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Abstract
Traditional planar diffractive optical elements (DOEs) are challenged in imaging systems due to diffraction efficiency and chromatic dispersion. In this paper, we have designed a microfluidic diffractive optical element (MFDOE), which is processed by digital micromirror device (DMD) maskless lithography (DMDML) assisted femtosecond laser direct writing (FsLDW). MFDOE is a combination of photoresist-based multi-layer harmonic diffraction surface and liquid, realizing diffraction efficiency of more than 90% in the visible band. And it shows achromatic characteristics in the two bands of 469 nm (±20 nm) and 625 nm (±20 nm). These results show that MFDOE has good imaging performance.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Diffractive optical elements (DOEs) can be made into flat plate devices [1–6], and thus the overall thickness can be significantly decreased as compared with lens [7–10], revealing the great potential for integrated microsystem applications. Generally, DOEs can be classified into single-layer diffraction optical elements (SLDOE) and multi-layer diffraction optical elements (MLDOE). The chromatic dispersion of SLDOE is large, and the diffraction efficiency in the deviating wavelength range is low, which results in poor optical performance in a wide band [11]. MLDOE has a high diffraction efficiency in a wide band but generally suffers from a large chromatic dispersion [12]. Moreover, MLDOE usually consists of microstructures based on two or more materials, which makes manufacturing more difficult. And the alignment of different layers can cause misalignment, which results in poor imaging performance. Recently, the integration of micro-optical elements into microfluidic devices has attracted considerable attention, revealing the great potential for applications in micro focusing/imaging, optical capture, fluid laser, and tunable optics [13–16]. Theoretically, it is possible to integrate MLDOE into microfluidic devices. In this way, liquids with different refractive indexes can be employed as the second material that matches the solid DOE to realize the achromatic function. On the other hand, traditional achromatic methods such as doublet lenses formed by different dispersive materials are unsuitable for MLDOE [17–18]. The theory of harmonic diffractive optical elements (HDOE) also confirms the possibility of achieving achromatic dispersion in multiple bands [19]. That is, the phase is quantized to an integer multiple of 2π to achieve the confocal effect at multiple central wavelengths of MLDOE. However, to this end, open problems with respect to the fabrication of complex DOEs and the integration with microfluidic devices, as well as the alignment of solid/liquid layers are still challenging.
In this paper, we combined the concept of optofluidic, HDOE, and MLDOE, forming a micro-fluid diffractive optical element (MFDOE). MFDOE demonstrates high diffraction efficiency and small chromatic dispersion in a wide band. Based on the structural characteristics of MFDOE, femtosecond laser direct writing (FsLDW) and DMD maskless lithography (DMDML) were adopted. MFDOE's serrated relief structure is suitable for the high precision and true three-dimensional (3D) FsLDW. The low-precision frame structure that protects the stability of the internal fluid can be machined quickly using DMDML technology. High precision and high-efficiency machining can be achieved using FsLDW and DMDML combined machining methods. This work provides a convenient option for manufacturing MFDOE and other optical components.
2. Design and experiment
2.1. Design
The optical design software ZEMAX was used to design the imaging system with Binary 2 as the diffraction plane, and the total phase of MFDOE to be modulated was obtained. The design wavelength is 625 nm, the entry pupil diameter is 300 mm, and the imaging focal length is 1386 µm. The overall diffraction efficiency of MFDOE is greater than 90% in the visible band (400 nm-760 nm), and it has an achromatic effect at 469 nm and 625 nm. For comparison, according to the optical characteristics of DOEs [20–21], we have formed the comprehensive phase that can be applied to various kinds of DOEs:
Here, m is the diffraction order, p is the design order, d is the height, ${\lambda _i}\; $ is the incident wavelength, ${\lambda _0}$ is the dominant wavelength, ${\lambda _{m{\lambda _0}}}$ is the resonance wavelength, and $\alpha $ is the phase retardation factor, ${n_{{\lambda _i}}}$ is the refractive index of material corresponding to ${\lambda _i}$, and ${n_{m{\lambda _0}}}$ is the refractive index of material corresponding to ${\lambda _{m{\lambda _0}}}$. Δ${\varphi _{{\lambda _i}}}(r )$ is the additional phase difference caused by the non-dominant wavelength ${\lambda _i}$, which determines the diffraction efficiency. ${\varphi _{{\lambda _i}0}}(r )\; $ is the ideal phase at the resonance wavelength, which determines the focal length. So, the focal length and the diffraction efficiency at different orders are:
For the above formulas, when p = 1 and d2(r), d3(r) = 0, they correspond to the SLDOE; when p = 1, d2(r) and d3(r) are not 0, they correspond to the MLDOE; when p = 3, m is 3 and 4, d2(r) and d3(r) are not 0, n1 = n3≠n2, they correspond to the MFDOE. The structures of all kinds of DOEs are shown in Fig. 1. All kinds of DOEs are designed with SU-8 Photoresist (n = 1.58) (NANO, MicroChem).
Based on this theory, we calculated the diffraction efficiency, wavefront, and chromatic dispersion of all kinds of DOEs. The chromatic dispersion results in focal length differences at different wavelengths. For all kinds of DOEs, the two-wavelength ranges selected for theoretical analysis are 449-489 nm (blue light) and 605-645 nm (red light). First, the wavefront is calculated by Matlab software, and then the external data of the phase at each wavelength is derived. Based on the grid sag surface shape, we import external data into the optical design software ZEMAX. Then we analyzed the modulation transfer function (MTF) for all kinds of DOEs with different wavelengths. The wavefront of all wavelengths includes the additional phase and the diffraction phase corresponding to the dominant wavelength. Here, we do not consider the energy loss caused by surface reflection and the energy loss caused by material absorption in our calculation. Different light incidents on the DOE surface at a small Angle, resulting in energy loss due to Fresnel reflection. As the refractive index of SU-8 photoresist changes from 1.61 to 1.58 in the wavelength range of 0.45-0.65, the difference is minimal, so the loss ratio is the same, 8% on average (double-sided). At the same time, the absorption of SU-8 within the band is almost the same (less than 2%). The overall loss can be approximately 10%. Hence, the actual energy is about 90% of the diffraction efficiency. The calculation result of SLDOE is shown in Fig. 2(a)–2(f). As shown in Fig. 2(a), the additional phase difference of SLDOE gradually increases as it deviates from the dominant wavelength. Figure 2(d) shows that the diffraction efficiency deviating from the dominant wavelength drops sharply. The diffraction efficiency of blue light is 50-70%, and that of red light is close to 100%. We optimized the design to MLDOE, as shown in Fig. 2(g)–2(l). Because the additional phase difference of MLDOE is minimal (Fig. 2(g)), its diffraction efficiency in the visible light band is above 90% (Fig. 2(j)). Moreover, SLDOE and MLDOE have the same ideal phase at each wavelength, resulting in chromatic dispersion. The chromatic dispersion curves of SLDOE (Fig. 2(b) and 2(c)) and MLDOE (Fig. 2(h) and 2(i)) show that the focal lengths of all wavelengths are different. The focal length of red light is 1386 µm, while blue light is 1847 µm, which cannot achieve achromatic performance. Diffraction efficiency and chromatic dispersion determine the MTF and affect image quality. Figures 2(e) and 2(k) show the imaging characteristics of SLDOE and MLDOE at the focal length of 1386 µm. The MTF of red light has good imaging characteristics, while blue light does not have good imaging characteristics. Similarly, when the focal length is 1867 µm, only blue light can obtain good imaging characteristics, while red light cannot, as shown in Fig. 2(i) and 2(l). Neither SLDOE nor MLDOE can achieve good imaging characteristics in wide bands. SLDOE and MLDOE have different focal lengths for the blue and red light. Theoretically, the MTF corresponding to the focal length of red light is close to 0.4 at 70 lp/mm, when the MTF of blue light is poor (Fig. 2(b) and 2(e)). The MTF is less than 0.3 at blue focal length, and the MTF of red light is very poor (Fig. 2(c) and 2(f)). This result indicates that blue light also has a worse MTF than red light at ideal locations. There are three main reasons for this result: Firstly, although the diameter of DOE remains unchanged, the focal length of blue light is much larger than that of red light, so the NA of blue light is smaller, and its airy spot radius (σ=λ/NA) is 8.671 µm, which is larger than that of red light (6.358 µm). Secondly, the chromatic dispersion curve shows that the blue light has a larger slope than the red light, indicating that blue light has a more serious chromatic dispersion than the red light. Thirdly, the calculation of diffraction efficiency shows that blue light's diffraction efficiency is worse than red light. Figures 2(f) and 2(l) show that the blue light resolution of MLDOE is close to 0.3 at 70 lp/mm, which is stronger than that of SLDOE because the diffraction efficiency of blue light for MLDOE is higher.
Fig. 2. Diffraction efficiency, wavefront, chromatic dispersion and MTF of SLDOE (a)-(f), MLDOE (g)-(l).
In order to optimize the DOEs performance, MFDOE was designed. Based on the above formulas, we calculated the properties of several liquids and found that the effects of ethylene glycol and methanol are more prominent. Where, glycol refractive index formula ${\textrm{n}_{\textrm{gly}}} = 0.01456{\ast }{\lambda ^{ - 2.181}} + 1.391$, methanol refractive index formula is ${\textrm{n}_{\textrm{met}}} = 0.3753{\ast }{\lambda ^2} - 0.5894{\ast }\lambda + 1.5479$. Figure 3(a) shows that the additional phase difference of MFDOE filled with ethylene glycol is very small, and its diffraction efficiency in the band is close to 100% (Fig. 3(c)). It is better than the diffraction efficiency of SLDOE and MLDOE. At the same time, the ideal phase is inversely proportional to the wavelength. The chromatic dispersion characteristic curve (Fig. 3(b)) shows that the focal length of the two wavelengths is close to achieving achromatically. Figure 3(d) shows that the MTF of red and blue light for MFDOE can reach more than 70 lp/mm at the theoretical focal length of 1386 µm. MFDOE has the same focal length for blue and red light, so NA is the same. The simulation results show that the radius of the Airy spot is 6.358 µm and 4.77 µm, respectively, which accords with the wavelength ratio of λ/NA of 450/620. However, Fig. 3(c) shows that the slope of blue light is larger than that of red light, indicating that the chromatic dispersion of blue light is stronger than that of red light. The MTF calculation shows the blue light is 0.3 at 70 lp/mm, lower than 0.4 of red light, which is caused by strong blue light chromatic dispersion. To illustrate the flexibility of MFDOE, we also present the calculation results of methanol filling (Fig. 3(e)–3(h)), which are very similar to those for ethylene glycol. It proves that MFDOE is suitable for multiple liquid matching.
Fig. 3. Diffraction efficiency, wavefront, chromatic dispersion, and MTF of MFDOE filled with ethylene glycol (a) - (d) and methanol (e) - (h).
2.2. Experimental setup
Three-dimensional (3D) printing is widely used in many fields such as micro-optics, microbiology, and microfluidics [22–34]. In order to process MFDOE, we prepared the self-made FsLDW system and DMDML system, as shown in Fig. 2(b). The DMD (Texas Instruments Inc.) chip is composed of 1024×768 micromirrors, each with a size of 13.68 µm × 13.68 µm, and the projection objective is a 2× objective (Olympus, NA = 0.055). The wavelength of the light source is 385 nm. FsLDW uses a 780 nm femtosecond fiber laser (80 MHz, 120 fs) with a 40× oil-immersed objective lens (Olympus, NA = 1.30). The used laser intensity is 7.5 mW. The fabrication parameters are slicing 0.4 µm, hatching 0.4 µm, and scan speed 50 mm/s. Both SLDOE and MLDOE are directly manufactured through FsLDW. Figure 4(a) shows the structure of MFDOE. In order to ensure the integrity of the structure during processing, an understructure of h = 5 µm was added to both layers. The edge is designed as a perforated support structure with a thickness of 10 µm. Figure 4(b) shows the processing flow of MFDOE. In order to achieve the alignment of the two processes, we prepared a circular mark on the glass substrate in advance, which also functions as an aperture stop. First, MFDOE is processed by FsLDW based on the center of the circular mark. The microchannel is only used to avoid the volatilization or flow of liquid after sealing, so high processing precision is not required during processing. In addition, the channel is 7 mm in length and 5 mm in width, which is a long processing time for FsLDW (more than 100 h). However, the total time of composite machining is only 4 h and 20 min (including alignment and movement time). Below, we introduce the detailed processing process. The circular markings were made using a DMDML system by exposing a cylindrical structure with a radius slightly larger than MFDOE on the SU-8 photoresist spin coating. After development, the substrate with cylindrical structure is coated with opaque Cr by magnetron sputtering. The coated cover glass is then rinsed successively with acetone, ethanol and deionized water to obtain a substrate with a circular marker (aperture stop). Clean substrates containing SU-8 2025 (NANO, MicroChem) are placed on hot plates and heated at 65 °C and 95 °C for 3 min and 30 min respectively, namely soft baking. The substrate with circular markers coated with SU-8 photoresist was placed in the FsLDW system, and the image processing method recognized the central position of circular markers (x1, y1). Move the processing data center of MFDOE prepared in advance to (x1, y1) to realize the first alignment machining. After FsLDW processing is completed, the substrate is moved to DMDML system for fixation. The image processing method again recognizes the center position of the circular mark (x2, y2). The center of the DMD mask map corresponding to the pre-designed microchannel was moved to (x2, y2) to realize the second alignment machining. After preparation, the sample was heated again at 65 °C for 3 min and 95 °C for 15 min, namely postbake. Heating can promote further cross-linking of the exposed resin. Then the sample was cooled to room temperature in air and immersed in SU-8 developer and cleaned by ultrasound for 3-5 min. Finally, rinse with deionized water for 1 min and blow-dry with nitrogen. After development, drilled polydimethylsiloxane (PDMS) plate is sealed to the upper layers of the structure. Figure 4(c) shows the sealing step. SU-8 microfluidic channel was sealed with PDMS (Sylgard 184, Dow Corning). PDMS prepolymer was mixed with a cross-linking agent at a mass ratio of 10:1 and heated at 95°C for 50 min on a hot plate. Then a PDMS plate was formed. After drilling, 3-aminopropyl triethoxysilane (APTES) was used to silanize the surface. And the PDMS plate was bonded to the SU-8 microfluidic channel and the upper layer of the glass substrate by oxygen plasma treatment. Finally, a SU-8 microfluidic channel with good sealing performance was obtained. MFDOE can be filled with more liquids. In this paper, we present the test results of MFDOE flushed with ethylene glycol. SU-8 2015 (GmbH) photoresist and PDMS were used in this experiment.
Fig. 4. (a) Schematic diagram of the three-dimensional structure of MFDOE. (b) Fabrication steps for the MFDOE. (c) The sealing step of MFDOE.
3. Experimental results
3.1. Surface quality and profile
To further characterize the surface quality and profile, we measured the lower layer of MFDOE using a three-dimensional (3D) microscope (KEYENCE VHX-5000). Due to the inability to measure the internal profile of the bilayer structure, we machined the underlying structures of multiple MFDOEs. The machining error of multiple measurements is basically kept within a certain range. Here, we present the results of one measurement. Figure 5(a) shows a clear relief surface profile. The radial surface profile plot demonstrates a great match between the designed profile and the actual fabricated profile (Fig. 5(b)). Figure 5(c) shows that the error value between the test and design profiles is within ±0.6 µm. We calculate the average diffraction efficiency in the band generated by the maximum height error in different radii. Put the measured $\varDelta d$ into Formula 3 to get $\varDelta \alpha $, and then put $\varDelta \alpha$ into Formula 4 to get $\varDelta \eta $ of different wavelengths. Finally, the average value of $\varDelta \eta $ is obtained, as shown in Table 1. The effect of small height error on image quality and diffraction efficiency is small or even negligible.
Fig. 5. (a) The 3D microscope image, (b) Surface profilometer and (c) surface profile error of the underlying structure of MFDOE.
Table 1. The relationship between Δdmax and the average Δη
Figures 6(a)–6(d) show the microscope (Olympus, Japan) images of all kinds of DOEs. Figure 6(c) shows the microscope image of the MFDOE integrated into the microchannel. The length and width of the entire frame are 7 mm and 5 mm, respectively. The width of the middle channel (380 µm) is slightly wider than that of the MFDOE. The results show high quality, good shape fidelity, and stable structure.
Fig. 6. The microscope images of SLDOE (a), MLDOE (b), micro-channel and MFDOE (c) and MFDOE (d). The scales are 50 µm.
3.2. Image test
We use an optical power meter to test the percentage of the energy in the focus area to the incident energy, as shown in Fig. 7. The specific test method is as follows. First, measure the energy of incident light passing through a circular aperture without all kinds of DOEs, denoted as E2. Then, a hole of the same size as the diffraction spot is placed near the all kinds of DOEs focus, and the energy E1 after the light incident into the circular aperture passes through all kinds of DOEs, and the hole is measured. Energy ratio = E1/E2. Because the aperture of all kinds of DOEs is very small, there must be some error in the test. In addition, about 10% energy loss caused by the reflection of front and rear surfaces and absorption of materials is not taken into account in the calculation, so the actually measured energy proportion is about 12% lower than the average theoretical diffraction efficiency.
We built an optical test path with replaceable light sources, as shown in Fig. 8. The light sources are narrow-band red, and blue LED light sources with central wavelengths of 625 nm (full-width half-maximum (FWHM) = 20 nm) and 469 nm (FWHM = 20 nm), respectively. The practical value of diffractive lenses ultimately depends on the quality of optical imaging. A USAF test target and a 5 µm diameter hole were placed 3 mm in front of the DOE, which was imaged by the DOE and received by the CCD. Figures 9(a)–9(p) describe the USAF test target and hole imaging at different image distances by SLDOE and MLDOE under the same light intensity. For SLDOE, Fig. 9(a) shows the line image (white dashed line) corresponding to 70 lp/mm has better resolution for red light at z = 2.5 mm. However, Fig. 9(b) shows the blue light cannot be imaged clearly. As shown in Fig. 9(i)–9(j), the blue light can be imaged at z = 4.5mm, but the red light cannot, and the line pair corresponding to blue light imaging is only 50 lp/mm. It also shows that the magnification of blue light is greater than that of red light. Due to the low diffraction efficiency of blue light, most of the light exists in the overall background as stray light, reducing the contrast. As shown in Fig. 9(c)–9(d) and 9(k)–9(l), the imaging results of MLDOE are consistent with SLDOE, but the contrast of blue light is better than that of SLDOE. This is because the diffraction efficiency of MLDOE at blue light is higher, and the corresponding stray light is reduced, so the contrast of MLDOE at blue light is better than that of SLDOE. Figures 10(a)–10(d) show that the MFDOE filled with ethylene glycol and methanol both have good imaging results at z = 2.5 mm. The ethylene glycol-filled MFDOE achieves a 70 lp/mm resolution at blue and red light. The methanol-filled MFDOE also achieved 70 lp/mm resolution for both lights. It can also be seen that the contrast of the two MFDOEs is slightly worse at blue light than the red light. This is due to the lower diffraction efficiency of the blue light than red light, which reduces contrast.
Fig. 9. (a)-(p) Image effects of SLDOE and MLDOE on USAF targets and 5 µm diameter hole at different locations. The energy normalization of SLDOE (q) and MLDOE (r) on the spot imaged by the circular aperture. The scales are 50 µm.
Fig. 10. (a)-(h) Image effects of glycol-filled MFDOE and methanol-filled MFDOE on USAF targets and 5 µm diameter hole at different locations. The energy normalization of glycol-filled MFDOE (i) and methanol-filled MFDOE (j) on the spot imaged by the circular aperture. The scales are 50 µm.
The hole imaging of all kinds of DOEs show the same results as the USAF test target imaging (Fig. 9(e)–9(h), 9(m)–9(p) and 10(e)–10(h)). Figures 9(q)–9(r) and Figs. 10(i)–10(j) show the energy normalization and FWHM of all kinds of DOEs on the spot imaged by the circular aperture. Referring to the diffraction efficiency tested, the normalized curve is processed according to the corresponding energy proportion, approximately representing the focusing efficiency of all kinds of DOEs. As shown in Fig. 9(q), the intensity of SLDOE at red light reaches 0.96, while the intensity at blue light is only 0.51. For MLDOE, the intensity of red light reaches 0.96, and the intensity of blue light also reaches 0.87, which is higher than that of SLDOE (Fig. 9(r)). The diffraction efficiency of MLDOE at blue light is stronger than that of SLDOE, which is consistent with theoretical calculations. The test results of half height and width agree with the theory. The test results of FWHM agree with the theory. As shown in Fig. 9(i)–9(j), the intensity of MFDOE red light reaches 0.98, and blue light can also reach 0.99. All the test results agree with the theoretical average diffraction efficiency. The comparison with the imaging results of SLDOE and MLDOE shows that the liquid-filled MFDOE achieves achromatic properties in two bands, and the diffraction efficiency is significantly enhanced, which proves the excellent performance of MFDOE.
4. Discussion
In general, we demonstrated a microfluidic diffractive optical element with high diffraction efficiency and achromatic dispersion in a wide band. We used the combination of FsLDW and DMDML to achieve high-efficiency and high-precision processing. MFDOE adopts a harmonic diffraction design to focus the 625 nm and 469 nm resonant waves to the same focal point, effectively eliminating chromatic dispersion. The matching calculation of liquid phase materials is used to improve the diffraction efficiency and achromatic characteristics in the band. This kind of MFDOE is small, combined with high-efficiency, high-precision composite processing, paving the way for developing high-efficiency, high-performance, and flexible optical elements.
Funding
National Natural Science Foundation of China (No. 61875036); Jilin Scientific and Technological Development Program (20190302049GX); Key Technology Research and Development Program of Shandong (2021CXGC0102020) .
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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