Demonstration of lateral resolution enhancement by focusing amplitude modulated radially polarized light in a confocal imaging system

Lateral resolution enhancement is demonstrated in a confocal imaging system with amplitude-modulated radially polarized (RP) light at the wavelength λ = 632 nm . Annular pupil fields and optimized amplitude distribution functions can be realized with a spatial light modulator. By comparing images obtained with full and amplitude modulated apertures of RP illuminations using a high numerical aperture (NA = 0.9), spatial resolution of d = 0.358 λ has been achieved experimentally. This result agrees very well with theoretical simulation results and will be helpful in improving performance of the non-fluorescent imaging systems.

(Some figures may appear in colour only in the online journal) Radially polarized (RP) beams have attracted increasing interest due to their unique focusing properties. In the previous work, it has been shown that a RP beam focused by a high numerical aperture (NA) objective can generate a sharp focal spot because of its strong longitudinal component near focus [1,2], which has potential in practical applications, such as optical tweezers and manipulation [3,4], optical data storage [5], accelerators [6] and super-resolution microscopy [7]. However, one limitation is that although the longitudinal component dominates in three components of the focal field, the transverse component still exists and has a donut shape. The transverse component affects the optical process, especially the imaging quality. Therefore, an appropriately shaped focal spot is essential in many applications, such as optical recording, photolithography and microscopy. Intensive efforts in phase, polarization and amplitude modulation [8][9][10] of the pupil field have been made to modify the relative ratio between longitudinal and transverse components of the intensity distribution in focus. One simple method is using an annular aperture pupil field to obtain a tighter focusing spot in a high NA system with RP beam illumination, although this happens at the expense of stronger side lobes [11,12]. It is shown that the longitudinal component of the focused spot can be, depending on the NA, 15% to 30% less than that of the classical Airy spot when shaping the amplitude of the RP pupil field that increases monotonically as a function of the pupil radius [13]. Spot-size reduction by means of focusing such an optimized RP beam with a high NA objective on a photoresist is confirmed experimentally and agrees with the theoretical analysis [14].
Conventional confocal imaging system is a very commonly used microscopic technique, especially in the research field of biology. Due to advantages of laser excitation, high resolution and 2D sections, it is widely applied in biological fluorescent samples. However, the lateral resolution is limited Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. by the Abbe diffraction limit. Our motivation for the present research is to implement an amplitude modulated RP beam in a confocal imaging set-up. This will provide general guidance for developing a higher resolution confocal imaging system, which can be not only applied for imaging biological objects but also for nanostructures.
The complete imaging process in a confocal system with a high NA objective illuminated by conventional, annular aperture and amplitude optimized pupil fields of RP beam to obtain a small focused spot is studied theoretically [15]. We first consider the case that the amplitude of the RP beam in the lens pupil is given by where a is the radius of the pupil of the objective, r p is the radial pupil coordinate, and r D p is the width of the annular ring. The second case is an optimized pupil field which gives the largest longitudinal component of the focused RP beam, for a given power P , 0 as derived in [13]: where the wave vector perpendicular to the optical axis is 2 with = k k n 0 the wave number in the medium with refractive index n, f 1 is the focal distance determined by the objective lens, l 0 is the wavelength in vacuum, e 0 and m 0 are the permittivity and permeability of vacuum, respectively. Figure 1 shows the advantage of modulating the amplitude of the pupil. Considering the normalized total intensity distribution with NA=0.9 at focus, the full width at half maximum FWHM≈0.7514λ of the spot size with linearly y polarized illumination, while FWHM≈0.5186λ for the case of linearly x polarized illumination. When the illumination is a conventional RP beam, the value of FWHM is the same as the condition of linearly x polarized excitation. However, the optimized pupil function has a FWHM of total intensity 0.434λ, which is 16.3% smaller than the case of conventional RP beam. By blocking 90% in terms of the pupil radius from the center, the value of the FWHM reduces to 0.3916λ, almost 24.5% sharper than the unmodulated conventional RP beam. In our previous simulation work, we regard subwavelength particles as electric dipoles, and to make full use of the narrow longitudinal component of the RP beam, two nearby dipoles with longitudinal dipole vectors are considered. It is demonstrated that the smallest distinguished distance of the two ideal longitudinal dipoles is 0.36λ with both annular and optimized pupil fields, i.e. beyond the diffraction limit of 0.68 λ [15]. However, for the annular pupil field, the light only propagates through the 10% unblocked area. As a consequence, the signal is very weak in the experiment. Strong side lobes can be produced in focus, which has a negative influence on imaging a non-isolated object.
The confocal set-up to demonstrate the effect of different focused RP beams is shown in figure 2(a). The He-Ne laser (l = 632 nm) passes through a single mode fibre and at the output of the fibre the laser is collimated into a large beam of about 8 mm diameter. The intensity distribution of the laser light is shaped by polarizers and spatial light modulator (SLM), with the latter being a reflected amplitude-only Holoeye LC-R2500.
The first polarizer is to produce linearly polarized light from the unpolarized light and should be aligned with the  orientation of liquid crystal molecules in the SLM to maximum the reflectance. The light after modulation passes through the second polarizer between the two beam splitters, which should be cross-polarized for the required amplitude modulation. After that, a liquid-crystal polarization convertor (THORLABS zero-order vortex half-wave retarder) is used to convert the beam from linear to radial polarization by rotating the linear polarization over an angle that depends on the azimuthal angle f in the pupil. The purpose of adding a 4f system between the SLM and the objective lens is to avoid the diffraction of modulated light after long distance propagation. Therefore, the modulated pupil field stays the same at the back focal plane as the one produced by the SLM. Then, the RP beam is tightly focused by an objective (NA=0.9) lens on a sample supported on a substrate. The detected sample is placed on a piezo-electric actuator operating by stepping in the x-y plane within its linear range. The reflected light goes back to the convertor to convert the light back to linear polarization so that the signal can be easily detected in the confocal system [15,16]. The final signal is detected after being filtered by the linear polarizer which can improve the image contrast and then collected by a single mode fiber (THORLABS SM600). The fiber with a lens of small NA acts as a pinhole to make an aperture giving 50% of the maximum intensity [17], which is necessary in the confocal microscope. The detector is a silicon photodiode coupled into a low noise amplifier. Figures 2(b)-(e) show the optimum amplitude function given by equations (2) and (3), the annular shaped mask which blocks the center of the beam up to NA=0.38 (42%), 0.57 (63%) and 0.81 (90%) described in equation (1), respectively. All these modulated pupil fields can be realized by the SLM. The sample is composed of random structures of paint on a glass substrate (n glass =1.5) with a very thin layer (∼20 nm) of TiO2 (n TiO2 =2.3897) on top of it. The thin layer functions as a substrate with guided mode excitation to further enhance the resolution and sensitivity [17][18][19][20]. A wide view of the sample provided by the digital microscope KEYENCE VHX-6000 is shown in figure 3(a) with the magnification ×30. The area in the red dashed box amplified as an inset is the final research target, which is zoomed in by 2000 times in figure 3(b). Here, we need to draw attention to the magnification defined by Keyence microscope, which is very high and thus different from the normal optical magnification. In fact, there is a multiplication factor of ∼22 after the calibration. One group of strips which can be distinguished are separated by m = d 1.49 m. Figures 3(c)-(g) display the images of the area obtained by our confocal imaging system with the excitations of a scanning focused spot corresponding to the conventional RP beam (c), to the optimized RP beam (d) and the annular mask with 42% (e), 63% (f) and 90% (g) of the light being blocked. The stripes with various distances in the structure are useful to determine the spatial resolution. The marked stripes with a distance of m = d 1.49 m in figure 3(b) can be seen in all the images obtained with the amplitude modulated RP beams (figures 3(d)-(g)), except in the case of the conventional RP beam ( figure 3(c)). In figure 3(d), after the sample illuminated by the RP beam with the optimized pupil field as described in equations (2) and (3), even the distance of l 226.24 nm 0.358 ( ) between two stripes can be observed clearly. The highly resolved distance agrees well with the resolution of l = d 0.36 as mentioned in our previous theoretical calculation [15]. For the annular pupil fields, the medium size of the ring aperture (63% blocked) gives the best imaging result. This is reasonable, since with the increase of the blocked area ( figure 3(g)), the effect of the side lobes becomes significant. Therefore, in the experiment, the image quality is not so good with the illumination of the RP beam of the annular aperture (90% blocked) as predicted in the simulations. Another important reason is that the sample is not the ideal longitudinal dipole anymore in the experimental work. Although the image quality in figure 3(e) with 42% of the pupil light being blocked is worse than the other two annular aperture cases (figures 3(f) and (g)), it is better than the unmodulated conventional condition (figure 3(c)). Therefore, the RP beam with the optimized amplitude of pupil field gives the most amount of detailed information and the best resolution. The RP beam with the pupil field of an annular ring also has advantages in the application of imaging, but the size of the ring mask should be chosen properly.