the collection lens portion 104 is designed to map the focal line 134 to the pixels of the photodetector 462. Such a BICI lens 100 may resolve depth information independent of OCT.

[0126] In the above-described embodiments, the illumination and collection lens portions 102 and 104 are usable areas for illumination and imaging, and other areas of the BICI lens 100 distributed around the illumination and collection lens portions 102 and 104 (e.g., area 106 shown in FIG. 1A ) are unusable areas that are prohibited or otherwise disallowed for use (optically unusable (e.g., opaque) or not allowed for use).

[0127] 21 is a schematic diagram showing a BICI lens 100 (hereafter referred to as a "Bijective Illumination Collection Ellipsometry (BICE)" lens) for high speed, high resolution ellipsometry. As shown, the BICE lens 100 includes two illumination lens sections 102 and two collection lens sections 104 in the xy plane of the BICE lens 100 (similar to the lens 100 shown in FIG. 12). Preferably, the illumination and collection lens sections 102 and 104 have the same size and circular shape.

[0128] Each illumination and collection lens section 102 and 104 is positioned at a distance away from the optical axis. The two illumination lens sections 102 are located at two diagonal anti-symmetries (or two diagonal opposite sides of the optical center 108) and are symmetrical about the optical center 108. The two collection lens sections 104 are located at the other two diagonal anti-symmetries (or two diagonal opposite sides of the optical center 108) and are symmetrical about the optical center 108. The illumination and collection lens sections 102 and 104 are symmetrical about each axis.

[0129] The illumination and collection lens units 102 and 104 are generally the same as those described above (see also Reference 62). More specifically, the illumination and collection lens units 102 and 104 are generally focused within a continuous focal line 134 along the optical axis (i.e., the z-axis), thereby ensuring high resolution imaging along the entire depth range. As described above, this requires all incident rays with the same distance to the optical axis to be bent at the same angle toward the optical axis when projected onto the lens unit 102 or 104.

[0130] In these embodiments, the metasurfaces of the two illumination lens sections 102 are used to illuminate light rays of two orthogonal polarization states onto the material, and the metasurfaces of the two collection lens sections 104 are used to collect light rays of two orthogonal polarization states from the material.

[0131] Each illumination and collection lens section 102 and 104 includes a metasurface that allows light rays of each polarization state to pass through the lens section. In the embodiment shown in FIG. 21, the illumination lens section 102 is designed to focus light rays of different circular polarization states to a focal line 134. For example, as shown in FIG. 22, the illumination lens section 102A is designed to focus light rays 502 of left circular polarization (LCP) to a focal line 134, and the illumination lens section 102B is designed to focus light rays 504 of right circular polarization (RCP) to a focal line 134. In these embodiments, the metasurface of each illumination and collection lens section 102 and 104 changes the polarization state of the light rays 502 or 504 passing through the lens section, for example, from LCP to RCP or from RCP to LCP.

[0132] The collection lens unit 104 is designed to collect the LCP and RCP light rays from the material within focal line 134, which correspond to the excitation or illumination light rays incident from illumination lens units 102A and 102B, respectively. For example, as shown in FIG. 23, the collection lens unit 104A is designed to collect the LCP light rays 512, and the collection lens unit 104B is designed to collect the RCP light rays 512.

[0133] In some embodiments, the illumination beams 502 and 504 may be separated or otherwise isolated by time division multiplexing and / or frequency division multiplexing. For example, in one example, interferometry is used to isolate the illumination beams 502 and 504 when the beam 504 incident on the illumination lens portion 102B is time delayed relative to the beam 502 incident on the illumination lens portion 102A. In another example, the beams 502 and 504 incident on the illumination lens portions 102A and 102B are modulated at different frequencies to be isolated from each other and demodulated accordingly at the receiving end.

[0134] In the example shown in Figure 24, a single illumination lens portion (e.g., LCP illumination lens portion 102A) is used to illuminate material within focal line 134 with LCP light illumination 502. In these embodiments, lens 100 may not include RCP illumination lens portion 102B. Figure 25 shows collected light rays 512 and 514 under LCP light illumination 502.

[0135] In the example shown in Figure 26, a single illumination lens portion (e.g., RCP illumination lens portion 102B) is used to illuminate material within focal line 134 with LCP light illumination 504. In these embodiments, lens 100 may not include LCP illumination lens portion 102A. Figure 27 shows collected light rays 512 and 514 under RCP light illumination 504.

[0136] In the above embodiment, RCP and LCP polarization states are used, which are suitable for ellipsometry of linearly birefringent materials.

[0137] In other embodiments, any other suitable two orthogonal polarization states may be used. For example, in some embodiments, a linear polarization state may be used, for example for materials that have significant optical activity (e.g., circular birefringence).

[0138] In the examples shown in Figures 22-27, the collected beams 512 and 514 resulting from LCP and / or RCP excitation may be separated by using different time delays and / or different modulation frequencies. Figure 28 is a schematic diagram illustrating an ellipsometry system 600 using a BICE lens 100 with collected beams 512 and 514 separated using different time delays according to some embodiments of this disclosure.

[0139] In the ellipsometry system 600 shown in FIG. 28, a light beam 604 emitted from a light source 602 is split by a beam splitter 608 into two light beams 610 and 612, each of which contains light of two orthogonal polarization states.

[0140] The light beam 610 is further split by a polarizing beam splitter 614 into two polarized light beams 616 and 618 with different polarization states. Each of the two polarized light beams 616 and 618 passes through a respective quarter-wave plate (QWP) 620 to obtain a respective phase-shifted polarized light beam 622 and 632, respectively. Then, one of the phase-shifted polarized light beams (e.g., the phase-shifted polarized light beam 632) is directed by a number of reflectors 634 and 636 to an additional propagation path that introduces, for example, a time delay. In these embodiments, the introduced additional propagation path may be adjustable to adjust the introduced time delay of the phase-shifted polarized light beam 632.

[0141] Phase-shifted polarized beams 622 and 632 (beam 632 is also time delayed) are then directed to beam conditioning module 624, which outputs illumination beams 502 and 504 that are incident on BICE lens 100 for illuminating the material within focal line 134. BICE lens 100 collects reflected and / or refracted light from the material, as described above, and outputs collected polarized beams 512 and 514 that are directed to beam conditioning module 624.

[0142] Beam conditioning module 624 outputs polarized beams 628 and 638 that are passed through respective QWPs 646 for phase shifting. The phase shifted polarized beams 652 and 654 output from QWP 646 are then directed to polarizing beam combiners 656 and 658, respectively.

[0143] The beam 612 output from the beam splitter 608 is further split by the polarizing beam splitter 704 into two polarized beams 706 and 708 with different polarization states. Each of the two polarized beams 706 and 708 is directed to an additional propagation path that introduces a time delay, for example, by multiple reflectors 714 and 716 for the polarized beam 706 and multiple reflectors 724 and 726 for the polarized beam 708. In these embodiments, the additional propagation paths of the polarized beams 706 and 708 may be adjustable to adjust the introduction time delay of the polarized beams. Furthermore, the time delays introduced to the polarized beams 632, 706, and 708 may be different.

[0144] The time delayed polarized beams 706 and 708 are then directed to polarizing beam combiners 656 and 658, respectively.

[0145] Polarizing beam combiner 656 combines beams 652 and 706 having the same polarization state and then outputs combined beam 802 that is directed to a photodetector 806 (labeled "Detector X" in FIG. 28).

[0146] Polarizing beam combiner 658 combines beams 654 and 708 having the same polarization state (orthogonal to the polarization states of beams 652 and 706) and then outputs combined beam 812 that is directed to photodetector 816 (shown as "Detector Y" in FIG. 28).

[0147] 28 also shows several other optical components that may be required (depending on the implementation), such as lenses 606, 804, and 814, which optionally shape light beams 604, 802, and 812, respectively, and optical reflectors 630, 702, 718, 722, and 728, which optionally redirect the paths of light beams 618, 612, 706, and 708, respectively. Ellipsometry system 600 may include other optical components as required.

[0148] 29 is a schematic diagram illustrating an ellipsometry system 600 using a BICE lens 100 with collected light beams 512 and 514 separated using different frequencies according to some embodiments of this disclosure. The ellipsometry system 600 in these embodiments is similar to the ellipsometry system 600 shown in FIG. 28, except that instead of an additional propagation path for light beam 632, the ellipsometry system 600 in these embodiments includes an optical modulator 822 that adjusts the frequency of light beam 622 and an optical modulator 824 that adjusts the frequency of light beam 632.

[0149] Figure 30 is a schematic diagram showing a beam conditioning module 624 that uses knife-edge prisms and mirrors to separate the beams and couples the illumination and collection beams from the BICE lens 100 to the rest of the system 600. Figure 31A shows the path of the illumination beam, and Figure 31B shows the path of the collection beam.

[0150] Polarized light beam 622 is directed to a reflector 842 (e.g., a mirror) which reflects polarized light beam 622 to a knife-edge prism 844, as indicated by arrow 840. Knife-edge prism 844 directs polarized light beam 622 to a primary knife-edge prism 846, which outputs polarized light beam 622 as illumination light beam 502 that enters the BICE lens 100.

[0151] Similarly, polarized light beam 632 is directed to a reflector 852 (e.g., a mirror) which reflects polarized light beam 632 to a knife-edge prism 854, as indicated by arrow 860. Knife-edge prism 854 directs polarized light beam 632 to primary knife-edge prism 846, which outputs polarized light beam 632 as illumination beam 504 that enters BICE lens 100.

[0152] As described above, BICE lens 100 collects light from focal line 134. It directs collected light beam 512 to primary knife-edge prism 846 of beam conditioning module 624 which directs collected light beam 512 (renumbered as 628) to knife-edge prism 844, as shown by arrow 880. Knife-edge prism 844 then directs collected light beam 628 to reflector 856, outputting collected light beam 628 from beam conditioning module 624.

[0153] Similarly, collected beam 514 is directed to primary knife-edge prism 846 of beam conditioning module 624 which directs collected beam 514 (renumbered as 638) to knife-edge prism 854, as shown by arrow 890. Knife-edge prism 854 then directs collected beam 638 to reflector 858, outputting collected beam 638 from beam conditioning module 624.

[0154] The BICE lens 100 disclosed herein combines the principles of ellipsometry with those of the BICI lens to provide high speed, high resolution ellipsometry over a relatively large depth range.

[0155] In some embodiments, the BICE lens 100 can be easily implemented into an endoscopic setup using fiber optic components and a gradient index (GRIN) lens to collimate light toward the BICE lens 100 placed at the tip of the endoscope.

[0156] Although embodiments have been described above with reference to the accompanying drawings, those skilled in the art will appreciate that variations and modifications can be made without departing from the scope as defined by the appended claims.

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Claims

1. an optical center and an optical axis passing through the optical center; One or more lens portions; Including, the one or more lens portions include at least a first lens portion; wherein the at least a first lens portion refracts light rays of a given polarization state that impinge on the first lens portion perpendicularly from a first side towards the optical axis at a second side at a constant bending angle, thereby defining a focal line at the second side along the optical axis.

2. The lens of claim 1 , wherein the at least a first lens portion is positioned a distance away from the optical center.

3. the at least first lens portion includes the first lens portion and a second lens portion; the centers of the first and second lens portions are diagonally opposite to the optical center; 3. A lens as claimed in claim 1 or 2, wherein the first and second lens portions are configured to pass the light rays of orthogonal polarization states.

4. The one or more lens portions include 4. The lens according to claim 1, further comprising at least a third lens section configured to refract light rays impinging on said lens section at said constant bending angle on said second side in a direction parallel to the optical axis from said focal line to said first side.

5. the at least third lens portion includes the third lens portion and a fourth lens portion, the centers of the third and fourth lens portions are diagonally opposite to the optical center; The lens of claim 4 , wherein the third and fourth lens portions are configured to pass the light rays of orthogonal polarization states.

6. 6. The lens of claim 5, wherein in a two-dimensional (2D) coordinate system defined by the lens having an origin of the 2D coordinate system at the optical center, each of the one or more lens portions is positioned in a respective quadrant of the 2D coordinate system.

7. The lens of claim 6 , wherein the centers of each circumferentially adjacent pair of the one or more lens portions are perpendicular to the optical center.

8. The lens of any one of claims 1 to 7, wherein the bend angle is 21 degrees.

9. The lens of any one of claims 1 to 8, wherein each of the one or more lens portions has a circular shape.

10. 10. The lens of claim 9, wherein each of the one or more lens portions has a diameter of 1.1 millimeters (mm).

11. The lens of claim 1 , wherein each of the one or more lens portions comprises a metasurface coupled to a substrate.

12. The lens of claim 11 , wherein each metasurface includes a plurality of nanopillars in a pattern of arcs, the arcs being part of a plurality of concentric circles centered about the optical center.

13. the plurality of nanopillars have a cubic shape with a square cross section; The lens of claim 12 , wherein the nanopillars have the same height and varying widths.

14. The lens of claim 13 , wherein the width of the nanopillars is between 80 nanometers (nm) and 300 nm.

15. The lens of claim 14 , wherein the height of the nanopillars is 750 nm.

16. 16. The lens of claim 14 or 15, wherein adjacent pairs of the nanopillars have a center-to-center distance of 370 nm.

17. A lens according to any one of the preceding claims, wherein the lens is opaque except for the one or more lens portions.

18. an axicon, the apex of the lens being the optical center; The lens of any one of claims 1 to 17, wherein the one or more lens portions are defined by the axicon.

19. a polarizing beam splitter for splitting the light beam into a first polarized light beam and a second polarized light beam of orthogonal polarization states; a beam conditioning module configured to receive the first and second polarized beams and output the first and second polarized beams to a lens according to any one of claims 1 to 18; an adjustment module that introduces a time delay into at least one of the first and second polarized beams and / or adjusts a frequency of at least one of the first and second polarized beams prior to inputting the first and second polarized beams into the beam condition adjustment module; An imaging device comprising:

20. The lens is a lens according to claim 6 or any one of claims 6 to 18 dependent on claim 6, The beam conditioning module includes: A primary knife-edge prism; a first knife-edge prism that directs the first polarized light beam toward the primary knife-edge prism; a second knife-edge prism for directing the second polarized light beam toward the primary knife-edge prism; Including, The primary knife edge prism is outputting the first and second polarized light beams to a lens; receiving a third light beam and a fourth light beam from the lens; directing the third light beam toward the first knife-edge prism; Directing the fourth light beam to the second knife-edge prism. The imaging device according to claim 19 , configured as follows:

21. A method for producing a lens according to any one of claims 1 to 18, comprising the steps of: depositing an amorphous silicon (a-Si) layer on the substrate using plasma enhanced chemical vapor deposition; applying a layer of negative photoresist to the a-Si layer; generating an etching pattern in said layer of negative photoresist using electron beam lithography (EBL); using deep reactive ion etching to produce a-Si nanopillars that form the metasurface of one or more lens portions; The method includes:

22. 22. A method according to claim 21 when dependent on claim 12, wherein the etching pattern corresponds to the pattern of arcs.

23. 22. The method of claim 21 when dependent on claim 12, wherein the etch pattern corresponds to a plurality of concentric circles.

24. 24. The method of claim 23, further comprising opaquely masking one or more unusable areas.

25. A method of using a lens according to claim 5 or any one of claims 6 to 18, comprising the steps of: directing a first light beam at a first lens portion; collecting a third light beam and a fourth light beam from a third lens portion and a fourth lens portion, respectively; At least one of the first light beam has a cross-sectional size that matches the size of the first lens portion; method.

26. an optical center and an optical axis passing through the optical center; a plurality of lens sections including a first lens section and a second lens section on first and second quadrants on diagonally opposite sides of a plane perpendicular to the optical axis for refracting a light ray from a first side to a second side, and a third lens section on a third quadrant of the plane for refracting a light ray from the second side to the first side; having the first and second lens portions are configured to refract light rays impinging on the lens portions at right angles from the first side towards the optical axis at the second side at a constant bending angle, thereby defining a focal line at the second side along the optical axis, and the third lens portion is configured to refract light rays impinging on the lens portions at the second side from the focal line at the constant bending angle towards the first side parallel to the optical axis, or the third lens section is configured to refract light rays impinging on the lens section at right angles from the second side towards the optical axis at the first side at the constant bending angle, thereby defining the focal line at the first side along the optical axis, and the first and second lens sections are configured to refract light rays impinging on the lens section at the first side from the focal line at the constant bending angle towards the second side parallel to the optical axis. lens.

27. 27. The lens of claim 26, wherein the lens portions are spaced apart from the optical center.

28. 28. A lens as claimed in claim 26 or 27, wherein the centres of the first and third lens sections or the centres of the second and third lens sections are perpendicular to the optical centre.

29. the plurality of lens portions further includes a fourth lens portion on a fourth quadrant of the plane; 29. The lens according to any one of claims 26 to 28, wherein the fourth lens section is adapted to refract light rays impinging on said lens section from the focal line on the second side at the constant bending angle to the first side parallel to the optical axis, or to refract light rays impinging on said lens section perpendicularly from the second side towards the optical axis on the first side at the constant bending angle, thereby towards the focal line on the first side.

30. A lens according to any one of claims 26 to 29, wherein the bend angle is 21 degrees.

31. A lens according to any one of claims 26 to 30, wherein each of the one or more lens portions has a circular shape.

32. 32. The lens of claim 31 , wherein each of the one or more optics has a diameter of 1.1 mm.

33. 33. The lens of claim 26, wherein each of the one or more lens portions comprises a metasurface bonded to a substrate.

34. 34. The lens of claim 33, wherein each metasurface comprises a plurality of nanopillars in a pattern of arcs, the arcs being part of a plurality of concentric circles centered about the optical center.

35. the plurality of nanopillars have a cubic shape with a square cross section; 35. The lens of claim 34, wherein the nanopillars have the same height and varying widths.

36. 36. The lens of claim 35, wherein the width of the nanopillars is between 80 nm and 300 nm.

37. 37. The lens of claim 36, wherein the height of the nanopillars is 750 nm.

38. 38. The lens of claim 36 or 37, wherein adjacent pairs of the nanopillars have a center-to-center distance of 370 nm.

39. the lens comprises an axicon, the apex of the lens being the optical center; A lens according to any one of claims 26 to 38, wherein the one or more lens portions are defined by the axicon.

40. A lens according to any one of claims 26 to 39, wherein the lens is opaque except for the one or more lens portions.

Images