Scanning fiber microdisplay: design, implementation, and comparison to MEMS mirror-based scanning displays

: In this study, we propose a compact, lightweight scanning ﬁber microdisplay towards virtual and augmented reality applications. Our design that is tailored as a head-worn-display simply consists of a four-quadrant piezoelectric tube actuator through which a ﬁber optics cable is extended and actuated, and a reﬂective (or semi-reﬂective) ellipsoidal surface that relays the moving tip of the ﬁber onto the viewer’s retina. The proposed display, oﬀers signiﬁcant advantages in terms of architectural simplicity, form-factor, fabrication complexity and cost over other ﬁber scanner and MEMS mirror counterparts towards practical realization. We demonstrate the display of various patterns with ∼ VGA resolution and further provide analytical formulas for mechanical and optical constraints to compare the performance of the proposed scanning ﬁber microdisplay with that of MEMS mirror-based microdisplays. Also we discuss the road steps towards improving the performance of the proposed scanning ﬁber microdisplay to high-deﬁnition video formats (such as HD1440), which is beyond what has been achieved by MEMS mirror based laser scanning displays.


Introduction
Head-worn displays (HWD) typically utilize a micro-scanning unit that displays a two-dimensional (2D) image or video on the users retina.As the distance between the microdisplay and the viewer's eye is usually smaller than the closest distance at which human eye can focus, a blurred image forms on the retina.To overcome the blurring, relay optics are placed in between the microdisplay and the eye that conventionally consist of multiple lenses to form a magnified version of the displayed image beyond 25 cm that the eye can focus [1].Microdisplay-based lightweight HWD designs that incorporate a single magnifier lens usually provide a restricted field-of-view (FOV) [2].The addition of extra components to improve FOV and compensate aberrations, result in a bulky system that is not convenient as a HWD.For instance, high-end military-type display may support a FOV of ∼ 150 degrees, while incorporating > 10 lenses to compensate the aberrations and weighting over 1 kg (2.2 pounds) [3].
Scanning fiber endoscopy has been introduced in early 2000's, where a fiber optic cable is mechanically actuated with a four-quadrant piezoelectric cylinder.The back-emitted light from the tissue, is then captured with either the illumination fiber or using different fiber(s), and is directed to a photo detector element for image formation [4].Such scanning endoscopic systems have been adapted to a plethora of optomedical imaging modalities, including but not limited to, optical coherence tomography (OCT), multi-photon endoscopy, confocal endoscopy and Raman spectroscopy [5][6][7][8].Scanning fiber based devices have also been demonstrated as a display, through a modulated laser source to show the desired content to the viewer.However, previous scanning fiber displays utilize multiple optical components that makes the overall device bulky.Furthermore the optical components are placed on the optical axes, making such displays only suitable as virtual reality (VR) devices [9,10].Here, we demonstrate a fiber-scanning HWD type (small form-factor) microdisplay design and implementation that only incorporates an elliptic or ellipsoidal reflective mirror (or partially reflective for augmented reality applications) surface to map the fiber tip onto the retina.In the upcoming sections, we present the technical details of our design, backed up by simulations and analytical performance metrics, together with its experimental demonstration.For a general review on HWD technology (both scanning and 2D matrix-based) we refer the readers to other literary work [3] in the field.

Scanning fiber microdisplay
Our scanning fiber microdisplay design, illustrated in Fig. 1, comprises of a piezoelectric cylinder actuator, an extended fiber cable (having length L) whose effective anchor point is placed on one of the foci ( f 1 ) of the ellipse.The effective anchor point of the scanned fiber is 1  3 L away from its true anchor point [11], as detailed in Fig. 1.The viewer's eye lens is located at the second focus ( f 2 ).The laser beam, exiting the tip of the scanned fiber is quasi-collimated once hitting the elliptic surface.At the second focus, where the viewer's eye lens is located, the chief rays of collimated beams arriving from all angles, at a time-multiplexed manner, intersect.Then the eye lens focuses the collimated beams onto retina forming the relayed image.In this regard, the ellipse act as a relay element by itself as it (i) collimates the incoming beam and (ii) maps the collimated beam, without lateral shift, on the viewers lens at all scan angles.The degree of collimation achieved by the ellipse is typically improved through optimization of the freeform optical surface.Figure 1c illustrates an alternative implementation using a spherical surface and a beam splitter as opposed to an ellipse.The alternative optical architecture utilized with a free form on-axis aspherical surface, would indeed result in an aberration-free performance.In this study, we focus our efforts to the implementation with single elliptic surface, due to its simplicity (only necessitates a single optical component) and form-factor.
Figure 2 illustrates the optical simulation, performed with Zemax software, demonstrating the tracing of the laser beam, which exits the ± 0.6 mm (±12 • , in accordance with experimental conditions) scanned fiber tip (having initial tilt of 10 • with respect to the optical axis) and then is relayed to the retina via the elliptic surface.Throughout both the simulations and the experiment, we use an extended fiber length of 4.2-mm, a reflective ellipse having 25 mm and 50 mm focal lengths and the viewers eye that is modeled with an f = 25.4 mm lens and a detector plane (retina).These specific distances and element sizes were chosen in accordance with typical HWD dimensions.The spot diameter on the detector plane is simulated to be ∼ 8 µm at any scan angle, on the retina.As the scan line on the retina is ∼ ± 1.4 mm long, for ±12 • fiber scan angle, one can calculate the number of resolvable spots on the retina (N r etina ) to be 350 for the given conditions, through dividing the scan length on the retina to the spot diameter.Meanwhile, the number of resolvable spots generated at the fiber tip (N f iber ) could be found through dividing the scan length of the fiber to the Full-width-half-maximum (FWHM) mode-field-diameter (taken as ∼2.55 µm based on a typical SMF fiber specifications, such as Thorlabs SM-600), which is found to be 470.We attribute the difference among N r etina and N f iber to the aberrations introduced both by the elliptic surface and the viewers eye.Thus, N f iber sets an upper limit on N r etina .It is noteworthy to mention that with thorough optimization of the elliptic surface one can further increase N r etina .Fig. 2. Optical simulations: ray tracing of the full system.spot size is found to be ∼8 µm for all scan angles.Note that the scan angle displayed in this figure is exaggerated for visual purposes.

Comparison with MEMS mirror-based displays
In this section, we present an in-depth comparison between microdisplays based on electromechanical steering of the laser beam (typically employed with MEMS mirror scanners) vs. fiber scanning.MEMS mirror based scanners have been studied for more than two decades and they are quite advanced.They can deliver high quality repeatable scan patterns with integrated angle sensors and closed-loop controllers.Figure 3 illustrates the optical architecture of a typical MEMS mirror (bi-axial) scanner based display.One easily notices the simplicity of our optical design that eliminates all the optical components till the intermediate plane, as opposed to a typical MEMS mirror display.This advantage is obvious when Figs. 1b, 3 are compared.

Resolution
Figure 4 illustrates the scanning parameters of a MEMS mirror-based display and a fiber scanning display, from which we derive a common ground for comparison.The number of resolvable spots for a MEMS mirror-based scanner (N M E M S ) is related to the total optical scan angle ((θ M E M S )), MEMS mirror diameter (D M E M S ), the wavelength of illumination (λ), and a shape factor (a, where 0.75<a<2) that is determined by the spot size definition (amount of overlap between adjacent spots) such that [12] N   Similarly, one can define the total optical scan angle (θ f iber ) for the fiber scanning display system (Fig. 4a), and formulate it with respect to the effective length (2L/3) and the fiber tip displacement (d), as: On the other hand, as there is no mirror for the fiber scanner, one would have to back-trace the exiting rays to form a virtual diameter (D f iber ), as illustrated in Fig. 4a.Note that: where N A f iber is the numerical aperture of the laser beam that is exiting the scanned fiber.
Calculating the scanned angle and diameter product for the fiber scanner, we get the number of resolvable spots (N f iber ): As expected, the deduced expression for number of resolvable spots is also in line with the fiber scan length (d) to the spot diameter (δ xy ) ratio: Field-of-view (FOV) and exit pupil size (ExP) are important metrics for head-worn displays.The product of FOV and ExP the two is equal to the product of the scan line length and fiber NA.The actual values of the FOV and ExP depend on the relay optics design.If fiber NA is increased by way of reducing the mode-field diameter of the fiber, while keeping the output single mode, then the resolution as well as FOV.ExP product of the system increases.However, if the fiber NA is increased by using other means, such as scattering nanoparticles at the tip of the fiber, then resolution of the system would remain the same but ExP size increases (i.e, scattering at an intermediate image plane acts like an exit pupil is expander) [13].

Frame rate
Alongside resolution, the frame rate is another crucial parameter for display systems.Two distinct strategies have been employed in fiber scanning based on the scan pattern, namely spiral and Lissajous scanning.Here we present the cons and pros among both strategies and relevant formulas.

Spiral scanning
Spiral scanning has allowed for highest-achievable frame-rates for fiber scanners.The spiral scan is typically created through applying a sinusoidal voltage with 90 • phase shift between adjacent electrodes of the piezocylinder actuator.The amplitude of the sinusoidal drive voltage is modulated to form concentric circles one after the other.In summary, the drive signals for all four electrodes (±X, ±Y) are summarized below [4] where A(t) is a time dependent ramp (or other monotonically increasing) function to create enlarging concentric circles and f is the mechanical resonance frequency of the extended fiber cable, which is determined by its material properties as well as its dimensions [4].Within one period of fiber scan (T = 1 f ) a circle is formed that crosses both horizontal and vertical axes twice.In this regard to achieve N f iber resolvable spots in both horizontal and vertical directions, N f iber /2 concentric circles should be displayed.Once all N f iber /2 circles are completed (within N f iber /2f duration), a breaking strategy is employed on the drive signal to bring the fiber back to its original position.Nevertheless, the breaking period takes significantly less of the duration to complete all circles [14], thus the frame time could be approximated by totalling the duration to scan all circles (N f iber /2f).The speed of the scan in frames-per-second (FPS) for spiral scanning (FPS spir al ) can be formulated based on the reciprocal of the duration that it takes to complete one frame: Eq. ( 7) highlights the drawback between the speed (FPS spir al ) and the resolution along a line (N f iber /2) of a fiber scanning display, exploiting spiral scan.At the end of this section the reader is referred to Fig. 5 and Table1, showing a comparison among fiber scanned displays having different fiber lengths, and how they compare to MEMS mirror-based displays.

Lissajous scanning
Lissajous scanning is typically employed, owing to its i) simpler actuation drive strategy [15], ii) improved illumination uniformity [16] and iii) its capability to provide the preview of the entire image within a very small fraction of the frame.The frame rate for a Lissajous pattern is given based on the orthogonal scan frequencies, such that [17] : where f x and f y are the drive frequencies for orthogonal directions and n x and n y are smallest integers satisfying Eq. ( 8).Lissajous scan pattern is created through driving the orthogonal electrodes of the piezoelectric actuator at different frequencies.However, the mechanical resonances of an extended fiber optic cable in orthogonal directions are theoretically the same due to its cylindrical symmetry, and practically only slightly different due to assymetric anchoring condition (assymetric spread of fixing epoxy etc.) [15].Various strategies are employed to differentiate the orthogonal resonances through off-resonance actuation [18], employing additional microfabricated components to break the cylindrical symmetry [19][20][21], and utilization of polarization maintaining fibers, thanks to the asymmetry in their geometry and intrinsic stress [22].As already mentioned, Lissajous scanning offers imaging / display of the preview of an image within a tiny fraction of the frame rate (thus could potentially be operated above the fps values that is given in Eq. ( 8), via smart selection of drive frequencies [23] .However, sub-frame rate Lissajous scanning strategy is mostly useful for sparse content, thus is more suitable for certain imaging applications (such as in-vitro cell culture imaging [17] rather than display applications.Thus, in this work, we focus our efforts and discussion to spiral scanning.

Piezo scanning vs. MEMS mirror microdisplays
Figure 5 summarizes the performance estimates of fiber scanning displays with different speeds (scanned fiber lengths and fiber diameters) along with state-of-the-art MEMS mirror-based display studies presented in literature, for comparison.Table 1 compares the state-of the art MEMS mirror scanner based display [24] in literature with two cases of piezo scanning, where a conventional thickness (125 µm diameter) fiber having L = 4.2-mm (to match the experimental condition) is considered.Note that initially L=4-mm was targeted in the experiment, where we ended up getting a slightly longer extended fiber.Table 1 also shows the performance of a shorter and optimized fiber scanner having L = 1.3-mm length.For a cylindrical resonating beam, the resonance frequency can be found with the following formula [25]: where E is the Young's modulus and ρ is the density of silica, R is the fiber cladding radius (R = 62.5 µm), L is the extended fiber length, and β is a constant related to the vibration mode (β = 3.52 for 1ŝt eigenmode).Based on Eq. ( 9), the mechanical resonance is found as 5.6 kHz for the longer piezo-scanner (L = 4.2 mm) and 53 kHz for the shorter fiber scanner (L = 1.3 mm).Note that higher order modes in fiber scanning could potentially be utilized to simultaneously increase the scan angle and the resonance frequency [26], while we have exploited 1ŝt order mode in our simple and compact optical design.We consider both mechanical limitations (yield stress) and optical limitations (bending losses) to estimate maximum scan angle for the fiber scanner.The maximum stress (σ max ) induced on a beam, is given as [11]: where F is the force exerted on the beam, and I is the area moment of inertia.Note that for a cylindrical beam such as the extended fiber, the area moment of inertia (I f iber ) is given as [27] Inserting Eq. ( 11) into Eq.( 10), we get: Hooke's Law suggests a linear relationship between the force and the out-of-plane displacement ( d 2 ) as: . The stiffness of a cylindrical beam (k f iber ) can be written as [27] k f iber = 3E πR 4 8L 3 (13) Replacing Eq. ( 13) into Eq.( 12), we get: From Eq. ( 14), the displacement could be expresses in terms of maximum stress as: Using Eq. ( 2), we can express the maximum total fiber scan angle θ in terms of maximum stress: Eq. ( 15) suggests low radius-of-curvature bending (and thus high scan angle) of the fiber, for a maximum tensile and yield stress of ∼6Gpa [28] for fused silica.The reduced ROC values would indeed result in significant increase of optical losses [29].Although the increase of optical losses is a significant drawback for fiber communication applications that necessitate kilometers of long fibers, the HWD design that is proposed here only requires 1 meter long fiber even if the light sources are located at user's beltpack.Thus we are less concerned with optical losses than the mechanical fatigue that the fiber might undergo.Total number of pixels/sec is proportional to the product of N 2 f iber and FPS , such that : Note that f f iber × d (KHz.mm)product is constant and depends only on the material properties and sets an upper limit on the resolution and frame rate considering the mechanical parameters of the fiber.Overall pixel rate can be increased by reducing the output spot diameter of the single mode fiber, thereby, increasing the output NA of the fiber.If the NA of the fiber is increased by other means, such as using scattering nanoparticles, the impact would be increasing the eyebox size for the display, at the expense of reduced brightness.Furthermore, the resolution of the fiber scanning display still would remain the same, once the eyebox size is enlarged through using scattering particles at the fiber tip.Figure 5 illustrates the resolution that can be achieved with a fiber scanning microdisplay unit (both in Megapixels and as optical angle & virtual mirror diameter product) as a function of FPS, based on the formulation presented above.In summary, FPS was calculated based on Eqs. ( 5) and (7) for fibers having different lengths and NA.The resolution was calculated based on Eqs. ( 4) and (15).Note that different fiber NA'a have been considered whose values range between 0.1 to 0.6.A typical single-mode fiber (SMF) showcases an NA of 0.1-0.2, while tapering of the fiber as well as utilizing special photonic crystal fiber designs leads to 0.2-0.6NA's for the visible region [30].Although, the elliptic surfaces would have to be tailored based on fiber NA, as well as the enlarged scan angle.Without loss of generality, our design is tailored for the fiber used in our experiments (Thorlabs SM-600, NA=0.15).The performance of the State-of-the-art (SOA) 2D MEMS mirror [31] together with the experimental conditions is also labeled in Fig. 5.
The curves in Fig. 5 were generated through plotting the resolution and FPS values acquired for fiber lengths: L = 1-10-mm.FPS was calculated based on Eq. ( 7), Note that the optimal fiber scanning unit can significantly exceed the performance of SOA MEMS display at L = 1.1 mm, for NA = 0.6.Note that HD720 level resolution at 60Hz FPS could be achieved with an off-the-shelf, low-cost 0.2 NA single-mode fiber, and furthermore SOA MEMS mirror display performance could even be reached with an NA = 0.3 fiber.
Figure 6 compares the fiber scan angles, at the ultimate tensile strength, achieved with the analytical formulation presented above (Eq.( 15)) with that found with COMSOL finite-element software.The results match to a great extend for L > 2 mm, and reveal ∼ 30 % error for short fiber lengths.
Table 1 summarizes the comparison between SOA MEMS unit, experimental conditions (fiber scanner #1) and an optimal fiber scanning unit (fiber scanner #2).
Overall, Table 1 highlights the roadmap for an optimized fiber scanning microdisplay (Fiber scanner #2) for operation with higher performance as opposed to the state-of-the-art MEMS mirror-based display.Furthermore, the optical architecture simplicity offered in Fig. 1, as opposed to that of a typical MEMS mirror scanner based display, coupled with the ease of fabrication   1 also highlights the performance and conditions for the experimentally demonstrated fiber scanning microdisplay (Fiber scanner #1).Note that the calculated parameter values for fiber scanner #1 and #2 do not scale in accordance with the analytical formulation given above.As fiber scanner #1 reflects experimental conditions where the scanning was not pushed to the stress limits.Realistically, the fiber is to be scanned with a stress safety factor (SSF), which reflects the ratio of the ultimate stress to the fiber stress during scanning to the ultimate stress.Figure 7 illustrates the performance of the optimal fiber scanner (NA=0.6)as a function of the safety factor.Note that each data point on Fig. 7 satisfies 60 Hz frame rate.We observe that an SSF of up to ∼2.5 results in an HD1440 display, while 2.5 < SSF < 4 results in an HD1080 level resolution at 60 Hz, which is still superior with respect to the best 2D MEMS Mirror scanner.Furthermore one can achieve an HD720 display with an SSF of as large as 8.In Fig. 5,the experimental data point falls short of the corresponding NA line, as it was performed with a large SSF of 25.Yet, we managed to showcase a VGA level performance at 25 Hz.Note that, the optimized fiber scanner and the utilized elliptic mirror results in a 3 mm eyebox size and 20 degrees of FOV.For the mentioned eyebox size and FOV, one can achieve very bright displays using mW-level laser sources.The resolution predictions based on Eq. ( 4), illustrated in Figs.5,7 and Table 1, reflects an ideal scenario that neglect the aberrations presented by the elliptic surface.Nevertheless, despite possible degradation of the display performance due i) aberrations, ii) slight discrepancies in scan angle calculations between analytical and FEA findings, along with iii) sub-maximum stress level actuation of the fiber will still enable HD1440 and HD1080 level display performance.The wide SSF ranges mentioned in the above paragraph corresponding to each display resolution provides a reasonable and practical safety margin to enable realization of the claimed resolution levels.

Conclusions and discussion
We've proposed a lightweight scanning fiber microdisplay architecture that is suitable for HWD adaptation.Although, the simulations and experiments were performed for a reflective ellipse (suitable for virtual reality applications) as a relay element, the ellipse could simply be replaced by a partially reflective counterpart for augmented reality applications.FOV and ExP size product of the display increases with the resolution of the fiber based display.ExP size can be further expanded by scattering the light at the tip of the fiber output [34].
With its simple and low-cost optical architecture, the proposed display offers important advantages over MEMS mirror scanners in terms of fabrication and optical architecture simplicity towards practical realization.Furthermore, scanning fiber microdisplays offer similar optical throughput (only minor optical losses due to fiber coupling and bending) with MEMS mirror scanning displays, and superior energy density and thus wall-plug efficiency as opposed to electrostatic and electromagnetically actuated MEMS counterparts.Overall pixel rate (pixels/second) of the fiber scanning system can be increased by increasing the output NA of the fiber by way of reducing the emission spot size.We demonstrate the display of a checkerboard pattern with ∼VGA resolution.Although MEMS mirror scanners are quite advanced with integrated angles sensors and controllers, fiber scanners have very good potential.As demonstrated with further improvements, through exploiting of high NA PCF or tapered fibers, the proposed fiber scanning architecture has the potential to display HD1440 resolution videos at 60 fps, which is beyond what has been demonstrated by a MEMS mirror scanner based display.

Fig. 1 .
Fig. 1.Scanning fiber microdisplay: a) general view b) detailed schematic of the design.c) Alternative implementation using a spherical surface and a beam splitter.

Fig. 3 .
Fig. 3. Optical architecture of a bi-axial MEMS mirror-based display unit.This figure is dedicated for comparison with Fig. 1b.

Fig. 4 .
Fig. 4. Optical architecture of a bi-axial MEMS mirror-based display unit.This figure is dedicated for comparison with Fig. 1b.