Abstract

State-of-the-art autostereoscopic displays often do not comply with mandatory requirements for outdoor use, because of their limitations in size, luminance, number of 3D viewing zones, and maximum 3D viewing distances. In this paper we propose a concept for a modular autostereoscopic multi-view laser display with sunlight readable luminance, theoretically up to several thousand 3D viewing zones, and maximum 3D viewing distances of up to 70 meters. Each picture element contains three laser diodes, a cylindrical microlens, as well as a MEMS mirror, which deflects the collimated light beams to the left and right eyes of multiple viewers in a time-multiplexed manner. To demonstrate the principle, we have developed a prototype display with 5 x 3 picture elements.

© 2014 Optical Society of America

1. Introduction

Stereoscopic perception means that the viewer’s eyes see two slightly different images, which the human brain combines into a corresponding three-dimensional (3D) model of the observed scene. Widely used glasses-based 3D displays with active shutter or passive polarization glasses use rapid flickering shutters and polarizing lenses to present different images to each eye. These displays are, however, inappropriate for many applications, especially for large-scale outdoor displays where the number of viewers might be very large (e.g. public screening) or viewers only briefly watch the displayed content (e.g. digital signage). State-of-the-art autostereoscopic, i.e. glasses-free, concepts incorporate optical elements such as lenticular arrays or parallax barriers [1] in front of, e.g., a liquid-crystal display (LCD) panel in order to send the image information of a subset of the LCD’s pixels to distinct tightly constrained directions—so-called 3D viewing zones. The main disadvantage of these displays is that the native resolution of the underlying LCD as well as the luminance is reduced by a factor equal to the number of viewing zones, which significantly reduces both image quality and sunlight readability. Some alternative concepts for autostereoscopy circumvent the loss of resolution and can also be applied to large-scale displays but are not suitable for outdoor applications due to their low luminance [2,3]. In this paper we propose a technology, where most of the limitations of state-of-the-art autostereoscopic techniques are nonexistent or at least substantially relaxed.

Our autostereoscopic display consists of arrays of separate picture elements—so-called “trixels”. Each trixel contains an integrated light source with three individually controllable lasers with associated monitor photodiodes, a common cylindrical microlens, and a rotating micro-electro-mechanical systems (MEMS) mirror which deflects the collimated light beams to the left and to the right eyes of the viewers. By synchronizing the micromirror actuation with the 3D image information, i.e. the laser diode driving signals, each trixel can display a multitude—theoretically up to several thousand—of autostereoscopic views [4]. Unlike concepts with conventional video projectors [5], the trixel’s cylindrical microlens collimates the beams in only one spatial dimension, readily generating a horizontal parallax.

To demonstrate the proposed principle, we have developed an autostereoscopic prototype laser display with an array of 5 x 3 trixels using red laser diodes and a trixel pitch of 12 mm. For comparison, state-of-the-art two-dimensional (2D) LED displays for outdoor applications have pixel pitches of 6 mm to 18 mm. Our prototype display is capable of sending different image information, e.g. patterns or single characters, to the left and right eyes of multiple viewers in a time-multiplexed manner, effectively proofing the proposed technique for achieving an autostereoscopic effect.

This article is organized as follows: The basic principle of the 3D laser display is introduced in Sec. 2. In Sec. 3 optical properties like maximum 3D viewing distance, number of 3D viewing zones, and luminance are analyzed. Section 4 describes the prototype display.

2. Basic operation principle

2.1 Time-multiplexed autostereoscopic effect

Figure 1 shows the basic operation principle of a single trixel. Light emitted from a red, green, and blue individually controllable laser diode is collimated by a microlens and deflected by a scanning MEMS mirror. By synchronizing the image information to be displayed in a particular 3D viewing zone with the mechanical mirror deflection, the viewer can see different image information with the left and the right eye. In the example of Fig. 1 the optical beam direction changes by an angular offset Δγ within the time interval Δt while the displayed image information changes from Im to Im+1. In contrast to state-of-the-art autostereoscopic techniques like lenticular arrays or parallax barriers, our time-multiplexed approach does not reduce the resolution of the display, i.e. both eyes of the viewers can receive image information from all trixels and not only from subsets thereof.

 

Fig. 1 Basic time multiplex principle of a single trixel: (a) image information Im is displayed at the time instance t = t0 for the viewer’s left eye and (b) a different image information Im+1 is displayed at the subsequent time instance t = t0 + Δt for the viewer’s right eye.

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The divergence angle θ of the collimated scanned beams (cf. Fig. 1) is the most important parameter of the system as it directly influences the maximum viewing distance. The beam divergence is defined as 1/e2 half-angle of the collimated “fast axis” of the elliptical Gaussian laser beam. An autostereoscopic effect can only be perceived in a viewing position at distance d from the display if the width of the 3D viewing zone dVZ = 2d tan(θ) is smaller than or equal to the average human eye distance se, i.e. dVZse. The average distance between the human eyes is se = 6.5 cm for adult males and se = 6.3 cm for adult females [6]. In the following the lower value for female adults will be used. For a given divergence angle θ the maximum viewing distance is given by dmax = se/(2 tan(θ)).

2.2 Trixel components

Figure 2(a) shows a schematic of the integrated laser light source. Three laser diodes and three associated monitor photodiodes are assembled on a common submount. While in future 3D RGB laser displays three different laser diode chips—one each for red, green, and blue—will be incorporated, the trixels presented in this paper contain three identical red GaAs laser diodes with a wavelength of λ = 635 nm due to the limited availability of bare die green and blue GaN laser diodes. By assembling and operating three individual chips we can proof in hardware the feasibility of aligning the focal points of the cylindrical microlens to the active laser diode areas. The monitor photodiodes continuously measure the optical power emitted from the back facets of the laser diodes in order to estimate the optical output power irradiated from the front facets. This information is used to compensate for potential color shifts in RGB displays caused by temperature variation as well as aging effects and to guarantee eye safety.

 

Fig. 2 Schematics of (a) integrated laser light source and (b) trixel including MEMS mirror and MID substrate.

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In front of the three laser diodes is a single collimating microlens. The submount and the microlens are attached to a common heat sink element. The prototype of our integrated light source has a volume of only 0.07 cm3, but includes three laser diodes, three monitor photodiodes, a submount, a heat sink, as well as a microlens.

The plano-convex cylindrical microlens collimates the beams from the light source in only one transverse direction, the so-called “fast axis” [7], which here is equal to the z-axis. In the orthogonal y-direction, the so-called “slow axis”, the light beams pass the microlens uncollimated. In the far field of the integrated light source this produces a Gaussian beam characteristic with large ellipticity. The residual “fast axis” divergence angle is lower-bounded by diffraction according to θLDλ/(π f θ0) = 0.34 mrad, where λ = 635 nm and θ0 ≈ 28° (1/e2 half-angle) are the wavelength and the divergence angle of the beams emitted by the laser diodes, respectively. The focal length f of the microlens is constrained by the physical dimensions of the lens as well as the refractive index of the lens material. For our prototype display applying red laser diodes of wavelength λ = 635 nm the focal length is f = 1.2 mm. In order to minimize spherical aberrations, the convex surface of the lens is aspheric. Strictly speaking, this diffraction limit is valid only for paraxial beams. However, experiments show that it also describes quite well the transformation of beams emitted by typical laser diodes [4].

Figure 2(b) shows a schematic of the trixel including the MEMS mirror, the common substrate, and the integrated light source. The prototype display incorporates quasi-static electromagnetic 1D MEMS mirrors with an optical scanning amplitude of αmax = ± 10°. In its idle position, the micromirror deflects the beams by 90°. The substrate is fabricated applying the molded interconnect device (MID) technique, comprising an injection-molded thermoplastic base material with tailored metallization lines on its surface for electrical wiring purposes.

3. Optical properties

3.1 Maximum 3D viewing distance

Due to tolerances arising from the manufacturing and assembly process the divergence angle θ, and hence the maximum 3D viewing distance dmax is in general different for each individual trixel. Assuming perfect aberration-free components, the theoretical diffraction limit θDL introduced in Sec. 2 can only be reached by perfectly aligning the center of the light emitting area at the front facets of the laser diodes to the focal points of the microlens. In [4] we have presented both measurements and simulation results of the cumulative distribution function (CDF) of the divergence angle, which reflect the fact that due to the manufacturing tolerances the diffraction limit cannot be reached in practice, i.e. θθDL.

If the reflecting surface of the MEMS mirror is not perfectly flat and smooth, the divergence angle of the reflected beam is increased even further. Since the peak-to-valley flatness of the micromirror model incorporated in the first prototype display of approximately 3 µm is significantly larger than the surface roughness, only the influence of the former parameter is analyzed in the following.

We have modeled the surface profile of the micromirror as a sphere with radius of curvature R, where R = ∞ corresponds to a perfectly flat surface. Figure 3 shows the 99% confidence intervals of the divergence angle as well as the corresponding maximum 3D viewing distances dmax as a function of the reciprocal micromirror curvature. Measurements based on beam optics have shown that the micromirror incorporated in the first prototype has a curvature of 1/R ≈ 3.6 m−1. The mean value of the divergence angle of a trixel with a perfectly flat micromirror equals μΘ = 0.44 mrad while it is μΘ = 6.12 mrad for a trixel with a mirror curvature of 1/R = 3.6 m−1. The corresponding maximum 3D viewing distances are dmax = 70.5 m and dmax = 5.1 m, respectively. Meanwhile, MEMS mirrors with curvatures of some 1/R ≈ 0.2 m−1 are available, leading to a maximum 3D viewing distance of dmax = 58.6 m.

 

Fig. 3 Divergence angle θ and maximum 3D viewing distance dmax as a function of the reciprocal micromirror curvature (99% confidence intervals; the dashed lines represent the mean values).

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3.2 Number of 3D viewing zones

Assuming a perfectly flat micromirror, the theoretical maximum number of 3D viewing zones is determined by the maximum optical scanning angle αmax and the diffraction-limited divergence angle θDL according to NVZ,max = αmax/θDL. Our prototype display has a theoretical maximum number of NVZ,max ≈ 500. Future 3D laser displays with optimized MEMS mirrors and integrated laser light sources have the potential for up to several thousand viewing zones by increasing αmax and decreasing θDL, respectively. The latter can be achieved by increasing the focal length f of the lens as well as by optimized laser diodes with increased “fast axis” divergence angles θ0.

3.3 Luminance and eye safety

The irradiance in the far field of one laser diode of a single trixel in cylinder coordinates is given by

Ee(ρ,φ,y)E0rect(φ2αmax)HorizontalMEMSmirrorscanningw0,SA2wSA2(ρ)exp(2y2wSA2(ρ))VerticalGaussian“slowaxis”profile,
where E0 is the peak irradiance. In the vertical y-direction the profile is Gaussian due to the uncollimated “slow axis” of the laser diodes with corresponding divergence angle θ0,SA, beam waist w0,SA, and beam radius wSA(ρ). In the angular coordinate φ the profile is approximately invariant and constrained by the MEMS mirror scanning angle αmax, which is here modeled by the rectangular function with rect(ξ) = 1, |ξ| < ½ and rect(ξ) = 0, |ξ| > ½. By converting Eq. (1) to spherical coordinates the radiant intensity Ie(r,ϑ,φ) = Ee(r,ϑ,φ) r2 is given by
Ie(r,ϑ,φ)I0rect(φ2αmax)(λπsin(ϑ)tan2(θ0,SA))2exp(2tan2(ϑ)tan2(θ0,SA)).
Since Eq. (2) does not depend on the radial distance r, the peak radiant intensity I0 is defined by the normalization
φ=02πϑ=0πIe(ϑ,φ)sin(ϑ)dϑdφ=KP0,
where P0 is the optical output power of the laser diode. The parameter K takes into account the MEMS mirror flyback duration, which will be described in Sec. 4, and the absorption by the microlens, the MEMS mirror, and the package window.

The luminance of an autostereoscopic laser display is given by LvIv/dPIX2, where Iv = 683 V(λ) Ie is the luminous intensity with V(λ) as the eye intensity function and dPIX is the pitch between adjacent trixels. Our first prototype display with a trixel pitch of dPIX = 12 mm and three red laser diodes per trixel with a “slow axis” divergence angle of θ0,SA ≈ 6.4° and a wavelength of λ = 635 nm (resulting in V(λ) = 0.22) can achieve peak luminance values of, e.g. Lv ≈ 32,000 cd/m2 with an optical output power as low as P0 = 1 mW per laser diode when viewing the display at a polar angle of ϑ = 90°. The luminance of our first prototype display is significantly larger than for state-of-the-art sunlight-readable 2D LED outdoor displays, which have luminance values of, e.g. Lv = 5,000 cd/m2. An eye safety analysis based on [8] has shown that the maximum permitted luminance value of a 3D RGB laser display for long term viewing is Lv,max ≈ 100,000 cd/m2.

4. Prototype display

Figure 4(a) shows the first prototype display with an array of 5 x 3 trixels. The volume of a single trixel including the package is only 0.96 cm3, which to our knowledge is the smallest MEMS-based optical light module with three individually controllable laser diodes to date [9]. This enables to achieve a small pitch between adjacent trixels of only 12 mm, which would not be possible with state-of-the art commercial MEMS projectors.

 

Fig. 4 (a) Prototype display and (b) different image information in viewing zones m and m + 1 at the maximum viewing distance of the first prototype of dmax = 5.1 m.

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The driving electronics are located on a separate PCB. All MEMS mirrors are actuated with the same triangular signal at a frequency of fM ≈ 60 Hz. Image information is only displayed during one micromirror movement direction within a time interval of 2/(3 fM), while all laser diodes are switched off during the flyback duration of 1/(3 fM). The laser diode driving signals are pulse-width modulated (PWM) with a slot duration of tPWM ≈ 10 ns. This fine temporal granularity allows for an 8-bit color depth for each of the laser diodes—resulting in a 24-bit color depth of a future RGB laser display. Both, the laser diode and the MEMS mirror driving signals are generated by a field-programmable gate array (FPGA) on a separate development board.

Figure 4(b) shows an example of two out of NVZ = αmax/μΘ different test patterns in 3D viewing zones m and m + 1, which are spatially separated by the eye distance se = 6.3 cm. This effectively proofs that our prototype display is capable of sending different image information to the left and right eyes of viewers, which by definition is the main principle of autostereoscopy. Unlike state-of-the-art autostereoscopic displays, where the image information displayed in individual viewing zones is inherently repeated after, e.g. 8 views [1], our system is capable of displaying different image information in each of the NVZ viewing zones.

5. Summary and conclusion

We have designed an autostereoscopic large-scale multi-view laser display targeted for outdoor use. The individual “trixels” of our display incorporate laser light sources, leading to sunlight readable luminance. MEMS mirrors deflect the emitted light and form different images for the left and right eye of the viewer to achieve the autostereoscopic effect in a time-multiplexed manner without any loss of resolution. The proposed concept allows for a modular display, imposing no limits on the total size.

In this paper, we explain the principle of this system and characterize the optical properties of the first prototype with 5 x 3 trixels. We calculate the maximum distance, at which a 3D effect can be perceived, the maximum number of 3D viewing zones, as well as the luminance of the display. Assuming perfectly flat reflective surfaces of the MEMS mirrors, maximum viewing distances of up to approximately 70 meters can be achieved. The volume of a single trixel including the package is only 0.96 cm3 resulting in a trixel pitch of 12 mm. Our prototype display is capable of sending different image information to the left and right eyes of multiple viewers, effectively proofing our proposed approach.

Acknowledgments

This work has been partly funded by a grant for scientific research, No. 839656 (“3D Laser Display”), from the Austrian Research Promotion Agency (FFG).

References and links

1. B. Lee, “Three-dimensional displays, past and present,” Phys. Today 66(4), 36–41 (2013). [CrossRef]  

2. O. Eldes, K. Akşit, and H. Urey, “Multi-view autostereoscopic projection display using rotating screen,” Opt. Express 21(23), 29043–29054 (2013). [CrossRef]   [PubMed]  

3. T. Balogh, P. Kovacs, and A. Barsi, “Holovizio 3D display system,” in Proceedings of 3DTV Conference 2007, (Kos Island, Greece, 2007) pp. 1–4. [CrossRef]  

4. J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013). [CrossRef]  

5. J. Jurik, A. Jones, M. Bolas, and P. Debevec, “Prototyping a light field display involving direct observation of a video projector array,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition Workshops, (Colorado Springs, 2011) pp. 15–20. [CrossRef]  

6. L. Lipton, Foundations of the Stereoscopic Cinema (Van Nostrand Reinhold, 1982), Chap. 2.

7. V. Sturm, H. Treusch, and P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” Proc. SPIE 3097, 717–726 (1997). [CrossRef]  

8. International Electrotechnical Commission, “Safety of laser products - Part 1: Equipment classification and requirements,” IEC (EN) 60825–1 Ed. 2.0 (IEC, 2007).

9. L. Kilcher and N. Abelé, “MEMS-based micro projection system with a 1.5cc optical engine,” Proc. SPIE 8252, 825204 (2012). [CrossRef]  

References

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  1. B. Lee, “Three-dimensional displays, past and present,” Phys. Today 66(4), 36–41 (2013).
    [Crossref]
  2. O. Eldes, K. Akşit, and H. Urey, “Multi-view autostereoscopic projection display using rotating screen,” Opt. Express 21(23), 29043–29054 (2013).
    [Crossref] [PubMed]
  3. T. Balogh, P. Kovacs, and A. Barsi, “Holovizio 3D display system,” in Proceedings of 3DTV Conference 2007, (Kos Island, Greece, 2007) pp. 1–4.
    [Crossref]
  4. J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013).
    [Crossref]
  5. J. Jurik, A. Jones, M. Bolas, and P. Debevec, “Prototyping a light field display involving direct observation of a video projector array,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition Workshops, (Colorado Springs, 2011) pp. 15–20.
    [Crossref]
  6. L. Lipton, Foundations of the Stereoscopic Cinema (Van Nostrand Reinhold, 1982), Chap. 2.
  7. V. Sturm, H. Treusch, and P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” Proc. SPIE 3097, 717–726 (1997).
    [Crossref]
  8. International Electrotechnical Commission, “Safety of laser products - Part 1: Equipment classification and requirements,” IEC (EN) 60825–1 Ed. 2.0 (IEC, 2007).
  9. L. Kilcher and N. Abelé, “MEMS-based micro projection system with a 1.5cc optical engine,” Proc. SPIE 8252, 825204 (2012).
    [Crossref]

2013 (3)

B. Lee, “Three-dimensional displays, past and present,” Phys. Today 66(4), 36–41 (2013).
[Crossref]

O. Eldes, K. Akşit, and H. Urey, “Multi-view autostereoscopic projection display using rotating screen,” Opt. Express 21(23), 29043–29054 (2013).
[Crossref] [PubMed]

J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013).
[Crossref]

2012 (1)

L. Kilcher and N. Abelé, “MEMS-based micro projection system with a 1.5cc optical engine,” Proc. SPIE 8252, 825204 (2012).
[Crossref]

1997 (1)

V. Sturm, H. Treusch, and P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” Proc. SPIE 3097, 717–726 (1997).
[Crossref]

Abelé, N.

L. Kilcher and N. Abelé, “MEMS-based micro projection system with a 1.5cc optical engine,” Proc. SPIE 8252, 825204 (2012).
[Crossref]

Aksit, K.

Bolas, M.

J. Jurik, A. Jones, M. Bolas, and P. Debevec, “Prototyping a light field display involving direct observation of a video projector array,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition Workshops, (Colorado Springs, 2011) pp. 15–20.
[Crossref]

Debevec, P.

J. Jurik, A. Jones, M. Bolas, and P. Debevec, “Prototyping a light field display involving direct observation of a video projector array,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition Workshops, (Colorado Springs, 2011) pp. 15–20.
[Crossref]

Eldes, O.

Fidler, F.

J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013).
[Crossref]

Gartner, W.

J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013).
[Crossref]

Jones, A.

J. Jurik, A. Jones, M. Bolas, and P. Debevec, “Prototyping a light field display involving direct observation of a video projector array,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition Workshops, (Colorado Springs, 2011) pp. 15–20.
[Crossref]

Jurik, J.

J. Jurik, A. Jones, M. Bolas, and P. Debevec, “Prototyping a light field display involving direct observation of a video projector array,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition Workshops, (Colorado Springs, 2011) pp. 15–20.
[Crossref]

Kilcher, L.

L. Kilcher and N. Abelé, “MEMS-based micro projection system with a 1.5cc optical engine,” Proc. SPIE 8252, 825204 (2012).
[Crossref]

Lee, B.

B. Lee, “Three-dimensional displays, past and present,” Phys. Today 66(4), 36–41 (2013).
[Crossref]

Leeb, W.

J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013).
[Crossref]

Loosen, P.

V. Sturm, H. Treusch, and P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” Proc. SPIE 3097, 717–726 (1997).
[Crossref]

Reitterer, J.

J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013).
[Crossref]

Saint Julien-Wallsee, F.

J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013).
[Crossref]

Schmid, G.

J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013).
[Crossref]

Schmid, U.

J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013).
[Crossref]

Sturm, V.

V. Sturm, H. Treusch, and P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” Proc. SPIE 3097, 717–726 (1997).
[Crossref]

Treusch, H.

V. Sturm, H. Treusch, and P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” Proc. SPIE 3097, 717–726 (1997).
[Crossref]

Urey, H.

Opt. Express (1)

Phys. Today (1)

B. Lee, “Three-dimensional displays, past and present,” Phys. Today 66(4), 36–41 (2013).
[Crossref]

Proc. SPIE (3)

L. Kilcher and N. Abelé, “MEMS-based micro projection system with a 1.5cc optical engine,” Proc. SPIE 8252, 825204 (2012).
[Crossref]

V. Sturm, H. Treusch, and P. Loosen, “Cylindrical microlenses for collimating high-power diode lasers,” Proc. SPIE 3097, 717–726 (1997).
[Crossref]

J. Reitterer, F. Fidler, F. Saint Julien-Wallsee, G. Schmid, W. Gartner, W. Leeb, and U. Schmid, “Large-scale autostereoscopic outdoor display,” Proc. SPIE 8648, 86480G (2013).
[Crossref]

Other (4)

J. Jurik, A. Jones, M. Bolas, and P. Debevec, “Prototyping a light field display involving direct observation of a video projector array,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition Workshops, (Colorado Springs, 2011) pp. 15–20.
[Crossref]

L. Lipton, Foundations of the Stereoscopic Cinema (Van Nostrand Reinhold, 1982), Chap. 2.

T. Balogh, P. Kovacs, and A. Barsi, “Holovizio 3D display system,” in Proceedings of 3DTV Conference 2007, (Kos Island, Greece, 2007) pp. 1–4.
[Crossref]

International Electrotechnical Commission, “Safety of laser products - Part 1: Equipment classification and requirements,” IEC (EN) 60825–1 Ed. 2.0 (IEC, 2007).

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Figures (4)

Fig. 1
Fig. 1 Basic time multiplex principle of a single trixel: (a) image information Im is displayed at the time instance t = t0 for the viewer’s left eye and (b) a different image information Im+1 is displayed at the subsequent time instance t = t0 + Δt for the viewer’s right eye.
Fig. 2
Fig. 2 Schematics of (a) integrated laser light source and (b) trixel including MEMS mirror and MID substrate.
Fig. 3
Fig. 3 Divergence angle θ and maximum 3D viewing distance dmax as a function of the reciprocal micromirror curvature (99% confidence intervals; the dashed lines represent the mean values).
Fig. 4
Fig. 4 (a) Prototype display and (b) different image information in viewing zones m and m + 1 at the maximum viewing distance of the first prototype of dmax = 5.1 m.

Equations (3)

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E e (ρ,φ,y) E 0 rect( φ 2 α max ) Horizontal MEMS mirror scanning w 0,SA 2 w SA 2 (ρ) exp( 2 y 2 w SA 2 (ρ) ) Vertical Gaussian “slow axis” profile ,
I e (r,ϑ,φ) I 0 rect( φ 2 α max ) ( λ πsin(ϑ) tan 2 ( θ 0,SA ) ) 2 exp( 2 tan 2 (ϑ) tan 2 ( θ 0,SA ) ).
φ=0 2π ϑ=0 π I e (ϑ,φ) sin(ϑ)dϑdφ=K P 0 ,

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