1. Introduction

Recently, tightly focused multifocal spot arrays with high-NA objective lens have attracted great attention due to their broad applications in real-time molecular tracking, optical manipulation, laser micro/nano-fabrication and multifocal microscopic imaging etc. [1–4]. With multifocal spots, both parallel optical imaging and parallel lithography can be realized with significantly improved measurement or processing efficiency [5–9]. Accompanied with a high-NA objective lens, each of the focal spot in multifocal spots reserve high spatial resolution and accuracy. There are distinct ways of generating multifocal spots in the focal region with the high-NA objective lens. One simple way is using optical elements, like microlens arrays [10–12] and diffractive optical elements (DOEs) [13,14]. These methods can split a single incident beam into multiple beams to generate multifocal spots on the same focal plane. The other is through modulating the phase or amplitude of the beam at the pupil plane of the objective lens [7,9,15–17] by a spatial light modulator (SLM) [9]. SLM provides the cability of dynamically loading phase maps to realize complex beam patterns and distributions. Thus, SLM is one of the most widely used devices for generating multifocal spots.

In recent years, various algorithms have been developed to generate phase maps for SLM and realize phase modulation of multifocal spots. Iterative methods developed based on Fourier transform (FT) were primarily used in phase modulation, like Gerchberg–Saxton (GS) algorithm and weighted Gerchberg-Saxton (WGS) algorithm [18–20]. However, iterative methods typically require a large number of iterations, lacking flexibility and may not produce a unique phase distribution related to the desired light distribution [7,9]. Currently, some non-iterative algorithms have been proposed. Compared to the aforementioned iterative algorithms, non-iterative algorithms have two major advantages. One is the high time efficiency of computing phase distribution. The other is the realization of flexible control of multifocal spots with different light distributions. For instance, Zhu et al. [21] proposed a method of multizone plate to generate multifocal spot arrays with the focal positions and polarization controllable. Deng et al. [22] proposed an approach method with a specially designed hybrid phase plate (HPP). In their algorithm, several optical parameters of multifocal spots, e.g., positions, orbital angular momentum states, number of spots and their diameters, can be modulated. Guan et al. [9] designed a type of dartboard phase filter (DPF) map, which is divided along with polar coordinates. Compared to the complex iterative algorithms, it is easier to control focal position and polarization with DPF.

However, these methods are more-or-less flawed in applications with a high-NA objective lens, for bioimaging, molecular tracking and photofabrication. For instance, these methods are normally evaluated by reflective imaging, laser beam analyzer or numerical simulations only. When applying these methods in an inverted fluorescence microscope with a high-NA objective lens, the actual beam patterns on the focal plane can be highly different, as can be seen from Fig. 1. When the multifocal spots generated by SLM with a single lens ($f = 250$ mm) is captured by a camera, the effect of zeroth-order light of SLM can be simply eliminated with blazed grating (BG) method, as shown in Fig. 1(a). However, on the focal plane of a high-NA objective lens, as shown in Fig. 1(b), the influence of zeroth-order light can be hardly eliminated with BG method. This is also an obstacle in the application of parallel imaging and laser direct writing.

 

Fig. 1. Generation of multifocal spots in different experimental diagrams. (a) Multifocal spots generated by SLM with optical lens ($f = 250$ mm). The image of multifocal spots is directly captured by CCD with the lens. (b) Multifocal spots captured using inverted fluorescence microscopy with high-NA objective lens (Nikon PL APO 63X NA1.4 oil-immersion).

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In this investigation, we propose a non-iterative strip segmentation phase (SSP) method, which can achieve good uniformity and multifocal spots quality as supported by both numerical simulations and experiments, including high-NA objective applications. The advantages of the SSP method include:

In section 2, a phase-only analysis for controlling multifocal spots is derived based on the Fourier transform (FT) of Debye diffraction integral. Then, based on the phase-only analysis, we propose an SSP method composed of a large number of segmentation regions, which contain different phase maps of focal spots. In section 3 and 4, we use the SSP method to generate multifocal spots with high quality and uniformity, which are further evaluated by both numerical simulations and experiments of fluorescent imaging through inverted fluorescence microscopy. Then, we demonstrate that by dynamic loading the phase maps on the SLM, flexible control of the multifocal spots for parallel laser direct writing has been realized. Finally, section 5 is the discussion and conclusion.

2. Principle and method

2.1 Principle of changing the position of the focal spot

The diagram of numerical simulation with Debye diffraction integral is shown in Fig. 2, where a high-NA aberration-free objective lens is compatible. Here, for simplification, we omit the constant coefficients. Then, the electric field intensity of light at point o can be expressed with Fourier transform [24–26]:

 

Fig. 2. Schematic diagram showing tightly focusing field distribution through objective.

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Thus, we can control the position of the focal spot by applying different $\Delta x$ and $\Delta y$ in Eq. (3).

2.2 Strip segmentation phase method for multifocal spot generation

In this investigation, we advanced a strip segmentation phase method for generating tunable multiple spots in the focal region of the objective lens. Different to the previously reported methods (e.g. Reference [6]), SSP can generate a multifocal spot array with the position of each spot controllable at the focal region of the objective lens. Accompanied by the phase function in Eq. (3), a highly flexible multifocal spot array can be generated, regardless of low or high-NA objective lens.

The SSP method is schematically described in Fig. 3. To generate multifocal spots, we divide the aperture stop radius into N strip segments (1,2,$\cdots N$) with equal interval $R/N$, as shown in Fig. 3(a). The segmentation generates N main areas in half of the aperture plane. Then, each main area is further divided into M smaller subareas, in which each strip has equal height, given by $R/NM$ and $N > M$, as shown in Fig. 3(b). M is also the number of spots generated using this SSP method. Each of the subareas is filled with phase distribution calculated from Eq. (3) using different $\Delta x$ and $\Delta y$ parameters. To further illustrate the SSP method, one example of generating two spots using $N = 3$ and $M = 2$ is shown in Fig. 3(c). The aperture plane is divided into 6 main areas, each of which has a width of $R/3$. The phase distributions in the subareas according to the 2^nd main area is shown in Fig. 3(e). Since $M = 2$, two subareas are present in the main area.

 

Fig. 3. Schematic of generating multifocal spots by SSP method. (a) Segmentation of phase map on the pupil plane of the objective. Half of the phase map has been divided into N main areas. One of the main areas has been highlighted by the yellow lines. (b) Zoom-in of the main area in (a). The main area is constituted of M subareas. (c) Two spots are generated by SLM through the SSP method. (d) The corresponding phase map of generating the two spots in (c) by SSP method, where $N = 3$, $M = 2$. A typical main area has been highlighted. (e) The phase distributions in the subareas according to the selected main area.

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3. Numerical simulations on realizing multifocal spots

The feasibility of realizing multifocal spots with SSP has been supported with numerical simulation in this section. Generation of multifocal spots with the previously reported non-iterative methods [9,21,17] has been rarely realized in fluorescence microscopy and parallel laser direct writing. However, stable and flexible generation of multifocal spots in a microscope is of great significance to the imaging field. Here, multifocal spots are successfully generated in a fluorescence microscope by combing the blazed grating with the SSP method.

As an example, we show how to generate arbitrary multifocal spots with circularly polarized Bessel-Gaussian (CPBG) beam (639 nm wavelength) using a NA1.4 oil-immersion objective lens (${n_t} = 1.518$). The apodization function of the Bessel-Gaussian (BG) beam can be written as [27]:

Figure 4 shows an example of flexibly controlling each of the multifocal spots by the SSP method to realize a continuously writing of “NWU”. Figure 4(a) shows the phase distribution of generating “N” with 7 points. In the SSP method, seven types ($M = 7$) of phase distributions with different position parameters are applied. According to Eq. (4), the position parameters according to the 7 spots are $({\Delta x,\Delta y} )= ({ - 4\lambda ,4\lambda } )$, $({ - 4\lambda ,0} )$, $({ - 4\lambda , - 4\lambda } )$, $({0,0} )$, $({4\lambda ,4\lambda } )$, $({4\lambda ,0} )$, $({4\lambda , - 4\lambda } )$. The corresponding “N”-shape intensity distribution on the focal plane of the objective lens is shown in Fig. 4(d). Similarly, we can generate a 9-point “W” shape and a 7-point “U” shape by letting $({\Delta x,\Delta y} )= ({ - 8\lambda ,4\lambda } )$, $({ - 6\lambda ,0} )$, $({ - 4\lambda , - 4\lambda } )$, $({ - 2\lambda ,0} )$, $({0,4\lambda } )$, $({2\lambda ,0} )$, $({4\lambda , - 4\lambda } )$, $({6\lambda ,0} )$, $({8\lambda ,4\lambda } )$ and $({\Delta x,\Delta y} )= ({ - 4\lambda ,4\lambda } )$, $({ - 4\lambda ,0} )$, $({ - 4\lambda , - 4\lambda } )$, $({0, - 6\lambda } )$, $({4\lambda ,4\lambda } )$, $({4\lambda ,0} )$, $({4\lambda , - 4\lambda } )$. The corresponding phase maps have been shown in Fig. 4(b) and (c), with the multifocal spots of “W” and “U” realized in Fig. 4(e) and (f), respectively.

 

Fig. 4. Phase maps generated according to Eq. (4) in the SSP method, where (a) $N = 30$, $M = 7$, (b) $N = 30,$ $M = 9$ and (c) $N = 30,$ $M = 7$. (d), (e) and (f) are the corresponding light intensity distributions of CPBG beams ($\beta = 1.5$) in the focal plane of the objective lens, which are modulated by the phase distributions shown in (a), (b) and (c). The dynamic control of each focal spot in the focal plane of the objective lens is realized flexibly based on the SSP method (see Visualization 1).

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According to the analysis above, we can see that multifocal spots with NWU-shape can be created using the SSP method shown in Fig. 4. It is easy to generate continuously and dynamical varying multifocal spots by simply changing the phase distribution. Visualization 1 shows an example of flexibly controlling N-, W- and U-shaped multifocal spots. To the best of our knowledge, it is more flexible to adjust the position of multifocal spots with the SSP method relative to the iterative methods.

Uniformity of the focal spot is an important parameter to evaluate the quality of multifocal spots generation. It can be defined by a factor as [6]:

The uniformity of the multifocal spots generated by the SSP method is primarily dominated by N, as can be found from Fig. 5. When $N = 10$, the generated multifocal spot image shows diverse and scatterd light spots. The five-spots image has a Q factor of only 0.79. When N is increasd to 25, the scatterd light spots are significantly reduced. The Q factor increases to 0.92 which indicates an improvement of uniformity. When N is increasd to 30, the scatterd light spots are nearly dissappeard. The five spots show excellet uniformity with $Q > 0.99$. From Fig. 5(g), it can be concluded the larger the N used in SSP, the better uniformity of the multifocal array is. As $N > 30$, a good uniformity with $Q > 0.99$ can be stably realized. Note, the maximum value of N is determined by the resolution of the SLM.

 

Fig. 5. Uniformity of multifocal spots changes with N. (a-c) shows the phase maps generated by the SSP method at $M = 5$. (a) $N = 10$, (b) $N = 25$ and (c) $N = 30$. (d-f) shows the corresponding light intensity distributions of (a-c). (g) Q factor varies with N.

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4. Experimental validation of flexibly generating multifocal spots

In previous studies, it is rarely reported that non-iterative method has been used to flexibly generate multifocal spots with high-NA objective lens, which is crucial for parallel fluorescent imaging and parallel laser direct writing. To support the feasibility of the SSP method in practical applications with high-NA objective lens, we first test the method in an inverted fluorescence microscope to generate multifocal fluorescent spots. Then, the multifocal spots generated by the SSP method are used for laser direct writing (LDW) fabrication.

4.1 Experimental setup and procedure for both fluorescent imaging and LDW

The experimental system is diagramed in Fig. 6(a). A dual-beam system has been built to realize both fluorescent imaging and LDW.

 

Fig. 6. (a) Schematic of the optical system for fluorescent imaging and LDW. SPF is spatial pinhole filters; L is a collimation lens; ${\textrm{R}_1}$ and ${\textrm{R}_2}$ are reflective mirrors; DM is dichroic mirror (SEMROCK ZT488/647/780rpc); P is a polarizer; BS is a beam splitter; SLM is a liquid-crystal-on-silicon spatial light modulator; WP is a quarter-wave plate. (b) Illustration of the phase map. The SSP method and blazed grating method are combined to realize multifocal spots with inhibited zeroth-order light. (c) Excitation and emission spectra of Cy5 fluorescent dyes (the data is from Bridgen).

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4.1.1 Experimental setup and procedure for fluorescent imaging

In the application of fluorescent imaging, a 639 nm continuous-wave laser (MW-RL-639/400 mW, CNI) is used as a light source. After modulated by a spatial pinhole filter (SPF) (OptoSigma, SFB-16DM), the beam is collimated by lenses (L1) to realize improved beam quality. The beam passes a dichroic mirror (DM) (SEMROCK, ZT488/647/780rpc, 639 nm HT) and subsequently, a polarizer (P) to generate a linearly polarized beam, of which the polarization direction is consistent with the long side of the liquid crystal plate of the SLM (LETO, HOLOEYE Photonics AG, Germany, PLUTO-NIR-011, 420 nm∼1100 nm). The beam passes through a beam splitter (THORLABS, BS 400 nm∼800 nm) and reaches the SLM. The beam after modulation is converted to circular polarization by a quarter-wave plate (THORLABS). Finally, the excitation beam is imported into an inverted fluorescence microscopy system (NIB900, NEXCOPE, China). The microscope has a filter set, including a dichroic mirror (SEMROCK, Di01-R488/543/635, 405 nm HR, 639 nm HR) and a bandpass filter (CHROMA, ZET488/640 m). The 639 nm beam is reflected by the dichroic mirror and focused with a high-NA objective lens (Leica, PL Apo 63X, NA 1.4). The fluorescent spots pass through the same dichroic mirror and the bandpass filter sequentially and finally captured by a SCMOS (PCO AG, Kelheim, Germany, PCO. edge 4.2 m) camera.

In the experiment, CY5 (Bridgen) was used as fluorescent dye. It has an excitation peak at 651 nm and emits fluorescence at 670 nm (see Fig. 6(c)). During sample preparation, CY5 solid powder is first dissolved by deionized water (DI) for a concentration of $1.25$ µM. Then, we mixed the dye solution with refractive index matching liquid Mowiol 4-88 (Sigma-Aldrich) under a ratio of 3:2. The Mowiol 4-88 liquid has a refractive index of 1.518 which is consistent with that of the coverslip and immersion oil. Thus, the difference of refractive indices between solution and coverslip can be significantly reduced, accompanied by the smaller influence of aberration caused by refractive index mismatch [28]. During measurement, several drops of the mixed solution were placed on a coverslip. The fluorescent images were later captured when the water in the mixed solution had been evaporated.

4.1.2 Experimental setup and procedure for LDW

In the realization of LDW, another optical path with a 405 nm continuous-wave laser (MW-RL-405/500 mW, CNI) as the fabrication light source has been added to the optical system (shown in Fig. 6(a)). The beam consequently passes a spatial filter (SFB-16DM, OptoSigma) and a collimating lens to improve the beam quality and collimate. Then, the fabrication beam also passes the same polarizer, a beam splitter (THORLABS, BS 400 nm∼800 nm) before reaching the SLM (LETO, HOLOEYE Photonics AG, Germany, PLUTO-UV-043, 350 nm∼420 nm). The beam modulated by SLM is subsequently converted to circular polarization by the quarter-wave plate (THORLABS). Finally, the fabrication beam is imported into the inverted fluorescence microscopy system and focused on the photoresist with the same high-NA oil-immersion objective lens (Nikon, PL APO 63X, $\textrm{NA }1.4$). In the experiment, a positive photoresist (Germany, ALLRESIST, AR-P 3740) is spin-coated with 4000 rpm over 60 s on the surface of a coverslip. Then, it was baked at 100 ℃ for 1 min on a hot plate. After exposure, the photoresist was immersed in a developing solution (Germany, ALLRESIST, AR 300-47) for 90 s, and then rinsed in deionized water for 30 s. At last, the structure of the photoresist could be observed by a Leica microscope (Germany, Camera AG, Leica, DMi8).

4.2 Validation by multifocal fluorescent spots

In the experiment, to inhibit the influence of zeroth-order light due to spatial light modulator pixilation [29], a blazed grating method has been applied accompanied by SSP method. Accordingly, the phase distribution can be finally expressed as:

 Figure 7(a) shows the phase distribution of generating $\textrm{N}$-shape multifocal spots, which is experimentally observed in Fig. 7(d). Similarly, the W- and U-shape multifocal spots, realized by applying the phase distributions in Figs. 7(b) and (c), have been precisely generated as shown in Figs. 7(e) and (f) accordingly. All the spots can be flexibly controlled to achieve independent movement, as can be seen from Visualization 2. By evaluating the uniformity of the multifocal fluorescent spots of the experiment according to Eq. (8), we found the values of Q in Figs. 7(d) and (e) are all more than 96%.

 

Fig. 7. Phase distributions applied on SLM and the corresponding multifocal fluorescent spots generated in the inverted fluorescence microscope. (a-c) Phase distributions applied on SLM to generate multifocal spots. Here, in SSP method, $N = 90$. $M = 7$, $9$ and $7$ for (a-c) respectively. (d-f) The corresponding fluorescent intensity distributions recorded by SCMOS camera. (see Visualization 2 for dynamic changing).

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Besides, relative to the previous researches [7,9], with the SSP method, we can generate more multifocal spots of the same shape with good uniformity at relatively smaller N. As shown in Figs. 8(a)-(c), more multifocal fluorescent spots are generated when the number of phase division N is only 30 and 1080${\times} $1080 pixels of SLM have been applied. The Q factors are all above 95%.

 

Fig. 8. Experimental results of generating more spots using SSP method (see Visualization 3 for dynamical changing of the spots). Here, $= 30.$ $M = 7$, $9$ and $7$ for (a-c) sequentially.

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4.3 Flexible and parallel fabrication of continuous structures with LDW

In the following section, we flexibly and simultaneously control the movement of each focal spot with different displacement parameters, to realize parallel LDW of the NWU-shape structures. During fabrication, the laser is turned on first. In the meanwhile, the phase map is loaded on the SLM. In the fabrication of the structures shown in Fig. 9, a sequence of phase maps (4 frames) is loaded one after another. Each phase map is kept for 800 ms and the time interval between two loadings is around 17 ms. The overall time cost for fabrication is around 3.25 s. The laser power is 0.75 mW. Multiple characters can be directly written at one time, as can be seen from Figs. 9(a)-(c). Each of the focal spots in the multifocal arrays moves according to Visualization 3(a)-(c). The fabrication resolution is on submicron scale (${\sim} 0.875$ μm) as shown in Fig. 9(b). The results indicate SSP method provide a flexible and potentially high-throughput approach for future laser direct writing.

 

Fig. 9. Experimental results of parallel laser direct writing, where $N = 30$. (a) $M = 7$, (b) $M = 9$ and $M = 7$ respectively. Here, a 40X air objective (Leica, PL Apo 40X, NA 0.6) was applied to observe the fabrication results.

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5. Conclusion

In this investigation, we have proposed a non-iterative method, named strip segmentation phase method, to realize multifocal spots with high uniformity and flexibility. The segmentation method is simple for designing phase map. The performance of the segmentation method has been supported by both numerical simulations and experiments. Especially, a parallel laser direct writing of an NWU-shape structure has been realized by the method. Compared to the iterative method, the phase-only pattern targeted to flexible realizes arbitrary-shape structure by shifting the multifocal spots using the proposed SSP method. This method can also be combined with the blazed gratings to produce multifocal fluorescent spots in an inverted fluorescence microscope system with a high-NA objective lens. According to the superior performance, the SSP method of generating multifocal spots has wide applications in laser direct writing, fast scanning microscope and multifocal Stimulated Emission Depletion microscope and optical data storage etc.