1. Introduction

High diffraction efficiency Fresnel lens (HDFL) provides alternative solution for next generation 10 m scale space telescope due to relaxed surface figure tolerance, higher foldable ratio and light weight, compared to traditional refraction-reflective optics [1–3]. Optical-polyimide membrane with good space environmental adaptability became a potential substrate material for primary lens on which diffractive patterns are sculptured. The adoption of membrane materials can further decrease weight of HDFL and provide better adaptation to launching vibration [4–7]. In order to construct 10 m aperture primary lens, over 70 pieces of large aperture off-axis Fresnel lenses (LAOFL) should be stitched precisely and co-phased. However, directly sculpturing diffractive patterns on membrane is technologically challenging and repeting fabrication on dozens of substrates is time consuming and costly. Fortunately a two-step method was put forward that a master silica template is made by lithography and then a membrane with complementary structure is replicated through casting and curing [8]. It was found that microrelif profile can be well replicated thus final profile precision is almost determined in lithography process and near 60% of average diffraction efficiency of coaxial 4-level Fresnel lens were reported in recent years [9–14]. The deviation of diffraction efficiency from theoretical 81% was discussed mainly due to alignment errors in overlay etching process [15,16].

In this paper, we adopted laser direct writing (LDW) system as pattern generation tool and reactive ion etching system (RIE) as pattern transfering tool to fabricate LAOFL, and investigated the diffraction efficiency distribution. We adopted verniers in X direction and Y direction to straightforwardly display alignment errors horizontally and vertically, and discussed factors influencing average diffraction efficiency and its standard deviation.

2. Results and discussions

The LAOFL is a part of primary lens constructing the segmented large-scaled lightweight diffractive telescope (SLLDT) previously built in our laboratory aiming at astronomical observation [17]. The key optical parameters of the telescope are shown in Table 1 and technical specification of LAOFL is shown in Table 2.

Table 1. Key optical parameters of SLLDT

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Table 2. Technical specification of LAOFL

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The primary lens diameter is 1.5 meters consisting of eight identical LAOFLs and one 710 mm aperture coaxial Fresnel lens, with F number at 7 and field of view at 0.12 degrees and working waveband from 550 nm to 650 nm. Each 4-level LAOFL is made in Φ390 mm aperture optical quality fused silica substrate with Φ352 mm aperture diffractive pattern, and the smallest linewidth is 2.1 µm. It is necessary to mention that linewidth increases from outer edge to inner edge with the largest linewidth at 3.7 µm. Etching depth of each level is the same 330 nm across whole diffractive pattern.

The photolithography of LAOFL is based on LDW system (VPG800, Heidelberg, Germany) with capability of 800 mm×800 mm substrate size and 100 nmpositioning error (3σ). The pattern transfer process is based on Reactive Ion Etching machine (RIE600, developed by Institute of Optics and Electronics, China). Schematic diagram of LAOFL pattern fabrication process is shown in Fig. 1 below.

 

Fig. 1. Schematic diagram of LAOFL pattern fabrication process. There are six major steps including two rounds of exposure, development and pattern transfer in which the first round generates a 2-level pattern and the second round generates a 4-level pattern.

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Before the pattern fabrication process, chromium cross marks were made on fused silica substrate through commercial photomask fabrication process, helping LDW lens system have a better contrast and higher positioning accuracy. In pattern fabrication process, substrate was firstly coated with a layer of 1 µm thick AZ1500 photoresist (AZ technology, USA) by spin coater (SM900, SAWATEC, Switzerland) and hot plate (HP900, SAWATEC, Switzerland). Then the substrate with photoresist was placed in LDW system under first exposure followed by first development, generating a layer of photoresist diffractive pattern as well as primary verniers pattern.The first pattern transfer was carried out afterwards using RIE600 machine and residual photoresist was washed away using acetone liquid, generating a layer of 2-level diffractive pattern with smallest linewidth at 2.1 µm as well as primary verniers pattern on fused silica. After that, the susbstrate was coated with a layer of photoresit again and followed by the second exposure in LDW system. Notice that in the first and second exposure, laser head determined its coordinates by finding chromium cross marks central positions. The second development and second pattern transfer were implemented afterwards, generating a layer of 4-level diffractive pattern with smallest linewidth at 4.2 µm as well as secondary verniers pattern on fused silica.

The positioning cross mark and vernier pattern is illustrated in Fig. 2 below. The positioning chromium cross mark is 15 µm wide and 300 µm long, uniformly distributed across effective aperture with 60 mm distance away from each other. The vernier pattern is consisting of primary vernier and secondary vernier both in X and Y directions. The primary vernier pattern is fusioned in diffractive pattern data and generated in the first exposure. The secondary vernier pattern is fusioned in diffractive pattern data and generated in the second exposure. The primary vernier consists of 21 lines with 2 µm width and 2.1 µm space, while the secondary vernier is composed 21 lines with 2 µm width and 2 µm space. Therefore, the reading accuracy of vernier pattern is supposed to be 100 nm in both X and Y directions.

 

Fig. 2. Illustration of positioning cross mark and vernier pattern. There are 29 sets of cross mark and vernier pattern uniformly distributed in effective aperture, and each set consists of a positioning chromium cross mark, a primary vernier and a secondary vernier in horizontal and vertical directions.

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The picture of real fabricated LAOFL is shown Fig. 3 below. Macrophotograph of the sample is shown in Fig. 3(a) that outer edge and inner edge are marked up and down respectively. Typical microscopic photo of vernier pattern in X and Y directions are shown in Fig. 3(b) and (c) respectively, where primary vernier seems to have lower contrast than secondary vernier because the former is etched in fused silica and the latter is still on photoresist.

 

Fig. 3. The picture of real fabricated LAOFL. (a) Macrophotograph of fabricated LAOFL; (b) Typical microscopic photo of vernier in X direction; (c) Typical microscopic photo of vernier in Y direction.

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The diffraction efficiency (DE) of LAOFL is one of the most important parameters evaluating comprehensive performance of LAOFL and a key indicator reflecting fabrication precision. The highest theoretical DE of the 4-level lens is 81% according to Eq. (1) where η stands for diffraction efficiency, L refers to number of levels.

In real fabrication process, misalignment introduce DE decrease according to scalar diffraction theory. In Eq. (2) the complex amplitude distribution of a 4-level surface with phase deviation at specific location is marked as C, where Δφ₁ stands for phase deviation raised by the first diffractive pattern and Δφ₂ stands for phase deviation raised by the second diffractive pattern. The final η equals to C squared.

Due to variation of line width and line angle of diffractive pattern illustrated in Fig. 4, different locations correspond to different relative overlay erors under misalignment. The largest linewidth is 3.7 µm at outer edge with radius of R₁ and the smallest linewidth is 2.1 µm at inner edge with radius of R₂, while the angles between line and X direction vary from −17 ° to 17 ° with maximum value at radius of r.

 

Fig. 4. Illustration of line width and line angle variation on diffractive pattern. For each LAOFL the smallest radius of diffractive lines is 421 mm and the largest radius of diffractive lines is 750 mm with the largest angle 17 degrees between line and horizontal direction at radius of 576 mm.

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For a certain alignment error on X and Y direction, the relative overlay error is expressed in Eq. (3) below, where E_r refers to relative overlay error, Δ_X and Δ_Y refer to alignment error on X and Y respectively, α means line angle and L stands for linewidth.

We calculated the influence of alignment errors on DE distribution through numerical simulation, and the statistical results are shown in Fig. 5 below. It is found that alignment errors on Y direction basically determine DE average value and alignment errors on X direction mainly influence DE degree of divergence. In Fig. 5(a) DE average value decreases from around 80% to lower than 60% when alignment error on Y direction increases from 0 to 500 nm, and the trend line is quite linear. The increase in alignment error on X direction almost imposes no influence on DE average value when error on Y direction is above 100 nm, but the RMS value of DE increases substantially with error increment on both directions shown in Fig. 5(b) below.

To visualize the distribution of DE throughout whole diffractive pattern, supposing that alignment error on X and Y direction vary from 100 nm to 400 nm, we simulated DE distribution shown in Fig. 6(a) to (d) below. The simulation area is 350 mm long and 350 mm wide, and color bar indicating DE value ranges from 0 to 80%. When alignment error on both X and Y equals 100 nm, DE average value is 76.6% with RMS value at 1.1% as shown in (a). When alignment error on both X and Y equals 200 nm, DE average value is 72.2% with RMS value at 2.2% as shown in (b).When alignment error on both X and Y equals 300 nm, DE average value is 67.8% with RMS value at 3.2% as shown in (c).When alignment error on both X and Y equals 400 nm, DE average value is 63.3% with RMS value at 4.3% as shown in (d).It is noticeable that DE value at bottom left corner is higher than its counterpart at top right corner. This DE distribution trend is due to distribution of line width and line angle, where lines at top right corner tend to be thinner and perpendicular to misalignment direction and lines at bottom left corner tend to be thicker and parallel to misalignment direction.

 

Fig. 5. Statistical analysis of theoretical DE influenced by alignment errors. (a) Influence of Δ_Y on DEaverage value; (b) Influence of Δ_X on DE RMS value.

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Fig. 6. Simulated DE distribution at different alignment errors.(a) X/Y error both at 100 nm; (b) X/Y error both at 200 nm;(c) X/Y error both at 300 nm;(d) X/Y error both at 400 nm.

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The influence of etching depth error on DE can be found in relevant literatures and our previous work that 10% of relative etching depth error causes less than 1% of DE decrease [12,15]. In our experiments, the real average etching depth of each level is measured to be 320 ± 7 nm where relative etching depth error is less than 5% from theoretical value thus the influence of etching depth error on DE can be neglected here. Therefore, only influence of alignment error on DE distribution is concerned and analysed in following discussions.

The real alignment errors, measured from 29 uniformly distributed vernier patterns, of fabricated LAOFL samples are listed in Table 3 below. For Sample 1 the average alignment error on X direction and Y direction is around 321 nm and 359 nm respectively. For Sample 2 the average alignment error on X direction and Y direction is around 79 nm and 176 nm respectively.

Table 3. Measured alignment errors of fabricated LAOFL samples

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The DE measurement was carried out on a customized set up developed in our laboratory, the principle and method was described in our previous work [12,18]. The measured DE distribution of two fabricated LAOFL samples mentioned above is shown in Fig. 7(a) and (b) below. For Sample 1 the DE average value is 62.7% with RMS value of 6.4%, and Sample 2 presents DE average value at 75.9% and RMS value at 2.8%, indicating a similar distribution pattern with simulated results.

 

Fig. 7. Measured DE distribution of two fabricated LAOFL samples. (a) DE distribution of Sample 1; (b) DE distribution of Sample 2.

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The existance of three curved lines in the pattern area is due to lack of diffractive data where vernier patterns and positioning marks exist. Note that bottom left part is obviously higher than top right part in DE value, demonstrating that anaysis of simulated DE distribution is reasonable.By comparing the experimental results between Sample 1 and 2, we understood that decrease of alignment error on Y direction from over 350 nm to below 200 nm extensively enhanced DE average value from 60% level to over 70% level, noticing that alignment error on X direction almost remained at the same level. From fabrication point of view, alignment errors showed random behavior to some extent, resulting unstable DE distribution thus different optical performance of LAOFL between each other. The reason behind partly attributes to positioning error of LDW system caused by temperature variation and limitation of imag recognition algorithm. Besides, design and distribution of cross marks also influence alignment errors in a way that better constrast of mark edges improves image recognition accuracy and more distributed cross marks reduces accidental errors on positioning and image recognition.

3. Conclusions

In conclusion, we have presented a LAOFL with Ф350 mm effective aperture and 2 µm critical dimension fabricated through overlay etching technique by LDW system. Influence of alignment errors both horizontally and vertically on DE distribution was simulated mathematically. Certain distribution pattern of DE was observed and analysed, which is resulted from line width and angle variation. We have achieved over 75% average DE experimentally, and measured DE distribution is in accordance with theoretical simulation. This work presented the best results to our knowledge among the same field with similar aperture and critical dimension in open publications, and layed a solid foundation for future large aperture diffractive telescope development. In the following work, better design and distribution of cross marks will be investigated. Further improvement of overlay accuracy relys on higher alignment precision of laser system and better positioning marks distribution strategy.