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Abstract
Dark-field confocal microscopy (DFCM) facilitates the 3D detection and localization of surface and subsurface defects in high-precision optical components. The spatial resolution of conventional DFCM is commonly undermined owing to complementary aperture detection. We employed a radially polarized (RP) beam for illumination in DFCM. The RP beam creates a sub-diffraction-sized longitudinal optical component after being focused and effectively enhances the lateral resolution by 30.33% from 610 nm to 425 nm. The resolution improvement was verified by imaging a 2D sample containing sparsely distributed gold nanorods along with a 3D neodymium glass containing surface and subsurface defects.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Dark-field confocal microscopy (DFCM) is a promising technique that merges the capability of high-resolution imaging and imaging contrast [1–3]. In contrast to confocal bright-field microscopy (CBFM), dark-field imaging schemes exploit the scattered light from localized changes in the refractive index of scattering materials, which enables label-free 3D visualization of features that are undetectable in CBFM. In a typical DFCM system, an annular beam is used for illumination, where the reflected beam displays an annular intensity distribution. A spatial filter is placed in the collection path to block the reflected light while keeping the scattered light in the central region [4–6]. The rejection of reflected light provides DFCM with improved abilities to image biological structures, nanoparticles, and subsurface defects [7–11].
Despite an enhanced imaging contrast, DFCM tends to obtain a degraded spatial resolution compared with conventional confocal microscopy after annular beam illumination [2], limiting further application in the field of subcellular organization inspection or nano defect detection. To retrieve information with higher resolution using a confocal configuration, several protocols have been proposed to manipulate the total point spread function (PSF), which consists of illumination and detection PSF. For instance, the differential scheme modulates the illumination process with a double exposure. Super-resolution results were obtained by subtracting images using different illumination beams [12,13]. Similarly, in the detection path, subtraction between images acquired with different pinhole diameters also enables resolution enhancement [14]. Moreover, replacing the point detector with array detectors can improve the resolution by a factor of two [15–17]. In addition, other methods such as pupil filters, spatial mode sorters, and polarization modulation have been employed in confocal microscopy systems to overcome the diffraction limit [18–20]. Nonetheless, all these methods are employed in bright-field mode, and few investigations to realize resolution enhancement for DFCM have been proposed considering the requirement of complementary aperture detection. Thus, to achieve higher resolution imaging with confocal dark-field microscopy, it is necessary to keep the central dark spot stable while modulating the illumination beam.
In recent years, vector beams with a spatially inhomogeneous state of polarization (SOP) have been investigated because of their cylindrical symmetry in both polarization and phase [21,22]. As one of the fundamental modes among them, a radially polarized (RP) beam produces a relatively weak transverse electrical component along with a strong longitudinal component, due to which it can be tightly focused to a spot of sub-diffraction scale with a high-numerical-aperture objective [23–26]. The spot size was numerically verified to be compressed to less than λ/6 and a spatial resolution better than 150 nm using confocal detection [27]. The highly focused spot brought by RP beam has been proved compatible with confocal microscopy [28,29]. The resolution can be further enhanced when binary optics elements are added to properly choose the pupil filtering functions [30–33]. Considering the uncertain SOP in the central region, the RP beam inevitably appears in an annular shape, and the dark spot is stable, which allows it to combine perfectly with DFCM.
In this paper, we utilize vector beam illumination in a DFCM system to obtain resolution enhancement of dark-field imaging. A vortex retarder is placed in the illumination path to generate an RP beam from a linearly polarized input. Distinct from the bright-field mode, the transformation from a hollow-core reflected RP beam to a solid linear polarized beam by a polarization convertor placed in the detection path can be omitted to maintain the doughnut shape of the reflected light. The tightly focused beam excites scattering in a sub-diffraction-scale region. After removing the reflected annular beam, pure scattered light, which contains information pertaining to super-resolved sample features, was collected via confocal detection. We first demonstrate the physical model for DFCM with vector beam illumination based on vectorial diffraction theory. Then, the resolution enhancement is investigated by both simulation and experiments for imaging the 3D distribution of non-fluorescence samples. An improvement of lateral resolution from 610 nm to 425 nm was realized when an objective of 0.9 NA is applied.
2. Method
2.1 Focus of RP beam illumination
A schematic diagram for RP-DFCM is illustrated in Fig. 1. The polarization converter (PC) transforms the linearly polarized input to an RP beam with a dark spot at the center, which can be utilized for annular illumination in DFCM. When focused by a high numerical aperture (NA) objective with a maximum divergence angle of ${\theta _1}$, the electric field at the focus ${\vec{E}_{ill}}$ can be calculated according to the vectorial Debye integral:
Fig. 1. Schematic diagram of high-resolution DFCM with RP beam illumination. (a) Illumination path of conventional confocal microscopy applying RP beam. (b) Illumination path of RP-DFCM involving the axicon pair.
Fig. 2. (a) Distribution of the transverse component of the focused electric fields from RP beam. (b) Longitudinal component of the counterpart. (c) The total field distribution. (d-e) Inspection of the field distribution in x-z plane.
Distinct from conventional RP beam-assisted confocal microscopy, manipulation of the RP beam is performed in DFCM to generate a larger dark spot. Figure 1(b) illustrates the modified configuration of the illumination path of RP-DFCM. A pair of axicons was placed in front of the PC to create an annular beam with an adjustable inner diameter, which can be controlled up to 9/10 of the outer diameter. The PC then converts the SOP of the pre-generated annular beam to the RP state. With a larger inner diameter, the integral can be modified by replacing the lower limit from 0 to θ2, leading to a significant decrease in the intensity of the transverse component while maintaining the longitudinal component. Consequently, the longitudinal field accounts for the majority of the total electric field, and hence largely dominates the intensity distribution of the focal spot. A comparison of the total focused electric field with and without beam shaping by the axicon pair is depicted in Fig. 3(a-f). Assuming an objective with an NA of 0.9 is applied and the illumination wavelength is 532 nm, the theoretical lateral FWHM of the illumination PSF when applying solid beam illumination is 0.61λ/NA, which equals 360.6 nm. When the illumination is transformed to an RP beam with a small dark spot, the normalized intensity PSFs inspected in the x-y and x-z planes are shown in Fig. 3(a) and (b), respectively, and the corresponding component intensity distribution along the radial direction is shown in Fig. 3(c). The calculated FWHM of PSFs along the x- and z-direction denoted as FWHMx and FWHMz are 509.3 nm and 665.6 nm, respectively, which are larger than the diffraction limit. After intensity-modulation to an annular beam, where the ratio between the maximum divergence angles of the outer and inner edges θ2/θ1 was set to 2/3, the size of the focal spot was effectively compressed, which tended to breach the diffraction limit in the transverse plane, as depicted in Fig. 3(d). The FWHMx drops dramatically to 259.8 nm. Nonetheless, the compression of the focal spot in the x-y plane is accompanied by an obvious expansion of PSF along the axial direction, which is acknowledged to lead to an extended depth of field [29], yet a degraded axial resolution. With the same value of θ2/θ1, FWHMz expands to more than 1µm. Furthermore, the degree of intensity compression in the transverse direction and expansion in the axial direction can be intensified by continually enlarging the inner diameter of the annular illumination, as illustrated in Fig. 3(g-i). Considering the lower level of intensity and poorer axial resolution with increasing θ2/θ1, we chose a ratio of 2/3 for the following research in RP-DFCM.
Fig. 3. (a-f) Intensity PSF distribution of RP beam with (a-c) and without (d-f) intensity modulation brought by the axicon pair. (g, h) Intensity PSF along x-direction (g) and z-direction (h) under different θ2/θ1 of 1/6, 1/3, 1/2, 2/3, 5/6. (i) Evolution of FWHM of PSF along both x- and z-direction with distinct θ2/θ1.
The narrower focal spot effectively facilitates the spatial resolution enhancement which is shown in Fig. 4. Compared with the annular illumination with linear polarization (LP), the focal spot of RP beam is compressed. The linewidth of focal spot profile of LP beam is calculated as 348.8 nm and the counterpart of RP beam is 259.8 nm as mentioned above, which represents a 25.6% improvement in terms of lateral size of focal spot.
Nonetheless, the polarization modulated by conventional polarization convertors is commonly not fully accurate and tends to deviate from perfect radial polarization in practical application. Considering the imperfect polarization modulation, the azimuthal component in Eq. (1) is nonzero and the electrical field vector can be denoted as:
Fig. 5. Intensity profile of focal spot along the radial direction with distinct azimuthal component proportion η between 0 and 1.
2.2 Total PSF of RP-DFCM
The detection path is illustrated in Fig. 1. Distinct from the CBFM applying RP beam illumination, where the polarization converter is included in the detection path to transform the SOP of the collected light back to linear, RP-DFCM aims to block the reflected light and let the scattering signal through, which can be utilized for label-free imaging. The reflected light follows the original trajectory and eventually exhibits an annular shape as an illumination beam. In contrast, scattering occurs in all directions, filling the central area with the reflected light. Therefore, we adopt a diaphragm in front of the collective lens (L) whose aperture corresponds to the inner diameter of the reflected annular beam to fully block it. Consequently, the effective divergence angle limit of the detection path can be denoted as θ2.
Then, based on the dielectric scatterers model, the vector electric field of the scattered light at the detector plane ${\vec{E}_{det}}$ can be represented as [29]
Here, α denotes the divergence angle of collection at the pinhole. With the electric field at the detection plane, the detection PSF can be given as:
Furthermore, scattering detection-based dark-field detection is based on coherent imaging. Hence, the total PSF of the RP-DFCM is expressed as the multiplication of the illumination and detection electric fields:
Considering the tight focusing characteristic of RP beam as depicted in Fig. 3 and Fig. 4, the resolution improvement ratio brought by the narrower illumination PSF is expected to be kept after involving the detection PSF.
3. Experimental setup
The DFCM setup, which combines annular beam shaping and vector beam illumination, is illustrated in Fig. 6. A linearly polarized laser with a wavelength of 532 nm was injected through a single-mode fiber and collimated by a fiber collimator (RC04FC-P01, Thorlabs). Then, a variable optical beam expander (BE, BE02-05-A, Thorlabs), whose magnification can be adjusted between 2X to 5X, cooperates with a diaphragm (D1) to expand the waist of the input and filter out the part with stronger light intensity at the mean time. A beam with a diameter of 5 mm and a uniform distribution is generated and propagates towards a pair of axions (A, AX255, Thorlabs), which further shapes the solid beam to an annular distribution. Here, the inner diameter of the annular beam is adjusted by controlling the distance between the axions and the beam waist of the input. After the beam shaping process, a liquid crystal vortex retarder (VR1-532, LBTEK) is placed, acting as a polarization converter (PC) that aims to transform the linearly polarized input to a spatially variable vector beam. Specifically, when adjusting the SOP of the input to the fast axis of the PC via a half-wave plate (λ/2, WPH05M-532, Thorlabs), the output was radially polarized. The generated RP beam propagates through a non-polarizing beam splitter (BS, CCM1-BS013, Thorlabs), followed by a high-NA objective (UPLFLN60X, Olympus) with a magnification of 60X and NA of 0.9. The objective focuses the RP annular beam on the sample under test, generating a focal spot with a highly constrained scale in the lateral direction, as previously investigated. In this study, a 3-axes high-precision piezo stage (P-517.3 CLP-517.3 CD, PI) was applied to support the sample and conduct fast 3D scanning; when the focal spot passes a uniform area of the sample, light is reflected and collected by the same objective, forming an annular reflected beam whose intensity distribution is identical to the illumination. If an abrupt change in the refractive index exists within the focal spot, scattering is excited to fill the original dark spot at the center. Then, both reflected and scattered light are directed to the detection path by the BE. A second diaphragm (D2) was placed to specifically block the reflected light while passing the pure scattered light. Thus, the aperture of D2 tends to be set as the inner diameter of the annular reflected light. Finally, a collective lens (CL, MAD410-A, LBTEK) with a focal length of 150 mm focuses the scattered light on the core of a multi-mode fiber connected to a highly sensitive photomultiplier (APD430A, Thorlabs) to conduct confocal detection.
4. Results
4.1 Intensity distribution of RP beam
First, we verified the radial-polarization of the illumination. The RP beam revealed spatial-dependent SOPs at different spots. Compared with other types of vector beams, such as azimuthally polarized beams, the polarization direction at each spot is parallel to the radial direction.
After being modulated by the axicon pairs and the PC, the illumination reveals an annular intensity distribution with a high diameter ratio of the inner and outer circle. Moreover, when the SOP of the input is aligned to the fast axis of the PC, the RP beam is theoretically generated. A polarizer with an adjustable orientation was introduced to filter out the corresponding polarization components. The transmitted beam was recorded by a CCD with an exposure time of 10.8 µs. As depicted in Fig. 7(I-VIII), the transmitted beam experiences a polarizer-dependent intensity distribution evolution that presents a petal shape. The intensity along the orientation of the polarizer was maintained, while a dark interval appeared in the perpendicular direction. The consistency between the orientation of the polarizer and the filtered petal confirms the radial polarization of the illumination.
Fig. 7. Intensity distribution of radially polarized illumination after passing through a polarizer with different polarization directions.
4.2 Imaging of the gold nanorods with enhanced resolution
A verification experiment was carried out in which gold nanorods (GNRs) with a length of 200 nm and a width of 20 nm were imaged in the dark-field imaging mode. We first diluted the GNR solution and oscillated the solution so that the gold particles could be sparsely distributed. Then, a small amount of the solution was placed on the glass slide to allow it to evaporate to dryness. The samples were imaged using both conventional DFCM and RP-DFCM (Fig. 6). In the former case, the PC in Fig. 6 was removed, and the annular illumination beam was linearly polarized. The diameter ratio of the outer and inner circle of the annular beam was adjusted to 2/3 in both cases, and the NA was set to 0.9.
The 2D visualizations acquired by both modes are presented in Fig. 8(a) and (b). Several bright spots were observed, which represent the GNRs. We investigated the two observed regions. One contains a cluster of particles and the other, a single particle, which are marked as regions ① ③and ② ④, respectively. The images of the clusters in regions ① and ③ are magnified in Fig. 8(c). When the cluster is imaged by RP-DFCM, four nanorods can be identified with clear gaps between the intense peaks. Nonetheless, the particles imaged by conventional DFCM are blurred because of the lower resolution. The 1D intensity distributions sectioned along the dashed lines in Fig. 8(c) are plotted in Fig. 8(d), which further compares the performance of the system in resolving adjacent nanoparticles. The resolution enhancement caused by RP beam illumination leads to a higher peak-to-valley ratio of the second peak, which can hardly be identified when a linearly polarized annular beam is employed. Considering that the relatively strong scattering signal in the 2D dark-field images tends to originate from the contributions of several particles with overlapping positions, we selected a particle with moderate signal intensity to investigate lateral coverage, which is represented as ② and ④. Note that the 2D tomograms were recorded at the depth where the particles were marked. The linewidths of the peaks under the two distinct imaging modes are 610 nm and 425 nm, respectively, which represents a 30.33% improvement in the lateral spatial resolution under the same experimental condition. A representative distribution of sparse nanorods imaged by scanning electron microscopy (SEM) is given in Fig. 8(f) which verifies the size of particles of 20 nm in width and about 200–300 nm in length. The resolution improvement ratio in the experiment is close to the theoretical compression ratio of the illumination focal spot, in accordance with the simulations. A relatively higher resolution improvement is experimentally obtained which is mainly caused by the polarity of GNRs. The RP beam illumination tends to suppress the scattering intensity fluctuation related to particle orientation and enhance the imaging robustness. Note that in the dark-field detection path, the effective collection aperture is smaller than the aperture of the objective to block the reflected annular beam and maintain the scattering signal, which leads to a decreased spatial resolution that is larger than the diffraction limit. Meanwhile, the spatial resolution is also influenced by SNR of the collected scattering signal.
Fig. 8. 2D dark-field images of the gold nanorods recorded by (a) RP- and (b) conventional DFCM. (c) Magnified view of the region numbered as ① and ③. (d) 1D sectioning along the dashed lines in (c). (e) The peaks corresponding to the single nanorod marked as ② and ④.(f) Representative SEM image of GNRs.
4.3 Imaging of the defects of neodymium glass
DFCM was first designed to detect defects in high-power optical components. Thus, we chose a neodymium glass with surface and subsurface defects to verify the 3D dark-field imaging ability of the proposed scheme. Figure 9 shows the measurement results obtained using both the conventional DFCM and RP-DFCM. The lateral and axial scanning ranges were 10 µm and 5 µm, respectively, with the same step of 50 nm. The three-dimensional morphology of the defects is illustrated in Fig. 9(a), and one of the axial sections recorded by RP-DFCM is shown in Fig. 9(b). Note that the surface of the neodymium glass sample was located via bright-field confocal detection with a depth of z = 0 µm, which is not shown in Fig. 9. The RP beam illumination introduced to DFCM leads to a slightly extended depth of focus, which has been observed through the pre-measured axial envelope obtained by the two dark-field imaging schemes. The comparison is given in Fig. 9(c), which illustrates a linewidth of 1.75 µm in the axial direction for RP-DFCM and 1.45 µm for conventional DFCM. Thus, the decrease in axial resolution caused by the RP beam is not significant in the experiments and has little impact on the axial tomography capability of the DFCM system. The lateral tomograms acquired by RP- and conventional DFCM at a depth of 1 µm are shown in Fig. 9(d, e), respectively. The tomograms of the defects contained within the white dashed box at four distinct axial positions (z = 0, 0.5, 1 µm and 1.5 µm) are investigated in detail in Fig. 9(f). These defects can be divided into three parts with slightly distinct depths. With the axial position of the focal spot scanning from 0 µm to 1.5 µm, the intensity distribution evolves with a detectable scale, which verifies the axial sectioning ability of RP-DFCM. The resolution enhancement is further confirmed by comparing the intensity distribution sectioned along the dashed line in Fig. 9(d, c), as shown in Fig. 9(g). The adjacent defects can be distinguished by the RP-DFCM, and the distance between the two peaks representing the positions of the two defects is approximately 250 nm. However, the two defects are blurred and can hardly be distinguished by conventional DFCM.
Fig. 9. (a) 3D dark-field image of the neodymium glass containing surface and subsurface defects. (b) Axial section of the 3D measurements. (c) Axial envelope of RP- and conventional DFCM. (d) Tomography at depth of 1 µm recorded by RP-DFCM. (e) Tomography at depth of 1 µm recorded by conventional DFCM. (f) Detailed intensity distribution of the defects contained within the dashed boxes in (d) and (e) at distinct depths. (g) 1D intensity traces along the dashed line in (d) and (e).
4.4 Reliability and robustness of imaging results
To investigate the reliability and accuracy of RP-DFCM, we used another silica glass sample with defects on the surface for the control experiment. A high-resolution atomic force microscopy (AFM, Dimension HPI, Bruker Optics) was applied to finely scan the surface morphology which in turn can reflect the distribution and topology of the defects. A field of view (FOV) of 30 µm ×15 µm is scanned and the image recorded by AFM is shown in Fig. 10(a). Then, we focused on the same region and conduct imaging by RP-DFCM. The 2D sectioning along the transverse direction is illustrated in Fig. 10(b) which corresponds to the depth of 0, representing the surface location. The scan step is 100 nm in both x and y direction and interpolation was performed at 20 nm intervals during the post-processing. Most of the defects inspected by AFM are detected by DFCM with a high degree of coincidence in relative position, verifying the reliability of RP-DFCM.
Fig. 10. (a) Defects on a silica glass recorded by atomic force microscopy (AFM). (b) RP-DFCM imaging of the defects in the same region. (c-f) Images recorded by RP-DFCM with the field of view marked by white box in (b) when the axis of input beam is away from the ideal direction by 0°, 10°, 20° and 30°. (g) Enlarged AFM view of defects marked by yellow box in (a). (h) Intensity trace sectioned along the dashed line in (g). (i) Enlarged image of defects marked by yellow box in (b) taken by RP-DFCM. (h) Intensity trace with different polarization mismatch.
In addition, the reliability and robustness of the defects visualization in RP-DFCM is yet influenced by the polarization deviation. Ideally, the polarization direction should be adjusted to be aligned with the fast axis of the PC to generate a quasi-pure RP beam. A deviation of input polarization tends to distort the RP polarization which will result in a broadened illumination PSF as demonstrated in section 2.1. Moreover, the extra azimuthal component is prone to bring polarity sensitivity to the scattering image. Specifically, the polarity of the sample induced by orientation and constituent tends to cause scattering intensity fluctuation with imperfect RP beam illumination, which may eventually undermine the reliability. We manually rotated the input polarization to deviate it from ideal direction by Δφ and imaged the sample region marked by white dashed box in Fig. 10(b). The dark-field images with Δφ of 0°, 10°, 20° and 30° are presented in Fig. 10(c-f) respectively, which reveal obvious intensity distinctions within the region corresponding to the defects contained by the yellow box. According to the ground truth obtained by AFM, the morphology in Fig. 10(g) shows three peaks that indicate three distinguishable defects. The distance between first two of them are measured as 490 nm. With pure RP beam illumination (Δφ=0°), the three peaks are identified clearly. However, with the increase of polarization deviation, the second peak vanishes gradually and the mismatch appears between the intensity distribution recorded by DFCM and the AFM image as illustrated in Fig. 10(j).
5. Conclusion and discussion
Conventional DFCM commonly suffers from a decrease in spatial resolution resulting from the complementary detection aperture, which may result in false or missed detection of defects in optical components. In this study, we introduced RP beam illumination to the DFCM system to enhance the spatial resolution. The RP beam illumination tends to create a tight focal spot that is smaller than the diffraction limit, using a high-NA objective if the diameter ratio of the inner and outer circle of the annular beam is sufficiently large. The focusing characteristic, in turn, leads to an improvement in the lateral resolution.
By calculating the focal spots and the PSF of the RP-DFCM, the enhancement of the lateral resolution was verified theoretically. Furthermore, a 2D sample of sparsely distributed GNRs was employed to experimentally investigate the actual spatial resolution of the proposed scheme, which confirms a lateral resolution of 425 nm. The comparison with the measurement of the conventional DFCM with the same experimental conditions indicates a 30.33% spatial resolution improvement. In addition, RP-DFCM was applied to detect the defects contained in a neodymium glass sample to investigate its 3D imaging ability.
The enhanced resolution tends to facilitate highly accurate defect detection and positioning in the optical components. Moreover, the RP beam illumination offers opportunities to acquire the polarization information of the scattering signal, which is correlated with the polarity of the sample under test. However, to obtain a high diameter ratio between the inner and outer circle of the annular beam with the axicon pair, severe energy loss occurs. Thus, other schemes for polarization modulation and adjustable annular beam generation should be further investigated.
Funding
National Natural Science Foundation of China (51905133, 51975159).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data underlying the results presented in this letter are not publicly available at this time, but may be obtained from the authors upon reasonable request.
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