A novel method of beam steering enables a large field of view and reliable single chip light detection and ranging (lidar) by utilizing a mass-produced digital micromirror device (DMD). Using a short pulsed laser, the micromirrors’ rotation is frozen in mid-transition, which forms a programmable blazed grating. The blazed grating efficiently redistributes the light to a single diffraction order, among several. We demonstrated time of flight measurements for five discrete angles using this beam steering method with a nano second 905nm laser and Si avalanche diode. A distance accuracy of < 1 cm over a 1 m distance range, a 48° full field of view, and a measurement rate of 3.34k points/s is demonstrated.
© 2017 Optical Society of America
Laser beam steering technology is essential for light detection and ranging (lidar) systems. For this reason, beam steering technologies have been actively researched. Along with mechanical and completely non-mechanical beam steering, Micro-Electro-Mechanical-Systems (MEMS) are one of the emerging beam steering fields that are especially suitable for lidar.
Mechanical scanning including gimbals, fast-steering mirrors, Risley prisms, rotating polygon mirrors and gratings have been used for wide wavelength ranges . Although mechanical beam scanning modalities are widely adopted, having fewer or no moving parts and smaller component inertia is more desirable for fast and compact beam steering devices so that size, weight, cost, and power consumption can be reduced [2, 3]. These qualities are especially required for autonomous vehicle and robotics applications.
In contrast, completely non-mechanical scanning such as programmable spatial light modulators, modulo 2π optical phased arrays, solid state phase arrays, and liquid crystal electro-optic scanners are emerging [1, 4–7]. These non-moving part devices enable large steering angles and are expected to be highly reliable, and are now actively researched.
In terms of small component inertia, Micro-Electro-Mechanical Systems (MEMS) are promising due to their small size and weight, low production cost, high energy efficiency, and applicability to wide wavelength ranges. These MEMS devices include single resonant mirrors and shifting lenslet arrays [2, 8, 9]. However, in lidar applications for autonomous vehicles, a large steering angle as well as large beam size are needed to cover a large angle of scanning and minimize beam divergence due to diffraction. Unfortunately, resonant mirrors and shifting lenslet arrays are limited in angular range and maximum accommodated beam size. Current high-end resonant mirror MEMS scanning systems have moderate fields of view at 36° and scan rates of 21 kHz [2, 10]. However, a resonant mirror’s maximum beam diameter is only increased at the expense of decreasing the maximum scan rate . An optical amplification of the steering angle by an inverse telescope design has been reported; however, this design requires a reduced beam diameter to conserve the Lagrange invariant, which would limit the effective delivery of light over large distances due to beam spreading by diffraction [11, 12].
Thus, a beam steering system for use in lidar would ideally have a large beam size, a wide field of view, and a high scan rate while minimizing the number of moving parts. To simultaneously satisfy these requirements, we propose and demonstrate a new beam steering method by utilizing the commercially available Digital Micromirror Device (DMD) with a short pulsed laser. We also demonstrate its application to lidar with a large field of view, high scan rate and potentially a large beam size.
In chapter 2, the key idea of the beam steering, freezing the micromirror movement by nano-second laser pulse to form a programmable blazed grating is discussed, followed by a diffraction analysis of this programmable grating. The beam steering theory is experimentally demonstrated for three kinds of sub microsecond pulsed light sources: a collimated laser beam, a focused laser beam, and a quasi-collimated beam from a light emitting diode. In chapter 3, implementation of the beam steering method in a single chip DMD lidar system is discussed with experimental results of distance measurement accuracy and live image capturing. Finally, we will address possible optical design solutions to overcome the limited number of scanning points available to meet modern requirements for lidar systems.
2. Discrete and continuous beam steering by DMD
In Fig. 1, the DMD is schematically depicted. This beam steering setup utilizes a 608x684 (horizontal by vertical) DMD chip (DLP3000, Texas Instruments). The micromirrors are positioned in a diamond configuration with a corner to corner period of 10.8μm as shown in Fig. 1(a). On this DMD, an array of micromirrors flip between an “on” and “off” state by rotating +/− 12° about an axis defined by the diagonal of the mirror. Thus, a DMD is designed for binary spatial light modulation and is not intended to be used for angular beam steering, unless additional optics to convert the spatial modulation to angular modulation are incorporated at the expense of light throughput .
The DMD mirrors move continuously between the “on” or “off” states with a typical transition time in the order of micro seconds . This unused transitional state of the DMD is utilized by a short pulsed laser whose pulse duration is much shorter than the transition time of the mirrors. With the short pulsed laser, the micromirror movement is “frozen” at an angle between the stationary “on” and “off” states. Thus it is feasible to form a programmable blazed diffraction grating to discretely steer a laser beam with a collimated beam. It is also feasible to create a continuously scanned and diverging beam if the laser beam is focused on a single DMD mirror by eliminating the diffraction grating effects.
2.1 Analysis of discrete beam steering with plane wave illumination
The principle of the beam steering for plane wave illumination is first numerically modeled. Each mirror was modeled as a series of point sources with an associated phase and optical path length (OPL) induced by the tilt of mirror while taking into account the angle of incidence of the incoming beam. Figure 2 shows the OPL of a 5 x 5 mirror area with the micromirrors tilted at −12 degrees and a plane wave incident angle of + 3 degrees. The field contributions from each point source are added together by the Huygen-Fresnel integral to calculate the electric field on the observation screen located 250 mm away from the DMD .
The results from a model containing a 70x3 mirror array is depicted in Fig. 3. The top five rows in Fig. 3 show “snap shots” of the diffraction intensity patterns normalized to the 0th order of diffraction. The very bottom row of Fig. 3 shows a “long exposure” shot. The diffraction orders from left to right model micromirror rotation angles of −10.3, −5.8, 0, + 4.9, and + 12 degrees, respectively. The incident plane wave is diffracted into one of the specific diffraction orders with diffraction efficiencies close to 100% since the frozen state of the tilted DMD mirrors is equivalent to a blazed grating where the slope of the mirror is set to the blaze angle. The diffraction pattern is further evaluated by modeling the reflectivity of the DMD’s cover glass, 4% with an optimized antireflective coating and 23% without, as described in detail in section 4.3.
2.2 Experimental demonstration of discrete beam steering of plane wave
Experimental setup for the beam steering of a plane wave is illustrated in Fig. 4. The source is an 8ns, 905nm laser diode (LS9-220-8-S10-00, Laser Components, Germany). The laser pulse is collimated by a 20x and NA 0.4 microscope objective lens (80.3071, Rolyn Optics) and directed toward the DMD surface at an incident angle of 30 degrees. The implementation of an optional focusing lens to focus light onto a single DMD pixel is further discussed in section 2.4.
The DMD driver contains an external trigger port that was used to switch the mirror array between the “on” and “off” state by displaying an all-white or all-black bitmap image. Both the DMD driver and the pulsed laser source were controlled by a microcontroller (Arduino Uno, Arduino) by sending delayed trigger signals to synchronize the laser pulse with the movement of the micromirrors.
We experimentally determined that the micromirrors start transitioning about 218μs after the external trigger pulse is sent to the DMD driver and take about 2μs to complete transitioning. The complete timing diagram is depicted in Fig. 5. To increase timing precision, we added a serially programmable timing element (DS1023, Dallas Semiconductor) between the Arduino and laser source which adds an additional delay with 0.25ns timing precision. This allows the Arduino micro controller to produce virtually any time delay between triggering the DMD and laser with 0.25ns precision.
Figure 6 shows a captured image of the progression of a horizontal scan, showing the five discrete diffraction orders. This image was captured with a CMOS camera (DCC1545M-GL, Thorlabs) and an infrared lens (12VM1040ASIR, Tamron) by imaging the viewing screen placed 250 mm away from the DMD as illustrated in Fig. 4. The integration time of the camera was set to be tens of milliseconds which is substantially slower compared to time interval among laser pulses. Each picture in Fig. 6, except for the picture of the bottom, was taken over a number of pulses which are diffracted to the specific order by tuning the laser pulse timing. Milliseconds of exposure time confirms that stable beam steering is done since no other diffraction orders, except for the 0th order specular cover glass reflection, are observed. The last “Long Exposure” picture captures all the 5 sequential scans.
2.3 Discrete beam steering with light emitting diode illumination
Since diffraction dominates the performance of DMD beam steering, quasi monochromatic and incoherent light sources are also usable. The laser source in Fig. 4 was replaced with a green LED (L-7113GT, Kingbright) and modulated and synchronized to the movement of the DMD mirrors. Figure 7 shows snapshot pictures and a long exposure picture while the beam is scanned over the five diffraction orders. The LED used was not collimated to the degree of the laser used in plane wave illumination, causing larger spot sizes. Even with larger scan spots, beam steering by using LED is feasible. One may notice that diffraction spots surround the central spots. Those unnecessary spots can be optically filtered out by employing a 4-f imaging optics with a horizontal slit located at the Fourier plane of the lens.
2.4 Continuous beam steering with focused laser illumination
With a collimated laser or quasi collimated LED illumination, continuous scanning is not possible due to the diffraction effects of the relatively small DMD pixels. As an opposite case, we illuminated a single DMD pixel with a nano second 532 nm laser (Vector 532-1000-20, Coherent). The laser was focused by a microscope objective (20x, Swift Optical Instruments) and controlled with the same synchronizing electronics. In this way, the diffraction effects no longer dominated the scan pattern. A CMOS camera (DCC1545M-GL, Thorlabs) and lens (12VM1040ASIR, Tamron) imaged the viewing screen, shown in Fig. 8.
3. Integration into lidar system
The proposed beam steering method requires pulsed beams, thus it is well suited for lidar systems based on a Time of Flight (TOF) measurement. To demonstrate this application of DMD beam steering, we integrated DMD based beam steering into a 1D line scanning lidar system. This lidar system makes TOF measurements along each of five diffraction orders within the DMD’s field of view of 48 degrees.
To make TOF measurements, an avalanche photodiode (APD) (C12702, Hamamatsu) and a fold mirror were added to the optical setup as illustrated in Fig. 9(a). A 3D printed mount to reduce cross talk between transmitting and receiving optical passes was also added as illustrated in Fig. 9(b). The 3D printed mount held the APD, fold mirror, and DMD in such a way that allowed outgoing pulses to be spatially isolated from the APD, but still allowed incoming pulses to be detected. As illustrated in Fig. 9(a), the laser pulse travels from the collimating objective through an adjustable aperture and is directed by a fold mirror onto the DMD at a 30° incident angle. The reflected light retraces this path through the DMD to the APD.
Figure 10 shows a block diagram of the electronic circuit for the TOF measurements. A time to digital converter (TDC7200, Texas Instruments) was used to measure the TOF of each pulse. The rising edge of the Arduino’s trigger pulse to the laser module was the “start” signal and the rising edge of the APD’s electrical response was the “stop” signal.
After measuring the TOF, the data is retrieved through a serial interface and transferred to a host computer. The data is sent through the Arduino’s built in serial monitor for real time data collection. Alternatively, for off-line and faster data collection, the data is sent to a static random access memory (SRAM) chip (23LC1024, Microchip) via serial peripheral interface (SPI). The SPI interface was used because much higher data transfer rates could be achieved compared to the Arduino’s serial monitor. The Arduino serial monitor allowed data points to be read at a 433Hz rate whereas saving data points to the SRAM via the SPI interface allowed data points to be saved at a speed of 3.34kHz.
4. Experimental results
4.1 Diffraction efficiency test
The diffraction efficiencies and the angles of diffraction for all five horizontal diffraction orders are tabulated in Table 1. The angles of diffraction were measured with respect to the 0th order in the horizontal plane. Positive angles were measured in a counterclockwise direction. Table 1 contains both the measured and predicted diffraction angles.
The transmitted power was measured by aiming the diffracted beams onto the sensor of a CMOS camera (DCC1545M-GL, Thorlabs). The mean counts of each captured image were proportional to the incident power. Table 1 provides the diffraction efficiencies normalized to the 0th order diffraction power for each diffraction order as well as the absolute diffraction efficiency.
4.2 Maximum measurable distance test
The maximum measurable distance test was performed to quantify the system’s distance measurement accuracy. To do this, we performed a linear conversion from the reported digital number to reported distance. White paper targets (25mm by 25mm square) were placed at different distances to calibrate each arm.
Distance tests were performed from 10cm to 50cm. However, the + 2 diffraction order was only able to detect objects up to 40cm. The + 2 order had the lowest diffraction efficiency as shown in Table 1. Additionally, due to the large tilt angle of the micromirrors and the 30° beam incidence angle to the DMD, the projected collection area of the DMD is smallest for the + 2 order as shown in Fig. 9. To quantify the repeatability of the measurements, N data collects were averaged together to produce one measurement and N was varied from 1 to 10. These reported average distance measurements are shown in Fig. 11 for N = 1 and N = 10. The shapes of the curves in Fig. 11(a) are very similar to the curves in Fig. 11(b), suggesting a low noise content. To show the noise content in the distance measurements, the standard deviation (STD) of measurements made of objects placed at 50cm for each scan angle are tabulated in Table 2. The root-mean-square (RMS) errors for N = 1, N = 2, N = 5, and N = 10 averaging for object distances of 10cm to 50cm is also tabulated in Table 2 to show the degree of repeatability of distance measurements.
The 0th order is a special case such that the Fresnel reflection from the cover window provides more optical power than the other diffraction orders as shown in Table 1. The DLP3000 DMD contains a Corning Eagle XG glass protective window with an antireflective coating optimized for visible light . When using infrared light, this coating creates a strong specular Fresnel reflection that overlaps with the 0th order of diffraction. We experimentally measured this Fresnel reflection to be about 20% with a 30° incident angle. This extra power gave the lidar system a much longer range and a lower RMS error in the 0th order. The range of the 0th order was extended to 120cm as shown in Fig. 12.
4.3 Object motion capture test
The object motion capture test was performed to illustrate the capabilities of the lidar system in measuring distances of moving objects in real time. The lidar system captured live footage of a pendulum swinging within its field of view. The pendulum consisted of a white paper cube with a side length of 25mm. This cube was suspended from a thin wire about six feet long. The live video was captured with a digital camera (PowerShot D30, Canon). The lidar output and the live video were then combined using MATLAB. A representation of the videos consisting of a series of snapshots is shown in Fig. 13 to illustrate the performance of the lidar system in real time.
Note that in Fig. 13(c), artifacts appear in the −2, −1, + 1, and + 2 diffraction orders when the object swings through the 0th order. It was experimentally determined that these artifacts appear when the pendulum was closer than about 40 cm to the lidar system. This demonstrates the presence of crosstalk between the 0th order and all other orders, which is explained further in section 5.
4.4 Random object distance measurement test
The random object distance measurement test quantified the ability of the lidar system to measure objects with varying reflectivities, sizes, and distances. High and low reflectivity targets (white paper and brown cardboard respectively) were used as targets. Small (25mm x 25mm), medium (50mm x 50mm), and large (100mm x 100mm) sized targets were randomly placed in the system’s field of view. One such measurement is shown in Fig. 14. From left to right the targets used were medium size high reflectivity, medium size low reflectivity, small size high reflectivity, small size low reflectivity, and large size low reflectivity.
This experimental demonstration confirms that measurement accuracy is currently less than 1cm over a half meter range for all of the 5 diffraction orders for N = 1. In Fig. 12, one can notice that the 0th order can reach far objects at 1m but cross talk exists from adjacent diffraction orders when the object is located closer to the DMD chip. The origin of this artifact can be explained as follows. When the micromirrors steer the beam, for example the + 1 order diffraction angle, there is also a specular reflection from the cover glass towards the 0th order diffraction angle. As the object approaches the DMD, both the + 1 and 0th order beams illuminate the object. As a result, the system recognizes the object in the + 1 order as an object in the 0th order. Each frame of the video represented in Fig. 13 is the sum of all objects detected in one left to right five point scan. Thus, multiple object points are plotted for one single object located close to the DMD in the 0th order. The mechanism causing the artifact is confirmed by the fact that the DMD cover glass has a high specular reflectivity. Indeed, the reflectivity of the Corning Eagle XG DMD cover glass was measured to be about 20% for 905nm light at a 30° angle of incidence, this reflectivity agrees with literature . We expect that the artifacts can be eliminated by an appropriate antireflection coating since the artifact only occurs for near objects in the 0th diffraction order .
Currently, the number of scanning angles is limited to 5, which is equal to the number of diffraction orders available when using 905nm light. The number of scanning angles can be further increased by employing a larger DMD micromirror pitch, and/or a shorter wavelength as well as cascading multiple DMDs. As a matter of fact, the Texas Instruments model DLP9500 DMD has a 15.3µm corner to corner pixel pitch, which produces seven horizontal diffraction orders using 905 nm light at a 30° incident angle. In addition, the number of scanning angles can be further increased by using multiple arrayed light sources as shown in the following analysis.
Here, we present one possible solution for increasing the total number of scanning angles by using a stacked laser diode (LD) array. We first assume the case of illuminating the DMD surface with normal incidence. The angle between the 0th and + 1 diffraction order is defined as θ+1 in Eq. (1) where, p, is the corner to corner DMD pixel pitch, as described in Fig. 1, and λ is wavelength. Note that a factor of 2 is included in the expression which is necessary if the DMD has diamond-shaped pixels, such as the DLP3000 and DLP9500.
Thus, we wish to divide this angular space with NLD laser beams to increase the total scanning resolution of the system by a factor of NLD. In this configuration, only one of the diffraction orders from one of NLD laser diodes is used, and scanning is employed in a sequential manner, for example −2nd to + 2nd orders of 1st LD, followed by the same sequence for the 2nd LD and repeat the sequence up to NLD. The experimental demonstration is considered as a case for NLD = 1. These multiple laser beams are assumed to originate from a stack of NLD laser diodes placed at the back focal plane of a collimating lens and these beams are directed at the DMD, as depicted in Fig. 15.
The maximum spatial extent of the laser diode stack is . The output laser beams thus have a maximum angular divergence of . These two quantities are related by Eq. (2), where d is the laser diode pitch.
The DMD is assumed to have an area of Arec, thus the maximum linear dimension of the DMD is proportional to . It is assumed that the collimating lens has a numerical aperture of NAcol and that the DMD area is completely illuminated. The focal length of the collimation lens, fcol, can thus be described by Eq. (3).
Arec is related to the maximum measurable range, R, and is given by Eq. (5) . ET and ES are the transmitted and received powers respectively, Ailm is the area of the illumination spot, σ is the cross sectional area of the object being detected, and α is the reflectivity of the object. The transmission of the atmosphere and the system are given as ηatm and ηsys, respectively.
The maximum point scan rate of a DMD-based lidar system is equal to the pattern refresh rate of the specific DMD used. The line scan rate will be defined as the pattern refresh rate divided by the total number of points within the scan field of view, which is equal to the number of laser diodes, NLD, times the number of diffraction orders supported by the DMD at the current wavelength used, NOrder, as shown in Eq. (7).
We will now use Eq. (4) and Eq. (6) to calculate the approximate range and resolution for lidar systems using the DLP3000 and DLP9500 (Texas Instruments) under optimal conditions: σ = Ailm, ηatm and ηsys = 1, and α = 1. Equation (7) will be used to calculate the maximum line scan rate given that the maximum pattern refresh rate of the DLP3000 and DLP9500 is 4kHz and 23kHz respectively. Common laser diode stack pitches range from 0.35mm to 2mm, but stack pitches as low as 0.15mm have also been reported . NA values for collimating lenses of 0.5 have commonly been reported for Petzval lens types . The active area of the DLP3000 and DLP9500 are 0.24cm2 and 2.40cm2 respectively. Currently, the sensitivity of the APD used in the demonstration is 23 kV/W. APD sensitivities of up to 1 MV/W have been reported for commercial APD’s . Also, the peak optical power (defined by pulse energy divided by the pulse length) of the current laser diode used is 73 W for 600 nJ/pulse, 8 ns pulse length, but state of the art commercial infrared semiconductor laser diodes have peak optical powers up to 100W . By scaling the variables in Eq. (6), a rough estimate of the performance of a single-chip DMD lidar system under optimal conditions and using state of the art components was calculated. Table 3 summarizes the estimated performance of lidar systems using such parameters for 905nm and 1550nm light. Note that the average optical power over the DMD area for the system tabulated in Table 3 is on the order of mW whereas the maximum allowable average power for DLP9500 is 25W, therefore the systems operates way below the damage threshold of DMD device .
To show the feasibility of such systems described in Table 3, a ray trace model was constructed in ZEMAX using the DLP3000 and a stack of five 905nm laser diodes to create 25 scan angles as illustrated in Fig. 16. Diffraction efficiencies over the 25 diffraction orders are numerically calculated in Fig. 16(c). An array of laser diodes (NLD = 5) with laser diode pitch d = 0.15 mm is collimated by a NAcol = 0.5 collimating lens (fcol = 4.24 mm) and redirected to the DMD by a fold mirror. The returning beam from the object is redirected to the NArec = 0.14 receiving lens (frec = 17.0 mm) by the DMD and imaged onto the APD (detection diameter = 3mm). The relationship between the collimating lens focal length and receiving lens focal length can be geometrically calculated assuming the entire area of the APD is filled as described in Eq. (8). The diameter of the APD photosensitive area is dAPD and the focal length of the receiving lens is frec.
As simulation result in Fig. 16c shows, the multiple laser diode approach for NLD = 5, total scanning angles of 25, shows fairly high efficiencies over 70% across the field of view. One may notice that the scanning angles are not uniformly spaced with angular spacing of 1.6 to 4.4 degrees due to the inherit nonlinearity between the incident and diffracted angles upon diffraction by blazed grating. The scanning angle spacing can be further equalized by reducing angle of incidence of the incoming beam to DMD and/or with an additional aid of optics such as prism array.
In terms of scanning speed, currently a scan rate of 3.34k points/s is demonstrated in our lidar system using the DLP3000. This corresponds to a line scan rate of 668 lines/s with 5 scanning points and a single laser diode. Our analysis shows that a line scan rate of 256 lines/s with 90 scanning points is feasible when a faster DMD is used, such as the DLP9500 which features a 23kHz point scan rate, which is equal to pattern refresh rate of the DMD.
When making distance measurements, our system currently uses a constant voltage threshold value in the TOF circuitry and contains no pulse shaping circuitry. This provides a disadvantage in that the reported TOF is affected by the shape of the return pulse. Factors such as surface reflectivity and measurement distance have an effect on the amplitude of reflected pulses. To further increase measurement accuracy, implementation of additional circuitry and signal processing could increase the accuracy of this lidar system. An analog DC detector offset to place the voltage threshold level in the center of the noise distribution has been reported to increase accuracy in lidar systems . In addition, analog filtering that shapes the return pulse has also been reported to increase accuracy .
For the first time, to the best of the authors’ knowledge, we experimentally demonstrated a single chip lidar with an efficient DMD-based discrete beam steering capable of live imaging at 3.34k points/s and a 48° full field of view. Based on the results of the demonstration, we performed a mathematical modeling of such a single chip lidar system given reasonable physical and optical design constraints. Our model predicts that range finding over 175 m with scanning rates of (256 lines/s) x 90 (points/line) = 23k points/s and a field of view over 60° with 0.65° resolution is attainable. Such a system would still have the benefits of single chip DMD-based lidar, such as reliable Micro-Electro Mechanical System based scanning, flexible selection of wavelengths, and a large beam diameter.
References and links
1. W. C. Stone, M. Juberts, N. G. Dagalakis, J. A. Stone Jr., J. J. Gorman, “Performance Analysis of Next-Generation LADAR for Manufacturing, Construction, and Mobility,” NIST Interagency/Internal Report (NISTIR) – 7117, (2004).
2. A. R. Cho, A. Han, S. Ju, H. Jeong, J. H. Park, I. Kim, J. U. Bu, and C. H. Ji, “Electromagnetic biaxial microscanner with mechanical amplification at resonance,” Opt. Express 23(13), 16792–16802 (2015). [CrossRef] [PubMed]
3. C. Niclass, K. Ito, M. Soga, H. Matsubara, I. Aoyagi, S. Kato, and M. Kagami, “Design and characterization of a 256x64-pixel single-photon imager in CMOS for a MEMS-based laser scanning time-of-flight sensor,” Opt. Express 20(11), 11863–11881 (2012). [CrossRef] [PubMed]
4. C. T. DeRose, R. D. Kekatpure, D. C. Trotter, A. Starbuck, J. R. Wendt, A. Yaacobi, M. R. Watts, U. Chettiar, N. Engheta, and P. S. Davids, “Electronically controlled optical beam-steering by an active phased array of metallic nanoantennas,” Opt. Express 21(4), 5198–5208 (2013). [CrossRef] [PubMed]
5. R. Dou and M. K. Giles, “Programmable phase grating and beam steerer by operating a LCTV,” Proc. SPIE 2566, 26 (1995).
6. S. Davis, S. Rommel, S. Johnson, G. Farca, N. Rebolledo, S. Selwyn, and M. Anderson, “Electro-optic steering of a laser beam,” SPIE Newsroom (2011).
7. E. Ackerman, “Quanergy Announces $250 Solid-State LIDAR for Cars, Robots, and More,” IEEE Spectr. , 7 (2016).
8. A. Tuantranont, V. M. Bright, J. Zhang, W. Zhang, J. A. Neff, and Y. C. Lee, “Optical beam steering using MEMS-controllable microlens array,” Sensor Actuat. A 91(3), 363–373 (2001).
9. Mirrocle Technologies Inc., “Mirrorcle Technologies MEMS Mirrors – Technical Overview,” Gimbal-les Two-Axis Scanning Micromirror Devices technical overview, 2016.
10. T. Sandner, M. Wildenhain, C. Gerwig, H. Schenk, S. Schwarzer, and H. Wölfelschneider, “Large aperture MEMS scanner module for 3D distance measurement,” Proc. SPIE 7594, 75940D (2010). [CrossRef]
11. R. Moss, P. Yuan, X. Bai, E. Quesada, R. Sudharsanan, B. L. Stann, J. F. Dammann, M. M. Giza, and W. B. Lawler, “Low-cost compact MEMS scanning LADAR system for robotic applications,” Proc. SPIE 8379, 837903 (2012). [CrossRef]
13. Texas Instruments, “DLPTM System Optics,” Application Report, July 2010.
14. T. Kaeriyama, Damped Control of a Micromechanical Device, U.S. Patent Application No. 10/749,432, filed December 31, 2003.
15. J. D. Gaskil, Linear Systems, Fourier Transforms, and Optics (John Wiley & Sons, Inc., 1987), Chap. 10.
16. Texas Instruments, “Wavelength Transmittance Considerations for DLP® DMD Window,” Application Report, May 2012 revised March 2014.
17. P. McManamon, Field Guide to Lidar (SPIE, 2015).
18. R. Feeler and E. Stephens, “High Density Pulsed Laser Diode Arrays for SSL Pumping,” Northrop Grumman Cutting Edge Optronics Application Note 15, 2010.
19. W. Smith, Modern Lens Design (McGraw-Hill Professional, 2004).
20. Analog Modules, Inc., “High Sensitivity APD Optical Receiver,” Model 7510–1 Datasheet, May 2015.
21. E. Technologies, “PGA Series of Single- and Multi-epi 905 nm Pulsed Semiconductor Lasers,” Datasheet Photon Detection, 2013.
22. T. Instruments, “DLP9500 DLP(R) 0.95 1080p 2x LVDS Type A DMD,” (accessed 6 June 2017), www.ti.com.
23. PulsedLight, Inc., “LIDAR-lite Operating Manual,” (accessed 13 Feb 2017), www.pulsedlight3d.com.