Nanostructured birefringent optical element and microscope equipped with nanostructured birefringent optical element

Abstract

1. A birefringent optical element for converting an incident light beam into two spatially separated output light beams having orthogonal linear polarizations, comprising: a transparent substrate having an input surface for receiving the incident beam, an output surface, and a uniform thickness between the input and output surfaces, the substrate having non-uniform birefringence in a plane parallel to the input surface, the birefringence being provided by a plurality of nanostructures randomly disposed in the substrate and configured to shear the incident beam within the substrate into two output beams having orthogonal linear polarizations and wavefronts at an angle to each other, such that the output beams leave the output surface spatially separated along a shear direction parallel to the output surface, each nanostructure having an oblate spheroid shape with an elliptical cross section in the plane parallel to the input surface, the direction of the elliptical cross section providing a slow axis orientation of the birefringence and the size of the oblate spheroid shape providing a retardance value of the birefringence, the direction and size varying among the nanostructures to provide the non-uniform birefringence of the substrate.

Description

[Technical field]

[0001] This invention was made with United States Government support under Grant No. GM101701 awarded by the National Institutes of Health. The Government has certain rights in this invention.

[0002] The present invention relates to nanostructured birefringent optical elements and to the use of such optical elements in differential interference contrast microscopy. [Background technology]

[0003] A Wollaston prism is an optical element that can be used to manipulate polarized light. Propagation through a Wollaston prism converts an input light beam into an output that comprises two linearly polarized output light beams with wavefronts at an angle to each other, such that the two output beams are spatially separated with diverging propagation directions. A Wollaston prism is formed from two right-angled prisms or wedges of birefringent material that are cemented together with their hypotenuses abutting and the optical axes of the two wedges perpendicular to each other. The difference in refractive index provided by the orthogonal directions of the optical axes causes the ordinary and extraordinary components of the propagating light beam to diverge, resulting in two separate output beams. The divergence angle depends on the wedge angle. Uniaxially birefringent crystalline materials such as quartz or calcite may be used for the wedges.

[0004] A related device is the Nomarski prism, which also contains two prisms or wedges of birefringent material with orthogonal optic axes. However, while in a Wollaston prism both of the optic axes are parallel to the input and output faces of the prism, in a Nomarski prism the input wedge has its optic axis oriented at an angle to the input face. As a result, the angled wavefronts of the two output beams converge to a focal point outside the prism, rather than the spatially separated output beams diverging. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] National Patent No. 7233434 [Patent Document 2] U.S. Pat. No. 7,564,618 [Patent Document 3] International Publication No. 2019 / 158910 [Patent Document 4] US Patent No. 2020 / 109767 [Patent Document 5] US Patent No. 2020 / 109768 [Non-patent literature]

[0006] [Non-Patent Document 1] JM Desse and F Olchewsky, “Use of Wollaston prism for dual-reference digital holographic interferometry”, https: / / doi.org / 10.1364 / DH.2019.Tu4B.4 [Non-Patent Document 2] RD Small, VA Sernas and RH Page, “Single Beam Schlieren Interferometer using a Wollaston prism”, https: / / doi.org / 10.1364 / AO.11.000858 Summary of the Invention [Problem to be solved by the invention]

[0007] Cutting and polishing a wedge from a bulk crystal, followed by bonding to create a prism, can lead to a complex, difficult and costly finished product.

[0008] An important application of Wollaston and Nomarski prisms is differential interference contrast (DIC) microscopy. This is a type of microscope that produces a monochromatic shadow-cast image of the light path (refractive index) gradient in a transparent sample, allowing the observation of the structure and movement of unstained living cells and isolated organelles. A more sophisticated version is the direction-independent DIC microscope. In both types of microscopes, imaging is achieved by passing a pair of spatially separated and orthogonally polarized light beams through the sample to be observed, which introduces the necessary optical path difference between the two beams. To deliver the two beams, Wollaston and / or Nomarski prisms are used. The first prism is placed in front of the sample and is associated with a focusing lens that collimates the beams for propagation through the sample. An objective lens collects the beams after their interaction with the sample and focuses them into a second prism, where the beams recombine into a single beam for observation.

[0009] Besides the cost of Wollaston and Nomarski prisms (which can be exacerbated by the requirement for small wedge angles), a further difficulty is that the prisms must be tailored to the specifications of the model and design of the microscope for which they are intended, and cannot be interchanged between different microscopes. Also, in order to be installed in the microscope, the prisms must be removed and cut to a specific shape. However, microscope manufacturers do not always provide prisms that are suitable for their microscopes. Thus, delivery times for newly ordered prisms are typically six months or more, which can cause significant delays in new projects.

[0010] There is therefore interest in alternatives to Wollaston and Nomarski prisms. [Means for solving the problem]

[0011] Aspects and embodiments are set out in the accompanying claims.

[0012] According to a first aspect of certain embodiments described herein, there is provided a birefringent optical element for converting an incident light beam into two spatially separated output light beams having orthogonal linear polarizations, the birefringent optical element comprising: an input surface for receiving the incident beam; an output surface; and a transparent substrate having a uniform thickness between the input and output surfaces, the transparent substrate having non-uniform birefringence in a plane parallel to the input surface, the birefringence being provided by a plurality of nanostructures randomly disposed within the substrate, configured to shear the incident beam within the substrate into two output beams having wavefronts at an angle to each other with respect to the orthogonal linear polarizations, the output beams leaving the output surface spatially separated along a shear direction parallel to the output surface, each nanostructure having an oblate spheroid shape with an elliptical cross section in the plane parallel to the input surface, the orientation of the elliptical cross section providing a slow axis orientation of the birefringence, and a size of the oblate spheroid shape providing a retardance value of the birefringence, the orientation and size varying among the nanostructures to provide the non-uniform birefringence of the substrate.

[0013] According to a second aspect of certain embodiments described herein, there is provided an optical assembly for converting an input light beam into two spatially separated output light beams having orthogonal linear polarizations, the optical assembly comprising a first birefringent optical element according to the first aspect, a second birefringent optical element according to the first aspect, and an optical rotator sandwiched between the first and second birefringent optical elements.

[0014] According to a third aspect of certain embodiments described herein, there is provided a differential interference contrast microscope comprising one or both of a birefringent optical element according to the first aspect, arranged to shear an illumination light beam in the microscope into two spatially separated light beams having orthogonal linear polarizations for illuminating a sample placed in the microscope, and a birefringent optical element according to the first aspect, arranged to receive, by transmission or reflection, the two spatially separated light beams having orthogonal linear polarizations from the sample and to focus the two spatially separated light beams into a single output light beam for observation or detection.

[0015] According to a fourth aspect of certain embodiments described herein, there is provided an orientation independent partial interference contrast microscope comprising one or both of an optical assembly according to the second aspect, the optical assembly being arranged to shear an illumination light beam in the microscope into two spatially separated light beams having orthogonal linear polarizations for illuminating a sample placed in the microscope, and an optical assembly according to the second aspect, the optical assembly being arranged to receive two spatially separated light beams having orthogonal linear polarizations from the sample by transmission or reflection and to focus the two spatially separated light beams into a single output light beam for observation or detection.

[0016] These and further aspects of certain embodiments are set forth in the accompanying independent and dependent claims. It will be understood that the features of the dependent claims can be combined with each other and with the features of the independent claims in other combinations than those expressly set forth in the claims. Furthermore, the approach described herein is not limited to the specific embodiments as set forth below, but includes and contemplates any suitable combination of features presented herein. For example, devices and apparatuses may be provided according to the approach described herein, suitably including any one or more of the various features described below.

[0017] For a better understanding of the present invention and to show how the same may be carried into effect, reference will now be made, by way of example, to the accompanying drawings in which: [Brief description of the drawings]

[0018] [Figure 1] 1 is a schematic diagram of a first example of a differential interference contrast microscope in which a nanostructured birefringent optical element according to examples and embodiments of the present invention can be used; [Diagram 2] 1 is a schematic diagram of a second example of a differential interference contrast microscope in which a nanostructured birefringent optical element according to examples and embodiments of the present invention can be used. [Diagram 3] FIG. 3 is a schematic diagram illustrating the structure and operation of a beam-shearing prism as conventionally used in differential interference contrast microscopes of the type shown in FIGS. 1 and 2. [Figure 4] FIG. 1 is a schematic plan view of a first embodiment of a nanostructured birefringent optical element according to an aspect of the present invention, showing a graphical representation of the proposed birefringence profile. [Diagram 5] 5 is a photograph (taken using a polychromatic polarizing microscope and a color CCD camera) of a nanostructured birefringent optical element fabricated to include the proposed birefringence profile of the example of FIG. 4. [Figure 6A] 1 is an image of a sample taken using a differential interference contrast microscope with a conventional beam-shearing prism attached. [Figure 6B] 6B is an image of the same sample as shown in FIG. 6A taken with the same differential interference contrast microscope, but fitted with the nanostructured birefringent optical element shown in FIG. 5. [Figure 7] FIG. 2 is a schematic plan view of a second embodiment of a nanostructured birefringent optical element according to an aspect of the present invention, showing a graphical representation of an alternative proposed birefringence profile. [Figure 8] 8 is a photograph (taken using a polychromatic polarizing microscope and a color CCD camera) of a nanostructured birefringent optical element fabricated to include the proposed birefringence profile of the example of FIG. 7. [Figure 9A] 1 is an image of a sample taken using a differential interference contrast microscope with a conventional beam-shearing prism attached. [Figure 9B] 9B is an image of the same sample as shown in FIG. 9A taken with the same differential interference contrast microscope when fitted with the nanostructured birefringent optical element shown in FIG. 8. [Figure 10] 1 is a schematic diagram of a first example of an orientation-independent differential interference contrast microscope in which a nanostructured birefringent optical element according to examples and embodiments of the present invention is used; [Figure 11]FIG. 2 is a schematic diagram of a second example of an orientation-independent differential interference contrast microscope in which a nanostructured birefringent optical element according to examples and embodiments of the present invention is used. [Figure 12] 1 is a simplified schematic diagram of individual oblate anisotropic nanopores or nanostructures in a substrate to provide birefringence in a nanostructured optical element according to the present invention; FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0019] In this specification, aspects and features of specific examples and embodiments are discussed / described. Some aspects and features of specific examples and embodiments may be implemented in a conventional manner, and they are not discussed / described in detail for the sake of brevity. Thus, it will be understood that aspects and features of the apparatus and devices discussed in this specification that are not described in detail may be implemented according to any conventional technique for implementing such aspects and features.

[0020] A differential interference contrast (DIC) microscope is a beam-shearing interference system in which a reference or illumination light beam is sheared by a small amount (typically slightly less than the diameter of an Airy disk) before being transmitted through the sample under observation. "Sheared" means that the beam is split into two spatially separated beams, where a Wollaston or Nomarski prism is traditionally used to generate the shear, so that the beams also have orthogonal linear polarization states. By illuminating the sample with the sheared beam, the microscope produces a monochromatic shadow-cast image that shows the gradient of the optical path. Those regions of the sample where the optical path along the reference direction increases appear brighter (or darker), while regions where the optical path difference decreases appear with the opposite contrast. As the gradient of the optical path becomes steeper, the contrast of the image is significantly improved. Another important feature of the DIC technique is that it produces an effective optical sectioning of the sample. This is especially evident when high numerical aperture objectives are used in conjunction with high numerical aperture focusing illumination.

[0021] FIG. 1 is a schematic diagram of an example of a DIC microscope according to a known configuration, in which illumination light is transmitted through a sample for detection or observation. The DIC microscope 10 comprises a light source 12 that emits a monochromatic plane wave reference light beam 14 by which the sample can be illuminated. The light beam 14 passes through a polarizer 16 at an azimuthal angle of 45° to set the polarization state of the light beam 14 into ordinary and extraordinary components 15 at the appropriate orientation. The light beam 14 is then incident on the input face of a first Wollaston prism 18 that is oriented such that its orthogonal optical axes are parallel to the ordinary and extraordinary components of the light beam 14. The Wollaston prism 18 thus has an azimuthal angle of 0° (angular orientation in a plane perpendicular to the light propagation direction). The Wollaston prism 18 acts to split or shear the incident beam 14 into two spatially separated plane wave light beams 14a, 14b having orthogonal linear polarizations 15a. The linearly polarized light beams 14a, 14b leave the output face of the Wollaston prism 18 with divergent propagation directions separated by a splitting or shearing angle ε1, which is characteristic of the Wollaston prism 18, along a shearing direction parallel to the output face of the Wollaston prism 18. The divergent linearly polarized beams 14a, 14b propagate from the Wollaston prism 18 to a focusing lens 20 placed at a focal length fc and spaced apart along the shearing direction by a shearing amount d in order to reorient the propagation directions and make the linearly polarized beams 14a, 14b parallel to each other. The linearly polarized beams 14a, 14b are transmitted through a sample 22 mounted on a rotation stage 24 that allows the azimuth angle to be changed, the transmission through the material of the sample creating an optical path difference δ between the linearly polarized beams 14a, 14b. The beams 14a, 14b are collected by the objective lens 26 and have their propagation directions converged at an angle ε2 selected to match the shear or split angle of a second Wollaston prism 28 (also with an azimuth angle of 0°) placed behind the objective lens 26 at a distance fob, which is the focal length of the objective lens 26.The second Wollaston prism 28 receives the converging spatially separated linearly polarized beams 14a, 14b and spatially coincides them to output a single output light beam 14c in which the optical path difference δ introduced by the sample 22 is preserved and supplemented by the optical path difference bias Γ introduced by the second Wollaston prism 28 to give a total optical path difference Γ+δ. The output beam 14 is passed through an optical analyzer at an azimuth angle of 45° before reaching an eyepiece or image sensor 32 for observing or detecting a shadow cast image of the sample 22, allowing visualization of the phase inhomogeneity of the sample 22.

[0022] The inset to FIG. 1 shows that the second Wollaston prism 28 may be replaced by a Nomarski prism 34 placed beyond the focal length fob of the objective lens 26.

[0023] 2 is a schematic diagram of a second embodiment of a DIC microscope according to a different known configuration in which an illumination light beam is reflected from a sample. A light source 12 conventionally emits an illumination light beam 14, which passes through a filter 36 and reaches a semi-transparent beam splitter 38. A portion of the light beam 14 reflected by the beam splitter 38 passes through a polarizer 16 (at an azimuth angle of 45°), a Wollaston prism 18 (at an azimuth angle of 0°) and a collecting lens 20, conventionally providing two spatially separated, parallel and orthogonal linearly polarized beams 14a, 14b, which reach the sample 22. Instead of passing through the sample 22 as in the example of FIG. 1, the light beams 14a, 14b are reflected from the sample 22 and pass again through the lens 20, the Wollaston prism 18, and the polarizer 16, which act as the objective lens, the second Wollaston prism, and the analyzer of the example of FIG. 1, to generate a single output light beam 14c with optical path difference information from the sample 22. A portion of the output light beam 14c passes through a beam splitter 38 (with a filter 36 that protects the light source 12 from reflections from the beam splitter) for detection or observation at an image sensor or eyepiece 32. This reflective configuration has fewer parts than a transmissive arrangement and results in a more compact microscope, but optical losses, especially in the beam splitter, tend to reduce the light intensity available for observation or detection, resulting in a dimmer image. As in the example of FIG. 1, the Wollaston prism may be replaced by a Nomarski prism.

[0024] However, DIC microscopy, as enabled by DIC microscopes such as the examples of Figs. 1 and 2, has several drawbacks. To achieve optimal imaging, it is necessary to ensure that the sample is properly oriented with respect to the optical system. Also, the results are not directly quantitative. To address these limitations, orientation-independent (OI-) DIC microscopes have been developed (Patent Documents 1 and 2). This allows rapid switching between bias and shear directions without the need to mechanically rotate or adjust the sample or prisms. Quantitative optical path length (phase) images of the sample can be obtained with high fidelity and resolution. In particular, each individual Wollaston or Nomarski prism is replaced by a beam-shearing assembly that comprises a switchable 90° rotator sandwiched between two Wollaston or Nomarski prisms at an azimuth angle of 90° to each other. The rotators can be embodied, for example, by liquid crystal devices.

[0025] As mentioned in the background section, an issue affecting DIC microscopes (both standard and orientation-independent) is the compatibility and availability of suitable Wollaston and Nomarski prisms. Prisms must be designed to fit a specific microscope model, of which there are many and they are commercially available from various manufacturers. Thus, a prism designed for an Olympus microscope cannot be used in microscopes made by other manufacturers, such as Zeiss, Leica, or Nikon. For compatibility, the prisms must have the appropriate optical properties (especially shear angle and bias) as well as being unmounted and cut to the shape required for the microscope design. However, microscope manufacturers may not provide the appropriate prisms for their microscopes, forcing users to obtain them separately, which can be costly and take several months. The high cost of Wollaston and Nomarski prisms is due to the need to cut and polish birefringent crystal material into the required wedge shape with the appropriate wedge angle (which is generally required to be small for DIC microscopes) and the subsequent step of mounting the prism in an optically suitable manner.

[0026] It is therefore proposed to provide an alternative prism to Wollaston and Nomarski prisms for use in DIC microscopes and other applications, which provides the same optical functions and performance in a simpler and less expensive format and which also allows the optical properties to be easily tailored to meet the requirements of a particular design of a microscope or other optical instrument.

[0027] To achieve this, an optical element is proposed that includes a substrate whose birefringence is imparted by nanostructures formed within the material of the substrate. The procedure for "writing" the nanostructures can be easily tailored to create nanostructures that mimic the beam-shearing function of Wollaston and Nomarski prisms and impart a profile of varying birefringence across the substrate, where the shear angle and bias can be set for any application. The optical element simulates the optical action of a prism by similarly transforming (splitting, splitting, shearing) one input beam into two output beams. The different birefringences achieved by appropriate shaping of the nanostructures correspond to the diverse birefringences generated by the tilted boundaries between the wedges of the prism. The substrate is a sheet of transparent optical material of uniform thickness, thus avoiding the manufacturing precision required for cutting, polishing, and bonding the wedges of Wollaston and Nomarski prisms. Also, the elimination of the need for optical crystals with natural, inherent birefringence allows inexpensive silica-based glasses to replace expensive crystalline materials such as quartz and calcite.

[0028] The nanostructures and the techniques for forming them will be described in more detail later. First, the working principles of Wollaston and Nomarski prisms are explained to understand the optical properties required to be replicated by the proposed birefringent optical elements, particularly with respect to their use in DIC microscopy.

[0029] As explained above, Figure 1 shows the shear amount or distance d over which the two orthogonally polarized beams produced by the first Wollaston prism are spatially separated. This distance is the spacing between the beams after they have been collimated by the focusing lens, and therefore depends on both the shear angle between the two beams produced by the Wollaston prism, and the distance behind the Wollaston prism where the beams meet the focusing lens and diverge along the shear angle, thereby increasing the spatial separation. The shear distance is an important parameter of DIC microscopy, determining its contrast, sensitivity, resolution, and optical section depth.

[0030] FIG. 3 is a schematic diagram of a prism (Wollaston or Nomarski) and its operation in shearing an incident beam. The incident or input beam 14 is a monochromatic plane wave propagating along a propagation direction z, with a wavefront Ex of an ordinary polarization component and an unordinary polarization component Ey lying in the xy plane orthogonal to the propagation direction z. The beam 14 is incident on the input face 18a of a prism 18, which is located in the xy plane. The birefringent structure of the prism, formed from two wedges with orthogonal optical axes, splits or shears the beam 14 into two separate linearly polarized beams with slightly different and diverging propagation directions (again, generally in the z direction) starting from the output face 18b of the prism 18, according to known principles. The first output beam 14a has a plane wavefront Ex and a linear polarization along the x direction, and the second output beam 14b has a plane wavefront Ey and an orthogonal linear polarization along the y direction. The shear direction, and therefore the shear plane in which both beams 14a, 14b lie, is parallel to the x-axis in this example. While the shear plane is perpendicular to the output face, the shear direction is also parallel to the output face. The propagation directions of the output beams 14a, 14b are separated by a shear angle ε (which depends on the optical properties and structure of the prism 18). As a result, the wavefronts Ex and Ey lie at the same angle ε with respect to each other and have an optical path difference along the propagation direction z. As can be seen from the geometry of FIG. 3, the shear angle ε (in radians) is equal to the derivative of the optical path difference Δ (alternatively, the bias or retardance of the prism 18) with respect to the coordinate x (shear direction), ε=dΔ / dx.

[0031] In a DIC microscope, the shear amount or shear distance d is set by passing a diverging beam through a focusing lens (see Figure 1). If the lens has a focal length f, the shear distance d is given by d = fε = ε Lt / M, where M is the magnification of the lens. Lt is the standard reference focal length of the tube lens for an infinity objective as adopted by several microscope manufacturers. For example, Olympus uses a reference focal length of 180 mm, Zeiss uses 164.5 mm, and Nikon and Leica use a reference focal length of 200 mm.

[0032] In order to replace certain conventional Wollaston or Nomarski prisms with the proposed birefringent optical element, the shear angle of the prism needs to be determined in order to reproduce this characteristic in the optical element. The retardance derivative with respect to the coordinate along the shear direction has been measured for many DIC microscope prisms to yield the shear angle according to the geometry of FIG. 3 (Patent Document 3). As an example, the retardance derivative of Olympus prism U-DIC40HR is 15 nm / mm and the corresponding shear angle is 15 μrad, and the retardance derivative of Olympus prism U-DIC20HR is 30 nm / mm and the corresponding shear angle is 30 μrad.

[0033] The birefringent optical element proposed here to replace the Wollaston or Nomarski prism is a simple planar substrate with a birefringence that is inhomogeneous and varies across the plane of the substrate; in use, the optical element is oriented so that this plane is orthogonal to the propagation direction of the incident optical plane wave. As for the DIC microscope already described, the plane of the substrate lies in the xy plane, and the substrate has a thickness along the propagation direction z. The required shear effect can be produced with a profile of varying birefringence. The profile is composed of the value of birefringence along the z direction, where different xy positions show different birefringence values ​​(the variation exists only along one of these directions, giving the shear direction, and not along the other). Thus, for an incident beam with a finite beam cross-sectional area, different parts of the beam in the cross section (in the xy plane) experience different birefringence. The birefringence at any position has two components: the amount of retardance and the direction (azimuth) of the slow axis (as is usual for birefringence). A variety of birefringence profiles can provide the required beam shearing, and the amount of shear (angular separation of the two output beams) and bias (optical path difference between the two output beams) achieved can be selected by tuning the retardance and slow axis direction across the profile. Two examples are described in detail.

[0034] The first example has a birefringence profile consisting of a variable retardance and a constant (fixed) slow axis direction. The second example has the opposite arrangement with a constant (fixed) retardance and a variable slow axis direction. More complex configurations in which both the retardance and the slow axis direction are varied are also envisaged. However, it is considered preferable if only one component of the birefringence is variable, as this can simplify the process for forming the nanostructures (described further below). Also, in the examples, the birefringence profile is one-dimensional, varying along one direction (x-direction as described, corresponding to the shear direction) and constant along the other direction (y-direction as described) in the plane of the substrate. This corresponds to a beam-shearing prism due to the shape of the wedge boundary. However, it is also possible to vary the profile along both the x-direction and the y-direction to achieve beam shearing.

[0035] (First Detailed Example) Assume that the substrate of the optical element has a birefringence profile defined within a field of X mm × Y mm in the XY plane. Considering that the incident beam is usually of circular cross section, a square field is practical. The birefringence profile therefore exists in the region 0 mm < x < X mm, 0 mm < y < Y mm, where X and Y are equal in the square field. To give the absolute retardance value Δ at any x position, the retardance derivative of α is needed along the x direction (so the shear direction is in the x direction). Along the x direction, the variable retardance is chosen to have a value of zero at the center of the field (x = X / 2), increases to a positive maximum at one end of the field (x = X) and a negative maximum at the opposite end of the field (x = 0), with the maxima being equal. In the half of the field with positive retardance, the direction of the slow axis φ is fixed and chosen to be parallel to the x direction. In the other half of the field, which has negative retardance, the slow axis direction is also fixed, but orthogonal to the slow axis direction of the positive half, and therefore parallel to the y direction, however the orthogonal slow axis direction may be reversed or angled with respect to the x and y directions.

[0036] Therefore, when the x - direction is selected as the horizontal direction and the y - direction is selected as the vertical direction, the birefringence profile (along the x - direction) can be mathematically described as follows.

[0037]

Number

[0038] Consider a specific example. The birefringence field is set to 10 mm×10 mm and can be described for 0 mm < x < 10 mm, 0 mm < y < 10 mm. The retardance derivative α is selected to be 15 nm / mm to correspond to the actual Olympus U - DIC40HR prism described above. Therefore, each half of the field in the x - direction has a width of 5 mm and gives the maximum retardance at the ends of the field. Thus, the birefringence profile is given by the following equation:

[0039]

Number

[0040] FIG. 4 is a schematic plan view of an optical element having this birefringence profile. The optical element 50 comprises a circular substrate 52 made of fused silica having a planar shape of constant thickness and diameter 25 mm. The birefringence profile is written across a square field 54 in the center of the substrate, over an area of ​​10 mm×10 mm. The direction of the slow axis φ in each half of the field is indicated by a double-ended arrow. As mentioned above, the direction is fixed or constant within each half, with the two halves located on either side of a centerline at x=5 mm. The vertical lines indicate where the value of retardance Δ is 0 mm at x=5 mm, −75 nm at x=0 mm, and +75 nm at x=10 mm. The change in retardance value along the x direction is indicated by shading, the saturation of which is proportional to the absolute magnitude of retardance (hence the maximum saturation is located at the edge of the field 54). The absolute value of retardance increases linearly with distance from the centerline, due to the dependence of Δ on α·x shown above. In other words, the retardance has a constant gradient.An optical element constructed according to the first embodiment is optically equivalent to a Wollaston prism.

[0041] Figure 5 is a photograph of an experimental optical element fabricated according to the present specification. The photograph was taken using a polychromatic polarizing microscope and a color CCD camera (Lumenera Infinity 3-1C). As can be seen, the shading pattern corresponds to the theoretical representation of the birefringence profile in Figure 4, indicating that the optical element was successfully fabricated according to the design.

[0042] To evaluate the performance of the experimental optical element of the first embodiment, images of a sample were taken using a microscope configured for DIC microscopy and compared with images of the same sample taken using the same microscope equipped with a conventional shear prism. The microscope used was an Olympus BX61 research microscope equipped with a 40x objective, a high-resolution DIC slider U-DICTHR, a bandpass filter 576 / 10 nm, and a monochromatic CCD camera Lumenera Infinity 3-1M for recording images. In the illumination path (i.e., the position of the prism between the light source and the sample, see FIG. 1), either a conventional DIC shear prism, the Olympus U-DIC40HR, or the experimental optical element of the first embodiment was placed. The U-DIC40HR has a shear angle of 15 μrad resulting from a retardance derivative of 15 nm / mm as described above, and the optical element of the first embodiment was also made to have this same retardance derivative (and therefore the same shear angle) as described above.

[0043] The specimen contained a short segment of glass rod used as a spacer for the liquid crystal cell, embedded in Fisher Permounting Medium (Fisher Scientific Company LLC). This was chosen because of its optical similarity to the transparent filaments in cell structures that are typically observed through DIC microscopy. The refractive index of the glass rod and permount at a wavelength of 546 nm was measured to be 1.554 and 1.524, respectively, using a Jamin-Lebedeff microscope (Zeiss). A drop of the suspension was placed between a microscope slide and a coverslip, and the prepared specimen was placed on the rotatable stage of the microscope as shown in Figure 1.

[0044] FIG. 6A shows an image of a sample recorded with a microscope equipped with a U-DIC40HR prism, and FIG. 6B shows an image of a sample recorded using a microscope equipped with the optical element of the first embodiment. As can be seen from the figures, both images are sharp and have the same contrast. Therefore, the optical element having a birefringence profile configured according to the first embodiment can easily replace the conventional DIC microscope prism without any loss of image quality. Furthermore, the flexibility in forming the birefringence nanostructure on the substrate of the optical element (discussed further below) provides the possibility that the optical element exhibits improved performance compared to the conventional DIC prism.

[0045] (Second Detailed Embodiment) In this embodiment, the birefringence profile of the birefringence field of the optical element has a constant (fixed) retardance and a variable slow axis orientation. Again, assume that the substrate of the optical element has a birefringence profile defined within a field in the x-y plane having dimensions of X mm × Y mm, where X and Y are equal in a square field, and the profile exists in the region of 0 mm < x < X mm, 0 mm < y < Y mm. To provide a shear direction along the x direction, the direction or azimuth angle φ of the slow axis changes along the x direction. The variation is uniform in that the value of the slow axis azimuth angle has a constant gradient across the field. Therefore, the value of the slow axis azimuth angle is proportional to the value of x. Since the retardance Δ is fixed at a constant value along the x direction, there is the same amount of retardance at all x positions. In this embodiment, a retardance value that is half of the wavelength λ of the intended incident light beam is selected, although other values may also be used.

[0046] Therefore, if the x direction is selected as the horizontal direction and the y direction as the vertical direction, the birefringence profile (along the x direction) can be mathematically described as follows.

[0047] [Number]

[0048] This design results in an optical element where the evolution of the wavefront propagating through the substrate obeys geometric phase principles.

[0049] Consider a concrete example. The birefringence field is taken to be 10 mm × 10 mm, and can be taken to be 0 mm < x < 10 mm, 0 mm < y < 10 mm. The slow axis rotation gradient β is chosen to be 5.5° / mm. The wavelength λ is chosen to be 560 nm, and the retardance Δ is half this value, 280 nm.

[0050] FIG. 7 is a schematic plan view of an optical element with this birefringence profile. The optical element 50 has a circular substrate 52, also made of silica glass, and has a planar shape of constant thickness and diameter 25 mm. The birefringence profile is written across a square field 54 in the center of the substrate, over an area of ​​10 mm×10 mm. The retardance Δ is fixed at 280 nm across the birefringence field. The direction of change of the slow axis φ is shown by the double-ended arrow. According to the above relationship, the direction of the slow axis is shown to have a constant gradient: at the left edge of the field, x=0 mm, so φ=0°; at the center of the field, x=5 mm, so φ=27.5°; at the right edge of the field, x=10 mm, so φ=55°, with a smooth transition between these positions for larger values ​​of x. The field shading used in the figure corresponds to the azimuthal angle of the polarization plane of the output beam. Because the retardance is set to half the wavelength, the output polarization plane is rotated by an angle twice the azimuthal angle of the slow axis. Therefore, the output polarization azimuth angle χ varies from 0° to 110° along the x direction, as shown in the figure.

[0051] Figure 8 is a photograph of an experimental optical element fabricated according to the present disclosure. The photograph was taken using a polychromatic polarizing microscope and a color CCD camera (Lumenera Infinity 3-1C). As can be seen, the shading pattern is consistent with the theoretical representation of the birefringence profile in Figure 7, indicating that the optical element was successfully fabricated according to the design.

[0052] When an optical element with a birefringent profile is illuminated by a linearly polarized beam with vertical polarization, the azimuthal angle χ of the polarization plane of the output beam is given by χ = 2βx (i.e. twice the azimuthal angle of the slow axis as described above). However, the rotation of the linearly polarized light by the angle χ can be written as a phase shift between two orthogonal circular (left and right) eigenwaves ψ, so that ψ = 2χ = 4βx. The derivative of the phase shift between the left and right circular eigenwaves is then given by dψ / dx = 4β. The optical path difference or retardance derivative ε can therefore be written as ε = (λ / 360°)dψ / dx = λ(β / 90°). (As an aside, the optical element of the second embodiment, which can be described as a geometric phase optical element, works similarly to a Fresnel triprism, which is a further example of a prism with beam-shearing capabilities, but uses a different beam polarization transformation principle.)

[0053] Note that the retardance derivative scales with the shear angle. In this example, λ = 560 nm, β = 5.5° / mm, so the shear angle introduced between the two orthogonal circularly polarized beams is 34 μrad (2 millidegrees). This is similar to the shear angle of the Olympus DIC prism U-DIC20HR, which is 30 μrad as mentioned above. Therefore, it is possible to compare the experimental optical element with the Olympus prism and evaluate its performance.

[0054] Thus, a similar experiment to the experimental optics of the first embodiment was performed by using the experimental optics of the second embodiment in a microscope configured for DIC microscopy to obtain images of a sample and comparing them with images of the same sample taken with the same microscope equipped with a conventional shear prism. The microscope was again an Olympus BX61 microscope, equipped with a 20x objective, a high-resolution DIC slider U-DITHCER, a bandpass filter 576 / 10 nm, and a monochromatic CCD camera, Lumenera Infinity 3-1M, for recording images. In the illumination path (i.e. the prism position between the light source and the sample, see FIG. 1), either a conventional DIC shear prism, in this case an Olympus U-DIC20HR (which, as mentioned above, has a similar shear angle as the optical element of the second embodiment), or the experimental optics of the second embodiment was placed. The same samples were used as in the experiment with the optical element of the first embodiment.

[0055] FIG. 9A shows an image of a sample recorded using a microscope equipped with a U-DIC20HR prism, and FIG. 6B shows an image of a sample recorded using a microscope equipped with the optical element of the second embodiment. Both images are of good quality, but the image obtained with the conventional prism may be perceived as having a more uniform field of view and slightly better contrast. One reason for this is that the shear angle of the optical element (34 μrad) is slightly higher than that of the Olympus prism (30 μrad), so the former is not a direct replacement for the latter, which creates a different shear distance inside the microscope and other components of the microscope are not optimized. Further studies have also revealed that the optical element of the second embodiment has manufacturing defects. However, if the shear angles are correctly matched (which can be achieved by changing the parameters of the process of forming the birefringent nanostructures in the substrate) and there are no defects, it is expected that the same image quality will be obtained. Thus, an optical element equipped with a birefringent profile constructed according to the second embodiment can also be easily substituted for a conventional DIC microscope prism without any loss of image quality.

[0056] Thus, a DIC microscope arranged as in the example of FIG. 1, or other similar arrangements for transmitting light to a sample, may be reconfigured by replacing the Wollaston or Nomarski prism with a birefringent optical element as described herein. Both prisms may be replaced, or only a single prism may be replaced (either the first prism in front of the sample or the second prism after the sample). If both prisms are replaced, the two optical elements may be the same or different. For example, one may be according to the first detailed embodiment, one may be according to the second detailed embodiment, or both may be according to the same detailed embodiment but with different azimuth angles or retardance values ​​in the birefringence profile (depending on the functionality with other components of the microscope). Similarly, the single Wollaston or Nomarski prism of the reflection type DIC microscope of the example of FIG. 2 may be replaced with a birefringent optical element as described herein, for example according to the first detailed embodiment or the second detailed embodiment.

[0057] Furthermore, the birefringent optical elements described herein may also be used in orientation-independent (OI-) DIC microscopes (Patent Documents 1 and 2). These have a similar structure to non-OI versions of DIC microscopes, with the key difference to enable orientation independence being that each beam-shearing prism is replaced by a beam-shearing assembly comprising a pair of beam-shearing prisms (Wollaston or Nomarski) with orthogonal optical axes and a 90° optical rotator sandwiched between them. The optical rotator may be, for example, a liquid crystal device. These prisms may be replaced by birefringent optical elements as described herein (e.g., according to the first or second detailed embodiment) to provide a beam-shearing assembly comprising a pair of birefringent optical elements sandwiching a 90° optical rotator therebetween.

[0058] FIG. 10 is a schematic diagram of an example of an OI-DIC microscope 70 using transmission of an illumination beam through a sample similar to the embodiment of FIG. 1, but with a birefringent optical element instead of a conventional beam-shearing prism. Components in common with the embodiments of FIG. 1 and FIG. 2 are given the same reference numerals for ease of comparison and explanation. The light source 12 emits an illumination beam 14 that passes through a 45° polarizer 16 and a phase shifter 56 in the 0° direction. The beam then reaches a first beam-shearing assembly 60, which includes a first birefringent optical element 61 with an optical axis at an azimuth angle of 0°, a second birefringent optical element 63 with an optical axis orthogonal to the first birefringent optical element 61, and a 90° optical rotator 62 sandwiched therebetween at an azimuth angle of 90°. The first beam-shearing assembly shears the input illumination beam into the required pair of orthogonally polarized beams (14a, 14b) that diverge at a shear angle (not shown for simplicity). The two beams 14a, 14b pass through a collecting lens 20 that collimates the beams, spaced apart by the shearing distance, as described above, and are transmitted through a sample 22 to obtain the path difference pattern to be observed. An objective lens 26 collects the beams 14a, 14b and focuses them into a second beam-shearing assembly 64, which also includes an optical rotator 66 sandwiched between a first birefringent optical element 65 and a second birefringent optical element 67 with an optical axis perpendicular to that of the first optical element 65. However, the second beam-shearing assembly 64 is rotated by 180° with respect to the first beam-shearing assembly 60, such that the optical axes of the first birefringent optical element 65 and the second birefringent optical element 67 are oriented at 270° and 180°, respectively. The second beam-shearing assembly 64 brings the beams into overlapping common alignment as described above and provides output beam 14c to the microscope which conveys path difference information induced by the sample 22. Output beam 14c passes through a displacement compensator 68 at -45° and an optical analyzer to an image sensor or other optical detector 32 for detection / observation.

[0059] FIG. 11 is a schematic diagram of an example of an OI-DIC microscope 71 that utilizes reflection of an illumination beam at a sample, similar to the example of FIG. 2, but includes a birefringent optical element instead of a conventional beam-shearing prism. Components in common with the embodiments of FIGS. 1, 2 and 10 are given the same reference numerals for ease of comparison and explanation. A light source 12 emits an illumination beam 14 that passes through a 45° polarizer 16 and a phase shifter 56 (similar to the arrangement of FIG. 10) at 0° before reaching a beam splitter 38 (similar to the arrangement of FIG. 2) that directs a portion of the beam 14 to the sample. The beam first passes through a displacement compensator 68 before reaching a beam-shearing assembly 60, which includes a first birefringent optical element 61 with its optical axis at a 0° orientation, a second birefringent optical element 63 with its optical axis orthogonal to the first birefringent optical element 61 and at a 90° orientation, and a 90° optical rotator 62 sandwiched between them, similar to the first beam-shearing assembly 60 in the arrangement of FIG. 10. The beam-shearing element 60 generates the two spatially separated beams 14a, 14b required for DIC microscopy, which are collimated by the collection lens 20 before reaching the sample 22, as described above. Here, the beams 14a, 14b are reflected and transmitted through the collection lens 20 and the beam-shearing assembly 60 to remove the spatial separation and provide a single output beam 14c, which then passes through a displacement compensator 68 and reaches the beam splitter 38, which transmits a portion of the output beam 14c at −45° through the optical analyzer 30 and finally through the image sensor 32 (similar to that described for the example of FIG. 2).

[0060] Thus, the birefringent optical element proposed herein can be successfully used in both orientation-independent and orientation-dependent DIC microscopes. The birefringent optical element is less expensive than conventional beam-shearing prisms and can be easily customized individually for each specific model or configuration of microscope (including commercial DIC microscopes where appropriate prisms are currently costly to obtain) by the manufacturing methods described below. Such customized optical elements are more precise and can be configured to correct for manufacturing and alignment errors in the microscope, providing better image contrast. Furthermore, the optical element exhibits negative birefringence and a low maximum retardance of about 200 nm. This is in contrast to conventional quartz beam-shearing prisms, which have positive birefringence and a much larger retardance of about 5000 nm. The negative birefringence and small amount of retardance can increase the field of view of DIC microscopes.

[0061] The birefringence of the optical elements described herein is provided by nanostructures formed within the optical elements. The nanostructures comprise a collection of nanopores that are periodically or randomly distributed in an optically transparent material, typically silica glass. Nanopores are nanometer-scale structural modifications or changes that alter the refractive index in the bulk material, providing negative birefringence. Although not yet fully understood, nanopores are thought of as voids within the bulk material. Nanopores have a shape and orientation that impart birefringent properties to the bulk material. Nanopores are formed and "written" by the action of ultrashort (femtosecond) pulsed laser light directed at the substrate. The optical properties of the pulse determine the shape and orientation of the nanopores. Thus, the birefringence properties can be tuned by modifying the pulse characteristics, and by appropriately controlling the laser pulse when applied to the substrate, a birefringence profile can be created in the substrate that emulates the beam shearing capabilities of a Wollaston or Nomarski prism.

[0062] The amount of optical energy delivered to the substrate (determined by factors including the power, duration, and repetition rate of the laser pulse) determines the type of nanostructure formed. The pulse can provide sufficient stored and lattice heat to induce permanent material modifications in the substrate. One type of nanostructure, called Type II (Patent Document 3), comprises nanolattices with a periodic distribution of self-organized nanopores that act as optical lattices, providing an anisotropic refractive index pattern and hence birefringence. The anisotropy is strongly dependent on the polarization of the laser pulse, so that the induced birefringence can be tailored to the required profile.

[0063] A more useful type of nanostructure for the purposes of this application has reduced light propagation losses compared to type II structures and is called type X (Patent Document 3). Type X nanostructures can be written using lower applied light pulse densities than are necessary to produce the self-organized periodicity of type II nanostructures. Although type X nanostructures exhibit birefringence less than about four times that of type II nanolattices, by appropriate beam shaping of the laser pulses, nanostructures can be written with relatively long lengths in the intended light propagation direction through the optical element. Lengths on the order of 50 μm or more, for example up to about 100 μm, can be written. This length of nanostructures located along the light propagation direction compensates for low birefringence, since the parameter required for birefringent operation is the phase retardance, defined as the product of birefringence and optical path length. The retardance parameter can be easily varied by adjusting the lens to control the length of the nanopores and by adjusting the laser energy and pulse dose to control the density of the nanopores, the aspect ratio and the volume of the individual nanopores.

[0064] Type X birefringent structural modifications comprise randomly distributed individual nanopores or nanostructures. However, periodicity of the nanostructures is not necessary to provide the desired birefringence, relying instead on the orientation of the individual structures within the bulk material. Thus, lack of self-organization is not an impediment to the fabrication of high quality optical elements. Type X anisotropy is also controlled by the polarization of the laser writing beam. Each nanopore defines its anisotropy by its shape, which may be oblate spheroidal (ellipsoidal) or lenticular. As mentioned above, the nanopores are randomly spaced within the substrate material, although typically within a layer of a certain depth behind the optical input surface of the optical element. The oblate spheroidal shape of each nanopore is oriented parallel to the direction of light propagation through the optical element, with the plane of its circular cross section perpendicular to the input surface of the optical element. The elliptical or oval cross section parallel to the input surface can have its major axis oriented at any angle, with the major axis perpendicular to the polarization of the writing light beam. The minor axis is parallel to the polarization of the writing light beam. Because the overall shape is lenticular, the extent of the nanostructure in the direction of light propagation, i.e., the length along the direction through the thickness of the optical element from the input face to the output face, may be the same as or similar to the long axis. The overall shape of the nanostructure is determined by the intensity distribution of the laser pulse near the focal point.

[0065] FIG. 12 shows, highly schematic and not to scale, an individual nanopore 86 in an optical element 80, which in this example comprises a birefringent optical element having a birefringent profile that provides a beam shearing effect. For clarity, only a single nanopore is shown, but as noted above, the nanostructure modification will in fact comprise a multitude of such nanopores arranged randomly in the case of a type X modification, or periodically in the case of a type II modification, within the material of the optical element substrate. The term "nanostructure" may refer to a single nanopore, or to an ensemble of nanopores (either a subgroup within a broader group, such as a nanolattice, or all of the nanopores present in the optical element). The optical element 80 has an input face 82 for receiving incident light, which propagates through the optical element along a propagation direction z parallel to the thickness t of the optical element, and departs through an output face 84 opposite the input face 82. A focused writing light beam I of femtosecond pulses is incident on the input face 82 and has a linear polarization E aligned in this example parallel to the y-direction, i.e., width direction, of the sample forming the optical element 10. In subsequent use of the fabricated optical element 80, the incident or input light beam I (such as the illumination light beam of a DIC microscope) is modified or transformed into an output light beam I' (sheared into two parts in this example, not shown) by the birefringence of the optical element 80 created by the writing process. The nanopore 86 has a length L substantially parallel to the thickness t of the optical element, which is typically 100 nm or less. The length L is perpendicular to the plane of the input face 12. The nanopore 86 has a cross-sectional shape in a plane parallel to the input face that has an elliptical, oval or oblate spheroid shape with a major axis or height H and a small minor axis or width W perpendicular to the height. The major axis is larger than the minor axis. The width W typically has a size of about 30 nm or less. Due to the oblate spheroidal shape of nanopore 86, length L and height H may be substantially equal, and a cross-section of nanopore 20 through length L and height H may be approximately circular. In some cases, the growth of the nanopore during the writing process along these two dimensions may evolve differently, resulting in a slight or more significant difference between length L and height H. For example, length L may be greater than height H.In general, however, L and H will be at least similar to each other when compared to width W, which is smaller than both. The input face 82 has a height dimension h and an orthogonal width direction b. The width W and height H of the nanostructure 20 form an angle with respect to the height h and width b, which sets the orientation of the nanopore 86, which is defined as lying along the height direction (long axis). Either H and W can be parallel to either h or b, or can be disposed at any angle between parallel alignments. This orientation (the direction of the long axis H) is the direction (azimuth) of the slow axis of birefringence provided by the nanostructure comprising the nanopore. The direction is set by the polarization E of the writing light beam I, with W being parallel to E and H being perpendicular to E. Thus, rotation of the polarization direction of the writing light beam controls the direction of the slow axis of the birefringence created. The length L of the nanopore 20, which is the dimension along the light propagation direction, determines in part the total retardance available from the birefringence, and can be varied by controlling the amount of light energy applied to form the nanopore. The contribution of the nanopore shape to the retardance varies with the nanopore volume and the ratio of W to H. The overall total retardance also depends on the density of nanopores and the length of the region or volume containing the nanopores. The total energy can be varied by changing parameters including pulse duration, individual pulse energy, pulse repetition rate, number of pulses, and numerical aperture of the pulse focusing. Thus, both the retardance and slow axis direction of the birefringence provided by the nanostructure can be easily controlled, and the birefringence change profile as described herein can be easily created.

[0066] In both type II and type X structures, it is common to irradiate the substrate material multiple times with ultrashort laser pulses to create consistent and uniform birefringence. For example, about 10, 50, 100, or more pulses may be used. The laser light of the writing beam is polarized and a defined polarization direction is required to obtain the anisotropy that shapes the nanopore into an oblate spheroid to produce the desired birefringence. The polarized writing light has an anisotropic electric field distribution that is enhanced at the equator of the initial spherical nanopore induced in the substrate by the laser pulse, causing the sphere to grow into an oblate shape with its longer dimension oriented perpendicular to the polarization direction of the laser light. Thus, writing nanopores of a specific birefringence into a substrate can be achieved with ultrashort laser pulses with a polarization direction or orientation selected to define the slow axis direction of the birefringence and an amount of light energy selected to define the level of birefringence retardance.

[0067] Writing of nanostructures can be performed using linearly polarized light to define the slow axis orientation of the birefringence. To provide a full orientation range, the polarization orientation needs to be variable between 0° and 180°, and is set using a variable retardance polarization element that generates a linear polarization state, such as an electro-optic modulator. Alternatively, elliptically polarized light can be used to write nanostructures into the substrate material, and the direction of the elliptically polarized light has been found to act in the same way as linearly polarized light to define the slow axis orientation of the birefringent nanostructures. Thus, elliptically polarized light can easily replace linearly polarized light. Furthermore, since the retardance of the birefringent nanostructures also depends on the ellipticity of the elliptically polarized light, this property can be utilized to control the retardance when writing nanostructures. This arrangement avoids the need to adjust the amount of optical power to obtain a particular retardance. A constant pulse power (and writing speed, pulse repetition rate, and other factors that determine the total amount of power delivered) can be used throughout the creation of a full variable birefringence profile, and only the polarization properties need to be varied.

[0068] Additional information regarding birefringent nanostructures and methods for writing them onto substrates can be found in WO 2019 / 158910 (Patent Document 3), WO 2020 / 109767 (Patent Document 4) and WO 2020 / 109768 (Patent Document 5).

[0069] An attractive feature of replacing the Wollaston and Nomarski prisms described herein with birefringent optical elements is the avoidance of expensive optically birefringent crystalline materials such as quartz and calcite used to manufacture such prisms. The bulk material of the substrate used to form the optical element is a transparent material (having high transmission at the wavelength of the writing laser pulse, significant transmission for at least some wavelengths across the spectrum from ultraviolet to near infrared (approximately 200 nm to 2500 nm), and for the wavelength of the illumination beam of the microscope for which it is intended). Usefully, the material may be an amorphous glass material. For example, it may be silica (silicon dioxide, SiO2), including fused silica. Silica or other glass materials may be doped with other materials to modify their optical properties (which may be interesting for certain applications). Examples of doped or multicomponent glasses may include materials such as Al2O3, B2O3, alkaline earth oxides, and Na2 / K2O, and other elements and compounds may be used, and the disclosure is not limited in this respect. The other material of the optical element may be any material capable of supporting laser-induced nanostructures, including materials in which nanolattices have previously been demonstrated, such as type II or type X modifications. This includes multicomponent glasses, GeO2 glasses, porous glasses, aerogel glasses, silicon and silicon materials, semiconductor materials, lithium niobate and other lithium oxide compounds. However, other materials are not excluded. The nanostructures are formed to be embedded within the volume of the substrate material of the optical element. They may be formed in a single layer, with layer thicknesses ranging from about 50 μm to about 500 μm to provide suitable birefringence effects, although other layer thicknesses are not excluded.

[0070] The time it takes to write the birefringent nanostructures into the substrate is proportional to the amount of retardance produced. As an example, the average retardance of a 10 mm x 10 mm square birefringent field in the optical element according to the first example may be 37.5 nm, while the optical element according to the second example may have a retardance of 280 nm. Thus, the writing time of the optical element of the first example may be at least five times that of the optical element of the second example, which may be the preferred configuration in some cases. However, if a larger birefringent field size or a larger average retardance is required, the optical element of the second example may be preferred. DIC microscopes with high resolution in the final image require a small shear distance, so the optical element of the first example is generally the better choice. On the other hand, DIC microscopes with high contrast in the final image require a large shear distance, so the optical element of the second example may be the better choice in this case.

[0071] The birefringent optical element described herein simulates the behavior of beam-shearing prisms such as Wollaston prisms, Nomarski prisms, and Fresnel triprisms. Its application is therefore not limited to use in DIC microscopes, but may additionally be used to replace conventional beam-shearing prisms in other optical devices, including digital holographic interferometers (Patent Document 6) and shearing interferometers (Patent Document 7). It may also be used to fabricate high-precision zero-order Soleil-Babinet compensators. The described optical element is effectively a zero-order birefringent wedge that can be oriented in the opposite direction and can be used to replace the quartz wedge of a Soleil-Babinet compensator without the need for any additional compensating birefringent plate. This improvement can provide improved precision and a wider angle of view.

[0072] The various embodiments described herein are presented only to aid in the understanding and teaching of the features described in the claims. These embodiments are provided only as representative samples of embodiments and are not exhaustive and / or exclusive. The advantages, embodiments, examples, functions, features, structures, and / or other aspects described herein are not to be considered as limitations on the scope of the invention as defined by the claims or limitations on the equivalents to the claims, and it is understood that other embodiments can be utilized and changes can be made without departing from the scope of the invention as claimed. Various embodiments of the invention may preferably comprise, consist of, or consist essentially of any suitable combination of the disclosed elements, components, features, parts, steps, means, etc., other than those specifically described herein. Furthermore, the present disclosure may include other inventions not currently claimed but which may be claimed in the future.

Claims

1. 1. A birefringent optical element for converting an input light beam into two spatially separated output light beams having orthogonal linear polarizations, comprising: a transparent substrate having an input surface for receiving an incident beam, an output surface, and a uniform thickness between the input surface and the output surface, the substrate having non-uniform birefringence in a plane parallel to the input surface, the birefringence being provided by a plurality of randomly disposed nanostructures in the substrate, the substrate being configured to shear the incident beam within the substrate into two output beams having orthogonal linear polarizations and wavefronts at an angle to each other, the output beams leaving the output surface spatially separated along a shear direction parallel to the output surface; A birefringent optical element, wherein each of the nanostructures has an oblate spheroidal shape with an elliptical cross-section in a plane parallel to the input surface, the direction of the elliptical cross-section providing a slow axis direction of birefringence and the size of the oblate spheroidal shape providing a retardance value of birefringence, the direction and size varying between the nanostructures to provide non-uniform birefringence of the substrate.

2. 2. The birefringent optical element of claim 1, wherein the non-uniform birefringence has a birefringence profile across the substrate in which the birefringence varies along a first direction parallel to the shear direction and is constant along a second direction perpendicular to the shear direction.

3. The birefringent optical element of claim 2 , wherein the birefringence profile along the first direction has varying retardance values ​​and invariant slow axis orientations.

4. The birefringent optical element of claim 3 , wherein the retardance value has a constant gradient along the first direction between opposite ends of the birefringent profile.

5. 5. The birefringent optical element of claim 4, wherein along the first direction, the retardance value is zero at a center of the birefringence profile, increases to a maximum positive value at one end of the birefringence profile, and decreases to a maximum negative value at the opposite end of the birefringence profile.

6. The birefringent optical element according to any one of claims 3 to 5, wherein the birefringent profile along the first direction has a first slow axis orientation between a first end of the birefringent profile and a center of the birefringent profile, and a second slow axis orientation perpendicular to the first slow axis orientation between the center and a second end of the birefringent profile opposite the first end.

7. 7. The birefringent optical element according to claim 6, wherein one of the first slow axis orientation and the second slow axis orientation is parallel to the first direction, and the other of the first slow axis orientation and the second slow axis orientation is parallel to a second direction.

8. The birefringent optical element of claim 7 , wherein the retardance value is positive when the slow axis orientation is parallel to the first direction and negative when the slow axis orientation is parallel to the second direction.

9. 9. The birefringent optical element according to claim 3, wherein along the first direction, the birefringence profile has a retardance value Δ defined by Δ=αx-αX / 2 and a slow axis orientation φ defined by x<X / 2 when φ=90° and x>X / 2 when φ=0°, where x denotes a position along the first direction between 0 and X, X is the size of the birefringence profile along the first direction, and α is the derivative of the retardance Δ with respect to x.

10. The birefringent optical element of claim 2 , wherein the birefringence profile along the first direction has a constant retardance value and a varying slow axis orientation.

11. The birefringent optical element of claim 10 , wherein the slow axis orientation has a constant gradient along the first direction between opposing ends of the birefringent profile.

12. 12. The birefringent optical element of claim 10 or 11, wherein the slow axis orientation is parallel to the second direction at a first end of the birefringent profile and rotates toward an orientation parallel to the first direction at a second, opposite end of the birefringent profile or at a constant speed relative to an orientation parallel to the first direction.

13. A birefringent optical element according to any one of claims 10 to 12, wherein the invariant retardance value is half the value of the intended wavelength of the incident beam.

14. 14. The birefringent optical element of claim 10, wherein along the first direction, the birefringence profile has a retardance value Δ defined as Δ=λ / 2 and a slow axis orientation φ defined as φ=β-x, where λ is the intended wavelength of the incident beam, x indicates the position along the first direction, and β is the magnitude of the gradient of the rotation of the slow axis orientation.

15. A birefringent optical element according to any one of claims 2 to 14, wherein the birefringence profile has a square shape such that its size along the first direction is equal to its size along the second direction.

16. A birefringent optical element according to any preceding claim, wherein the substrate comprises quartz glass.

17. 1. An optical assembly for converting an input light beam into two spatially separated output light beams having orthogonal linear polarizations, comprising: A first birefringent optical element according to any one of claims 1 to 16, A second birefringent optical element according to any one of claims 1 to 16, an optical rotator sandwiched between the first birefringent optical element and the second birefringent optical element; An optical assembly comprising:

18. 20. The optical assembly of claim 17, wherein the optical rotator is configured to provide a rotation of 90 degrees, and the first birefringent optical element and the second birefringent optical element are arranged such that their optical axes are orthogonal to each other.

19. A birefringent optical element according to any one of claims 1 to 16, arranged to shear an illumination light beam in a microscope into two spatially separated light beams having orthogonal linear polarizations for illuminating a sample placed in the microscope; A birefringent optical element according to any one of claims 1 to 16, arranged to receive, by transmission or reflection, two spatially separated light beams having orthogonal linear polarizations from a sample, and to focus the two spatially separated light beams into a single output light beam for observation or detection; A differential interference contrast microscope equipped with one or both of the above.

20. 19. An optical assembly according to claim 17 or 18, arranged to shear an illumination light beam in a microscope into two spatially separated light beams having orthogonal linear polarizations for illuminating a sample placed in the microscope; 19. An optical assembly according to claim 17 or 18, arranged to receive two spatially separated light beams having orthogonal linear polarizations from a sample by transmission or reflection, and to focus the two spatially separated light beams into a single output light beam for observation or detection; An orientation-independent differential interference contrast microscope having one or both of the above.

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