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Abstract
Spiral-phase-contrast imaging, which utilizes a spiral phase optical element, has proven to be effective in enhancing various aspects of imaging, such as edge contrast and shadow imaging. Typically, the implementation of spiral-phase-contrast imaging requires the formation of a Fourier plane through a 4f optical configuration in addition to an existing optical microscope. In this study, we present what we believe to be a novel single spiral-phase-objective, integrating a spiral phase plate, which can be easily and simply applied to a standard microscope, such as a conventional objective. Using a new hybrid design approach that combines ray-tracing and field-tracing simulations, we theoretically realized a well-defined and high-quality vortex beam through the spiral-phase-objective. The spiral-phase-objective was designed to have conditions that are practically manufacturable while providing predictable performance. To evaluate its capabilities, we utilized the designed spiral-phase-objective to investigate isotropic spiral phase contrast and anisotropic shadow imaging through field-tracing simulations, and explored the variation of edge contrast caused by changes in the thickness of the imaging object.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
A vortex beam is a crucial and intriguing type of light that carries orbital angular momentum (OAM) along its propagation axis owing to the formation of a helical phase wavefront [1–3]. To generate a vortex beam, a spiral phase element is generally used, such as a spiral-phase-plate (SPP), which implements the optical surface in the form of a spiral shape, or a spatial-light-modulator (SLM) that can implement a fork interference fringe with a computer-generated hologram [4–7]. Additionally, liquid-crystal displays (LCDs) [8] and metasurfaces [9] have been proposed to generate vortex beams. Most recently, a reflection-type spiral phase mirror (SPM) with wavelength-tunability characteristics was developed to overcome the disadvantages of the transmission-type SPP, which optimally operates only at a single wavelength [10].
Given the unique optical properties of vortex beams, which have doughnut-shaped intensity profiles and carry OAM, various studies have been conducted using them. For example, micron- or submicron-scale doughnut-shaped beams, created by focusing a vortex beam with an objective, have been used as optical tweezers to trap and manipulate dielectric particles [11,12]. In addition, studies on stimulated emission depletion (STED) microscopy [13,14], which overcomes the diffraction limit of spatial resolution using donut-shaped beams that selectively deactivate fluorophores, and spiral-phase-contrast (SPC) microscopy, which enhances edge contrast using a spiral phase element as a spatial Fourier filter, have been actively conducted [15–17].
SPC microscopy has been extensively studied as an alternative to existing phase contrast (PC) and difference interference contrast (DIC) microscopy techniques to improve the image contrast of biological samples with low optical contrast [18–21]. SPC microscopy offers high-contrast imaging of biological samples because of its spatial Fourier filter that enhances both the phase contrast and shadow effects, which are characteristics of PC and DIC microscopy, respectively. To implement SPC imaging in a general optical microscope, a spiral phase element must be added after light is transmitted or reflected from the imaging object, making it a post-optical process. When the spiral phase element is placed on the Fourier plane in the optical pathway after light is transmitted through (or reflected from) an object, SPC imaging is achieved by integrating the convolution between the donut-shaped point spread function (PSF) with a helical phase profile and the object within an azimuthal angle (phase; θ) range of 2π [22]. Subsequently, the image-carrying wave that scatters or diffracts in the region of the object edge with a phase gradient is not cancelled during the integration process, leaving behind an image signal. In contrast, for an object region without a phase gradient, the image signal disappears owing to cancellation during the integration process. Consequently, the edge contrast of an object is significantly improved compared to that of conventional optical microscopy. In addition, SPC imaging is effective for both amplitude and phase objects, making it more advantageous than other PC imaging techniques. Moreover, if the singularity of the spiral phase element is decentered from the optical axis, a shadow image can be obtained, allowing for the visualization of the object’s phase landscape. However, implementing SPC imaging in a general microscope requires an additional Fourier plane outside the microscope body for installing a spiral phase element. This Fourier plane is formed by placing two lenses in front of and behind the spiral phase element, and the formation of a collimated beam is essential before and after focusing the beam with two lenses in the 4f configuration (see Fig. 1(a-c)). Thus, additional structural modifications and space allocations are necessary to incorporate SPC imaging into existing optical microscopy systems.
Fig. 1. Schematic diagrams of the optical configurations for the SPC microscopy. (a) The microscopy setup for SPC imaging using a standard objective and an SLM. (b) The setup for SPC imaging using a standard objective and an SPP. (c) The setup for SPC imaging using a standard objective and an SPM. (d) The simplified setup for SPC imaging using a designed SPO, which includes an SPP.
In recent developments in SPC imaging, nanostructures such as metasurfaces were actively utilized as spiral phase elements. Through these approaches, the synchronous acquisition of SPC imaging and bright-field imaging has been demonstrated [23] along with the application of spin-dependent metasurfaces allowing for the selection of either bright-field or SPC imaging based on polarization characteristics [24]. Furthermore, the potential applications of existing SPPs have been expanded by implementing quantum edge-enhanced imaging based on combining the SPC imaging technique with single-photon imaging [25]. Additionally, SPC imaging using infrared light has been achieved by converting to the visible range through a nonlinear spatial filter that combines a SPP and a second-harmonic-generating BBO crystal [26]. Nevertheless, the metasurfaces and SPPs utilized in these studies primarily employ the 4f configuration to achieve SPC imaging.
In this study, we propose a novel hybrid design for a spiral-phase-objective (SPO) that enables straightforward and simple implementation of SPC microscopy. The SPO is designed such that the spiral phase plate (SPP) is located at the back focal plane, which corresponds to the Fourier plane of the objective. Specifically, when the SPO is used with a commercial-grade standard microscope, the SPP is automatically positioned on the Fourier plane between the tube lens and objective within the microscope. Therefore, the conversion from standard bright-field microscopy to SPC microscopy is achieved by simply mounting the SPO onto the standard revolving nosepiece, which uses the usual objective, except for the corrections to increase the spatial coherence of the illuminated light. In the case of broadband incoherent light sources, a bandpass filter and a very small aperture are typically required. Figure 1(d) shows a simplified SPC microscope achieved using the SPO presented in this study.
Table 1 presents the respective strengths and weaknesses (or advantages and disadvantages) of the four optical configurations, for SPC imaging.
Table 1. Characteristics of the four optical configurations for SPC imaging.
Designing and verifying the SPO, which must consider the geometric optical performance of the focused beam and generation of a vortex beam with a helical phase wavefront, relying solely on ray-tracing simulations, has limitations. In this study, we present a new hybrid design approach that sequentially combines ray-tracing and field-tracing simulations, which are available for manufacturing and provide predictable performance values. The optical design of the SPO includes the optimization and analysis of optical performance, such as the modulation transfer function (MTF), wavefront error, field curvature, and distortion through ray-tracing simulations. The intensity and phase distribution of a high-quality focused vortex beam with a topological charge of l = 1, which was produced by the designed SPO, were confirmed by calculating the wave propagation and phase values through a field-tracing simulation. Additionally, variations in the edge enhancement for SPC and shadow imaging owing to changes in the thickness of the imaging object were investigated in detail using SPC imaging through ray-tracing simulations based on the designed SPO.
2. Design of spiral-phase-objective and its verification
The SPO was designed using both ray-tracing and field-tracing. Figure 2 shows a flowchart of the SPO hybrid design. First, the required specifications of the SPO are determined, and then the basic design is performed using the ray-tracing method based on Zemax OpticStudio (ANSYS), as in the usual optical design of an objective. Then, the objective was initially designed with a plane plate instead of an SPP with a spiral structure within the parfocal length, and the objective design was achieved through an optimization process. Because the optical performance of the objective in Zemax is typically evaluated with respect to a Gaussian beam and there is no general metric to quantitatively evaluate the optical performance of a vortex beam, a plane plate of the same thickness was used instead of the SPP inside the SPO. After confirming the optical performance of the SPO, the Zemax data based on ray-tracing were converted into VirtualLab Fusion (LightTrans international GmbH) data based on field-tracing. VirtualLab Fusion is a physical optics software designed for optical simulation based on field tracing [27]. In these simulations, the optical configuration encompassing a light source, SPO including SPP, lenses, and detector are modeled by dividing each component into subdomains. During the propagation of a beam, Maxwell’s equations are solved for subdomains such as space, time, frequency, and the k-field. The selection of suitable subdomains for each optical component is achieved through domain-to-domain field switching, thereby enhancing accuracy within a shorter processing time [28]. The process involves the application of advanced Fourier transform techniques, including fast Fourier transform, semi-analytical Fourier transform, and pointwise Fourier transform, for domain-to-domain field switching. To ensure the reliability of the converted SPO data, we verified that the optical performance was maintained in VirtualLab Fusion. Subsequently, a field-tracing simulation of the SPO, including an SPP instead of a plane plate, was conducted. A field-tracing simulation of a vortex beam formed by an optical surface with a spiral structure was verified in our previous study [10]. The hybrid SPO design was completed by confirming the generation of vortex beams. Furthermore, the optical configuration for SPC microscopy was established, and SPC imaging, including the characteristic structure of the SPP, such as a spiral shape, could be carried out through field-tracing simulations.
Fig. 2. Flow chart of the hybrid design process for the SPO. The SPO was designed using a hybrid approach that combines ray-tracing and field-tracing methods.
In this study, an SPO with 20x magnification and a numerical aperture (NA) of 0.5 was designed for an infinity-corrected microscope with narrowband illumination ranging from 623 to 643 nm. These illumination conditions can be easily achieved using bandpass filters in a standard microscope. Detailed specifications of the design parameters used in Zemax are listed in Table 2. These parameters were chosen to be almost identical to the physical dimensions of the commercially available NA 0.5 objectives, making them sufficiently compatible with most conventional microscopes. The parfocal length, which is the distance from the shoulder of the objective to the focal plane on the sample, varies among manufacturers (e.g., 45, 60, 75, and 95 mm). With the shortest parfocal length of 45 mm, the SPO can be used with several manufacturers’ microscopes using a parfocal length extender to match the parfocal lengths.
Table 2. Specification of the designed SPO. The magnification is given for a tube lens with a focal length of 200 mm. The Rayleigh criterion for resolution is determined using 0.61*λ/NA at λ = 633 nm. EFL, NA, WD, and FOV represent the effective focal length, numerical aperture, working distance, and field of view, respectively.
Table 3 lists the optical parameters for the eight lenses that constitute the SPO, which were obtained by optimizing the ray tracing process in Zemax. All the lens surfaces were designed using only spherical surfaces, considering the manufacturing conditions. In this step, L1, which has a spherical surface of infinite radius, acts as a plane plate with a thickness of 2.5 mm, and is replaced by an SPP with a spiral structure in the subsequent field-tracing.
Table 3. Optical parameters of each lens (from L1 to L8) in the designed SPO. The applied materials are commonly used materials selected from the list of SCHOTT.
In the context of designing an SPO using ray- and field-tracing simulations, the reflectivity of the SPP as a crucial optical component could be a significant factor. Typically, when dealing with an uncoated SPP, interference arises because of multiple reflections in a manner similar to what occurs in a Fabry–Perot etalon owing to the finite reflectivity of the SPP. This could act as a practical design limitation, potentially leading to the degradation of imaging performance. Previous studies have shown that a beam transmitted through an uncoated SPP can have an intensity profile with a periodic modulation as a function of azimuthal angle, whereas the reflected beam can generate high-contrast angular intensity fringes [29,30]. To address this potential problem, anti-reflection (AR) coatings are commonly utilized to reduce overall transmission loss, minimize stray light, and prevent back reflection. Typically, in the visible range, an uncoated optical element made from fused silica has a reflectance of around 4% at normal incidence. The application of AR coatings can reduce the average reflectance to < 0.5%; thus, anti-reflection (AR) coatings should be considered not only for the SPP itself but also for all other lenses within the SPO to enhance the performance of SPC imaging by reducing this reflectance.
Figure 3 shows the optical layout and performance of the NA 0.5 SPO consisting of the eight optical elements listed in Table 2. The most important aspect of the SPO design is that the SPP is located in the Fourier plane inside the objective. The back focal plane (BFP) in the objective is equivalent to the Fourier plane between the objective and tube lens in the microscope optical system. Thus, as shown in Fig. 3(a), L1 (SPP) is located on the leftmost side of the SPO configuration and the right-side surface of L1 (which becomes a spiral structure in the field-tracing stage) is designed to match the BFP of the SPO. The parfocal length, WD, and FOV of 45, 2, and 1.2 mm, respectively, satisfies the physical dimensions presented in Table 1. Figures 3(b), (c), (d), and (e) show the results of the main optical performance of the Gaussian beam focused by the SPO with a plane plate. Figure 3(b) shows the performance of field curvature and distortion, respectively. For field curvature, the distance between focusing points and the rightmost focal plane of the tangential and sagittal rays at the end (0.6 mm) of the FOV are approximately 0.81 and 0.83 µm, respectively, at 633 nm. The difference is approximately 0.02 µm, indicating a small astigmatic value. In addition, for the other two wavelengths, 623 and 643 nm, the differences are very small, similar to the case of 633 nm. The distortion is only approximately 0.4% at the FOV of 0.6 mm, which is the same for all three wavelengths. Figures 3(c) and (d) show the results of the MTF curve and the wavefront error as a function of the FOV, respectively. In Fig. 3(c), the MTF performance approaches the diffraction limit in all FOVs, with a modulation of approximately 55.2% at 650 cycles/mm and an FOV of 0 mm. For Fig. 3(d), the RMS wavefront error is also less than 0.07 λ in all FOVs, satisfying the criterion of the diffraction limit. Finally, Fig. 3(e) shows the PSF of the focused Gaussian beam, and the diameter of the focused beam at 1/e2 is 0.90 µm.
Fig. 3. Results of the NA 0.5 objective and its optical performances designed in Zemax. (a) Optical layout of the NA 0.5 objective designed with the plane plate (L1) over the FOV. (b) Field curvature and distortion as a function of the FOV. (c) MTF at each FOV and diffraction limit. (d) Wavefront error as a function of the FOV. (e) PSF of the focused beam.
After completing the design of the objective with a plane plate without a spiral structure in Zemax, the data were converted to VirtualLab Fusion for vortex beam formation and SPC imaging. Figure 4(a) shows the optical layout of the NA 0.5 objective that was converted from Zemax to VirtualLab Fusion. To ensure the reliability of the conversion to VirtualLab Fusion, the PSF, MTF, and RMS wavefront errors of the converted data were verified. After conversion, the PSF of the focused Gaussian beam (blue line) in Fig. 4(b) shows that the beam diameter (1/e2) is 0.91 µm, which is almost identical to the value (0.90 µm) calculated by Zemax. The MTF and RMS wavefront errors in VirtualLab Fusion were 57.9% and 0.005 λ, respectively, based on an FOV of 0 mm at 633 nm, and these values are also almost identical to the results calculated by Zemax. As shown in Fig. 4(c), the distributions of the 2D intensity and phase of a well-defined focused Gaussian beam at 633 nm are maintained after conversion.
Fig. 4. Results of the NA 0.5 objective converted from Zemax to VirtualLab Fusion and the focused beam images. (a) Optical layout of the NA 0.5 objective, converted from Zemax to VirtualLab Fusion. (b) PSFs of the focused Gaussian beam (blue line; with the plane plate) and vortex beam (red line; with the SPP) obtained at 633 nm. The intensities are normalized for comparison of the shapes of the two PSFs. The beam diameter (1/e2) of the focused Gaussian beam is 0.91 µm. Intensity and phase distributions of the focused (c) Gaussian and (d) vortex beams obtained at 633 nm. (e) Intensity distributions of the focused Gaussian and vortex beams obtained at a (f) narrow bandwidth with half the intensity at 623 and 643 nm with respect to 633 nm.
After validating the reliability of the data converted from Zemax to VirtualLab Fusion, the plane plate is replaced with the SPP for the final SPO design, and the formation of a vortex beam is achieved by conducting field-tracing simulations. Figure 4(d) shows the 2D intensity and phase distributions of the vortex beam obtained at 633 nm from the designed SPO. Unlike the phase in Fig. 4(c), the phase of the focused vortex beam rotates by 2π. Compared with the focused Gaussian beam in Fig. 4(b), the intensity distribution of the focused vortex beam exhibits a well-defined annular shape, which is a typical characteristic of OAM l = 1. The intensity distributions of the focused Gaussian and vortex beams obtained with a narrow bandwidth, where the intensity is half at 623 and 643 nm with respect to 633 nm, are shown in Fig. 4(e) and (f). This result is almost similar to that obtained at a single wavelength of 633 nm (see Fig. 4(c) and 4(d)), because the OAM values at the wavelengths of λ = 623 and 643 nm are 1.02 and 0.99, respectively, which show little difference from the OAM value of l = 1 at 633 nm.
3. Spiral-phase-contrast imaging based on the spiral-phase-objective
After verifying the generation of vortex beams by the designed SPO through a field-tracing simulation, an optical layout for SPC imaging, which is one of the main applications, was configured. Figure 5(a) shows the overall configuration of the SPC microscope obtained using a field-tracing simulation comprising an SPO, tube lens, and CCD camera. Its configuration closely resembles that of Fig. 1(d), to which it is nearly identical except for the omission of the beam splitter, which modifies the optical path toward the CCD. An ideal lens, which acts as a thin lens in VirtualLab Fusion, with a focal length of f = 200 mm was used as the tube lens for the 20x magnification of an SPO with an EFL of 10 mm. Our configuration is the same as that of an infinity optical microscope system, which combines an objective (with a parfocal length of 45 mm) with a tube lens (with a focal length of 200 mm), such as a commercial microscope system (e.g., the Leica microscope). To achieve the full capacity of the infinity optical microscope system, the BFP positioned at the end of the parfocal length (or BFP) of the objective must be matched with the position of the front focal length of the tube lens. The distance between the SPO and tube lens becomes 197.85 mm owing to the refraction of light rays by the SPP. In this configuration, the rays scattered by the sample propagate through the SPO and tube lens before entering the detector. Figure 5(b) presents an enlarged image of the SPO in Fig. 5(a), which shows that the rays scattered by the imaging sample are focused on the BFP, where the SPP is located at the right end of the SPO. The spiral patterned surface of the SPP is located on the BFP. The SPP consists of a structure in which the spiral pattern is formed on a 2.5-mm-thick plate, as shown in Fig. 5(c). Considering the characteristics of the spiral phase optical element, as the OAM can generate a well-defined vortex beam with only an integer value (l = 1) for a specific single wavelength, the SPP is designed for a single wavelength, λ = 633 nm, which is the center wavelength of a narrow bandwidth. The spiral height of the SPP corresponding to an OAM of l = 1 at a wavelength of λ = 633 nm is given by hSPP = l ·λ / (n - 1) = 1.39 µm, where n (refractive index of fused silica) = 1.46, and the OAM l = (n-1) hSPP / λ. The material, structure, and thickness of the SPP are the same as those of commercial SPPs (e.g., Vortex Photonics). The imaging sample used for SPC imaging is KBSI characters made of fused silica, as shown in Fig. 5(d).
Fig. 5. (a) Field-tracing-based optical layout for SPC microscopy using the designed SPO and the tube lens. (b) An enlarged view of the SPO shows that the rays scattered by the sample are focused at the back focal plane (BFP). (c) The spiral structure of the SPP, and (d) the structure of the KBSI characters phase object with a 100-µm-thick substrate for SPC imaging.
Figure 6 shows the results of SPC imaging obtained by varying the thickness of the imaging object. The thicknesses of the imaging objects (h) in Figs. 6(a), 6(b), 6(c), and 6(d) are h = 0.35 µm, h = 0.70 µm, h = 1.04 µm, and h = 1.39 µm, respectively, corresponding to 1/4, 1/2, 3/4, and 1 of the hSPP, within the detection area of 10 × 10 mm and obtained by considering the three wavelengths of 623, 633, and 643 nm under the narrowband condition mentioned in Figs. 4(e) and 4(f). In this case, the intensities at 623 and 643 nm were taken as half the intensity at 633 nm, e.g., as shown in Fig. 4(f). Except for Fig. 6(d) obtained at the thickness h = 1.39 µm, 6(a), 6(b), and 6(c) exhibit the isotropic enhancement of edge contrast (with respect to the center of the 2D image), which is a typical characteristic of SPC imaging, although the brightness varies. Among them, the enhanced intensity of edge contrast is maximized when h is 0.70 µm, which is half the hSPP, providing the clearest imaging of the KBSI object. In contrast, if the thickness of the imaging object is exactly h = 1.39 µm (equal to the hSPP), as shown in Fig. 6(d), the imaging is not visible at all. This is because when the thicknesses of the phase object are (2n-1)π and 2nπ (n is a positive integer), the phase gradients that form the image contrast have maximum and minimum values, respectively. In other words, when the thickness of the phase object is half the hSPP, the edge regions of the phase object, which undergo different phase shifts, lead to a relative phase difference of π. Thus, the edge signals can be significantly increased during the closed integration of the convolution, unlike the case of 2π. In a typical biological sample, where height changes gradually, the intensity of the edge contrast is also expected to change continuously, resulting in varying brightness. However, the intensity of the flat region with no height variation within the sample remains at 0.
Fig. 6. Results of SPC imaging for the KBSI characters that are presented in Fig. 5(d). The thicknesses of the KBSI characters are (a) h = 0.35 µm, (b) h = 0.70 µm, (c) h = 1.04 µm, and (d) h = 1.39 µm. The thickness of each structure is 1/4, 1/2, 3/4 and 1 of hSPP. The intensities of 6(a), 6(c), and 6(d) are normalized with respect to the maximum intensity obtained in Fig. 6(b).
We further investigated SPC imaging using a target with gradual height variation. We designed character samples similar to the previous target with gradually increasing heights, as shown in Fig. 7(a). The height of the target starts from 0 at the left end of the letter “K” and gradually increases until it reaches a height of 1.39 µm at the right end of the letter “I”. The SPC imaging results for this configuration are depicted in Fig. 7(b). No signal is detected at the left side of the “K” or the right side of the “I” at heights of 0 and 1.39 µm, respectively, whereas a maximum-intensity signal is obtained around the region with a height of 0.70 µm (near the letter “B”). This trend coincides with the SPC imaging results shown in Fig. 6.
Fig. 7. (a) The structure of the KBSI characters phase object with gradual height ranging from 0 to 1.39 µm. (b) Result of SPC imaging obtained using this target.
Among the results of isotropic SPC imaging depicted in Fig. 6, the two cases shown in Figs. 6(b) and 6(c) (corresponding to h = 1/2 and h = 3/4 of the hSPP, respectively) exhibit relatively high contrast and brightness. To obtain anisotropic (or shadow) SPC images, the SPP was shifted by 50 µm to the right with respect to the SPP singularity in both cases. Figures 8(a) and 8(c) show the results of the isotropic SPC imaging shown in Figs. 6(b) and 6(c), respectively, normalized to the maximum intensities of the respective SPC images. As the intensity of each image is normalized, the edge contrast enhancements in the SPC images in Figs. 8(a) and 8(c) are, unlike those in Figs. 6(b) and 6(c), not significantly different from each other. In contrast, when comparing Figs. 8(b) and 8(d), which are the images acquired after shifting the SPP by 50 µm to the right, the characteristics of the anisotropic (or shadow) SPC image are more prominent in Fig. 8(d). Focusing on the variation of the edge intensity of the KBSI characters in Figs. 8(b) and 8(d), it is seen that, in Fig. 8(d), the edge intensity of the left side of each character is stronger than that of the right side; by contrast, in Fig. 8(b), there is little difference in intensity between the left and right sides of each character. This shows the characteristics of anisotropic (or shadow) SPC images, which include a 3D-like effect produced by the shifting of the SPP. By contrast, isotropic SPC imaging, in which the focused beam transmits the singularity of the SPP, produces a 2D image with a symmetrically uniform edge intensity [18]. Further, if the SPP is shifted by 50 µm to the left with respect to the singularity, the difference between the left and right edge intensities of each character is reversed. As shown in Figs. 8(e), 8(f), 8(g), and 8(h), this effect can be analyzed quantitatively by comparing the line profiles (corresponding to y = 0) across the center of the 2D SPC images shown in Figs. 8(a), 8(b), 8(c) and 8(d). The results on the right sides of Figs. 8(f) and 8(h) show that the intensity difference between the adjacent line profiles in Fig. 8(h) is larger and the increase in the intensity of the inner region of the KBSI characters emphasizes the 3D-like image more than in Fig. 8(f).
Fig. 8. Anisotropic (or shadow) SPC images obtained by shifting the SPP to the right by 50 µm. (a) Results of SPC imaging (intensity normalized) at h = 0.70 µm (1/2 of hSPP). (b) Anisotropic (or shadow) SPC imaging obtained after shifting the SPP to the right by 50 µm. (c) Results of SPC imaging (intensity normalized) at h = 1.04 µm (3/4 of hSPP). (d) Anisotropic (or shadow) SPC imaging obtained after shifting the SPP to the right by 50 µm. (e), (f), (g), and (h) show the line profiles (corresponding to y = 0) across the center of the 2D SPC images of (a), (b), (c), and (d), respectively.
Here, a subtle but important distinction is that for isotropic SPC imaging before the SPP shift, relatively brighter edge-enhanced SPC imaging was obtained at the imaging object with a thickness of half the hSPP. However, for anisotropic (shadow) SPC imaging after the SPP shift, SPC imaging with a relatively 3D-like effect was acquired for the imaging object with a thickness of three-fourths of the hSPP. This suggests that the thicknesses of the imaging object for the optimal conditions of isotropic and anisotropic (shadow) SPC imaging may be slightly different. Such differences can be investigated by SPC experiments on imaging objects, such as nanostructures, where their heights can be well defined quantitatively.
4. Conclusion
In this study, we achieved SPC imaging for edge contrast enhancement and shadow imaging in a simple and convenient manner using a newly designed single SPO that does not require the structural modification of standard microscopes. This approach differs from the typical SPC imaging method, which requires a 4f-optical configuration to form a Fourier plane in addition to the standard microscope. The SPO was designed using a new hybrid approach that sequentially combines ray-tracing and field-tracing simulation. It was found to have conditions that are practically manufacturable and exhibit predictable performance. Using the designed SPO, we implemented isotropic and anisotropic SPC imaging through field-tracing simulations. A comparison of the two approaches for SPC imaging obtained by changing the thickness of the imaging samples showed that their optimization conditions had subtle but clear differences. These findings will be further investigated in future through SPC imaging experiments, and the potential contribution of the SPO design, which can be easily applied to various applications, including optical tweezers and STED microscopy, will be explored.
Funding
National Research Foundation of Korea (NRF2021R1F1A104940713, NRF2021M3D1A204643713); Korea Basic Science Institute (D300600); Korea Basic Science Institute (D300300).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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