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Abstract
We present a method for the fabrication of an arrayed one-axis scale grating for a two-probe optical linear encoder using a dual-beam interference lithography (IL) system with a compact diode laser source. We employ a multiple-exposure stitching method to form an arrayed scale grating. This allows a scale grating with small line spacing to be achieved over a large width. This stitched scale grating integrates well with a newly developed two-probe optical encoder, allowing the measurement results to be numerically connected. Since neither the gap width nor the grating phase of the two adjacent gratings must be controlled, the fabrication process is both simplified and made more robust. This flexible and cost-effective fabrication technique can benefit many precision measurement applications. Experiments are carried out to demonstrate the feasibility of this technology.
© 2017 Optical Society of America
1. Introduction
Scale gratings are a key component of optical linear encoders. The grating spanning width directly determines the measurement range of the encoders. Scale grating wider than 100 mm is required for long measurement ranges [1–5]. Interest in grating fabrication technology has been growing. Currently, scale grating fabrication is being done using engine ruling (ER), projection lithography (PL) and interference lithography (IL) [6].
For the engine ruling technique, a master grating is fabricated by a ruling engine, which removes the material of a substrate in a line-by-line fashion [7,8]. The pattern of the master grating can then be imprinted on a soft substrate to form a replica grating for mass-production. Engine ruling can offer a good surface finish and complicated grating shape, but a sophisticated motion stage is required, which is bulky and expensive. Although fabricated blazed grating patterns with periods of 0.5 – 20 μm are available,, for complicated shapes, such as square or sinusoidal the grating period is always limited to several μm due to the limitations of the cutting tool size, which is not suitable for grating interferometry applications [9]. In projection lithography (PL), a mask is required. The mask is usually prepared by using focused ion beam (FIB) etching or scanning electron beam (EB) etching. The PL process can fabricate a grating pattern with small line spacing and high precision. However, fabrication of the masks and the transformation of the pattern over a large area is time-consuming. Also, a PL system is too costly for many research groups [6].
Compared to the ER and PL techniques, the IL technique, in which two coherent beams interfere with each other and generate dark and bright fringes patterns which are exposed onto light sensitive material for pattern transformation, is more suitable for fabrication of scale gratings with equal line spacing structure over a relatively large area [10–14]. In IL technology, the grating spanning width is related to the coherence length Lc of the laser source. Thus, bulky, costly lasers with a large Lc are necessary such, as Kr + and He-Cd lasers. Although these lasers can provide an Lc up to 300 mm and theoretically ensure a grating width up to several hundred mm when a wavelength-level grating pitch is set, the grating width is always limited to be several tens of mm due to the limits of the expanded beam’s Gaussian distribution and the geometric parameters of commercial optics. To increase the grating spanning width, two kinds of stitching methods were proposed [15, 16]. In [15], a scanning beam IL technique was introduced, in which a small area of interference fringes with high uniformity was exposed on a large substrate coated by photo resist. The substrate was mounted on an X-Y air bearing stage and moved precisely. The fringes were scanned on the substrate surface to form a larger grating area. In [16], a mosaic type grating stitching technique was introduced, in which multiple exposures were carried out over the same substrate, rather than scanning. Phase continuity of the two adjacent exposure was observed and controlled by a phase locking loop (PLL). Both of these methods ensured the grating patterns continuity over a large width, which is beneficial for many applications. However, both methods require a precision motion system, a PLL unit for feedback control, and a large grating substrate, which makes the system costly, complex, and inflexible.
However, for linear encoder applications, the grating pattern does not need to be continuous over the entire grating surface. Multiple, highly uniform grating patterns can provide the same measurement performance, as shown in the newly proposed multi-probe surface encoders with mosaic gratings [17, 18]. In this method, multiple scale gratings, not multiple grating areas over a single grating substrate, are stitched to form a mosaic grating. Two probes are projected onto the two adjacent gratings, respectively. The two probes can read displacements of the mosaic grating in the same manner. When one of the two probes enters into the gap between the two gratings, the other one can offer outputs, and the measurement results of the two independent probes can be numerically connected. In this way, the optical encoder can work over the whole grating width, and neither the gap nor the phase difference between the two adjacent gratings would influence the measurement.
Thus, a novel IL technique for the fabrication of scale gratings for optical linear encoders is introduced. In this method, a cost-effective and compact laser diode rather than an expensive, bulky laser is used as a laser source. By effectively selecting the grating line spacing, the single exposure width can reach 7 mm. Stitching multiple exposures allows the arrayed scale grating to be larger than 100 mm. Especially, since these groups of the grating pattern structures are fabricated on the same grating substrate, the measurement error the optical encoder system can be reduced compared with the mosaic grating with several separate substrates that is mentioned above. Furthermore, these arrayed scale gratings can be connected and the grating spanning width can theoretically reach unlimited length. As mentioned above, neither the distance nor the phase of the gap is required to be controlled, so the fabrication system is greatly reduced and small area grating substrates can also meet the requirements. This method benefits many scale grating fabrications and applications. In this work, we introduce the principles of the two-probe encoder with arrayed scale grating and the generation of the arrayed scale grating. We then discuss the design and construction of the experiment, and fabricate and evaluate the scale gratings.
2. Principle
Figure 1 shows the setup of the linear optical encoder using an arrayed one-axis scale grating and a two-probe reading head. This transmission type arrayed one-axis scale grating includes multiple single grating areas. The gaps between two adjacent areas are δi(i = I, II, III, …, N). Two optical probes (A and B) a distance of L apart are projected onto the arrayed scale grating. According to the grating interferometry principle, incremental displacements and the direction of motion of these two probes can be obtained by [9]:
where k represents the entire range of numbers that the probe spans over the grating surface, and g is the grating pitch. IAC(90°), IAC(0°), IBC(90°), and IBC(0°) are the AC-components of the IA(90°), IA(0°), IB(90°), IB(0°) respectively, given by Eqs. (3) and (4). Either numerical programming or addition of reference arms can be used to remove the DC-components [19,20].As shown in Fig. 1(b), the two probes will pass these gaps one after the other. Thus, neither output of these two probes increases continuously with input displacement. The two outputs must be connected. It should be noted that the distance L between these two probes must be different than the grating width W to ensure that at least one probe can be projected onto the effective grating area. Assuming that the scale grating moves along the positive X-direction and Probe B passes gap I prior to Probe A, the output of this encoder can be obtained and is expressed by:
In this algorithm, δi(i = 1,3,5,…) with a small value represents the stable differences when the two probes have not yet entered or have passed the gap, which would be caused by the imperfect uniformity of these two probes. δi(i = 2,4,6,…) with a relatively large value denotes the stable differences when Probe A has passed the gap and the Probe has not yet entered the gap. For other motion conditions, the output can be obtained in the same manner by changing the subscript.
To achieve an arrayed one-axis grating structure, we propose a system based on interference lithography technology. As shown in Fig. 2, the separate grating area is fabricated by using IL. A beam from a laser source is collimated and then divided into two beams, which are then redirected by Mirrors 1 and 2. These two beams interfere with each other, pass through the window of the slit, and are exposed onto the photoresistant coated substrate. After the first exposure, the shutter is closed and the table is moved by a distance of W + δ for the next exposure. After finishing all the exposures, the substrate will be developed.
Fig. 2 Schematic of the fabrication of an array one-axis scale grating by using interference lithography for multiple exposures.
As mentioned above, neither the distance nor the phase of the gap δ have to be controlled, and no complicated phase locking loop is necessary. The single grating width W need not be large. Thus a compact and cost-effective diode laser can also work, which reduces the cost and space. What is more, all these groups of grating pattern structures are fabricated on the same substrate, the uniformity of these separate grating areas can be ensured, which allows a reduced measurement error. Compared with the setup in [17], Kimura et al, where multiple separate gratings are employed to construct a mosaic grating, the arrayed one-axis grating is less complex in alignment, which is also good for long-term operation stability. Details on the fabrication and evaluation of the arrayed one-axis scale grating are given in the following section.
3. Experiments and results
3.1 Theory
This arrayed type scale grating is composed of multiple single grating areas. Both the quality of a single grating area and the motion accuracy of the table determine the grating quality, which finally determines the measurement accuracy. The quality of the single grating area is related to the uniform grating pattern width that is determined by the quality of the laser source, including the coherence length and the beam profile. The stitching precision is determined by the accuracy of the moving stages, which can be previously calibrated and compensated for numerically.
Figure 3 illustrates the schematic of the interference lithography. Two coherent laser beams with a wavelength of λ spatially interfere with each other and generate bright and dark interference fringes with a pitch g, which is then exposed onto a photoresistant coated substrate, where the interference pattern is transferred. g can be expressed by:
When these two beam are symmetrically incident, that is, θ1 = θ2 = θ, the equation can be rewritten as
The width of a single grating area W also matters. W is related to the coherence length Lc, the aperture of the wavefront D, and geometric parameters of the optics [21]
The motion stage is employed to move the substrate for multiple exposures. The motion error of the stage influences the grating performance [22]. There are six types of errors, including three translational errors (Δx, Δy and Δz) and three rotational errors (θx, θy and θz), like those shown in Fig. 4. Of these six errors, Δx will influence the gap between two adjacent exposure areas. As mentioned above, this type of optical linear encoder is unaffected by the gap, and this error can be ignored. Because the grating width in the Z-direction is about four times of the diameter of the laser point, a slight error will still ensure that the probes are projected onto the grating surface, and Δz can also be ignored. For Δy, as illustrated in [11], Wolferen et al, when the two beam are symmetrically incident, the grating patterns are stable and kept constant along the normal direction (the Y-direction in this work), thus, a slight error in y-direction will not influence the grating shape uniformity. Error θy is due to the grating lines and the edge of the grating substrate not being parallel. Since the fabricated arrayed one-axis grating is adjusted when it is integrated into the optical linear encoder, the line and the edge being non-parallel need not be considered here The errors θx and θz influence the grating shape uniformity and grating period, respectively, which must be precisely aligned. In our work, a two-axis auto-collimation system with sub-arcsecond resolution was used to calibrate the errors θx and θz.
3.2 Grating width and diffraction efficiency calculation
Coherence length is measured using an interference setup, as shown in Fig. 5(a). The collimated laser beam passes through an aperture. Figure 6 shows the profile of the collimated beam. The target mirror was mounted on the linear stage and moved back and forth. The interference signal was detected and illustrated by Fig. 5(c). An enlarged area shows that the laser diode can provide an Lc of 0.41 mm. The grating width can then be calculated using Eq. (8). When the grating period is set to 2.5 μm, the uniform grating pattern can span about 2.5 mm when a 405 nm laser diode is used.
Fig. 5 Schematic of the Lc measurement layout (a), experimental setup (b), measured results (c), and details of an envelope (d).
The diffraction efficiency calculation was carried out to determine the grating shape. Figure 7 shows the usage stage of the diffraction grating and the calculated results of the first order diffraction efficiency. As with the optical encoder, a circularly polarized laser beam with a wavelength of 660 nm is projected onto the grating along its normal direction. The grating shape is characterized by the groove depth d and its duty cycle, denoted by Wl/g, where Wl is the linewidth and g is the grating period. The positive and negative first order diffraction beams used to generate the interference signal were calculated. Figure 7(b) shows the result. We find that the highest diffraction efficiency, 35%, can be obtained with a duty cycle of about 0.45 with a depth of 0.5 μm, and a grating pitch of 2.5 μm. Since the first order diffraction beams are not the only ones present, other orders of diffraction beams remove some amount energy. We note that the diffraction beams not used for measurement are blocked to avoid influencing the result. The simulation result is used as a reference for determining the grating fabrication process.
3.3 Experiments and results
Figure 8 illustrates the experimental setup. The simulated optical layout shown in Fig. 8(a) verifies that this system is greatly simplified. It has a footprint of only 200 mm ☓ 400 mm. The details of the configuration of slit and glass substrate are shown in Fig. 8(b). The glass substrate is mounted on a precise motorized linear stage (M-112.1DG, PI Corp.).
Fig. 8 Fabrication system: (a) simulated optical layout, (b) experimental setup, (c) details of the slit mount.
Experimental conditions were determined by matching the exposure energy of the interference field and the exposure thickness of the photoresist (Shipley S1805) [23]. The power of the expanded beam of the 405 nm laser diode is about 9 mW/cm2. The grating pitch was designed to be 2500 nm, and the angle of the two mirrors was aligned according to this value. The depth and duty cycle were set to be 400 nm and 0.5, respectively, for the highest diffraction efficiency. The exposure time and development time were determined to be 20s and 8s, respectively. Figure 9 shows the fabricated grating without a slit and its microstructure as measured by an atomic force microscope (AFM). The AFM images illustrate that the grating pattern is very uniform. The average grating constant and depth are 2502 nm and 405 nm, respectively, which are consistent with the design values of 2500 nm and 400 nm.
Figure 10 shows the diffraction efficiency of the fabricated grating. A circularly polarized beam was perpendicularly incident to the grating, which is consistent with that in the linear encoder. The positive first-order diffraction efficiency was tested. The incident beam for efficiency testing is of a diameter of 1 mm, similar with that in the optical encoder. Figure 10(b) shows the sectional shape of the incident beam. We see that the beam within a diameter 1 mm is highly uniform, with an intensity difference of less than 10%. Figure 10(c) shows the testing setup. The linearly polarized beam is divided by a PBS and the P-polarization beam passes through the PBS. The p-polarized beam is then modulated to be circularly polarized by a quarter-wave-plate (QWP), whose fast axis is set to be 45° off of the P-polarization direction. An observation plate is placed away from the grating and gives the first-order diffraction beam position. The grating is moved by a manual stage with intervals of 0.2 mm. The results are shown in Fig. 10(d). It can be seen from Fig. 10(d) that the effective grating area can be fabricated on a width of 6 mm. The highest diffraction efficiency within this area is about 36%, which is consistent with the simulated value, as shown in Fig. 5(b). However, the diffraction efficiency gradually reduces along the two sides. The main reason for this is the short Lc. According to the previous calculation, the width can reach 2.5 mm at an efficiency uniformity of about 80%. This result indicates that, when the efficiency is 80% of the maximum, that is, 28%, the width is about 2.3 mm, which is consistent with the design value.
Fig. 10 Diffraction efficiency measurement: (a) schematic of the measurement setup, (b) profile of the incident beam, (c) experimental setup for the efficiency measurement, (d) measurement result.
According to previous research, the linear encoder can identify the interference signal effectively when the diffraction efficiency is larger than 10%. In that case, the width can expand to be larger than 3 mm. However, efficiency uniformity is significant with our electronics design. Thus, for the arrayed grating pattern, the single grating area was determined to be 2 mm. A slit as shown in Fig. 7 is used to control the single grating width. The motorized stage (PI-Mercy, 112-2CD) moves the grating substrate. The distance between the slit and the substrate is about 0.2 mm and the edges were previously aligned using an auto-collimation system, as mentioned above. An interval of 0.3 mm between two grating exposures is determined to reduce the diffraction effect.
Figure 11 shows the picture and results of the arrayed one-axis grating. The exposure areas are preliminarily set to be 11 for observation of the arrayed grating. A similar setup is used to evaluate the efficiency and Fig. 11(b) shows the result. It can be seen that the diffraction efficiency is almost uniform over the whole width. Grating period evaluation was also carried out both by coarse observation of the diffracted light positions on the plate and fine measurement with an AFM. Positions of both the + 1 and −1 order diffracted light beams from different grating areas highly coincide. The improved grating uniformity verifies the advantage of the proposed method, groups of grating patter structures on the same grating substrate, over the conventional mosaic grating with several grating substrates. For fine evaluation of period values, each single exposure area is denoted by Ei (i = 1, 2, 3,……,11), and three points are measured by an the AFM. These averaged grating periods are used to identify the grating period. From these 33 averaged grating period values, the final grating period is 2502.4 nm, consistent with the designed values, 2500 nm, as shown in Fig. (c). The grating pitch deviation is smaller than 1%.
4. Conclusions
In this paper, we present a novel interference lithography system to fabricate a scale grating for a two-probe linear encoder. In this system, a multiple exposure stitching mechanism was designed and constructed to form an arrayed type scale grating over a relatively wide spanning range. Since neither the distance nor the phase connection of the gap between each two exposures needs be controlled, the fabrication process is greatly simplified. The system employed a compact 405 nm laser diode as the source, enabling a compact and accessible optical layout. A 2500 nm periodic grating with a width of up to 30 mm was achieved. The diffraction efficiency uniformity was as high as 80%. The grating period is highly consistent with the designed value and has a deviation of less than 1%.
Funding
National Natural Science Foundation of China (51427805); China Postdoctoral Science Foundation Funded Project (2016T90089), Shenzhen Science and Technology Plan (JSGG20150512162908714); National Key Research and Development Program (2016YFF0100704); Shenzhen Fundamental Research Program (JCYJ20160301153417873).
References and links
1. W. Gao, W. Kim, H. Bosse, H. Haitjema, Y. Chen, X. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann. 64(2), 773–796 (2015). [CrossRef]
2. Heidenhain, Sealed Linear Encoder LC catalog. (accessed April, 2017).
3. Renishaw, Optical Encoder catalog. (accessed April, 2017).
4. Magnescale, Laser scale, Linear scale catalog. (accessed April, 2017).
5. W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor driven planar motion stage integrated with an XYZ surface encoder for precision positioning,” Precis. Eng. 28(3), 329–337 (2004). [CrossRef]
6. C. J. Richard, Introduction to Microelectronic fabrication: Volume 5 of modular series on solid state devices, Prentice Hall, 2nd Ed., pp. 110–118 (2002).
7. Nikon, Ruling Engine No. 2, Recollections-Long-selling products (accessed April, 2017).
8. W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003). [CrossRef]
9. A. Teimel, “Technology and Applications of Grating Interferometers in High-precision Measurement,” Precis. Eng. 14(3), 147–154 (1992). [CrossRef]
10. S. R. J. Brueck, “Optical and Interferometric Lithography-Nanotechnology Enablers,” Proc. IEEE 93(10), 1704–1721 (2005). [CrossRef]
11. H. Wolferen, L. Abelmann, and T. C. Hennessy, Laser interference lithography (Lithography Principles Processes and Materials), Chap. 5 (2011).
12. X. Li, W. Gao, Y. Shimizu, and S. Ito, “A two-axis Lloyd’s mirror interferometer for fabrication of two dimensional diffraction gratings,” CIRP Ann. 63(1), 461–464 (2014). [CrossRef]
13. Q. Zhou, X. Li, K. Ni, R. Tian, and J. Pang, “Holographic fabrication of large-constant concave gratings for wide-range flat-field spectrometers with the addition of a concave lens,” Opt. Express 24(2), 732–738 (2016). [CrossRef] [PubMed]
14. X. Li, K. Ni, Q. Zhou, X. Wang, R. Tian, and J. Pang, “Fabrication of a concave grating with a large line spacing via a novel dual-beam interference lithography method,” Opt. Express 24(10), 10759–10766 (2016). [CrossRef] [PubMed]
15. P. T. Konkola, Design and analysis of a scanning beam interference lithography system for patterning gratings with nanometer-level distortions (Doctoral dissertation, Massachusetts Institute of Technology) (2003).
16. L. Shi, L. Zeng, and L. Li, “Fabrication of optical mosaic gratings with phase and attitude adjustments employing latent fringes and a red-wavelength dual-beam interferometer,” Opt. Express 17(24), 21530–21543 (2009). [CrossRef] [PubMed]
17. A. Kimura, K. Hosono, W. Kim, Y. Shimizu, W. Gao, and L. Zeng, “A two-degree-of-freedom linear encoder with mosaic scale gratings,” Int. J. Nanomanuf. 7(1), 73–91 (2011). [CrossRef]
18. Y. Shimizu, T. Ito, X. Li, W. Kim, and W. Gao, “Design and testing of a four-probe optical sensor head for three-axis surface encoder with a mosaic scale grating,” Meas. Sci. Technol. 25(9), 094002 (2014). [CrossRef]
19. W. Gao and A. Kimura, “A three-axis displacement sensor with nanometric resolution,” CIRP Ann. 56(1), 529–532 (2007). [CrossRef]
20. A. Kimura, W. Gao, W. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A sub-nanometric three-axis surface encoder with short-period planar gratings for stage motion measurement,” Precis. Eng. 36(5), 576–585 (2012). [CrossRef]
21. X. Li, Y. Shimizu, S. Ito, and W. Gao, “Fabrication of scale gratings for surface encoders by using laser interference lithography with 405 nm laser diodes,” Int. J. Precis. Eng. Manuf. 14(11), 1979–1988 (2013). [CrossRef]
22. Y. Shimizu, R. Aihara, Z. Ren, Y. L. Chen, S. Ito, and W. Gao, “Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd’s mirror interferometer,” Opt. Express 24(24), 27521–27535 (2016). [CrossRef] [PubMed]
23. http://www.microchem.com/PDFs_Dow/S1800.pdf (accessed April, 2017).
