1. Introduction
Planar encoders play a key role in precision positioning of linear stages due to their high resolution, high robustness, and relatively low cost [
1,
2,
3,
4,
5,
6,
7,
8,
9]. The key component in the planar encoder is a two-dimensional (2D) planar scale grating, on which typically surface relief square holes or sinusoidal hills with a period spacing from submicron to several microns are arrayed along two orthogonal directions.
Laser interference lithography (LIL), engine machining, and imprinting are three typical methods for fabrication of the scale grating. Compared with engine machining or imprinting, LIL is more convenient and cost-effective because only a coherent laser source is required and neither sophisticated precision positioning system nor expensive photolithography equipment and mask preparation are required. For fabrication of a 2D planar grating, according to the exposure times, the LIL process can be separated into two categories, double exposure and single exposure. For the two-beam two-exposure, it requires twice exposure procedures and the second time exposure requires rotation of the substrate by 90 degrees [
5,
10]. The exposure can be based on an amplitude-division type two-beam LIL, called two beam two exposures (TBTE) or a wavefront-division type Lloyd’s mirror type LIL, called one beam two exposures (OBTE) [
11]. TBTE is good at fabrication of gratings with a relatively large area up to 100 mm × 100 mm, while OBTE can be easily handled with a relatively simple and stable optical system. However, a big challenge existing in the method of the two-exposure process is that the grating structures generated in the first exposure will be influenced by the background light in the second exposure. Thus the depths of the grating structures will be different in two orthogonal directions. As a result, diffraction efficiencies of both the negative and positive diffraction beams will not be consistent. This is a critical problem for the encoder system since it directly affects the accuracy and the detecting limit of the interference signals. Therefore, efforts for solving this problem using a single exposure for 2D scale grating have been done these years. There are two trends for this motivation, multibeam LIL and one beam LIL. Multibeam LIL includes, but is not limited to, triple-beam and quadruple-beam interference technique. This technology can achieve the goal of 2D grating patterns with a single exposure. Some researchers invented a novel nanofabrication technique, called four-beam interference lithography, by using a two-dimensional grating [
12]. Nevertheless, it cannot be neglected that the multibeam interference lithography has complicated optical structure easily to be disturbed by external environment. Furthermore, the optical path difference (OPD) is also difficult to be manipulated.
In contrast, one beam LIL, represented by two-axis Lloyd’s mirror interferometer and a corner-like reflector interferometer, allows fabricating a crossed 2D grating with a single exposure [
13,
14,
15,
16,
17,
18]. For one beam LIL, one more proposal called the two-axis Lloyd’s mirror interferometer with polarization modulation technique, proposed in 2014, has the advantages of large grating area, easy handling, and stable grating patterns [
13]. However, optimization of the theoretical inclination in grating shape requires sophisticated in situ detection system for exposure and development. The inclination will influence the diffraction efficiency in a certain degree when it is directly used as a photoresist grating, though this influence might be reduced when a further etched process. On the other hand, the corner-like reflector interferometer, also called orthogonal type two-axis Lloyd’s mirror interferometer, also proposed in 2014, has the advantages on grating shape in depth direction, although the complicated interference patterns on the grating substrate require deep modification for application as a 2D scale grating [
14]. For modification of the grating patterns, Yuki and Chen took polarization modulation technique and results verified this technology has a great potential for 2D scale grating fabrication. But it should be noted that, introduction of the polarization modulation both reduce the grating area and bring a new challenge in the system stability [
16,
17,
18].
Thus, investigation of the orthogonal type two-axis Lloyd’s mirror interferometer based LIL without polarization modulation for a large grating area is carried out in this research. We constructed an orthogonal type two-axis Lloyd’s mirror interferometer and fabricated 2D scale grating under different polarization state. Design details, construction, experimental setup, and evaluation are presented in this paper.
3. Experiment and Results
According to the abovementioned theories about polarization modulation, we used half-wavelength plates to realize the optimal combination of initial polarization status. We used a linear polarizer to measure the initial orientation of polarization of the laser source, and use a half-wavelength plate to modulate it with 0 degrees; we marked it as s. We employed two HWPS, which is half-wavelength plates, to alter the orientation of polarization of beams 2 and 3. However, the basic requirement is that optical elements after the collimation lens are as few as possible, to keep a good wavefront and a relatively large effective exposure area. To a certain extent, if the degree of orthogonality is small enough as mentioned above, we can ignore the interference between beam 2 and 3. Therefore, experiments with half-wavelength plates were carried out to verify the effects of polarization modulation. Meanwhile, for the purpose of obtaining maximum fabrication area and simplification of the optical system, we conducted a bold attempt that abandoned employing the two half-wavelength plates. It is worth noting that the reflected beam had different polarization status with the change of incident angle according to Fresnel’s theories. For the sake of simplification, all the experiments were carried out under the constant condition of incident angle
θ = 71.8°. The fabricated 2D gratings could have the same grating pitch at two orthogonal directions (g
12 = g
13 = 1 μm).
Figure 5 shows the fabricated gratings without and with polarization, i.e., under polarization state of (s, s, s) and (s, −33.5°, 33.5°), respectively. It can be seen that the area of 2D grating fabricated without polarization status, i.e., initial polarization of the laser source (s, s, s) is larger than the modulated polarization status (s, −33.5°, 33.5°). The area of the 2D grating fabricated with the initial polarization status (s, s, s) and (s, −33.5°, 33.5°) are 25 mm × 25 mm and 10 mm × 10 mm, respectively. The enlarged grating area will be beneficial for grating interferometry application.
The fabricated grating shapes were then evaluated by using an atomic force microscope (AFM). The AFM (Bruker Dimension Icon) worked on a peak force tapping mode with a height sensor data density of 128 × 128 of an AFM image with a size of 10 μm × 10 μm. The grating surface material is photoresist, and AFM tip material is SiC and the shape aspect ratio is 1. The peak force setpoint and amplitude are 0.05 and 300 nm, respectively.
Figure 6a,b show the images of the fabricated 2D gratings under the initial polarization status of (s, s, s) and (s, −33.5°, 33.5°), respectively. First of all, it can be seen that the grating shapes under these two polarization status are all regularly uniform, a near pillar shape, and no obvious elliptical shape as illustrated in [
13] occurred. More than ten samples have been fabricated and results were highly consistent. Furthermore, the grating periods were evaluated as shown in
Figure 6, B-B’. The grating periods are all consistent with the designed value of 1 μm. It should be noted that, the period consistence is more importance than the absolute grating period value. From the A-A’ sectional data, we can see that the grating depth are about 500 nm, (s, s, s) is slightly lower than that of the (s, −33.5°, 33.5°), which are also consistent with the grating shape demand.
From
Figure 5 and
Figure 6, it can be concluded that the grating shape and area of these two polarization status are all consistent with the preliminarily designed value. However, before it can be employed to the grating interferometry system, grating diffraction efficiency that influencing the inference signals are required to be evaluated. An experimental setup, as shown in
Figure 7a, was constructed and the measurement point distribution is shown in
Figure 7b. As for the real interferometry system, the incident beam was polarized to be circular and pass through the fabricated grating. After the diffraction of the grating, four first-order diffracted lights appear on the observation screen. The power of each diffracted light can be read by the power meter, which was then divided by the output power of the laser source, thus we can get the diffraction efficiency. The measurement results were summarized by
Table 1 and
Table 2. Each diffraction efficiency is larger than 6%, and all the sum efficiency of all the first diffraction beam are larger than 50%. For the uniformity of the +1 and the −1 diffraction beams along the X- and Y-directions, the initial polarization is better than the modulated polarization, this may be because the intensity was redistributed by the two QWPs. The diffraction difference between the X- and the Y-direction is mainly due to the unideal intensity uniformity within the plane wavefront.
For comparison, we conducted experiments at the incident angle
θ of 60° and 85° without polarization modulation, i.e., (s, s, s), corresponding to the grating periods of 625 nm and 3586 nm, respectively. Under such polarization and incident angle, the
γ23 is larger than that of
θ of 71.8°.
Figure 8 shows the AFM images. This result reveals that the groove of 2D gratings deviated from square and was more inclined to elliptical shape, which cannot meet the interferometry application. Therefore, it is necessary for fabricating 2D grating to operate HWPs at 60° and 85°, as well as other angles. The specific values of modulation need to be calculated based on the three-dimensional polarization ray-tracing calculus [
20].
4. Discussion and Conclusions
We have designed and assembled the orthogonal type two-axis Lloyd’s mirror interferometer as the exposure system. Apart from removing of the unexpected beams 4 and 5, the grating shape uniformity is theoretically evaluated in terms of an undesired interference between beams 2 and 3 by an index of degree of orthogonality.
Experimental results reveal that the difference is not significant for the fabricated 2D gratings under the original polarization status (s, s, s) and the optimal combination polarization status (s, −33.5°, 33.5°) under a specific incident angle corresponding to a 1 μm grating period in both X and Y directions. The degree of orthogonality of beams 2 and 3 that fall in the same amounts level in the above two cases is the main reason. The degree of orthogonality of beam 2 and 3 are 0.07 and 0.048, respectively. The fabrication result under polarization was consistent with that shown in previous research, where similar initial polarization states (s, −45°, 45°) were employed [
18]. However, the grating area would be greatly enlarged without polarization as shown in
Figure 5a compared with all the simulations and experiments shown in [
18]; the optical system complexity was greatly reduced compared with the present technique, TBTE [
5,
10].
It is also confirmed that, under the condition of incident linear polarized light, the combination of initial polarization status of beams 2 and 3 corresponding to orthogonal polarization state in the orthogonal two-axis Lloyd’s interferometer does not exist. The microstructures of the fabricated gratings are all consistent with the designed value. However the diffraction efficiency uniformity, both in a relative large area and the four diffraction beams on a point, require improvement.
In summary, polarization modulation technique of the LIL system can bring a good grating shape despite grating area downsizing, while, without polarization, i.e., usage of the initial polarization under some specific angle that can reach a similar grating performance, with a reduced system complexity and an enlarge grating area.