Stimulated emission depletion (STED) microscopy is a potent technique for observing biological structures with sub-diffraction resolution, and is achieved by selectively quenching the fluorescence signal only in the peripheral area of the focal spot. This method employs two different excitation and depletion laser wavelengths, with the depletion focal spot requiring careful shaping for confinement [1–3]. STED microscopy enables a minimum five-fold enhancement in resolution [4]. However, the axial resolution generally lags behind the lateral resolution due to the elongated nature of the typical diffraction-limited focus along the optical axis. To address this limitation, isoSTED microscopy was developed to achieve isotropically improved resolution in three dimensions. It adopts a 4Pi geometry consisting of two opposing objective lenses that share a focal spot to generate an interference pattern on the depletion focal spot, thereby creating an axially sharp zero-intensity valley [5]. This approach gives a hollow-sphere-shaped focal spot using two depletion beams: One for lateral (STEDxy) and another for axial (STEDz) [6–8] resolution enhancements.

In the 4Pi cavity of a conventional isoSTED microscope, a polarizing beam splitter (PBS) and retarders are used, whereas a 4Pi microscope typically uses a beam splitter that splits intensity in a 50:50 ratio [6]. This approach incorporates a half-wave plate (HWP) before the PBS to equally split the powers of STEDxy and STEDz into two beam paths. Subsequently, another HWP is applied after the PBS to rotate the horizontally linearly polarized beams to a vertical orientation, aligning the transmitted and reflected light from the PBS in parallel. This alignment induces a phase difference of π between STEDxy and STEDz [9, 10], allowing STEDxy and STEDz lasers to generate constructive and destructive interferences, respectively. Hao et al. [11] additionally used a quarter-wave plate (QWP) before each objective to generate a circularly polarized beam for minimum selectivity to the fluorophore dipole orientation and optimal signal-to-noise ratio.

Misalignments of the retarders can lead to incomplete destructive interference at the center of the depleted focal spot, resulting in degraded resolution [12]. Furthermore, when a polarization-maintaining fiber (PMF) is used in the laser launch setup [11], the orientation of the PMF varies with temperature due to a proportional decrease in birefringence [13]. Therefore, achieving complete destructive interference becomes challenging as the intensities of the upper and lower beam paths in the 4Pi cavity undergo continual changes. Given these considerations, precise and rapid alignment of the retarders in the 4Pi cavity is crucial. In this study, we propose a method for evaluating the alignment of retarders in a 4Pi cavity using a single charge-coupled device (CCD) camera by simultaneously measuring the power of two laser beams with a single detector positioned outside the 4Pi cavity. Additionally, we built an interferometer and demonstrated the attainment of a completely destructive interference pattern using this method.

Figure 1 shows the experimental setup of the alignment module used to adjust the angle of the retarders in the 4Pi cavity of isoSTED microscopy. To reproduce a simplified 4Pi cavity, a fiber laser beam (OBIS LX 785 nm; Coherent Co., PA, USA) was collimated using a collimator (RC04APC-P01; Thorlabs, NJ, USA). A linear polarizer (GT10-B; Thorlabs) was used to generate a linearly polarized beam, which was then expanded using a beam expander (GBE05-B; Thorlabs). The beam subsequently passed through an iris diaphragm with a diameter of 1 mm (SM1D12; Thorlabs) and a neutral density filter (ND20A; Thorlabs). HWP1 (WPH10M-780; Thorlabs) rotated the orientation of the linearly polarized beam to 45° with respect to the splitting axis of the PBS (PBS25-780; Thorlabs). The PBS splits the beam into two equal-intensity beams: One with p-polarization transmitted through the PBS and the other with an s-polarization beam reflected by the PBS. In the upper beam path, HWP2 (WPH10M-780; Thorlabs) rotated the p-polarization beam to an s-polarization beam, enabling interference between both upper and lower beams. The upper beam propagated counterclockwise in the 4Pi cavity, passing through two QWPs (WPQ10M-780; Thorlabs) and becoming p-polarized before transmission through the PBS towards the upper-right direction. Similarly, the lower beam propagated clockwise in the 4Pi cavity, passing through the two QWPs and becoming p-polarized. After passing through HWP2, the lower beam reverted to s-polarization and was reflected by the PBS towards the upper-right direction. This optical setup replicated the configuration of polarizing components used in isoSTED microscopy. Both beams were directed towards the alignment module comprising a beam displacer (BD40; Thorlabs) and a CCD1 (UI-1240LE-NIR-GL; IDS Imaging Development Systems GmbH, Obersulm, Germany). Both beams were reflected by a foldable mirror and were incident normally onto the beam displacer, where two orthogonally polarized beams were separated in parallel and imaged using a CCD1, which simultaneously showed the profiles of the upper and lower beams. It was assumed that the diameters of both beams were identical, and so the optical power of each beam was measured by cropping the same number of pixels centered on the beam profile and calculating the sum of the intensity values for all pixels.

Figure 1. Schematic of alignment module for 4Pi cavity setup. HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarizing beam splitter cube; CCD, charge-coupled device. The red, blue, and green dashed lines indicate s-, p-, and circularly polarized beams, respectively. The split beams propagate following the arrows.

When all the retarders, including HWP1, HWP2, QWP1, and QWP2, are properly aligned, CCD1 observes equal powers of the two beams. In contrast, misalignments of the retarders lead to unequal beam powers or a decrease in the total beam power measured by CCD1. The alignment procedure using the proposed module begins by adjusting the fast axis of HWP1, with no other retarders present, to ensure that all beams are transmitted through the PBS, resulting in p-polarization. The transmitted beam, reflected by upper and lower mirrors, returns to the PBS and is then measured by CCD1 after transmission through the PBS towards the alignment module, yielding a single beam profile. HWP2 is then inserted and adjusted until the alignment module measures minimum power, indicating that all beams have become s-polarized. Ideally, the minimum power should be zero. Experimentally measured variations in beam power as the fast axis of HWP2 is rotated over 90° in 0.5° increments are shown in Fig. 2(a). Subsequently, QWP1 is inserted and adjusted until the maximum power is measured by the alignment module because the p-polarization component is maximized when the s-polarized beam is converted to a circular one. Figure 2(b) shows the variation in beam power with the orientation of QWP1. Finally, QWP2 is inserted and adjusted to convert the circularly polarized beam back to p-polarization, resulting in maximum power measured by the module, as shown in Fig. 2(c). Lastly, HWP1 is adjusted to equally split the upper and lower beams. As HWP1 is rotated, the second beam profile appears adjacent to the beam profile transmitted through the PBS on CCD1. This second beam is reflected by the PBS and converted into p- and s-polarization states by the QWPs and HWP2, respectively, before being reflected by the PBS towards the alignment module. According to Malus’ law, the relationship between the incident beam and the PBS-allocated beams can be expressed as

Figure 2. The normalized powers of a beam on the CCD1 camera measured at each rotation angle of (a) HWP2, (b) QWP1, and (c) QWP2, respectively, at 0.5° intervals. The x-axes in the graphs represent the angle of the rotation mount; Therefore, the angle does not correspond to the fast axis of the wave plates. CCD, charge-coupled device; HWP, half-wave plate; QWP, quarter-wave plate.

where I_T is the intensity of the transmitted light, I_R is the intensity of the reflected light, I₀ is the intensity of the incident beam, and θ_T is the angle between the orientation of the incident beam and the splitting axis of the PBS.

To ensure equal power allocation between the two beams, θ_T should be set at 45°, indicating that the fast axis of HWP1 should be oriented at 22.5° with respect to the axis of p-polarization. Figure 3(a) shows the power variations of the upper and lower beams, along with their average, as HWP1 is rotated over 90° in 0.5° increments. For precise adjustment of HWP1, power variations were measured by rotating HWP1 by over 1° in increments of 0.01°, as shown in Fig. 3(b).

Figure 3. Normalized power of two beams on the CCD1 camera at each rotation angle of HWP1: (a) over 90° with 0.1° intervals and (b) over 1° with 0.01° intervals. CCD, charge-coupled device; HWP, half-wave plate.

We validated our approach in realizing a destructive interference pattern using a Sagnac interferometer. Figure 4 shows the experimental setup of the interferometer based on the isoSTED setup. Each beam split by the PBS propagates through both the upper and lower beam paths while maintaining the same light path length before returning to the PBS. According to the Fresnel-Arago laws, orthogonally polarized beams cannot interfere. Therefore, a linear polarizer (LPVIS100-MP2; Thorlabs) set at a 45° angle relative to the splitting axis of the PBS was used.

Figure 4. Schematic of a Sagnac interferometer aligned with a half-wave plate (HWP); quarter-wave plate (QWP); polarizing beam splitter cube (PBS); and charge-coupled device (CCD) using the proposed method. The red, blue, green, and yellow dashed lines indicate s-, p-, circularly-, and 45°-polarized beams, respectively.

This configuration allows linearly polarized beams with identical orientation and equal power to pass through the linear polarizer. The linear polarizer was mounted on a piezo motorized rotation mount (CONEX AG-PR100P; Newport Co., CA, USA) for precise rotation. To adjust the orientation of the linear polarizer, the orientation of HWP1 was initially adjusted to ensure the transmission of all beams through the PBS. Subsequently, the beam circulated in the 4Pi cavity, in the absence of HWP2, QWP1, and QWP2, after reflection by the upper and lower mirrors. Upon returning to the PBS, the beam was transmitted through it. Then the linear polarizer was adjusted to prevent the beam from passing through it and precisely rotated to a 45° angle using the piezo motorized rotation mount. After the linear polarizer was set up, HWP2, QWP1, and QWP2 were sequentially inserted and adjusted using the proposed alignment module.

The interference patterns of these two beams were captured using a CCD2 (UI-1240LE-NIR-GL; IDS Imaging Development Systems GmbH), as shown in Fig. 5. Figure 5(a) shows the completely destructive interference pattern and intensity profile observed when all the retarders were well-aligned using the module. The normalized minimum intensity at which destructive interference occurred was 0.003. In contrast, the misalignment of the fast axis of HWP1 led to an increase in the minimum intensity required for destructive interference to occur. Figure 5(b) depicts the interference pattern with a normalized minimum intensity of 0.217 when the fast axis of HWP1 was rotated by 11°. The interference pattern disappeared when the fast axis of HWP1 was rotated by 22°, as shown in Fig. 5(c).

Figure 5. Interference patterns and corresponding intensity profiles: (a) When all retarders are well-aligned using our method, and when there are misalignments of HWP1’s fast axis (θ_e) with (b) 11° and (c) 22°, respectively. The intensity profiles are acquired by averaging intensities between the yellow dashed lines, which are 40 pixels apart.

We have developed an alignment method for a 4Pi cavity using isoSTED microscopy and experimentally validated our approach. In isoSTED microscopy, achieving a depletion focus with zero intensity at the center is essential to selectively quench fluorescence only in the periphery of the excitation focus. Otherwise, unwanted fluorescence inhibition occurs at the center, leading to decreased contrast and resolution degradation. Our proposed method enables simultaneous measurement of the power of two beams propagating clockwise and counterclockwise in the 4Pi cavity, in the unused part for imaging, where the beams are dumped. Therefore, this method allows for monitoring the power allocation between the upper and lower beam paths, which can change when a temperature-dependent PMF is employed in a depletion laser launcher. Additionally, our approach facilitates precise alignment of all the retarders in the 4Pi cavity of the isoSTED microscope. Experimental results demonstrate that our approach can generate complete destructive interference with zero intensity. This alignment method proves beneficial not only for aligning HWPs and QWPs in isoSTED microscopy but also in general optical systems.

This work was supported by the Soongsil University Research Fund (New Professor Support Research) of 2022.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

All data generated or analyzed during this study are included in this published article.