A photophoretic-trap volumetric display

Free-space volumetric displays, or displays that create luminous image points in space, are the technology that most closely resembles the three-dimensional displays of popular fiction. Such displays are capable of producing images in ‘thin air’ that are visible from almost any direction and are not subject to clipping. Clipping restricts the utility of all three-dimensional displays that modulate light at a two-dimensional surface with an edge boundary; these include holographic displays, nanophotonic arrays, plasmonic displays, lenticular or lenslet displays and all technologies in which the light scattering surface and the image point are physically separate. Here we present a free-space volumetric display based on photophoretic optical trapping that produces full-colour graphics in free space with ten-micrometre image points using persistence of vision. This display works by first isolating a cellulose particle in a photophoretic trap created by spherical and astigmatic aberrations. The trap and particle are then scanned through a display volume while being illuminated with red, green and blue light. The result is a three-dimensional image in free space with a large colour gamut, fine detail and low apparent speckle. This platform, named the Optical Trap Display, is capable of producing image geometries that are currently unobtainable with holographic and light-field technologies, such as long-throw projections, tall sandtables and ‘wrap-around’ displays.

displays gives rise to their unique ability to present "depth rather than depth cues" (ref. 6). Among volumetric systems, we are aware of only three such displays that have been successfully demonstrated in free space: induced plasma displays [7][8][9] , modified air displays 10,11 and acoustic levitation displays 12 . Plasma displays have yet to demonstrate RGB colour or occlusion in free space. Modified air displays and acoustic levitation displays rely on mechanisms that are too coarse or too inertial to compete directly with holography at present. The OTD advances the current state of the art by providing full-colour, free-space images with fine detail.
The OTD works by first trapping a micrometre-scale, opaque particle in a near-invisible (405-nm wavelength) photophoretic optical trap. The trapping sites are formed by a combination of oblique astigmatism and spherical aberration 2 . Once a particle is confined, the trap is scanned, moving the particle through a volume in the space that it shares with the user. A system of collinear RGB lasers then illuminates the trapped particle to create a highly saturated, full-colour, low-speckle 3D image in space by persistence of vision (POV), as shown in Fig. 1a, c. The resulting images can have image points smaller than ten micrometres and can be seen from every angle (with the possible exception of the line forming the optical axis).
The display reported here is based on photophoretic optical particle trapping. Photophoretic traps are especially useful for confining and manipulating micrometre-diameter absorbing particles [13][14][15] . Instead of radiation pressure and gradient forces, which are used by optical tweezer traps, photophoretic traps are thought to use thermal forces from 'thermal accommodation' and the radiometer effect. Forces arise on a particle because of uneven heating and thermal creep. Higher momentum is imparted to the particle from its hot side, leading to a net force pointing away from the heated region. A mathematical treatment of photophoretic effects for particles of different sizes is given in refs 16, 17. Our early trials were conducted using photophoretic traps that hold absorbing particles with greatly varying shapes and average diameters ranging from below 5 μ m to above 100 μ m-much larger than the mean free path of gas molecules (68 nm) at standard pressure and room temperature 18 . In this 'continuous' regime, the photophoretic force on a spherical particle is given as: where R is the gas constant, η the viscosity of the gas, M the molecular weight of the gas, p the gas pressure, ∇T the gradient of the temperature T and d the diameter of the particle (from ref. 16 Letter reSeArCH and the other in the diffraction mode. In the geometric trap, a lowvisibility 405-nm-wavelength beam was passed through a lens tilted at 1° from the optical axis. Cross-sections and trapping sites for this beam are shown in Fig. 1a. This geometric instantiation system has the advantages that it is light, efficient and straightforward to implement. This trap was also produced with a liquid-crystal-on-silicon (LCOS) spatial light modulator (SLM), as described in Extended Data Fig. 2.
The most critical display parameters are summarized in Table 1. These parameters were collected from multiple prototypes (see Methods for additional details). Simple images have been demonstrated at POV rates above the ten frames per second that are necessary for POV 21 . Figure 1c shows a vector image (1,307 vertices) traced at 12.8 frames per second (see Supplementary Video 1), which corresponds to 16,700 points per second, close to the maximum scanning rate of galvanometers (20,000 points per second). The volumetric image showed no noticeable flicker when viewed with the naked eye. An image of this complexity requires a particle velocity of 164 mm s −1 . Tests optimized for velocity (free from the processing delays and latency involved in image formation) show maximum achievable linear velocities greater than 1,827 mm s −1 , which suggests that it should be possible to obtain an order of magnitude increase in scan rate or image complexity for POV images without further optimization of either the trap or particle parameters. Supplementary Video 2 shows various particle movements including high accelerations. Accelerations in excess of 5g, where g is the acceleration due to gravity, have been measured.
Our early observations indicate that display performance depends strongly on the quality of the optical trap parameters. Several automatic tests were run to identify the sensitive parameters for particle trapping. The trapping beam power, wavelength and numerical aperture are the parameters that have shown the greatest influence on trap quality, as manifested by hold time and airflow tolerance. Highcontrast traps appear to hold best. Higher beam power is correlated with better trapping until the particle begins to disintegrate. Shorter wavelengths are associated with better trapping for both black liquor (cellulose) and tungsten particles. To give an example of common test parameters, a test consisting of 67 attempts and using 532-nm light at a power of 3.0 W has a pickup rate of 87% with an average hold time of 1.1 h. The maximum hold time recorded until now was in excess of | The Optical Trap Display. a, A low-visibility light traps a particle and uses it to scan a volume. The resulting levitated optomechanical system is illuminated by an RGB laser source that can vary the illumination power and position of the trapped particle.
As the particle scans the volume, images are formed by the POV method.
b, Photograph of an early OTD image. c, POV image. The particle in this image was scanned quickly enough (10 Hz) to produce an image by POV. A video of this OTD image is provided in Supplementary Video 1. Y logo from Brigham Young University Communications. Letter reSeArCH 17.2 h, obtained at a wavelength of 532 nm and optical power of 3 W (the measurement was terminated by the researcher), and the minimum hold power recorded was less than 24 mW (for 405-nm light). Successful trapping has been performed with 635-nm, 532-nm, 445-nm and 405-nm light. Given that the particles have sizes of ten micrometres or higher, the resolution of the display is also determined by the addressable points of the scanning apparatus. The highest image resolution so far is 1,600 dots per inch (dpi) for a projected total of 5 billion addressable points in a pyramidal volume with a maximum linear dimension of two inches on each side and a depth of approximately one inch, which was achieved with the proposed instantiation technique.
When considering image quality, such as optical geometry, colour and resolution, no effort was made to optimize for write speed. Instead, the images in Figs 2 and 3 were created by long exposure (exposure times are listed in Methods).
The OTD was used to demonstrate its ability to bend the light path. Figure 2 shows examples of OTD images produced using levitated optomechanics to successfully create optical geometries unachievable by holograms. These OTD images are not clipped at the display aperture (Fig. 2a), exhibit parallax and can be seen from all angles ( Fig. 2b-d). The OTD can create long-throw projections (Fig. 2e, f), tall sandtables (Fig. 2g) and images that wrap around physical objects (Fig. 2h).
Colour was obtained from low-cost, commercial diodes emitting red, green and blue laser light propagating collinearly with the 405-nm trap beam. The diode sources were driven using 8-bit pulsewidth modulation. Several colour tests were performed using the rastered images shown in Fig. 3. Figure 3a shows particles being illuminated by red, green and blue lasers. The colours are highly saturated, consistent with laser illumination. Figure 3b demonstrates the ability of the OTD to create additive colour and grayscale. Figure 3c shows an image frame with soft tones and no apparent speckle on an image of 3 cm by 2 cm. To demonstrate the resolution of the system, a 1-cm-diameter image of Earth was written above a fingertip at 1,600 dpi resolution (Fig. 3d).
The practical limitations imposed on the operation, scaling and complexity of OTD images include (i) finite mechanical scan speed, (ii) variable trapping conditions, (iii) airflow sensitivity and

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(iv) illumination splash. Image complexity in a single-particle display is constrained primarily by the speed of the scanning system. This limitation may be overcome by the use of solid-state scanning and parallelism. Parallelism is achieved by simultaneously manipulating multiple trapped particles. That is to say, instead of having one particle responsible for all of the points in an image (one particle per image volume), multiple particles may be trapped, manipulated and illuminated independently using solid-state SLMs. The scanning requirements are reduced as more particles are added. A line of trapped particles reduces the drawing complexity to a two-axis scan (one particle per image plane), a 2D array of trapped particles reduces the scan complexity to a single-axis scan (one particle per image line), and a 3D array of trapped particles could eliminate the need for scanning entirely (one particle for every image point). SLM trapping and SLM particle manipulation have been used previously 15,22-24 ; we have successfully trapped particles using an LCOS SLM, with the phase pattern designed to create an astigmatic aberration trap (see Extended Data Fig. 2). As an example, an OTD with a single-axis scan (one particle per image line), operating at the current maximum linear velocity of 1,827 mm s −1 , would be able to create images approximately180 mm high at POV refresh rates (10 Hz).
The strength of particle trapping and holding varies greatly because of the wide distribution of the particle sizes and shapes, as well as the presence of multiple axial trapping sites of different sizes and quality. Under poor trapping conditions, a particle may hop from one trapping site to another. The maximum achievable particle velocity and acceleration seem to depend strongly on these highly variable trap conditions. A clearer upper bound on the complexity of single-particle images will be obtained when the optimal particle and trap morphologies are identified and isolated.
Particles are sensitive to airflow. Under good trapping conditions, trapped particles are robust to low levels of airflow, including airflow generated by human breathing and hand gestures (estimated 25 airflow upper bound of one litre per second). However, it is unlikely that the display would function outdoors without an enclosure unless particles were much more strongly confined or steps were taken to refresh trapped particles regularly.
In general, some of the illumination light does not scatter, but instead continues along the optical axis to form a laser 'splash' . This can be overcome by carefully controlling the illumination focus, by directing the optical axis towards an absorbing surface or by using active particles. Examples of active particles are fluorescent particles or aerosol droplets trapped with an infrared beam and then illuminated with a low-power ultraviolet beam to induce coloured emission 26 . p-n junctions might also be levitated and optically pumped to create high-gain, lightemitting particles with no visible splash.
This study provides a proof-of-concept demonstration of a fullcolour, high-resolution, free-space volumetric POV display that can achieve display geometries beyond the capabilities of holography alone. The trapping strategy used in the OTD is both straightforward and efficient. The reported prototypes use commercial hardware and have low cost relative to other free-space volumetric displays. We anticipate that the device can readily be scaled using parallelism and consider this platform to be a viable method for creating 3D images that share the same space as the user, as physical objects would.
Online Content Methods, along with any additional Extended Data display items and Source Data, are available in the online version of the paper; references unique to these sections appear only in the online paper.

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MeThODS
Colour display experiments were performed using an RGB laser system (OEM Laser Systems) combined with a 200-mW 405-nm laser using dichroic mirrors. The beam was expanded and focused through a tilted spherical lens mounted on an active translation stage, immediately followed by a 30-mm-aperture x/y galvanometric scanning assembly.
All images shown in this paper were made with long exposures, with the exception of Fig. 1c, which was written at a rate of greater than ten frames per second. For all other images, the speed of writing was constrained by the method of colour display, which paused at each pixel point to allow time for the green laser to reach full power. The resulting long-exposure image times were as follows: Fig. 2a,  16.2 s; Fig. 2b-d, 8.4 s; Fig. 2e, f, 40.8 s; Fig. 2g, 45.4 s; Fig. 2h, 56.4 s; Fig. 3b, 34.3 s;  Fig. 3c, 18.9 s maximum; and Fig. 3d, 19 s. A portion of the 3D-printed surrounding scene in Fig. 2g was blacked out digitally.
The 532-nm frequency-doubled laser was swapped with a non-frequencydoubled, 520-nm diode laser with a 700-ns pulse generator for a faster modulation response time. The lasers were expanded to a beam waist of 30 mm and were caught by a positive, biconvex spherical lens tilted at an angle of 1° from the normal to the optical axis. The lens had a focal length of 125 mm. The x/y scanners had a maximum aperture of 30 mm with Al-coated mirrors. The galvanometric scanners were driven by a microcontroller. The focusing lens was mounted on a Physik Instrumente V-551.2B linear translation stage. The photographs in Figs 2 and 3 were taken through a 405-nm dichroic mirror that was used as an optical notch filter.
The early single-beam display prototypes were created using a 10-W Verdi laser operating at powers between 3 W and 4.06 W. The first instantiation system used a lens with 75-mm focal length and a single mirror constructed from an aluminized 100-mm silicon wafer, gimbal-mounted to scan over π steradians. This first instantiation system provided many of the results reported in this paper. An improved single-beam setup was created using a 125-mm lens and an OEM x/y scanning system with a 15-mm aperture. Early instantiation systems had both the trapping and illumination beams passing through the tilted lens. An iris was placed just before the lens to truncate the beam waist to improve pattern contrast at the focus. Particles were introduced into the trap either by scanning the trap into a retractable reservoir of particles or manually, by passing a plastic or metal instrument coated with particles away from the galvanometric scanner mirrors and through the focus. The retractable reservoir was composed of a piece of aluminium bar stock wrapped in aluminium foil. The aluminium foil was coated with a single layer of black liquor particles. The focused beam was pulled up and away from the aluminium surface to capture a particle. Once captured, the bar stock was pulled out of the write volume by a worm gear mechanism. The repeatability of trapping degraded gradually as a function of the number of pickup cycles. Efforts were made to reduce the airflow during trapping and image writing by placing foam core enclosures, baffles or table curtains around the write volume. Experiments were performed both within enclosures and in open air. Enclosures were found to improve trapping and hold times in some circumstances. The most commonly trapped particle in the experiments reported here was black liquor with approximately 70% solid content. Black liquor is a cellulose solution that is a common by-product of the paper-making process. Samples used in this work were obtained from a kraft pulp mill using southern pine.
The LCOS experiments were performed using a Hamamatsu X10468-01 phaseonly 792 pixel × 600 pixel SLM. The device was illuminated by a 100-mW, 405-nm diode laser approximately 10° from the normal. Owing to beam clipping, which is required for uniform illumination and internal reflections, the power delivered to the trap was only 48 mW. The phase image displayed on the LCOS was created numerically by combining the spherical aberration, astigmatism and coma that can be created by lenses. This was then combined with the factory-provided correction phase image and an offset grating to create the final phase image.
By using a beam-shaping SLM, the dynamic functions of the OTD can be changed to those of a solid-state display (Extended Data Fig. 2). The trap was also produced with an LCOS SLM with a phase pattern described by the following relations: where P SA , P A and P IMG stand for the spherical aberration, astigmatic aberration and total phase images, respectively. P CAL is a calibration phase image specific to the LCOS being used and is often provided by the manufacturer. The scalar coefficients A represent aberration weights (A A , weight for astigmatic aberration; A SA , weight for spherical aberration), q describes the rotation of the lens from the perpendicular, and ρ is the radial distance from the centre of the LCOS display. SLMs have previously been used for trapping and manipulating particles 27,28 . To achieve parallel, independent trapping, a fixed phase plate or an active SLM may be used to trap multiple particles for scanning simultaneously. A combination of two SLMs or a phase plate and an SLM would provide independent trapping and illumination. We have confirmed that a particle can be held with a phaseonly modulator displaying a diffraction pattern meant to both steer input light and modify the astigmatic and spherical aberration of the trap at the focus of the output lens. Data availability. The data that support the findings of this study are available from the corresponding author on reasonable request.