Abstract

A digital micromirror device (DMD) based holographic beam steering technique is reported that multiplexes fine-steering binary amplitude gratings with a coarse-steering programmable blazed grating. The angular spatial light modulation (ASLM) technique encodes the spatial pattern of the binary amplitude grating at the same plane as the angular modulation set by a phase map of the DMD-based beam steering technique. The beam steering technique is demonstrated at 532 nm and implemented into a 905 nm lidar system. The results of the lidar system tests are presented, achieving a 44° field-of-view, 0.9°×0.4° (H×V) angular resolution, 1 m max distance, 1.5 kHz sampling, and 7.8 FPS video. Scalability techniques are proposed, including max distance increases to over 100 m.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Large aperture area, wide Field-of-View (FOV), high speed, high resolution beam steering devices are needed for lidar systems, but these requirements are commonly conflicting. Rotating systems have been used for their larger collection area, but high-inertia mechanics limit scan rates [1]. A resonance MEMS mirror with kHz sampling was adopted for beam steering with an optically expanded FOV of 20° [2]. Resonance MEMS mirrors have relatively small mirror diameters (∼1 to 4 mm), and therefore relatively small output beam diameters, and optical expansion of the FOV further reduces the output beam diameter [3]. A small output beam diameter limits output pulse energy, limiting maximum range due to laser safety considerations [4]. Additionally, a resonance MEMS mirror’s limited receiver collection area prohibits it from being used in a lidar system with a common-path design in which the transmitter and the receiver share the same optical path. Unfortunately, a resonance MEMS mirror cannot support both a large FOV and a large area, because inverse relationships exist between the mirror’s size and its angular throw, and between the mirror’s size and its scan speed [5].

Spatial Light Modulator (SLM) based holographic beam steering has been applied to optical tweezers [6,7], optical interconnects [8,9], and object tracking [10]. Advancements have been made to improve the steering accuracy and efficiency of SLM-based holographic beam steering, for instance by use of phase-only SLMs that have significantly improved diffraction efficiency over amplitude-only SLMs [11]. Despite advancements, the angular extent of SLM-based holographic beam steering is limited by the SLM’s pixel pitch [12]. This has been resolved by combining an SLM with a galvo scanning mirror to great effect, but at cost to speed and system complexity [13]. In addition, the phase modulation speed of a liquid-crystal-based SLM is limited by the required material response time to induce a phase shift over the thickness of the liquid crystal material. Overdrive and restricted phase change techniques have reduced the material response time by nearly an order of magnitude, achieving a 250 Hz SLM reset rate [14], but the techniques are not scalable to additional order-of-magnitude improvements.

As stated above, the maximum scan angle for SLM-based holographic beam scanning is limited by the smallest element size: pixel pitch. For example, an SLM with a 10 um horizontal pixel pitch, operating at 905 nm, will have a maximum horizontal scan angle of ${\sin ^{ - 1}}[{{{905\textrm{nm}} / {({2 \ast 10\mathrm{\mu}\textrm{m}} )}}} ]$ = 2.6° for a full horizontal steering range of 5.2° (±2.6°) [12]. One or two orders-of-magnitude wider beam scanning is needed these days, for example 120° for an automotive application [15].

We previously demonstrated using a Digital Micromirror Device (DMD), a mass-produced Micro Electro Mechanical System (MEMS) based amplitude SLM, to efficiently steer a beam over 48° [16]. The DMD is a binary amplitude SLM comprising micromirror pixels. Each micromirror rotates between two landed states. In a typical digital projector, the landed states correspond to “on” and “off” directions, reflecting light either toward a projection lens to project a white pixel, or away from the projection lens to project a black pixel. Our wide-FOV beam steering technique illuminates the DMD with a nanosecond laser pulse during the micromirrors’ microsecond transition between the on- and off-states, effectively freezing the micromirrors at a synchronization-dependent angle. The frozen micromirrors form a blazed grating for highly-efficient beam steering with a programmable blaze angle. The arrayed structure of the DMD micromirrors limits the steering to discrete diffraction orders perpendicular to the micromirror axis of rotation. For instance, in the case of our demonstrated system using the DLP3000 DMD and 905 nm pulse illumination, we achieved 48° beam steering across 5 discrete output diffraction orders [16].

The DMD-based beam steering was converted to pattern steering for a single-plane angularly and spatially multiplexed system: the Angular Spatial Light Modulator (ASLM) [17]. The dual modulation is achieved by transitioning only the micromirrors of a programmable pattern on the DMD and pulsing illumination during the pattern array’s micromirror transition. The display output an array of angular- and time-multiplexed patterns and nearly doubled the étendue beyond binary-mode DMD implementations. The pattern steering technique was similarly applied to a holographic display application developed concurrently with the presented system [18].

We now report a scalable and single-chip MEMS-SLM based beam steering system having a moderate and beam footprint of 3.7×1.64 mm (scalable with larger currently-available DMDs), high angular resolution of 0.9°×0.4° (H×V), video frame rate of 7.8 FPS, MEMS sampling rate of 1.5 kHz, and a wide FOV of 44°, overcoming the pixel-pitch-imposed limitation on FOV in typical SLM-based holographic beam steering systems. We adopt an ASLM-based coarse-fine hybrid scanning approach. The coarse scanning is achieved by the angular modulation of our previously-presented wide-FOV discrete scanning by short-pulse illumination of transitioning micromirrors. The fine scanning is achieved by spatial modulation across the DMD by pre-selecting which micromirrors transition to form a pre-calculated hologram pattern to diffract light into an intended direction. The short-pulse illumination occurs during the transition of the select micromirrors, imparting an incident wavefront with both angular modulation from the pre-programmed blazed grating and spatial modulation of the pre-programmed hologram.

In Section 2, we review the beam steering and ASLM pattern steering techniques. In Section 3, we explain and experimentally demonstrate ASLM-based wide-FOV and high-resolution 2D holographic beam steering at 532 nm for visible inspection of the proposed method. In section 4, we apply the ASLM beam steering system to a wide-FOV lidar at 905 nm. In section 5, we discuss the impact on effective pixel pitch, FOV fill-factor compensation, and the quad-block reset limitation of the current MEMS-SLM system. In section 6, we present scalability of the system, including significantly improved speed, resolution, beam area, and diffraction efficiency.

2. Beam steering and pattern steering

2.1 DMD-based beam steering

We previously reported a lidar system using a DMD-based beam steering technique [16]. The DLP3000 DMD can switch between patterns at up to 4 kHz for a period of 250 µs [19]. The micromirrors are static (or settling) during most of the period since the transition between the binary states is only about 2.4 µs [16]. This is ideal for continuous illumination meant to be directed into binary states. Rather than continuous illumination, we illuminated a DMD with an 8 ns laser pulse during a simultaneous transition of all the mirrors. The nanosecond pulse illumination is three orders of magnitude shorter than the microsecond micromirror transition, effectively freezing the micromirrors transition during the illumination period. The frozen micromirrors form a blazed grating, theoretically with 100% diffraction efficiency (ignoring fill-factor and other loss factors), with a programmable blaze angle based on nanosecond synchronization of the illumination. The beam can be steered across discrete and selectable output diffraction orders, for example 5 orders with 905 nm illumination onto the DLP3000 DMD [16]. We synchronized illumination pulses by coarse, 62.5 ns clock cycle increments of an Arduino Uno microcontroller and fine, 250 ps increments of a DS1023 delay line integrated circuit (IC), but we found the 62.5 ns resolution increments to be sufficient to steer the output into one diffraction order at a time.

2.2 DMD-based pattern steering

Our previous DMD beam steering by programmable blazed grating produced an angular light modulation effect of directing light into selectable directions, but involved no spatial light modulation across the illumination plane [16]. The reported Angular Spatial Light Modulator (ASLM) system simultaneously modulates light in both the angular and spatial domains, creating more degrees of freedom from a traditional DMD across a greater angular extent [17].

The ASLM’s degrees of freedom include a programmable blazed grating phase mask, defined by the global angle of the mid-transition micromirrors and a programmable amplitude profile, created by pre-programming a pattern of which micromirror pixels will transition.

The three-step ASLM program sequence is as follows: (1) The DMD actuates to a fully black pattern to land all the micromirrors in the same state. (2) A diffraction-order-specific time delay between the micromirror actuation and illumination pulse is programmed for the next actuation, defining the next phase mask, and the next hologram pattern is loaded to the DMD, defining the next amplitude mask. (3) The DMD is then actuated, and the correct delay occurs during the transition of the pre-selected pattern of micromirrors before the illumination pulse occurs so that the pulse wavefront collects both the correct phase mask and amplitude mask at the plane of the DMD. The process is depicted in Fig. 1 for two different masks directed into two different diffraction orders.

 figure: Fig. 1.

Fig. 1. Phase (top) and OPL (bottom) maps of DMD micromirrors through the ASLM process. (a) Fully black pattern of mirrors at -12°. (b) “X” pattern of micromirrors actuated and, after time delay t1, illuminated during the transition at a mirror angle of -3° to project an “X” pattern in a diffraction order direction. (c) Transitioning micromirrors complete their transition to +12°. (d) All mirrors reset to -12°. (e) Square pattern of micromirrors actuated and, after time delay t2, illuminated during the transition at a mirror angle of +6° to project a square pattern into a different diffraction order. (e) Transitioning micromirrors complete their transition to +12°.

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3. ASLM holographic beam steering

3.1 Multiplexed beam steering and single-sideband filtering

The holographic beam steering system combines a coarse beam steering by DMD blazed grating based on the above mechanical tilt movement of micromirrors, and a fine beam steering by a pixelated binary amplitude Computer Generated Hologram (CGH) grating displayed across the DMD. The micromirror geometry is depicted in Fig. 2(a). With corner-to-corner pixel pitch p, pixels with the edge length of ${p / {\sqrt 2 }}$ are arranged in a diamond manner. The axis of tilt of the micromirrors is vertically oriented with a lateral spacing of ${p / 2}$.

 figure: Fig. 2.

Fig. 2. (a) Micromirror geometry on the DLP3000 DMD including micromirror axes of rotation and pixel coordinate addressing to compensate for the diamond pixel orientation. (b) Wavelength-normalized frequency domain of ASLM holographic beam steering output, including higher-order diffraction outputs and the single-sideband filter (gray with throughput boxes in white).

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Figure 2(b) depicts a spatial frequency domain representation of the diffraction from the DMD pixel geometry [20]. The binary amplitude grating forms an on-axis diamond-oriented frequency band area with extent of ${\pm} {1 / p}$ along the ${{{f_x}} / \lambda }$ and ${{{f_y}} / \lambda }$ axes. The 0th output diffraction order at the origin and the +1 and -1 output diffraction orders of the binary grating are limited to this extent. On the other hand, the higher order outputs (e.g., +2 and -2) overlap neighboring diffraction order band diamonds, but these points have reduced diffraction efficiency due to suppression by the $sinc({{{{f_x}} / {\lambda p}}} )$ envelope—the Fourier transform of the pixel function. The base diamond (dark black outline) is iterated in the ${{{f_x}} / \lambda }$ and ${{{f_y}} / \lambda }$ dimensions at ${2 / p}$ intervals. Higher-order cross-term diamond bands iterate as well. The tilt of the micromirror imparts a phase shift, shifting the $sinc({{{{f_x}} / {\lambda p}}} )$ envelope to neighboring bands on the ${{{f_x}} / \lambda }$ axis. The amount of phase shift is implemented in the synchronization of the illumination laser pulse and to control the tilt angle of the micromirrors. Consequently, several frequency bands beyond the central band become accessible to enable wide angle holographic beam steering.

We applied a single-sideband technique to multiple horizontal diffraction orders to spatially filter out extraneous conjugate and zeroth diffraction orders at a Fourier plane [21], as depicted by the grayed region and rectangular throughput white boxes in Fig. 2(b). This is a similar implementation of the single-sideband filter as another concurrent work implementing the DMD-based pattern steering into a holographic display [18].

3.2 Binary grating calculation and verification

Each binary CGH grating was calculated as a continuous function from interfering two plane waves, one at normal incidence and one at the prescribed steering direction, and binarized by hard thresholding of the intensity profile. The discrete pattern was created by sampling the continuous binary function at micromirror locations across the DMD-specific geometry. Steering of the +1 order was achieved by varying grating pitch and orientation.

We verified our calculation procedure by displaying a binary grating on the DLP3000 clocked at 45° with pitch equivalent to the DMD’s edge pitch and visually inspecting it through a microscope. The microscope setup used side-illumination, similar to the prescribed DLP3000 illumination for typical projection, to accurately image the on-state and off-state pixels onto a detector array. Figure 3(a) shows a region of pixels of the calculated hologram bitmap, and Fig. 3(b) shows the captured microscope image. The microscope capture demonstrates that we accurately calculated and mapped single-pixel 45° gratings on the DLP3000 with respect to the pixel coordinate addressing shown in Fig. 2(a) to compensate for the diamond micromirror geometry [19]. Spot artifacts are likely due to reflections by vias and micromirror sub-structure.

 figure: Fig. 3.

Fig. 3. (a) 7×7 pixels in the 45° single-pixel-pitch grating hologram with micromirror addressing corresponding to Fig. 2(a). (b) A microscope capture of a 7×7 micromirror region on the DMD displaying the same static binary hologram. Side illumination was used for accurate state viewing per pixel. Gold-highlighted pixels correspond between (a) and (b).

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3.3 Fourier filtering optical design and implementation

Figure 4 shows the single-chip holographic beam steering setup with 5 coarse output diffraction orders at 905 nm. A cylindrical lens (Rolyn #14.200, 80 mm focal length) is placed just after the DMD, with lens power in orthogonal to the plane of coarse steering, to create a 1D Fourier plane at a spatial filter array a focal length behind the first cylindrical lens. An extended cylindrical lens, comprised of three cylindrical lenses (Rolyn #14.200, 80 mm focal length) joined together, each equivalent to the first cylindrical lens, was placed a focal length after the spatial filter to re-collimate the beams. The lenses were joined at angles to maintain low angles-of-incidence for beams steered across the 48° output by the DMD.

 figure: Fig. 4.

Fig. 4. A beam (colored green, not depicting wavelength) in incident onto a DMD, coarse-steered across 5 diffraction orders (colored red), and fine-steered by binary grating on DMD (not shown). The single positive cylindrical lens, filter array, and 3-element positive cylindrical lens array comprise the single-sideband filter. The final 5-element negative cylindrical array compensates for the FOV fill-factor.

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3.4 FOV fill-factor and compensation

The individual collimated beams output from the second positive lens of the Fourier filter system maintain the same horizontal fill-factor as the spatial filter array depicted in Fig. 2(b) (i.e., a beam cannot be continuously steered horizontally due to the gaps between diamond bands on the ${{{f_x}} / \lambda }$ axis). We used one negative cylindrical lens (Rolyn #14.0825, -100 mm focal length), per diffraction order, to stretch the horizontal angular extent of the fine-steered beams to meet at the divide between neighboring diffraction orders. However, since only a single element was used, the individual beams are no longer collimated, and the beams only form a perfectly filled grid at one distance from the final lens array. We selected this approach to simplify the mechanical construction as it still shows the basis of 2D beam steering and is a sufficient proof-of-concept demo for short-range lidar testing. A more-accurate fill-factor compensating optical design is presented in Section 5.2.

3.5 Experimental setup and results

We demonstrated the system of Fig. 4 using a 532 nm laser source with nine output diffraction orders (-4 to +4). The non-off-state light was directed into diffraction orders -4 to +2 for coarse steering, and the off-state light of the non-transitioning pixels was directed into the off-state direction. “Non-off-state” refers to light from transitioning pixels, which may direct light into the on-state direction (e.g., diffraction order -4) or not (diffraction orders -3 to +2), as opposed to off-state light that is directed by non-transitioning pixels. The coarse steering diffraction orders are governed by the grating equation relating pixel pitch, micromirror slope angle, angle-of-incidence, and wavelength. The finite extent of the +/-12° micromirror rotation is not relevant to the diffraction order locations, but it does determine the number of diffraction orders for which the micromirrors can satisfy the blaze grating condition. For the DMD-based programmable blazed grating (for corner-to-corner rotating micromirrors), the maximum number of discrete beam steering diffraction order directions for normal incidence light is approximately given by dividing the full reflected angular extent by the diffraction order angular spacing, Norder = ${\textrm{floor}}\left( {\frac{{4 \ast {\theta_{\textrm{mirror}}}}}{{{{\sin }^{ - 1}}({{{2\lambda } / p}} )}}} \right)$, where θmirror is the micromirror’s half-angle mechanical rotational extent, λ is the wavelength of the illumination, p is the micromirror corner-to-corner pitch, and the floor function accounts for the restriction to integer diffraction orders. In this case of the DLP3000, with θmirror = 12°, p = 10.8 µm, and λ = 532 nm pulsed illumination, Norder = 8. However, before the floor function, Norder = floor(8.5) describes the cutoff of the micromirror angular sweep as between discrete diffraction orders. In practice, when the illumination angle-of-incidence is set to direct diffraction order -4 into the on-state direction, the off-state direction is between orders +3 and +4. The energy does not actually propagate in the direction between the two, but rather the energy is split across the two diffraction orders. Independent non-off-state beam steering is therefore restricted to seven diffraction orders, -4 to +2, while the off-state light is spread across two diffraction orders, +3 and +4. The total FOV of the fine-coarse multiplexed beam steering system including off-state light is slightly greater than the 48° angular extent of the DMD micromirror sweep. However, the FOV is reduced once the off-state diffraction orders are discarded. The final non-off-state FOV is therefore dependent on the output diffraction order directions [16,17]. Interestingly, the off-state light is sometimes directed into either diffraction order +3 or diffraction order +4 depending on the illumination timing. This is due to voltage reset pulses affecting the off-state pixels causing them to oscillate slightly in the landed off-state [22].

While steering the 532 nm pulsed laser, a total of 96 binary patterns, limited by the memory of the device, were loaded into the Lightcrafter EVM driving a DLP3000 DMD for sequential pattern display. Of the 96 patterns, 48 patterns were binary gratings corresponding to an 8×6 (H×V) array of output directions, and 48 fully black patterns were interleaved between the binary gratings to reset the micromirror positions after each grating actuation, as required by the ASLM sequence described in Section 2.2. Sequencing through 48 binary gratings, for fine steering, and seven coarse output diffraction orders results in 336 output scan points. The resolution of the fine-steering technique can theoretically be increased beyond the binary-pattern memory limit of the Lightcrafter EVM driving the DLP3000. The Lightcrafter has a 4 kHz nominal refresh rate. The max output scan rate by the DLP3000 is therefore 2 kHz due to the black pattern refresh required per output pulse, and 2 kHz was demonstrated and measured by oscilloscope. Figure 5 shows a long-exposure capture of the 432 scan points, including off-state diffraction orders +3 and +4, on an observation screen placed at the correct distance for compensated FOV fill-factor, as discussed in Section 3.4. The point array in Fig. 5 is captured on an observation screen 280 mm from the 532 nm illuminated DMD with independent non-off-state diffraction orders -4 to +2 covering a 2D FOV of 40°×2.0°.

 figure: Fig. 5.

Fig. 5. A long-exposure capture of an 8×6 array of points, finely-steered by binary gratings, iterated across nine course-steered diffraction orders for a total of 432 points. Diffraction orders +3 and +4 contain off-state light for each pulse illuminated into diffraction orders -4 to +2, so they cannot be employed for beam steering for lidar. 336 independent beam steering points are demonstrated across diffraction orders -4 to +2. The wide-angle capture portrays degraded resolution in diffraction order -4, but close inspection reveals similar performance as diffraction order -2. The attenuation in diffraction order +2 is caused by edge-clipping in the vertical-power cylindrical lens array of Fig. 4.

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4. ASLM-based beam steering for time-of-flight lidar

We implemented the presented beam steering technique into a single-detector lidar system using custom time-of-flight measurement electronics (Section 4.1) and a custom receiver (Section 4.2). Slight modifications for the lidar-specific transmitter were implemented (Section 4.3) for a 905 nm implementation, a common wavelength for lidar. Experimental results are detailed below, including: distance resolution (Section 4.4), angular resolution (Section 4.5), video capture (Section 4.6), and diffraction efficiency (Section 4.7).

4.1 Time-of-flight measurement by constant fraction discriminator

The distance measurement scheme we employed measures the Time-of-Flight (TOF) of a single short pulse transmitted from the system, reflected off a target in the FOV, and detected by a receiver. The time measurement occurs in a time-to-digital converter (Texas Instruments, TDC7200) IC. A digital “start” signal from a driving microcontroller (Arduino Uno) begins the internal timer. An analog signal from an Avalanche Photodiode (APD) in the receiver is converted into a digital signal by a comparator IC. The digital subsystem used in the presented lidar system were previously reported [23]. The TOF system of ICs is driven by the same Arduino Uno microcontroller used for beam steering. An additional analog subsystem was added as follows.

In receiver signal processing, amplitude-dependent signal walk commonly occurs due to varying target distance, reflectivity, and target surface orientation [24]. However, an additional concern for the presented system is that the amplitude of the output beam from the transmitter changes per output field point as discussed in the overall efficiency discussion in Section 4.7. We employed a Constant Fraction Discriminator (CFD) to avoid signal walk due to varying return signal amplitude [24].

Figure 6 shows the schematic of our custom constant fraction discriminator. A first op-amp (a) receives the signal from the APD, delays it, and sends it to a second op-amp (b) to sum the delayed pulse signal to the original. A comparator (c) then outputs a digital time-stamped signal based on the amplitude-independent inflection point. Power rails (d) and (e) and input threshold voltage (f) drive the ICs.

 figure: Fig. 6.

Fig. 6. Custom constant fraction discriminator design including: (a) delay op-amp, (b) summing op-amp, (c) comparator, (d) and (e) power rails, and (f) tunable threshold for comparator.

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Figure 7 shows the simulated output (OrCAD PSPICE) of our custom CFD from (a) the summing op-amp, including the input-amplitude-independent inflection point, and (b) the amplitude-dependent 0.2 ns signal walk of the comparator’s output, sufficiently low for the lidar demo. We implemented the combined digital and analog circuit (except APD) into a single printed circuit board (PCB) shield for the Arduino Uno in order to minimize wiring and signal noise. A non-inverting amplifier (HP 8447A, 20 dB) was added between the APD and CFD.

 figure: Fig. 7.

Fig. 7. (a) Summing op-amp output. (b) Comparator output with ∼0.2 ns amplitude-dependent signal walk.

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4.2 Receiver optics

The receiver is comprised of a 905 nm bandpass filter (Thorlabs, FL905-25) mounted onto an APD (Thorlabs, APD130A, Si Ø1 mm). The APD has an incident-angle-dependent response for an effective Numerical Aperture (NA), or equivalently a circular acceptance pupil. To match the horizontally-elongated scan to the circular acceptance pupil of the APD, a part of the vertical NA of the APD was reallocated to expand the horizontal NA by edge mirrors segmenting the vertical acceptance pupil of the APD. Figure 8(a) depicts the mirrors redirecting the upper and lower edges of the APD acceptance pupil. Figure 8(b) shows the initial APD acceptance pupil, and Fig. 8(c) shows the redirecting APD acceptance pupil covering the entire FOV region of interest. The APD acceptance pupil is only depicted as a hard cutoff—in reality, the APD angle-dependent source sensitivity rolls off at steeper angles due to decreasing cosine APD projected area increasing APD-surface reflectivity.

 figure: Fig. 8.

Fig. 8. (a) Mirrors redirecting the upper and lower portions of the APD acceptance pupil to the far left and right sides of the FOV. The acceptance pupil of the APD is shown (b) before mirror redirection, and (c) after.

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Since the focus of this work is on the ASLM-based beam steering transmitter, additional optics were not employed in the receiver to keep the results applicable and scalable. For instance, a lens could have been used between the APD and pupil-segmenting mirrors to optimize throughput across the FOV to the detector. However, this would have spread the lens-based vignetting issues at the edge of the FOV to the center of the FOV due to the pupil-segmenting mirrors. Rather, the use of bare APD, with pupil-segmenting mirrors to keep all high-angle targets at a small APD angle-of-incidence, maintains a relatively-ideal receiver with a 1 mm entrance pupil diameter across the entire wide-angle FOV. This simple receiver setup maintains the validity of the transmitter testing. It also enables easy scaling: adding receiver optics with a 10 mm diameter entrance pupil covering the entire FOV would enable a 100X signal improvement, or a 10X range improvement. This is explained further in Section 6.2.

4.3 Transmitter optics

The transmitter of the lidar system uses a 905 nm laser module (Laser Components, LS9-220-8-S10-00) emitting 8 ns, 1760 nJ pulses [25]. The laser module has a 3-element laser diode, each 235 µm × 10 µm element is separated by about 200 µm for a total emitting area of 235 µm × 400 µm [26]. When the output is collimated by a single lens, the output is of three narrow lobes with significant separation. The two side lobes were spatially filtered out to maintain a constant illumination angle-of-incidence on the DMD. The center lobe was also cropped by an iris to ensure illumination was confined to a single DMD quad-block (see Section 5.3) and was not clipped by the DMD active area edge. Each lobe has the energy of 1760/3 = 587 nJ, and we estimate the iris to pass 25% of the central lobe by area for the DMD to receive an approximate illumination pulse energy of 147 nJ.

As described in Section 3.5, the DMD has 8 diffraction orders at 532 nm, and the available angular extent for floor(8.5) diffraction orders causes the off-state light to be distributed equally into diffraction orders +3 and +4 when diffraction order -4 is directed in the on-state direction. By using the same Norder = $floor\left( {\frac{{4 \ast {\theta_{\textrm{mirror}}}}}{{{{\sin }^{ - 1}}({{{2\lambda } / p}} )}}} \right)$ equation, the DMD has 4 fully-independent diffraction orders at 905 nm across the 48° micromirror sweep. However, before the floor function, Norder = floor(4.97). Because 4.97 is so close to 5, we round it up and later address the marginal off-state crosstalk that occurs. In the transmitter, the collimated beam illuminated the DMD to output across four non-off-state output diffraction orders into the 1D spatial filter, similar to Fig. 4, and the off-state light was blocked by a baffle. Each of the four diffraction orders (-2,-1,0,1) scanned an 8×6 array of points for a combined array of 32×6 = 192 points. The FOV is anticipated to be reduced without the use of the off-state +2 diffraction order. However, the angular extent of the fine grating-based beam steering scales with wavelength, expanding the extent of the fine steering.

The transmitter’s output was projected onto a screen to measure the transmitter’s FOV. The transmitter subtended an FOV of 44°×2.2° (H×V). Given the 32×6 (H×V) sampling, the anticipated Instantaneous Field-of-View (IFOV) is 1.4°×0.4°.

4.4 Distance resolution measurement

Distance resolution was tested for a single DMD grating and diffraction order combination. Diffraction order -1 was used, neither an edge diffraction order nor 0 which contains the cover glass reflection, and a center grating of the 8×6 array was used, with neither the smallest nor the greatest diffraction deviation angle. 10 distance measurements were taken for each target distance from 15 cm to 100 cm at 5 cm increments. The distance accuracy is shown in Fig. 9(a) with a calculated root sum square (RSS) resolution of 10.1 cm. An earlier, higher-noise, breadboard version of the TOF circuit achieved 6.8 cm resolution in a different optical system with significantly more signal [23]. This new TOF PCB has demonstrated 3 cm distance resolution in tests of other optical systems with greater transmitter efficiencies. The RSS error is reduced to 4.1 cm when the 10 measurements of the presented system are averaged per target distance. It is therefore clear the distance resolution of this lidar system is limited by a combination of the electronics and the transmitter output energy, and not the DMD-based ASLM beam steering mechanism. The transmitter output energy of this system can be improved as outlined in Section 6.1.

 figure: Fig. 9.

Fig. 9. (a) Distance accuracy for diffraction order -1 and a center-most grating pattern on the DMD. (b) Horizontal, (c) vertical angular resolution testing by lidar capture of a single-pixel-wide target.

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The system was found to measure a target at distances slightly beyond 100 cm, but the distance resolution was significantly reduced, so the maximum distance for the current iteration was limited 100 cm.

4.5 Angular resolution measurement

A vertical line target was used to determine the horizontal angular resolution. The width of the target was decreased at a fixed target distance until only a single-pixel-wide line was captured by the lidar system. The same process was used with a horizontal line target determine the vertical angular resolution. The angular resolution was measured to be 0.9°×0.4° (H×V). The measured horizontal IFOV is finer than the transmitter’s anticipated 1.4° angular resolution. This deviation is likely due to the non-unity fill-factor of scan points (see gaps between points in zoom-in of Fig. 5). Figure 9 also shows the captures of the (b) vertical and (c) horizontal targets. The variable distance measured, particularly for the horizontal line target in Fig. 9(c), is likely due to part of the output pulse area missing the target. While the CFD ideally compensates for return signal magnitude variation, the design is imperfect.

The transmitter’s FOV was previously measured as 44°×2.2° (H×V). The full lidar system’s FOV was verified to be equivalent to the transmitter’s FOV by moving targets over the edge of the transmitter’s projected area and viewing live captures.

4.6 Video capture testing

The DLP3000 DMD has a binary refresh rate limit of 4 kHz [19]. The lidar sample rate is therefore 2 kHz due to the required black pattern reset between samples as described in Section 2.2. A 2 kHz sample rate across 192 points corresponds to a frame rate of 10.4 FPS. However, additional time is primarily required to transfer the TOF data from a time-to-digital converter (Texas Instruments, TDC7200) to the driving Arduino Uno, and to transfer the distance data points from the Arduino Uno to an SRAM memory chip (Microchip, 23LC1024) [23]. The ladder is necessary for longer video captures due to limited on-board memory on the Arduino Uno. Other small microsecond-scale delays were necessary for correct IC functionality. The frame rate was calculated by using the on-board timing function of the Arduino Uno across a 100-frame capture. Successive tests demonstrated a frame rate of 7.8 FPS. The average sample rate, including data-transfer time between frame captures, is 1.5 kHz. Improvements in the electronics would remove the Arduino Uno and IC bottlenecks and would be necessary for the 32 kHz DLP7000 implementation discussed in Section 6.2.

A highly reflective target (Styrofoam cup) pendulum swinging from the lab’s ceiling was used as a moving target. 100-frame lidar video captures were taken of the moving target with simultaneous RGB video captures. The two videos were synchronized for real-time playback. Visualization 1 shows the pendulum target swinging linearly across the FOV. Visualization 2 shows the pendulum target swinging in a circle across the FOV. Figure 10 is the first frame of Visualization 1 including the synchronized (a) RGB video and (b) lidar video.

 figure: Fig. 10.

Fig. 10. The first frame of Visualization 1, video capture of a swinging target, including synchronized (a) RGB video and (b) lidar video.

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The reflected signal from the target is significantly weaker at the side edges of the cup target due to the glancing angle-of-incidence, sometimes causing narrower target responses. The 0th order diffraction order has some energy from the cover glass reflection, not fully blocked by the single-sideband filter, causing significant noise when the target is in that direction.

4.7 Overall efficiency measurement

Diffraction and/or overall efficiency (nomenclature depending) has been reported for each DMD-based blazed grating beam steering [16], SLM-based holographic beam steering [27,28], and DMD-specific holographic beam steering [29,30]. The overall efficiency of simultaneous DMD-based blazed grating coarse beam steering and holographic fine beam steering is reported in Table 1 for the four diffraction orders for 905 nm at three different holograms spanning the full vertical deviation range.

Tables Icon

Table 1. Overall Efficiency (%) Across Diffraction Orders and Y-axis Range

The overall efficiency per beam steering direction was calculated by dividing a measured signal response from an APD capturing the output beam steered light by a later-measured signal response from the same APD receiving the DMD-input illumination (i.e., DMD physically replaced by APD). The same APD (Hamamatsu C12702-04) was used for all measurements, and it was affixed with a 10 mm diameter collecting lens to focus the full beam light onto the APD. The APD was precisely aligned for each beam steering direction, and a N=100 cycle averaging was used to reduce noise and per-pulse fluctuations. Special care was taken to ensure the same beam footprint illuminating the DMD was captured by the APD when the DMD was replaced with the APD.

The dynamic range of the APD was increased by adding neutral density filters for all beam steered measurements, removing them for the DMD illumination measurement, and back calculating the beam steered measurements without neutral density filters. The attenuation of each neutral density filter was measured using the same 905 nm laser and APD.

The hologram gratings were calculated by interfering two plane waves based on k-vectors: one along the z-axis normal to the DMD, and one calculated from input x-y direction cosines. For the 905 nm beam steering system, the 8×6 (H×V) array of points subtends the x-axis direction cosine $\vec{r} \cdot \hat{x} = \cos \alpha$ from -0.074 to +0.074, and the y-axis direction cosine $\vec{r} \cdot \hat{y} = \cos \beta$ from 0.018 to 0.08. The y-axis range starts at 0.018 to separate the 1st order range from the 0th order point for single-sideband filtering as shown in Fig. 2(b).

SLM-based holographic beam steering has been reported to have diffraction efficiency roll-off with increased 1st order deviation angle due to the sinc function envelope of the SLM in the frequency domain [27,28]. Overall efficiency was measured for three holograms covering the full vertical angular extent to observe the roll-off with increased angular deviation (i.e., with decreased hologram grating pitch). The horizontal deviation due to each hologram (or x-axis coordinate) is 0. The roll-off is demonstrated for each diffraction order in Table 1 across y-axis coordinates (or normalized vertical coordinates). The roll-off can be inferred to other directions of steering from previous reports [27,28].

DMD-based blazed grating beam steering anticipates reduced diffraction efficiency toward higher (positive) diffraction orders due to a variable fill-factor from the cosine projected area of the tilted micromirrors [17]. Moreover, the variable fill-factor also anticipates odd-order suppression—that odd diffraction orders have reduced diffraction efficiency [17]. Both of these anticipated characteristics are observed in Table 1, with the exception of the +1 diffraction order. As discussed in Section 4.3, we anticipated some off-state light being directed into diffraction order +1 because the micromirrors’ non-rounded angular extent spans up to floor(4.97) diffraction orders, barely missing 5. This likely caused some off-state light to be directed into the +1 diffraction order during the overall efficiency measurement. This is similar to the 532 nm setup in which the off-state light was spread across diffraction orders +3 and +4. This off-state crosstalk was not apparent in the lidar images, which can be explained by the CFD’s noise reducing threshold: the magnitude of the added off-state light in diffraction order +1 was smaller than any intended non-off-state diffraction order, therefore likely below the magnitude required to return a signal for TOF measurement. While this may have marginally reduced the accuracy of distance measurements in diffraction order -2 to 0, it may have also enhanced the accuracy of distance measurements in diffraction order +1.

The measured overall efficiency range can be justified through a combination of efficiency components as listed in Table 2 and described as follows. The DLP3000 has a 92% fill-factor, which must be considered for two efficiency components [19]. First, the fill-factor attenuates the beam geometrically: light incident on sub-structure between micromirrors is assumed to be absorbed, scattered, and/or reflected into the same direction as light reflected by the cover glass. Second, though a phase blazed grating has a theoretical diffraction efficiency of 100%, a reduced fill-factor will shift energy from the intended diffraction order to neighboring diffraction orders [31]. This is not double-counting the fill-factor because the first is geometrical attenuation and the second is diffractive redirection. The DLP3000 datasheet claims an 86% diffraction efficiency on this point [19], but this is a theoretical calculation based on an input F/3 broadband illuminated ideal DMD reflecting light into an F/2.4 projection aperture—not as applicable for a single wavelength with collimated illumination directing light into a single diffraction order (point rather than extended aperture). A DMD used as a binary switch for optical communications near 1550 nm satisfied the blaze condition to couple 88% of diffracted energy into a single diffraction order [29]. Our previous diffraction efficiency analysis at 905 nm [16] and crosstalk measurements at 532 nm [17] support the general range, so 88% was used as the anticipated single-order diffraction efficiency due to the fill-factor (amount of diffracted light directed into the selected diffraction order over the amount of light directed into all diffraction orders). The efficiency of an ideal binary amplitude grating is 10.1% [31], though the fill-factor is not considered again to avoid double-counting it. The DLP3000 has a Corning Eagle XG window with a visible Anti-Reflection (AR) coating designed for random polarization [19]. The window has a single-pass transmittance of about 85% at 905 nm at normal incidence [32]. The single-pass transmittance graph is only reported out to 800 nm for a 30° angle-of-incidence, but interpolating out to 905 nm at 23° angle-of-incidence supports a single-pass transmittance of 80%. Moreover, the anticipated single-pass transmission is further reduced to 78% to account for the s-oriented polarization of the 905 nm laser, since we anticipate p-oriented polarization to have higher transmission. The cover glass transmission is 60.8% in double-pass. The uncoated lens array assumes 96% transmission per surface due to Fresnel reflection. The negative lens array was removed during efficiency testing, so the total lens array transmission from four surfaces is anticipated to be 84.9%. The DLP3000 has aluminum micromirrors [19]. The DLP3000 datasheet claims an 88% micromirror reflectivity from 420 nm to 700 nm [19], though the average reflectivity for aluminum is about 91.3% for the same range [33]. The discrepancy may be due to the thinness or surface structure. The reflectivity of aluminum at 905 nm is about 89% [33], so we will assume an equivalent 3.3% margin to the micromirror reflectivity down to 85.7%. Multiplying all efficiency components finds an anticipated overall efficiency of 3.6%.

Tables Icon

Table 2. Efficiency Components and Anticipated Overall Efficiency

A DMD, used in a binary (non-transitioning) mode, was previously reported to steer 635 nm light within the “on” state diffraction order using programmable Fresnel zone plates for 3.8% overall efficiency [30]. This previous system is limited to holographic steering within the “on” state diffraction order, rather than across all diffraction orders between “off” and “on” as shown here. However, this is a very similar experimental setup and supports the measured overall diffraction efficiency reported in Table 2. The 3.8% overall efficiency is greater than the current reported system’s anticipated 3.6% overall efficiency primarily due to: (1) the previously reported system did not have two added lenses after the DMD which would improve the overall efficiency by 15.1%; and (2) the previous system was reported at 635 nm, with a cover glass double-pass transmission likely around 95% [32], increasing the overall efficiency by 34.2%.

The measured overall efficiency may have been further reduced beyond the anticipated overall efficiency by other attenuation factors: (1) variable angle-of-incidence upon second transmission through the cover glass (after DMD beam steering); (2) non-normal incidence through the lenses after the DMD; and (3) incorrect micromirror reflectivity identified.

5. Discussions

5.1 Effective Pixel Pitch

The grating equation dictates that, assuming normal-incidence, the maximum deflection angle of the ±1 diffraction orders from an SLM-based grating is ${\sin ^{ - 1}}[{{\lambda / {({2p} )}}} ]$, for wavelength λ and corner-to-corner pixel pitch p with a rectangular pixel grid [12]. The DLP3000 DMD has a corner-to-corner pixel pitch of 10.8 µm [19], corresponding to a maximum deviation angle of 2.4° at 905 nm, or a full FOV of 4.8°. The presented system, with a 44° full FOV (ignoring off-state light), achieves an effective corner-to-corner pixel pitch of 1.208 µm—about a 9X pixel pitch reduction. The ASLM-based holographic beam steering does not, of course, reduce the physical size of the pixels, but rather overlays a blazed grating phase map over the binary amplitude grating represented on a diamond offset pixel grid for a significant and programmable angular advantage.

5.2 Optical design for FOV fill-factor compensation

The following outlines a design to more accurately compensate for the horizontal FOV fill-factor while maintaining collimated output (see non-unity horizontal fill-factor of Fig. 2(b)). Figure 11(a) shows the far-field output of the ASLM holographic beam steering system with five output diffraction orders with accurate diffraction order angles at 905 nm (including off-state light for future development). Figure 11(b) shows a telescope array positioned across the five output diffraction orders to stretch each channel’s horizontal FOVs. The first elements are all equivalent plano-convex-conics, and the second elements are all equivalent plano-concave-conics, and different decenters across the different diffraction orders are used to compensate for the non-linear output diffraction order angles. Each lens is only tilted to be perpendicular to respective diffraction order’s optical axis. Figure 11(c) shows the horizontal equally-spaced far-field outputs of the compensated system.

 figure: Fig. 11.

Fig. 11. (a) Uncompensated far-field fill-factor. (b) Telescope array with diffraction-order-specific decenters. (c) Compensated far-field without gaps in FOV scanning

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5.3 DMD block refresh

The experimental setup employs the DLP Lightcrafter Evaluation Module with the DLP3000 DMD, equivalent to the reported ASLM display application [17], which has a quad-block refresh for which a phased reset occurs across four blocks of DMD micromirrors. The cascaded reset of the four quads causes a quad-dependent efficiency if the entire DMD is illuminated with a single short pulse into a transitional diffraction order. Figure 12 shows the quad-dependent efficiency change, where the micromirrors of each quad are at different angles mid-transition.

 figure: Fig. 12.

Fig. 12. Quad-block-dependent diffraction efficiency due to phased reset. Reprinted from [17].

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The quad-block reset allows the DMD to actuate one block of pixels while loading data to another block of pixels to achieve a higher reset rate. Other DMDs and drivers, such as the DLP7000 driven by the Discovery 4100, can use a global reset to actuate all micromirrors at once. We only illuminated one quad block through testing to maintain efficient beam steering, to prevent cross talk, and for convenience of the Lightcrafter Evaluation Module with the DLP3000. Until expanded to the DLP7000, the beam area is therefore limited to one quad block: 3.7×1.64 mm.

6. Future work

6.1 Light recycling techniques

The main optical efficiency limiting factor of the presented beam steering system is the 10.1% diffraction efficiency into each +1 and -1 diffraction orders due to the binary amplitude hologram. To adjust for this bottleneck, we previously presented light recycling techniques for DMD-diffraction-based lidar systems to increase the diffraction efficiency into intended beam steered directions [34]. Our work experimentally verified a previously-presented DMD-based phase modulation system [35], and we presented a concept employing a 1D retroreflector array to reflect light from the -1 diffraction order into the +1 diffraction order.

While binary amplitude holograms diffract light into the +1 and -1 diffraction orders each at a 10.1% diffraction efficiency, binary 0-to-π phase holograms diffract light into the +1 and -1 diffraction orders each at a 40.5% diffraction efficiency [31]. We propose merging the DMD-based phase modulation system with our DMD-based ASLM holographic lidar system to harness the phase hologram efficiency of 40.5%. Furthermore, employing a 1D retroreflector array to reflect the -1 hologram diffraction order into the +1 hologram diffraction order would increase the hologram diffraction efficiency to 81%, an 8X improvement factor. Figure 13 shows the effect of a 1D retroreflector array redirecting a +1 diffraction order from a binary grating into the opposite -1 diffraction order direction.

 figure: Fig. 13.

Fig. 13. Light reflection off a 1D retroreflector array from (a) a global perspective, and (b) a single-element perspective. Reprinted from [31].

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6.2 System scaling

The current receiver is a 1 mm diameter APD without collection optics other than pupil-segmenting mirrors (Fig. 8). The current max distance is 1 m. As stated above in Section 4.2, if collection optics were added with a 10 mm entrance pupil diameter, the 100X receiver area improvement would lead to a 10X max distance improvement to 10 m. A quick first-order calculation of étendue verifies that a 10 mm diameter entrance pupil diameter lens is feasible. The APD’s étendue can be calculated by EAPD=AAPDΩAPD/2, where AAPD is the 0.79 mm2 area of the APD, ΩAPD is the 2π str acceptance solid-angle of the APD, and the ½ factor assumes a Lambertian angular responsivity of the APD [3,4]. By conservation of étendue, additional collection optics would have an étendue limit of Eoptics=AopticsΩFOV=EAPD, where Aoptics is the entrance pupil area of the collection optics, and ΩFOV is the 2.2°×44°=0.03 str solid-angle of the lidar system’s FOV [3,4]. The maximum entrance pupil area is then Aoptics=EAPDFOV, for a maximum entrance pupil diameter of 10.3 mm.

As previously discussed in Section 5.3, the quad-block reset in the DLP3000 restricts our beam size from the full active area of the DMD, 3.70 mm × 6.57 mm, down to a single quad area, 3.70 mm × 1.64 mm. The output beam size must be considered since 905 nm is a water-permeable wavelength [4]. While 1550 nm is a “safe” wavelength, it is less ideal for certain weather conditions [4]. Since the irradiance of the beam is capped for the maximum permissible exposure of the eye, increasing the beam area scales linearly with maximum output energy. The maximum measurable distance of a lidar system with a collimated transmitter output scales with the square root of pulse energy [4]. Larger DMDs are available to scale the output beam footprint. The DLP7000 DMD has an active area of 10.5 mm × 14.0 mm and global reset capabilities (as opposed to quad-block) [36] for about a 24.2X beam area improvement factor—about a 4.9X max distance improvement factor above a max-energy eye-safe DLP3000 implementation.

Anti-reflection coatings on lenses (96% to 99% per surface) and the cover glass (78% to 97% single-pass [32]) could have a 75% power improvement, or about a 1.3X distance improvement factor. If the light recycling techniques of Section 6.1 were implemented, including the 1D retroreflector and the DMD-based phase-only modulation which would need more development, the theoretical diffraction efficiency of the binary grating would improve from 10.1% to 81%, an 8X power improvement factor, or a 2.8 distance improvement factor. Scaling from the presented system and incorporating all improvement factors leads to a theoretical max range of (1 m × 10 (receiver lens) × 4.9 (DLP7000 area) × 1.3 (AR coatings) × 2.8 (phase hologram and 1D retroreflector)) = 184 m (when factors not rounded). There are two caveats to this number: (1) eye-safety would be architecture-dependent so the maximum laser output may change; (2) the CFD is designed for a 100 mV input from the APD + amplifier to allow for a sizeable noise threshold, but improved electronics could significantly reduce noise and the required APD response for TOF measurement to increase the maximum ranging distance of the system.

A comparison of MEMS-based scanners’ output beam diameters and angular throws was previously reported [23]. Many competitive MEMS-based scanning mirrors have mirror diameters of 1 to 5 mm, with half-angle mechanical throws ranging from 1° to 20° [23]. However, for resonant MEMS mirrors, inverse relationships exist between a mirror’s size and its angular throw, and between a mirror’s size and its scan speed [37]. A DLP7000 implementation would be highly desirable with a 16 kHz scan rate (32 kHz binary pattern reset, and 2 binary patterns per scan point due to black pattern reset), 147 mm2 beam area, and 44° scanning field (before telescoping optics).

The DLP7000 DMD has a corner-to-corner pixel pitch of 19.3 µm—a 79% increase above the DLP3000 [19,36]. While this reduces the FOV of a typical grating hologram, the 48° angular sweep of the micromirrors is maintained, making more transitional diffraction orders of the DMD (accounting for off-state diffraction orders, the lidar FOV is still approximately 44°). The horizontal FOV is therefore maintained, the vertical FOV is decreased, and the horizontal and vertical IFOV is decreased for finer resolution scanning. The number of points is generally programmable as with any SLM-based hologram.

6.3 Additional DMD beam steering techniques

Additional DMD-based beam steering advancements have been explored. A multi-pulse lidar system was reported in which multiple pulses are incident on the DMD mirrors during one transition of the micromirrors to improve sampling rate [38,39]. If implemented into this ASLM holographic beam steering system, multiple blazed grating diffraction orders could be sampled with the same hologram output during a single transition of the DMD for higher sampling rates. A multi-beam lidar system was also reported, in which multiple sources are incident upon the DMD from different directions to improve the coarse diffraction order angular resolution [40]. Implementing the multi-beam technique into the presented system would enable higher angular resolution and continuous scanning of the FOV without fill-factor-compensating optics (e.g., negative lens array or telescope array). Multiple sources can also be used to increase the vertical FOV.

7. Conclusion

We have reported angular spatial light modulation (ASLM) at a single plane for a fine-coarse multiplexed beam steering technique merging DMD-based programmable blazed grating beam steering with SLM-based holographic beam steering. We have demonstrated a MEMS-level kHz sampling rate, a video frame rate, and a 44° wide FOV lidar system, and we have outlined paths toward a 32 kHz, large beam, high-efficiency system.

Funding

National Defense Science and Engineering Graduate; Air Force Research Laboratory; Achievement Rewards for College Scientists Foundation (Saba Scholar).

Disclosures

The authors have patents pending on aspects of the presented system.

References

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2. A. Kasturi, V. Milanovic, B. H. Atwood, and J. Yang, “UAV-Borne LiDAR with MEMS Mirror Based Scanning Capability,” Proc. SPIE 9832, 98320M (2016). [CrossRef]  

3. J. Greivenkamp, Field Guide to Geometrical Optics (SPIE, 2004).

4. P. McManamon, Field Guide to Lidar (SPIE, 2015).

5. Mirrorcle Technologies, Inc., “Mirrorcle Technologies MEMS Mirrors – Technical Overview,” https://www.mirrorcletech.com/pdf/Mirrorcle%20Technologies%20MEMS%20Mirrors%20-%20Technical%20Overview.pdf

6. M. Reicherter, T. Haist, E. Wagemann, and H. Tiziani, “Optical particle trapping with computer-generated holograms written on liquid-crystal display,” Opt. Lett. 24(9), 608–610 (1999). [CrossRef]  

7. C. Schmitz, S. Joachim, and J. Curtis, “High-precision steering of multiple holographic optical traps,” Opt. Express 13(21), 8678–8685 (2005). [CrossRef]  

8. E. Marom and N. Konforti, “Dynamic optical interconnects,” Opt. Lett. 12(7), 539–541 (1987). [CrossRef]  

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10. E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087, 13–23 (2003). [CrossRef]  

11. D. Engstrom, J. Bengtsson, E. Eriksson, and M. Goksor, “Improved beam steering accuracy of a single beam with a 1D phase-only spatial light modulator,” Opt. Express 16(22), 18275–18287 (2008). [CrossRef]  

12. Y. Soskind, Field Guide to Diffractive Optics (SPIE, 2011), pp. 48.

13. J. Kaakkunen, I. Vanttaja, and P. Laakso, “Fast Micromachining Using Spatial Light Modulator and Galvanometer Scanner with Infrared Pulsed Nanosecond Fiber Laser,” J. Laser Micro/Nanoeng. 9(1), 37–41 (2014). [CrossRef]  

14. G. Thalhammer, R. Bowman, G. Love, M. Padgett, and M. Ritsch-Marte, “Speeding up liquid crystal SLMs using overdrive with phase change reduction,” Opt. Express 21(2), 1779–1797 (2013). [CrossRef]  

15. P. Ross, “Luminar's Lidar Enters Mass Production,” IEEE Spectrum (2018). https://spectrum.ieee.org/cars-that-think/transportation/sensors/luminars-lidar-enters-mass-production

16. B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017). [CrossRef]  

17. B. Hellman and Y. Takashima, “Angular and spatial light modulation by single digital micromirror device for multi-image output and nearly-doubled etendue,” Opt. Express 27(15), 21477–21496 (2019). [CrossRef]  

18. Y. Takekawa, Y. Takashima, and Y. Takaki, “Holographic display having a wide viewing zone using a MEMS SLM without pixel pitch reduction,” Opt. Express 28(5), 7392–7407 (2020). [CrossRef]  

19. Texas Instrument, Inc., “DLP3000 DLP® 0.3 WVGA Series 220 DMD,” https://media.digikey.com/pdf/Data%20Sheets/Texas%20Instruments%20PDFs/DLP3000.pdf.

20. M.-C. Park, B.-R. Lee, J.-Y. Son, and O. Chernyshov, “Properties of DMDs for holographic displays,” J. Mod. Opt. 62(19), 1600–1607 (2015). [CrossRef]  

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23. B. Hellman, A. Gin, B. Smith, Y.-S. Kim, G. Chen, P. Winkler, P. McCann, and Y. Takashima, “Wide-angle MEMS-based imaging lidar by decoupled scan axes,” Appl. Opt. 59(1), 28–37 (2020). [CrossRef]  

24. M.-C. Amann, T. Bosch, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of unusual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001). [CrossRef]  

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27. D. Leyva, B. Robertson, C. Henderson, T. Wilkinson, D. O’Brien, and G. Faulkner, “Cross-talk analysis in a telecentric adaptive free-space optical relay based on a spatial light modulator,” Appl. Opt. 45(1), 63–75 (2006). [CrossRef]  

28. Z. Zhang, H. Yang, B. Robertson, M. Redmond, M. Pivnenko, N. Collings, W. Crossland, and D. Chu, “Diffraction based phase compensation method for phase-only liquid crystal on silicon devices in operation,” Appl. Opt. 51(17), 3837–3846 (2012). [CrossRef]  

29. W. Duncan, T. Bartlett, B. Lee, D. Powell, P. Rancuret, and B. Sawyers, “Dynamic optical filtering in DWDM systems using the DMD,” Solid-State Electron. 46(10), 1583–1585 (2002). [CrossRef]  

30. D. Benton, “Multiple beam steering using dynamic zone plates on a micromirror array,” Opt. Eng. 57(07), 1 (2018). [CrossRef]  

31. J. Goodman, Introduction to Fourier Optics, Third Edition (McGraw-Hill, 2004), problems P4.13-15.

32. Texas Instruments, “Wavelength Transmittance Considerations for DLP DMD Window,” http://www.ti.com/lit/an/dlpa031e/dlpa031e.pdf.

33. A. D. Rakić, “Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum,” Appl. Opt. 34(22), 4755–4767 (1995). [CrossRef]  

34. G. Chen, B. Hellman, J. Rodriguez, B. Smith, A. Gin, and Y. Takashima, “Light recycling beam steering on a DMD lidar,” Proc. SPIE 10757, 107570G (2018). [CrossRef]  

35. M. Hoffmann, I. Papadopoulos, and B. Judkewitz, “Kilohertz binary phase modulator for pulsed laser sources using a digital micromirror device,” Opt. Lett. 43(1), 22–25 (2018). [CrossRef]  

36. Texas Instruments, “DLP7000 DLP 0.7 XGA 2x LVDS Type A DMD,” http://www.ti.com/lit/ds/symlink/dlp7000.pdf.

37. Mirrorcle Technologies, Inc., “Mirrorcle Technologies MEMS Mirrors – Technical Overview,” https://www.mirrorcletech.com/pdf/Mirrorcle%20Technologies%20MEMS%20Mirrors%20-%20Technical%20Overview.pdf.

38. J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y. Kim, D. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3 K.7.

39. J. Rodriguez, B. Smith, B. Hellman, and Y. Takashima, “Fast laser beam steering into multiple diffraction orders with a single digital micromirror device for time-of-flight lidar,” Appl. Opt. (to be published). [CrossRef]  

40. J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018). [CrossRef]  

References

  • View by:

  1. S. I. Artamonov, N. A. Gryaznov, V. I. Kuprenyuk, N. A. Romanov, and E. N. Sosnov, “Selection of scanners for use in lidar systems,” J. Opt. Technol. 83(9), 549–555 (2016).
    [Crossref]
  2. A. Kasturi, V. Milanovic, B. H. Atwood, and J. Yang, “UAV-Borne LiDAR with MEMS Mirror Based Scanning Capability,” Proc. SPIE 9832, 98320M (2016).
    [Crossref]
  3. J. Greivenkamp, Field Guide to Geometrical Optics (SPIE, 2004).
  4. P. McManamon, Field Guide to Lidar (SPIE, 2015).
  5. Mirrorcle Technologies, Inc., “Mirrorcle Technologies MEMS Mirrors – Technical Overview,” https://www.mirrorcletech.com/pdf/Mirrorcle%20Technologies%20MEMS%20Mirrors%20-%20Technical%20Overview.pdf
  6. M. Reicherter, T. Haist, E. Wagemann, and H. Tiziani, “Optical particle trapping with computer-generated holograms written on liquid-crystal display,” Opt. Lett. 24(9), 608–610 (1999).
    [Crossref]
  7. C. Schmitz, S. Joachim, and J. Curtis, “High-precision steering of multiple holographic optical traps,” Opt. Express 13(21), 8678–8685 (2005).
    [Crossref]
  8. E. Marom and N. Konforti, “Dynamic optical interconnects,” Opt. Lett. 12(7), 539–541 (1987).
    [Crossref]
  9. D. C. O’Brien, R. J. Mears, and W. A. Crossland, “Dynamic holographic interconnects that use ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 33(14), 2795–2803 (1994).
    [Crossref]
  10. E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087, 13–23 (2003).
    [Crossref]
  11. D. Engstrom, J. Bengtsson, E. Eriksson, and M. Goksor, “Improved beam steering accuracy of a single beam with a 1D phase-only spatial light modulator,” Opt. Express 16(22), 18275–18287 (2008).
    [Crossref]
  12. Y. Soskind, Field Guide to Diffractive Optics (SPIE, 2011), pp. 48.
  13. J. Kaakkunen, I. Vanttaja, and P. Laakso, “Fast Micromachining Using Spatial Light Modulator and Galvanometer Scanner with Infrared Pulsed Nanosecond Fiber Laser,” J. Laser Micro/Nanoeng. 9(1), 37–41 (2014).
    [Crossref]
  14. G. Thalhammer, R. Bowman, G. Love, M. Padgett, and M. Ritsch-Marte, “Speeding up liquid crystal SLMs using overdrive with phase change reduction,” Opt. Express 21(2), 1779–1797 (2013).
    [Crossref]
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2020 (2)

2019 (1)

2018 (4)

D. Benton, “Multiple beam steering using dynamic zone plates on a micromirror array,” Opt. Eng. 57(07), 1 (2018).
[Crossref]

G. Chen, B. Hellman, J. Rodriguez, B. Smith, A. Gin, and Y. Takashima, “Light recycling beam steering on a DMD lidar,” Proc. SPIE 10757, 107570G (2018).
[Crossref]

M. Hoffmann, I. Papadopoulos, and B. Judkewitz, “Kilohertz binary phase modulator for pulsed laser sources using a digital micromirror device,” Opt. Lett. 43(1), 22–25 (2018).
[Crossref]

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

2017 (1)

2016 (2)

S. I. Artamonov, N. A. Gryaznov, V. I. Kuprenyuk, N. A. Romanov, and E. N. Sosnov, “Selection of scanners for use in lidar systems,” J. Opt. Technol. 83(9), 549–555 (2016).
[Crossref]

A. Kasturi, V. Milanovic, B. H. Atwood, and J. Yang, “UAV-Borne LiDAR with MEMS Mirror Based Scanning Capability,” Proc. SPIE 9832, 98320M (2016).
[Crossref]

2015 (1)

M.-C. Park, B.-R. Lee, J.-Y. Son, and O. Chernyshov, “Properties of DMDs for holographic displays,” J. Mod. Opt. 62(19), 1600–1607 (2015).
[Crossref]

2014 (1)

J. Kaakkunen, I. Vanttaja, and P. Laakso, “Fast Micromachining Using Spatial Light Modulator and Galvanometer Scanner with Infrared Pulsed Nanosecond Fiber Laser,” J. Laser Micro/Nanoeng. 9(1), 37–41 (2014).
[Crossref]

2013 (1)

2012 (1)

2008 (1)

2006 (1)

2005 (1)

2003 (1)

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087, 13–23 (2003).
[Crossref]

2002 (1)

W. Duncan, T. Bartlett, B. Lee, D. Powell, P. Rancuret, and B. Sawyers, “Dynamic optical filtering in DWDM systems using the DMD,” Solid-State Electron. 46(10), 1583–1585 (2002).
[Crossref]

2001 (1)

M.-C. Amann, T. Bosch, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of unusual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

1999 (1)

1995 (1)

1994 (1)

1987 (1)

1968 (1)

Amann, M.-C.

M.-C. Amann, T. Bosch, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of unusual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

Artamonov, S. I.

Atwood, B. H.

A. Kasturi, V. Milanovic, B. H. Atwood, and J. Yang, “UAV-Borne LiDAR with MEMS Mirror Based Scanning Capability,” Proc. SPIE 9832, 98320M (2016).
[Crossref]

Bartlett, T.

W. Duncan, T. Bartlett, B. Lee, D. Powell, P. Rancuret, and B. Sawyers, “Dynamic optical filtering in DWDM systems using the DMD,” Solid-State Electron. 46(10), 1583–1585 (2002).
[Crossref]

Bengtsson, J.

Benton, D.

D. Benton, “Multiple beam steering using dynamic zone plates on a micromirror array,” Opt. Eng. 57(07), 1 (2018).
[Crossref]

Bosch, T.

M.-C. Amann, T. Bosch, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of unusual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

Bowman, R.

Bryngdahl, O.

Chen, G.

B. Hellman, A. Gin, B. Smith, Y.-S. Kim, G. Chen, P. Winkler, P. McCann, and Y. Takashima, “Wide-angle MEMS-based imaging lidar by decoupled scan axes,” Appl. Opt. 59(1), 28–37 (2020).
[Crossref]

G. Chen, B. Hellman, J. Rodriguez, B. Smith, A. Gin, and Y. Takashima, “Light recycling beam steering on a DMD lidar,” Proc. SPIE 10757, 107570G (2018).
[Crossref]

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y. Kim, D. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3 K.7.

Chernyshov, O.

M.-C. Park, B.-R. Lee, J.-Y. Son, and O. Chernyshov, “Properties of DMDs for holographic displays,” J. Mod. Opt. 62(19), 1600–1607 (2015).
[Crossref]

Choi, H.

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y. Kim, D. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3 K.7.

Chu, D.

Collings, N.

Crossland, W.

Crossland, W. A.

Curtis, J.

Duncan, W.

W. Duncan, T. Bartlett, B. Lee, D. Powell, P. Rancuret, and B. Sawyers, “Dynamic optical filtering in DWDM systems using the DMD,” Solid-State Electron. 46(10), 1583–1585 (2002).
[Crossref]

Engstrom, D.

Eriksson, E.

Espinoza, A.

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref]

Faulkner, G.

Gin, A.

B. Hellman, A. Gin, B. Smith, Y.-S. Kim, G. Chen, P. Winkler, P. McCann, and Y. Takashima, “Wide-angle MEMS-based imaging lidar by decoupled scan axes,” Appl. Opt. 59(1), 28–37 (2020).
[Crossref]

G. Chen, B. Hellman, J. Rodriguez, B. Smith, A. Gin, and Y. Takashima, “Light recycling beam steering on a DMD lidar,” Proc. SPIE 10757, 107570G (2018).
[Crossref]

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref]

Goksor, M.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, Third Edition (McGraw-Hill, 2004), problems P4.13-15.

Greivenkamp, J.

J. Greivenkamp, Field Guide to Geometrical Optics (SPIE, 2004).

Gryaznov, N. A.

Haellstig, E.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087, 13–23 (2003).
[Crossref]

Haist, T.

Hellman, B.

B. Hellman, A. Gin, B. Smith, Y.-S. Kim, G. Chen, P. Winkler, P. McCann, and Y. Takashima, “Wide-angle MEMS-based imaging lidar by decoupled scan axes,” Appl. Opt. 59(1), 28–37 (2020).
[Crossref]

B. Hellman and Y. Takashima, “Angular and spatial light modulation by single digital micromirror device for multi-image output and nearly-doubled etendue,” Opt. Express 27(15), 21477–21496 (2019).
[Crossref]

G. Chen, B. Hellman, J. Rodriguez, B. Smith, A. Gin, and Y. Takashima, “Light recycling beam steering on a DMD lidar,” Proc. SPIE 10757, 107570G (2018).
[Crossref]

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref]

J. Rodriguez, B. Smith, B. Hellman, and Y. Takashima, “Fast laser beam steering into multiple diffraction orders with a single digital micromirror device for time-of-flight lidar,” Appl. Opt. (to be published).
[Crossref]

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y. Kim, D. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3 K.7.

Henderson, C.

Hoffmann, M.

Joachim, S.

Judkewitz, B.

Kaakkunen, J.

J. Kaakkunen, I. Vanttaja, and P. Laakso, “Fast Micromachining Using Spatial Light Modulator and Galvanometer Scanner with Infrared Pulsed Nanosecond Fiber Laser,” J. Laser Micro/Nanoeng. 9(1), 37–41 (2014).
[Crossref]

Kang, E.

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

Kasturi, A.

A. Kasturi, V. Milanovic, B. H. Atwood, and J. Yang, “UAV-Borne LiDAR with MEMS Mirror Based Scanning Capability,” Proc. SPIE 9832, 98320M (2016).
[Crossref]

Kim, D.

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y. Kim, D. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3 K.7.

Kim, Y.

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y. Kim, D. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3 K.7.

Kim, Y.-S.

Konforti, N.

Kuprenyuk, V. I.

Laakso, P.

J. Kaakkunen, I. Vanttaja, and P. Laakso, “Fast Micromachining Using Spatial Light Modulator and Galvanometer Scanner with Infrared Pulsed Nanosecond Fiber Laser,” J. Laser Micro/Nanoeng. 9(1), 37–41 (2014).
[Crossref]

Lee, B.

W. Duncan, T. Bartlett, B. Lee, D. Powell, P. Rancuret, and B. Sawyers, “Dynamic optical filtering in DWDM systems using the DMD,” Solid-State Electron. 46(10), 1583–1585 (2002).
[Crossref]

Lee, B.-R.

M.-C. Park, B.-R. Lee, J.-Y. Son, and O. Chernyshov, “Properties of DMDs for holographic displays,” J. Mod. Opt. 62(19), 1600–1607 (2015).
[Crossref]

Leyva, D.

Lindgren, M.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087, 13–23 (2003).
[Crossref]

Lohmann, A.

Love, G.

Marom, E.

McCann, P.

McManamon, P.

P. McManamon, Field Guide to Lidar (SPIE, 2015).

Mears, R. J.

Milanovic, V.

A. Kasturi, V. Milanovic, B. H. Atwood, and J. Yang, “UAV-Borne LiDAR with MEMS Mirror Based Scanning Capability,” Proc. SPIE 9832, 98320M (2016).
[Crossref]

Myllyla, R.

M.-C. Amann, T. Bosch, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of unusual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

O’Brien, D.

O’Brien, D. C.

Padgett, M.

Papadopoulos, I.

Park, M.-C.

M.-C. Park, B.-R. Lee, J.-Y. Son, and O. Chernyshov, “Properties of DMDs for holographic displays,” J. Mod. Opt. 62(19), 1600–1607 (2015).
[Crossref]

Pivnenko, M.

Powell, D.

W. Duncan, T. Bartlett, B. Lee, D. Powell, P. Rancuret, and B. Sawyers, “Dynamic optical filtering in DWDM systems using the DMD,” Solid-State Electron. 46(10), 1583–1585 (2002).
[Crossref]

Rakic, A. D.

Rancuret, P.

W. Duncan, T. Bartlett, B. Lee, D. Powell, P. Rancuret, and B. Sawyers, “Dynamic optical filtering in DWDM systems using the DMD,” Solid-State Electron. 46(10), 1583–1585 (2002).
[Crossref]

Redmond, M.

Reicherter, M.

Rioux, M.

M.-C. Amann, T. Bosch, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of unusual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2001).
[Crossref]

Ritsch-Marte, M.

Robertson, B.

Rodriguez, J.

G. Chen, B. Hellman, J. Rodriguez, B. Smith, A. Gin, and Y. Takashima, “Light recycling beam steering on a DMD lidar,” Proc. SPIE 10757, 107570G (2018).
[Crossref]

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

J. Rodriguez, B. Smith, B. Hellman, and Y. Takashima, “Fast laser beam steering into multiple diffraction orders with a single digital micromirror device for time-of-flight lidar,” Appl. Opt. (to be published).
[Crossref]

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y. Kim, D. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3 K.7.

Romanov, N. A.

Ross, P.

P. Ross, “Luminar's Lidar Enters Mass Production,” IEEE Spectrum (2018). https://spectrum.ieee.org/cars-that-think/transportation/sensors/luminars-lidar-enters-mass-production

Sawyers, B.

W. Duncan, T. Bartlett, B. Lee, D. Powell, P. Rancuret, and B. Sawyers, “Dynamic optical filtering in DWDM systems using the DMD,” Solid-State Electron. 46(10), 1583–1585 (2002).
[Crossref]

Schmitz, C.

Sjoqvist, L.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087, 13–23 (2003).
[Crossref]

Smith, B.

B. Hellman, A. Gin, B. Smith, Y.-S. Kim, G. Chen, P. Winkler, P. McCann, and Y. Takashima, “Wide-angle MEMS-based imaging lidar by decoupled scan axes,” Appl. Opt. 59(1), 28–37 (2020).
[Crossref]

G. Chen, B. Hellman, J. Rodriguez, B. Smith, A. Gin, and Y. Takashima, “Light recycling beam steering on a DMD lidar,” Proc. SPIE 10757, 107570G (2018).
[Crossref]

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref]

J. Rodriguez, B. Smith, B. Hellman, and Y. Takashima, “Fast laser beam steering into multiple diffraction orders with a single digital micromirror device for time-of-flight lidar,” Appl. Opt. (to be published).
[Crossref]

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y. Kim, D. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3 K.7.

Son, J.-Y.

M.-C. Park, B.-R. Lee, J.-Y. Son, and O. Chernyshov, “Properties of DMDs for holographic displays,” J. Mod. Opt. 62(19), 1600–1607 (2015).
[Crossref]

Soskind, Y.

Y. Soskind, Field Guide to Diffractive Optics (SPIE, 2011), pp. 48.

Sosnov, E. N.

Stigwall, J.

E. Haellstig, J. Stigwall, M. Lindgren, and L. Sjoqvist, “Laser beam steering and tracking using a liquid crystal spatial light modulator,” Proc. SPIE 5087, 13–23 (2003).
[Crossref]

Takaki, Y.

Takashima, Y.

Y. Takekawa, Y. Takashima, and Y. Takaki, “Holographic display having a wide viewing zone using a MEMS SLM without pixel pitch reduction,” Opt. Express 28(5), 7392–7407 (2020).
[Crossref]

B. Hellman, A. Gin, B. Smith, Y.-S. Kim, G. Chen, P. Winkler, P. McCann, and Y. Takashima, “Wide-angle MEMS-based imaging lidar by decoupled scan axes,” Appl. Opt. 59(1), 28–37 (2020).
[Crossref]

B. Hellman and Y. Takashima, “Angular and spatial light modulation by single digital micromirror device for multi-image output and nearly-doubled etendue,” Opt. Express 27(15), 21477–21496 (2019).
[Crossref]

G. Chen, B. Hellman, J. Rodriguez, B. Smith, A. Gin, and Y. Takashima, “Light recycling beam steering on a DMD lidar,” Proc. SPIE 10757, 107570G (2018).
[Crossref]

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref]

J. Rodriguez, B. Smith, B. Hellman, and Y. Takashima, “Fast laser beam steering into multiple diffraction orders with a single digital micromirror device for time-of-flight lidar,” Appl. Opt. (to be published).
[Crossref]

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y. Kim, D. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3 K.7.

Takekawa, Y.

Thalhammer, G.

Tiziani, H.

Vanttaja, I.

J. Kaakkunen, I. Vanttaja, and P. Laakso, “Fast Micromachining Using Spatial Light Modulator and Galvanometer Scanner with Infrared Pulsed Nanosecond Fiber Laser,” J. Laser Micro/Nanoeng. 9(1), 37–41 (2014).
[Crossref]

Wagemann, E.

Wilkinson, T.

Winkler, P.

Yang, H.

Yang, J.

A. Kasturi, V. Milanovic, B. H. Atwood, and J. Yang, “UAV-Borne LiDAR with MEMS Mirror Based Scanning Capability,” Proc. SPIE 9832, 98320M (2016).
[Crossref]

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Supplementary Material (2)

NameDescription
Visualization 1       Lidar capture of a pendulum swinging in a line.
Visualization 2       Lidar capture of a pendulum swinging in a circle.

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Figures (13)

Fig. 1.
Fig. 1. Phase (top) and OPL (bottom) maps of DMD micromirrors through the ASLM process. (a) Fully black pattern of mirrors at -12°. (b) “X” pattern of micromirrors actuated and, after time delay t1, illuminated during the transition at a mirror angle of -3° to project an “X” pattern in a diffraction order direction. (c) Transitioning micromirrors complete their transition to +12°. (d) All mirrors reset to -12°. (e) Square pattern of micromirrors actuated and, after time delay t2, illuminated during the transition at a mirror angle of +6° to project a square pattern into a different diffraction order. (e) Transitioning micromirrors complete their transition to +12°.
Fig. 2.
Fig. 2. (a) Micromirror geometry on the DLP3000 DMD including micromirror axes of rotation and pixel coordinate addressing to compensate for the diamond pixel orientation. (b) Wavelength-normalized frequency domain of ASLM holographic beam steering output, including higher-order diffraction outputs and the single-sideband filter (gray with throughput boxes in white).
Fig. 3.
Fig. 3. (a) 7×7 pixels in the 45° single-pixel-pitch grating hologram with micromirror addressing corresponding to Fig. 2(a). (b) A microscope capture of a 7×7 micromirror region on the DMD displaying the same static binary hologram. Side illumination was used for accurate state viewing per pixel. Gold-highlighted pixels correspond between (a) and (b).
Fig. 4.
Fig. 4. A beam (colored green, not depicting wavelength) in incident onto a DMD, coarse-steered across 5 diffraction orders (colored red), and fine-steered by binary grating on DMD (not shown). The single positive cylindrical lens, filter array, and 3-element positive cylindrical lens array comprise the single-sideband filter. The final 5-element negative cylindrical array compensates for the FOV fill-factor.
Fig. 5.
Fig. 5. A long-exposure capture of an 8×6 array of points, finely-steered by binary gratings, iterated across nine course-steered diffraction orders for a total of 432 points. Diffraction orders +3 and +4 contain off-state light for each pulse illuminated into diffraction orders -4 to +2, so they cannot be employed for beam steering for lidar. 336 independent beam steering points are demonstrated across diffraction orders -4 to +2. The wide-angle capture portrays degraded resolution in diffraction order -4, but close inspection reveals similar performance as diffraction order -2. The attenuation in diffraction order +2 is caused by edge-clipping in the vertical-power cylindrical lens array of Fig. 4.
Fig. 6.
Fig. 6. Custom constant fraction discriminator design including: (a) delay op-amp, (b) summing op-amp, (c) comparator, (d) and (e) power rails, and (f) tunable threshold for comparator.
Fig. 7.
Fig. 7. (a) Summing op-amp output. (b) Comparator output with ∼0.2 ns amplitude-dependent signal walk.
Fig. 8.
Fig. 8. (a) Mirrors redirecting the upper and lower portions of the APD acceptance pupil to the far left and right sides of the FOV. The acceptance pupil of the APD is shown (b) before mirror redirection, and (c) after.
Fig. 9.
Fig. 9. (a) Distance accuracy for diffraction order -1 and a center-most grating pattern on the DMD. (b) Horizontal, (c) vertical angular resolution testing by lidar capture of a single-pixel-wide target.
Fig. 10.
Fig. 10. The first frame of Visualization 1, video capture of a swinging target, including synchronized (a) RGB video and (b) lidar video.
Fig. 11.
Fig. 11. (a) Uncompensated far-field fill-factor. (b) Telescope array with diffraction-order-specific decenters. (c) Compensated far-field without gaps in FOV scanning
Fig. 12.
Fig. 12. Quad-block-dependent diffraction efficiency due to phased reset. Reprinted from [17].
Fig. 13.
Fig. 13. Light reflection off a 1D retroreflector array from (a) a global perspective, and (b) a single-element perspective. Reprinted from [31].

Tables (2)

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Table 1. Overall Efficiency (%) Across Diffraction Orders and Y-axis Range

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Table 2. Efficiency Components and Anticipated Overall Efficiency

Metrics