Holographic tomographic volumetric additive manufacturing

Optical configuration and light engine efficiency

The optical configuration of the holographic VAM is presented in Fig. 1. Unlike conventional TVAM^8,9, the DMD is arranged in a Fourier configuration, which allows the reconstruction of the projected holograms into the printing volume. We combine time-multiplexing³⁶ and tiled holograms^30,37 using the HoloTile method^38,39 to produce near speckle-free projections, as explained in the “method” section. A single (spatial)-mode laser at λ = 405 nm is used to achieve maximum spatial resolution in HoloVAM. A single-mode laser has less optical power than a multimode laser and thus power efficiency of the light engine is of high importance to obtain enough intensity at the build volume, keeping printing times short (~60 s). We first investigate the light efficiency difference between amplitude and phase encoding on a binary amplitude DMD spatial light modulator.

In VAM systems, due to the nature of the sparse intensity of the tomographic projections, most of the optical power incident on the 2D modulator is lost, with only a few pixels contributing to the projected image. This is exemplified in the histograms in Fig. 2b, where each pattern shows a large count of dark pixels. We estimate the light efficiency of each pattern using the following relation:

where n_g is the number of pixels in the image that have a gray level equal to g, and g_max is the maximum gray level value, where 8-bit images are used for amplitude tomographic projections, therefore $g_{\max }=255$. N_pixels is the number of pixels in the image, and ${\eta }_{DMD}$ is the pixel reflectivity of the DMD at the operating wavelength of 405 nm. As an example, the histogram using theoretical projections images of the Benchy boat at projection angles θ = 0° and θ = 90° shows a light efficiency ${\eta }_{patt}$ for amplitude modulation of 0.36 % and 0.42 % respectively (pixel reflectivity η_DMD = 65% at 405 nm). Experimentally, the light efficiency has been measured slightly below the theoretical value (0.34 % and 0.40 % respectively). Because of this low efficiency, the VAM system from Loterie et al.⁹ combines six high-power broad-area laser diodes with a nominal power of 6.4 W. The reason for this low light efficiency is that there is a one-to-one relation between the plane of the modulator and the plane of the image. In contrast to the above intensity-based projection, a holographic phase modulation with a computer-generated hologram (CGH) pattern has each pixel of the modulator contributing to the intensity pattern which yields a substantially higher light efficiency. Figure 2c shows the same reconstructed projection of the Benchy boat with a 28.6X improvement in light efficiency (see light efficiency measurements in the Supplementary Note 3).

Holographic encoding

Speckle is inherent in holographic projection^40,41. While a CGH can reconstruct the desired intensity distribution at the Fourier plane, the reconstruction quality is affected by the CGH design, the pixelated structure and type of spatial light modulator (phase-only or intensity-only), spurious unmodulated reflection, and optical aberrations^35,42. A typical intensity reconstruction from a CGH displayed on a pixelated 2D display is shown in Supplementary Fig. 2a–d), which exhibits speckle noise. To improve the reconstruction quality of phase-only holograms, a plurality of methods has been proposed such as using time averaging^36,43 and iterative algorithms applying bandwidth constraints^44–46.

Spatial and/or temporal tiling of holograms can be used to mitigate the effect of unwanted crosstalk between pixels^37,38,42,47. For this work, we use the HoloTile modality^38,39, described in detail in Supplementary Note 7, which consists of superimposing a first smaller hologram of the desired projection pattern which is spatially tiled on the available full area of the spatial light modulator and a second hologram—called here a PSF hologram which defines the shape of each reconstructed pixel in the image plane. The key aspect of tiling holograms is to provide high-speed computation, and separate reconstructed image points (modifying the original grid of image points by changing the size of the tiles). This technique essentially eliminates the uncontrolled interference at the reconstruction plane that gives rise to speckles^37,38,42.

The number of tiles N_t determines the dimensions of the sub-holograms $m\times m=\frac{L}{N_t}\times \frac{L}{N_t}$. Where L × L is the dimension of a full hologram size (the full size of the SLM display, in pixels). The sub-hologram ${\phi }_{SubH}\left(x,y\right)$ is calculated with the GS algorithm (see Supplementary Note 6). The sub-hologram is tiled in a L × L square hologram ${\phi }_{tile}\left(x,y\right)$, which is a mosaic of $N_t^2$ sub-holograms h(x, y). A PSF hologram of size L × L multiplies the tiled hologram h(x, y), which is then the final hologram displayed on the SLM. To experimentally investigate the effect of tiling the holograms on the reconstruction quality, six CGHs with the same target (“A” letter) but tiled with different N_t were generated using a flat-top PSF that produces a square pixel in the reconstruction plane (See Supplementary Note 7). The results of the reconstructions in the Fourier plane of a lens are shown in Fig. 3b. The reconstruction quality of the holograms compared to the desired pattern in the image plane (Fourier plane) is quantified with the following metrics: Mean Squared Error (MSE), and Peak Signal-to-Noise Ratio (PSNR). The MSE decreases and PSNR increases with the number of tiles Fig. 3c–e. A low MSE and increasing PSNR indicate a low level of speckle noise. We define the contrast over the region defined by the letter “A” as a “goodness” metric for the fidelity of the reconstruction. The higher the contrast, the better the fidelity. As the number of tiles increases, the contrast of the reconstruction increases (Fig. 3d), while the resolution decreases. In summary, there is a trade-off between speckle reduction and feature size. Since time multiplexing is applied in our approach, an initial evaluation was performed by time multiplexing six tiled holograms corresponding to N_t = 3–12 tiles. Figure 3b right shows the image recorded over an integration time corresponding to the projection time of the six holograms (50 ms each). Figure 3c, d shows that there is a clear trend towards increasing the PSNR and decreasing MSE when the number of tiles increases. This is due to the speckle noise reduction and smaller errors of the holographic projections with increasing number of tiles, with additional enhancement through time multiplexing.

The number of tiles and the sampling rate ∆x provide a relation to the number of controllable grid points in the reconstruction plane and the feature size respectively^37,38,42,48. The CGH is encoded as a binary amplitude hologram for experiments on the DMD modulator using the Lee method^32,33. Because of the use of a flat-top PSF, the projection’s minimal feature size is the distance between the grid in the reconstruction plane (Fig. 3f). We improve the speckle noise at the cost of an increased feature size. For example, with 3 tiles, the feature size is 23.09 μm. Smaller feature sizes can be realized with different PSF to make use of the space between grid points in the reconstructed plane.

Computation of holograms for tomographic projection

Figure 4 shows the pipeline to compute holographic projections for three different PSF: flat top (square output pixel), Bessel, and an Optical Vortex (OV), Fig. 4a, b, and c respectively (for PSF phase modification see Supplementary Note 7, 8). Two approaches were performed to achieve collimation of the projections. For the point spread function (PSF) generating square pixels, we extend the collimation range at each projection angle by sequentially projecting patterns at different depths z within the vial using time multiplexing. This is achieved by adding a Fresnel lens, for time-varying the reconstruction plane, to the tiled computer-generated hologram (CGH), which effectively “smears” the reconstruction of the projection over the axial direction, providing precise axial control. In the second approach, a Bessel beam PSF generated with an Axicon phase on the DMD⁴⁹ (see Supplementary Note 8) provides longer collimation of the projected image than when using a flat-top type PSF. Additionally, an Optical Vortex (OV) generated by a Helical Phase Plate (HPP) produces a low divergence beam with a donut intensity distribution that carries orbital angular momentum and has self-healing properties.

The final step in this process involves encoding the phase on a digital micromirror device (DMD) using the Lee method. Illustratively, a numerical reconstructed image for one projection is shown in Fig. 4a–c (bottom left) for a CGH with a number of tiles N_t = 4. The corresponding Lee hologram reconstruction of the same tiled hologram is shown in Fig. 4a–c bottom right for three distinct PSF shaping. For the case of the Bessel and vortex PSF, the depth of field is longer due to its “non-diffracting” characteristic, and thus there is no need to multiplex the reconstructed image at different depths.

Low étendue and multiplane reconstruction

With the aim of using a light engine based on phase encoding for TVAM, it is necessary to generate a beam with a low divergence that satisfies the collimation assumption of the Radon transform used to compute intensity patterns targets of the holographic projections (Supplementary Note 8). The parameter that defines spatial resolution is the etendue⁹. In this case, maintaining a collimated beam over the build volume produces a high-resolution printed part. We exploit PSF engineering to effectively reduce the divergence of the projected patterns. As mentioned, we used two approaches: first, we digitally modify the beam reconstruction using a sequence of Fresnel Lenses; second, a non-diffractive source, such as a Bessel beam, produces a beam with low etendue (Supplementary Note 8). Figure 5 shows simulations and experiments of a Flat -top PSF propagating over 10 mm. With a flat-top PSF, we sequentially display multiple CGHs at different depths along the optical axis, as shown in Fig. 5a. In the experiment, 25 CGHs were projected at a rate of 8 kHz. The incoherent sum of the projected patterns is experimentally captured by a camera on a motorized stage that moves along the depth step as the sequence of holograms is projected by the DMD (Fig. 5b). This effectively measures the optical dose that the photoresin would receive at a given angle. The propagation distance z = 10 mm is large compared to the intended object’s footprint (~2.5 mm). We see that simulation and experiment are in good agreement, Fig. 5c). A simulation with a Bessel beam and Optical Vortex PSF is shown in Supplementary Note 8. A single CGH using 4 tiles was used. This simulation showed good collimation of the projected pattern over 10 mm.

3D printed objects

We experimentally demonstrated the performance of our technique by printing in two different materials, an organic acrylate-based resin, and a cell-laden hydrogel. We used the CGHs described above to fabricate millimeter-scale objects. A commercial polyacrylate resin with Diphenyl (2,4,6-trimethylbenzoyl) phosphine oxide (TPO) as a photoinitiator was used as the photoresin. Parts were printed in less than 60 s. To increase the printability of small features, TEMPO (2,2,6,6-tetramethylpiperidin-1-yl)oxidanyl, a mediator in radical polymerization, was added to the photoresist⁵⁰. Because of its radical scavenging behavior, the addition of TEMPO increases the amount of printing time required per sample. Figure 6 shows the 3D printed results of a Benchy boat using holographic projections with different PSF shapes and different number of tiles. Pictures of the printed boat show that intricate high-resolution details, such as the sharp bow of the boat, the hollow cabin, or the chimney can be well resolved.

The pictures in Fig. 6a, b show objects printed with a Flat-top PSF, produced by time multiplexing 7 holograms (Fresnel lenses) per angle, with 3 and 4 tiles respectively. The printed parts displayed in Fig. 6c, d were achieved by projecting a single Bessel hologram per angle and using 3 and 4 tiles respectively. The 150 s printing time of the samples obtained when using TEMPO is still within the printing time of conventional tomographic VAM.

A well-defined hull with holes and a cylindrical chimney with a hole can be seen in the printed 3DBenchy boats in Fig. 6. The diameter of the hole in the hull was targeted at 161 μm. The prints with $N_t=3$ (Fig. 3a, c) show a hole diameter of 112 μm and 170 μm. The prints with $N_t=4$ (Fig. 3b, d) show a hole diameter of 118 μm and 140 μm. As the measurements in Fig. 3. show, the spatial feature size of the projections using N_t = 3 and N_t = 4 is expected to be 25.3 μm and 35 μm respectively, well within the resolution of the hull diameter. The variability of the printed hull diameter is attributed to overprinting and to the postprocessing of the parts.

The small positive features such as the cargo box in the back deck, where the thickness is 36 μm could not be printed with N_t= 4 tiles as it is too close to the minimal feature size (36.2 μm) but could be printed with N_t = 3 tiles (25.3 μm).

For these experiments, we measured and corrected the wobbling of the sample holder by adding a linear phase to the CGHs (Supplementary Note 10). This correction improved the straight columns of the cabinet and chimney.

Striations are observed similarly to conventional TVAM²⁴, but here the stria period changes with the number of tiles, matching the minimal feature size possible with each tile. For example, with a number of tiles N_t = 3, the distance between grid points is 23.09 μm, close to the observed striation period of the 20 μm. Similarly, with N_t= 4, the distance between grid points is 36.02 μm, matching the measured 35 μm striation period. And for N_t= 6, the stria period of 49 μm and the minimal feature size is 45.5 μm, as shown in Fig. 6a,

We hypothesize that the bright centers of the flat-top convolved tiles produce the striation, mainly through a self-focusing effect^51,52. Striation is particularly detrimental to print quality because it produces rough surfaces and objects appear white when they should appear mostly transparent. Stria reduction was quantified experimentally by modifying the point spread function of the CGH and adding time multiplexing (see Supplementary Fig. 8.4). We show that it can drastically reduce stria (Fig. 7b). The parts printed with PSFs other than the N_t= 3 Flat-top exhibit a smoother, shinier surface and are more transparent. We used microCT scans of the printed parts to obtain high-resolution images of their surface as shown in Fig. 7c. The inlets illustrate the side of the cabin of the boats, a region where striation occurs. The single N_t= 3 Flat-top PSF resulted in a rougher print. We measured the depth and the pitch of striation at the hull, the cabin, and the chimney from these microCT scans, and observed that tiling two vortices yielded prints with significantly shallower and smaller striation than using a single N_t= 3 Flat-top PSF (p = 0.223 and p = 0.001, respectively), as shown in Fig. 7d, e. The fidelity of the prints was evaluated using the Jaccard index between the micro CT scans and the model. Values between 0.82 and 0.86 were obtained (Supplementary Note 15 and Supplementary Fig. 12).

We validated the possibility to fabricate different geometries, we printed additional 3D structures in acrylate resins such as a cylinder with a hole, a Bucky Ball, and a pre-Columbian object called Poporo (Fig. 8).

Optical setup

The schematic of the experimental setup is shown in the Supplementary Fig. 1. It consists of one 40 mW CW laser diode at 405 nm (OBIS 405 nm LX SF 40 mW) coupled into a single-mode fiber (Thorlabs P3-405B-FC) to obtain a good quality Gaussian beam that is collimated to best approximate the Radon transform. For comparison, a 405 nm LED with an emission area of 1 mm² and emission angle of 170° has a space bandwidth product 10⁶ times larger than a single mode 405 nm laser diode (1 μm × 2 μm) emission area and 30° by 15°).

The collimated beam illuminates a DMD (Vialux DLP7000: $L\times W=768\times 1024$ micro-mirrors and pixel pitch = 13.6 μm) placed in a Fourier configuration and aligned to meet the blazed grating criteria for efficiency. After the Fourier lens L1 (f₁= 150 mm), a spatial filter (SF) was added to filter out the zero-order and keep the -1 order. L2 (f₂ = 150 mm) and L3 (f₃= 200 mm) form a 4-f system conjugating the Fourier plane and rescaling the holograms on the sample plane. The DMD was synchronized with the rotary stage (Zaber, RSW60C-E03T7-KX13A) using a Data Acquisition Card from National Instruments (X series DAQ, PCIe-6321) at a typical framerate of 1600 Hz. The rotatory stage holding the sample vial is set to rotate at a constant speed (30°/s) while a sequence of holographic projections is displayed every ∆θ = 0.6° synchronously on the DMD. The choice of 30 degree/s is a typical value for VAM printers. However, rotation speed could be increased as the projection rate of the DMD is 22’700 images (holograms) per second. An index-matching bath of vegetable oil is used to avoid lensing effects from the cylindrical vials containing the photoresin (n = 1.48).

Two inspection systems using lenses L4 (f₄ = 75 mm) and L5 (f₅ = 150 mm) with camera 1 (iDS UI307xCP-M), and lenses L6 (f₆ = 100 mm) and L7 (f₇ = 100 mm) with camera 2 (iDs UI327xCP), were implemented for the inspection of the polymerization process, and holographic projections respectively.

Tomographic amplitude projections

First, the 3D model (typically a.stl file) is voxelated and sliced (Supplementary Fig. 6). The y axis is selected parallel to the rotation axis of the vial. In tomographic printing, the Radon transform R(r, θ) is digitally computed to produce angular projections followed by the Filtered back-projections (FBP)⁵⁷.

These tomographic projections are the target intensities of the GS algorithm that generates the CGH. Projections were calculated over 360° with an angular resolution of 0.6°.

Computer generated holograms

Computer-generated holograms (CGHs) typically suffer from speckle noise, which generates grainy images^29,35,40,58. In the context of VAM, speckle noise needs to be avoided in the projected intensity image because they could create unwanted printed speckled voxels. To improve the reconstruction quality of the phase-only holograms, several methods such as time averaging iterative algorithms applying bandwidth constraints^44–46, and or camera in the loop⁵⁹ have been proposed. Due to the uncontrollable interference between adjacent pixels in a CGH caused by overlapping Airy disks, tiling holograms in space and/or time or by other output pixel separation methods can provide attenuation of unwanted noisy interference^{30,37,38,42,47}.

In general, the computational time for full-size CGHs scales as$M\log M$, where M² is the number of pixels in the image. An additional advantage of tiled holograms is the reduction of the computation time by at least an order of magnitude since the dimensions of the tiles (sub-holograms) are smaller than those of a full-size hologram and only the smaller sub-holograms need to be computed. Moreover, holographic projections give us the possibility to engineer the shape of the projected output “voxel shape” in 3D thanks to wavefront control.

Spatial Light Modulators (SLM) based on liquid crystals are typically used to modulate complex light fields; but they are not well suited for VAM due to their low frame rate (20–100 Hz) and reduced resistance to short wavelengths (<450 nm). Thus, we use a DMD, which is a binary amplitude SLM. To implement phase modulation on the DMD, we use the binary Lee hologram method^32,33. The synthesis of diffractive phase encoding using Lee holograms has been of increasing interest in various applications thanks to the high phase modulation rate of DMDs^31,33,35,60.

Peer review information

Nature Communications thanks Daniel Webber and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.