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A reflective-type photonic displacement sensor has been proposed and realized by taking advantage of a compact optical sensing head that incorporates a micro-optic beam shaper in conjunction with a rotary scale. The miniature beam shaper, which includes a pair of aspheric lenses, plays the role of optimally focusing a light beam emitted by a VCSEL source onto a rotary scale by utilizing efficient collimating optics. The focused beam is selectively reflected by a periodic grating pattern relevant to the scale; the beam then arrives at the photodetector (PD) receiver. Hence, an arbitrary displacement, encoded by the scale, could readily translate into an output signal available from the receiver. The proposed sensor was thoroughly designed through ray tracing based simulations and then analyzed in terms of the alignment tolerance for the VCSEL and code scale. The slim beam shaper was cost effectively constructed using plastic injection molding, and it was precisely integrated with the VCSEL and PD in a passive alignment manner, in order to complete the optical sensing head. In order to construct the displacement sensor, a code-wheel type scale containing alternate patterns of high- and low-reflection, was integrated with the optical head. The sensor was primarily characterized with respect to the evolution of generated beams for single-mode (SM) and multi-mode (MM) VCSELs, taking into consideration that the modulation depth of the output signal is elevated with decreasing focused beam size. For an embodied displacement sensor based on an SM VCSEL, leading to a focused beam spot of ~30 μm, a well-defined output with a modulation depth of 7% was obtained in response to the displacement of the rotary scale engraved with a grating of 10-μm pitch. The linear and angular resolutions were accordingly estimated to be better than 5 μm and 0.02°, respectively.
© 2014 Optical Society of America
1. Introduction
A displacement sensor, popularly known as an encoder, is considered to be an indispensable tool, preferably used for monitoring and tracking the positional and/or angular movement of an object [1, 2]. It has been applied in a vast range of fields, such as printing, machine control, factory automation, robot control, aerospace applications, bio sensing, etc [3–8]. Compared with its electrical counterparts, the photonic version of the displacement sensor is particularly advantageous in terms of its enhanced sensitivity, large dynamic range, light weight, and immunity to electromagnetic interference [9]. Such a photonic sensor, which comprises an optical sensing head, a scale, and a signal processing unit, is critically subject to two features, its footprint and its manufacturing cost [10, 11]. The type of sensor is classified as either reflective or transmissive, depending on the configuration of the light source, scale, and photodetector (PD) based receiver [12–20]. Due to its slim compact structure, the reflective-type device is distinctly preferred over the bulky transmission-type device. In terms of the properties of the light beam concerned, the case based on a collimated beam is known to inevitably require a special custom-designed array of PDs, unlike the case based on a focused beam [10, 11]. To date, the reflection type sensor with a code scale of 0.512-μm pitch has been reported to give the best resolution of 128 nm [7]. However, the sensor is considered to be practically unsuitable for consumer electronics products, owing to its critical reliance on the code scale of extremely small pitch and the complicated PD array in conjunction with the index grating.
In this paper, we aimed to develop a compact reflective-type displacement sensor, incorporating a rotary scale in conjunction with an optical sensing head, which takes advantage of a micro-optic beam shaper. For the proposed compact reflective displacement sensor, the light source is desired to allow for convenient integration, low cost, a small beam divergence, and a small aperture. In this respect, a VCSEL is believed to be the best candidate as the light source due to its well-known salient features [22]. The suggested beam shaper, including a pair of collimating and focusing aspheric lenses, has been introduced to appropriately modify the profile of incident light beam emerging from the VCSEL source and alter the beam’s travel path. It should be noted that the beam shaper could be efficiently created by plastic injection molding technique. As for the operation of the sensor, light generated by a VCSEL source is focused on the scale; it subsequently reflects off the surface of a rotary scale, which is engraved with alternately reflecting grating patterns, so as to arrive at the PD. Both single-mode (SM) and multi-mode (MM) VCSELs were individually assessed, in order to probe into the influence of their beam divergence and aperture on the transfer characteristics of the displacement sensor. The sensor was designed and analyzed by conducting ray tracing based simulations; it was then practically assembled through a fully passive alignment scheme, utilizing an alignment guide. The dependence of the sensor performance on the beam patterns was carefully examined in terms of a rotary scale, alongside the feasibility of the micro-optic beam shaper. We characterized the embodied sensor in terms of the modulation depth of the obtained output signals and ultimately the linear and angular resolutions.
2. Proposed reflective photonic displacement sensor and its design
The proposed reflective displacement sensor, as illustrated in Fig. 1, incorporates an optical sensing head in combination with a rotary scale conveying actual displacement. The optical head is made up of a VCSEL serving as a light source, a PD acting as a receiver, and a slim micro-optic beam shaper, which is used to modify the characteristics of incident beam and adequately route its path simultaneously. The compact and simple beam shaper contains a collimating lens and a focusing lens at the bottom and top sides, respectively, of a thin plastic substrate; the light emitted by the VCSEL is initially collimated by the lower aspheric lens and subsequently is optimally focused on the scale through one portion of the upper aspheric lens. The focused beam, reflecting off the scale, is appropriately directed toward the PD via the other portion of the upper lens. The rotary scale resembles a code wheel, which is alternately engraved with high- and anti-reflecting patterns with a periodicity of Λ. The output signal from the PD is presumed to be predominantly determined by the amount of light bouncing off the rotating scale.
The operation of the reflective displacement sensor can be explained by the propagation of optical rays, as described in Fig. 2(a). In order to facilitate the processing of output signals available from the PD, the modulation depth, which is defined as the ratio of the minimum to maximum levels of the signals, should be increased. For a sensor based on a focused beam, the modulation depth may be elevated by diminishing the beam spot. In this work, the collimating optics, established by the two aspheric lenses related to the beam shaper, satisfactorily focus the beam emerging from the VCSEL. The VCSEL beam is first collimated by the small aspheric lens on the lower side of the beam shaper, and is then focused by the left-hand portion of the focusing lens on the upper side, thereby forming a minimum spot on top of the grating patterns of the code wheel. The beam, stemming from the reflecting patterns of the scale, is accepted by the right-hand portion of the upper focusing lens to ultimately reach the PD. Therefore, a compact reflective displacement sensor could be efficiently accomplished, where both the light source and PD are placed on the same platform. Figure 2(b) presents the PD output with the displacement of the scale for different spot sizes of the focused beam, which is intended to affect the modulation of the output signal. Here, the beam is assumed to have a uniform irradiance distribution. The modulation depth is ideally 100% with the diameter D of the focused beam equivalent to Λ/2. However, the depth reduced to ~33% when the focused spot broadened to D = 3Λ/2. It was confirmed that the modulation depth is inversely proportional to the focused beam spot.
Fig. 2 Operation of the proposed displacement sensor (a) Propagation of light beams (b) PD output depending on the size of the focused beam spot.
The collimating and focusing lenses, constituting the beam shaper, have been designed by resorting to a ray tracing based tool, Code V, taking into account, where appropriate, the dimension and position of the VCSEL, PD and rotary scale. Major structural parameters relevant to the sensor are listed in Fig. 3.Here the VCSEL is considered to give a beam divergence of 30° in full angle, and the lens is made in a polycarbonate substrate with n = 1.586 at λ = 850 nm. The distance of the collimating lens from the VCSEL was chosen to be 0.7 mm. The collimating lens had the following aspheric structural parameters: a height of 300 μm, a radius of 0.40 mm, a conic constant of −2.47, and 4th, 6th and 8th coefficients of 0.19x10−5, −0.15x10−4 and 0.60x10−4, respectively. Also, the focusing lens was designed to have aspheric parameters, such as a height of 570 μm, a radius of 0.85 mm, a conic constant of −2.47, and 4th, 6th and 8th coefficients of −0.74x10−8, 0.62x10−8, and −0.21x10−8, respectively. In view of the practical mounting of the VCSEL and PD, the gap between them was determined to be 1.4 mm. The separation between the focusing lens and scale was fixed at 1.5 mm, so that the beam could be optimally focused on top of the scale, exactly along the central axis of the upper lens of the beam shaper. The offset between the beam shaper and the code scale was chosen to be as small as possible, in view of the sensor application to the aforementioned portable consumer electronics, including digital cameras and camcoders. The offset was ultimately determined to stably provide distinct signal outputs available from the sensor, leading to a target resolution of 5 μm. Next, the potential stray light coupling to the PD, induced by the Fresnel reflection at the surface of the beam shaper, was theoretically observed to be extremely weak, only accounting for <0.04% of the optical power of the VCSEL source.
A ray optic simulation tool, LightTools, has been primarily exploited to analyze the transfer characteristics of the proposed sensor device, by creating the light source by virtue of the Gaussian beam modeling. We first attempted to explore the effect of the focused beam diameter D on the relationship between the optical output of the sensor and the displacement of the scale. The scale was consistently treated as a grating with a pitch of 10 μm and a duty of 50%. In an attempt to enhance the accuracy of the simulations, we previously assessed SM and MM VCSELs from Oclaro with respect to the aperture size and divergence. Figure 4 reveals the propagation of the beam originating from the two VCSELs, as observed at distances of z = 0, 0.5, 1.0, and 1.5 mm. The SM VCSEL was observed to provide a beam with an aperture of 7 μm in dia. and a full-divergence of 20°, whereas the MM case exhibited a beam with a 15-μm aperture and a 30° divergence. As plotted in Fig. 5(a), for various focused spots ranging from 10 to 70 μm, the output was observed as a function of the displacement in the scale. As predicted, the modulation depth declined with increasing focused beam spot. The modulation depth progressively decreased from ~32% to 3% as the spot D was enlarged from 10 to 70 μm, as shown in Fig. 5(b). The focused beams of the SM and MM VCSELs were as small as 29 and 63 μm, respectively. Consequently, the modulation depth was estimated to be ~9% and 4% for the SM and MM cases, respectively, as shown in Fig. 5(b).
Fig. 5 (a) Optical response of the sensor as a function of the displacement for different focused beams (b) Modulation depth with the focused beam diameter for the SM and MM VCSELs.
We attempted to assess the proposed device, which is to practically act as a displacement sensor, in terms of the alignment tolerance mainly pertaining to the VCSEL and code scale. Taking into account that the sensor performance is chiefly determined by the size of the focused beam, the sensor was assumed to operate properly so as to offer the desired resolution of 10 μm with a satisfactory level of signal modulation depth, as long as the focused beam hardly exceeds 70 μm, as implied from the Fig. 5(b). The focused beam diameters with the VCSEL displacement along the x-, y-, and z-directions and with the code scale displacement along the vertical z-direction are shown in Fig. 6(a) and (b), respectively. The alignment tolerance was determined with reference to the aforementioned beam criteria of 70 μm. For the case of the SM VCSEL leading to enhanced modulation depths, the VCSEL tolerance was observed to be over 30 μm in all directions while the code scale tolerance was also over 30 μm along the z-direction. Consequently, the proposed sensor was proved to be highly alignment tolerant to enable practical passive assembly, as anticipated.
3. Implementation of the proposed displacement sensor and its characterization
It is worth noting that the proposed displacement sensor could be cost effectively embodied by a pick-and-place scheme while utilizing an alignment guide, enabling a fully passive assembly. As described in Fig. 7, the alignment guide was initially installed on the printed circuit board (PCB) via the board’s predefined holes. The VCSEL and PD chips were mounted on the PCB with reference to the line connecting the two holes embedded in the alignment guide. The assembly of the sensor was finished by permanently appending the beam shaper to the guide.
For the manufactured displacement sensor, the optical sensing head, with dimensions of 8x7.4x2.1 mm3, is displayed in Fig. 8(a).The beam shaper and alignment guide were produced in polycarbonate and polyimide, respectively, through the injection molding technique. Both SM and MM VCSELs from Oclaro were employed for the light source, while a silicon PIN PD with an active area of 0.54x0.54 mm2 was used for the receiver. The VCSEL and PD were first verified to be precisely mounted on the PCB within a tolerance of 10 μm. Figure 8(b) presents details on the built micro-optic beam shaper, having dimensions of 8x3.4x0.5 mm3. The fabricated collimating and focusing lenses were visually inspected to ensure agreements with their original design. The measured distance between the focusing lens and VCSEL was 0.72 mm, resulting in a slight deviation of 20 μm compared with the design; this could be easily compensated for by adjusting the position of the scale.
Fig. 8 (a) Completed optical sensing head with the beam shaper aligned with the VCSEL and PD (b) Micro-optic beam shaper consisting of the collimating and focusing lenses.
To evaluate the proposed displacement sensor, as shown in Fig. 9, the prepared optical sensing head was accurately aligned with a motor-driven rotary scale, mimicking a code wheel. The optical head was mounted on a precision stage, while the scale was connected to a holder, rotating at varying speeds. The rotary scale, engraved with a grating with a pitch of 10 μm, was considered to cause substantially selective reflectance of beyond and below ~95% and 5%. For the rotary scale, the center of the grating patterns is located along a circle with a radius of ~13.5 mm, indicating that a linear displacement corresponding to a single pitch of 10 μm is almost equivalent to an angular displacement of 0.04°. After ensuring that the gap between the focusing lens belonging to the optical head and the rotary scale was adjusted to 1.5 mm as intended, the output signal from the PD was monitored with the motor turned on.
Fig. 9 Test setup for the reflective-type displacement sensor based on a rotary scale resembling a code wheel.
We attempted to investigate the performance of the displacement sensor, chiefly in terms of the influence of the miniature beam shaper on the propagating beams; we then investigated the PD output as a function of the displacement of the rotary scale. In order to scrutinize the influence of the focused beam on the sensor performance, as shown in Fig. 10(a), the beam was first characterized immediately after the focusing lens, in terms of the distance along the z’ direction at 0.5 mm increments. The point where the center of the collimated beam hits the surface of the lens is designated as the origin, with a coordinate of (0, 0, 0). It should be noted that the z’ direction, representing the actual propagation of the focused beam, is expected to make an angle of 22° with the z-axis. The beam profile was checked along the z’ direction using a CCD camera linked to a zoom lens. For the cases of SM and MM VCSELs, a focused beam was obtained at a distance of z’ = 1.7 mm, which differs from the predicted distance of 1.85 mm due to a slight discrepancy of 20 μm in the VCSEL-to-focusing lens gap. The elliptic pattern of the beam was initially elongated along the y-axis on the lens surface. However, beyond the focusing point the pattern has been rotated so the stretched major axis is parallel to the x-axis, as anticipated. The 1/e2 spot size D of the focused beam was found to be ~30 and 70 μm for the SM and MM VCSELs, respectively, as plotted in Fig. 10(b).
Fig. 10 (a) Evolution of the beam tailored by the focusing lens (b) Irradiance profile of the focused beam.
Lastly, we undertook to examine the transfer characteristics of the proposed displacement sensor. The output signal from the PD was captured when the focused light beam, stemming from either the SM or MM VCSEL, was periodically reflected due to the rotary scale in motion. As plotted in Fig. 11, the output waveform continuously varied in accordance with the displacement of the grating patterns of the scale. The acquired output signal exhibited a period of 10 μm, in accordance with the pitch of the grating. The demonstrated modulation depth was about 7% and 3% for the SM and MM cases, respectively, signifying a good correlation between theoretical and experimental results. The resulting linear resolution of the prepared displacement sensor was estimated to be 10 μm by simply referring to the distance between the two consecutive peak levels. By possibly identifying half the period of the obtained signal, the resolution can be further enhanced to greater than 5 μm, leading to an angular resolution of ~0.02°. The proposed sensor may be compared with a commercially available product from Avago Technologies (Model AEDR 850), offering positional and angular resolutions of ~20 μm and 0.1° [21]. The figure-of-merit for the proposed sensor, which is defined as the product of the resolution and cost, is modestly thought to improve at least two fold compared with that for the commercial product.
Fig. 11 Measured transfer characteristics of the reflective displacement sensor exploiting an SM and MM VCSEL.
4. Conclusion
A compact reflective-type photonic displacement sensor was discussed based on a rotary scale combined with an optical sensing head consisting of a slim micro-optic beam shaper, which tailors the profile of the light beam and steers its traveling path. The sensor was cost effectively realized via passive assembly assisted by an alignment guide. When the optical head relying on an SM VCSEL was set underneath a rotary scale comprised of grating patterns with a 10-μm pitch, a highly discernible output signal was attained that exhibited a modulation depth of over 7%. The resulting linear and angular resolutions were better than 5 μm and 0.02°, respectively, which could be readily enhanced by use of advanced signal processing. Potentially, the resolution will be substantially elevated by diminishing the code scale pitch and accordingly the focused beam size.
Acknowledgments
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2013-008672, 2013-067321) and a research grant from Kwangwoon University in 2013.
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