## LED backlight designs with the flow-line method |

Optics Express, Vol. 20, Issue S1, pp. A62-A68 (2012)

http://dx.doi.org/10.1364/OE.20.000A62

Acrobat PDF (1923 KB)

### Abstract

An LED backlight has been designed using the flow-line design method. This method allows a very efficient control of the light extraction. The light is confined inside the guide by total internal reflection, being extracted only by specially calculated surfaces: the ejectors. Backlight designs presented here have a total optical efficiency of up to 80% (including Fresnel and absorption losses) with an FWHM below 30 degrees. The experimental results of the first prototype are shown.

© 2011 OSA

## 1. Introduction

1. J. C. Miñano, P. Benítez, J. Chaves, M. Hernández, O. Dross, and A. Santamaría, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE **5942**, 594202, 594202-12 (2005). [CrossRef]

8. K. Imai and I. Fujieda, “Illumination uniformity of an edge-lit backlight with emission angle control,” Opt. Express **16**(16), 11969–11974 (2008). [CrossRef] [PubMed]

1. J. C. Miñano, P. Benítez, J. Chaves, M. Hernández, O. Dross, and A. Santamaría, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE **5942**, 594202, 594202-12 (2005). [CrossRef]

## 2. Backlight architecture

1. J. C. Miñano, P. Benítez, J. Chaves, M. Hernández, O. Dross, and A. Santamaría, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE **5942**, 594202, 594202-12 (2005). [CrossRef]

## 3. Extended ray bundles and flow lines

*n*, be known, and let the collimator illuminates the beam slicer (in the cross section of Fig. 1) within an angle ±

*θ*. For the beam slicer design, consider an extended bundle of rays passing through the segment

*AB*within an angle ±

*θ*with respect to the

*x*axis. The edge rays of that extended bundle [9] are shown in Fig. 2 . For clarity, they have been represented as two subsets. Every point in the region bounded by the rays

*r*

_{1}and

*r*

_{2}is crossed by two edge rays (one ray of each edge ray subset). These subsets can be defined by two eikonal functions

*O*

_{1}(

*x,y*) and

*O*

_{2}(

*x,y*), whose constant values provide the wavefronts associated to those edge ray subsets.

*j = const*lines of the functionare the well-known flow lines of the bundle [1

**5942**, 594202, 594202-12 (2005). [CrossRef]

*O*

_{2}are just transformed into edge rays associated to eikonal

*O*

_{1}. This property will be used to design the top guide line and the guide segments of the bottom microstructured line to coincide with the flow lines.

*E*of the rays crossing a segment whose edge points lay on flow lines

*j*

_{1}and

*j*

_{2}>

*j*

_{1}is independent of the coordinates of those points (see Fig. 3(b)), and is just given by:

*x-*axis.

*R*, the incremental power is Δ

*P*=

*R*Δ

*E*= 2

*R*Δ

*j*. In order to provide uniform irradiance on the LCD (

*dP*/

*dx*= constant), the envelope of the microstructured line (at the limit of infinitesimally small ejectors), must fulfill the equation:where

*E*is the 2D etendue of the exiting bundle. Extrapolated to finite ejector sizes, Eq. (3) means that, for instance, if all the ejectors have the same projected size Δx, each ejector must intercept the same Δj.

_{out}*y*=

*y*(

*x*) in Eq. (3), it will fulfill the following differential equation:

## 4. Beam slicer design in two-dimensions

*conical*and

*linear*), both associated with the ray bundles already presented in Fig. 3(a), so step (1) is completed. For step (2), the flow lines in Fig. 3(a) consist of 3 segments (with C

^{1}continuity): a straight line (in region I of Fig. 3(a)), a parabola (in region II), and a hyperbola (in region III). This can be easily obtained by calculating the lines bisecting the edge rays in each region. In region I each point is intercepted by two edge rays forming the angle

*θ*in respect to the axis

*x*, thus the flow lines are straight lines

*y*=

*const*. In region II, one edge ray comes from an interior point of the strip

*AB*, while the other from an extreme point of the strip (

*A*or

*B*). Therefore, the flow lines are the parabolas with focus at

*A*or

*B*. Finally, in region III both edge rays come from points

*A*and

*B*, so the flow lines become the hyperbolas with foci

*A*and

*B*.

*y*= 0 as the top guide line. Finally, in step (4) the microstructured line must be calculated. For very small ejector sizes, this could be done by solving differential Eq. (4) with contour condition

*y*(0) = -

*d*

_{0}, where

*d*

_{0}is the collimator exit aperture size (in Fig. 3 the aperture is given by the strip CD). However, for better performance, we do the exact finite-facet construction. This is implemented by starting from the flow line passing though point C = (0, -

*d*

_{0}), alternating flow line segments (which are the guide lines) and the ejectors. We chose that these ejectors will all intercept the same etendue Δj, and with a tilt provided that all the rays are reflected by total internal reflection.

*y*

_{0}that defines points A = (0,

*y*

_{0}) and B = (0,-

*y*

_{0}), the aperture size

*d*

_{0}and angle

*θ*of the collimation, the minimum thicknesses of the beam slicer at its end,

*d*, which is fixed by manufacturing constraints. The purely geometrical efficiency (i.e, without considering absorption or Fresnel losses) is given by the ratio

_{min}*E*/

_{out}*E*, where

_{in}*E*= 2∙

_{in}*n∙d*

_{0}

*∙sin θ*is the étendue of the bundle exiting the collimator and entering the beam slicer. Note that fixing

*d*>0 implies some geometrical losses, given by E

_{min}_{l}, escaping at the end of the slicer (

*E*-

_{l}= E_{in}*E*).

_{out}*d*, and the length

_{max}*l*are computed. Since

*d*and

_{max}*l*are more practical input parameters, we match them by varying

*d*

_{0}and

*θ*.

*y*

_{0}is small enough that flow lines inside the beam slicer contain not only straight line segments but parabolic and hyperbolic ones too (i.e. the slicer is designed in regions I-III), the design will be called

*conical backlight*here. When

*y*

_{0}tends to infinity, the bundle has only region I, so all the flow lines inside the beam slicer are straight lines, therefore the design will be called

*linear backlight.*

*AB*= 5

*mm*,

*θ*= 10°,

*d*= 0.5

_{min}*mm*,

*d*= 2.9

_{max}*mm*,

*p*= 1

*mm*(where

*d*and

_{min}*d*are the smallest and the biggest thicknesses, and

_{max}*p*is the distance between two ejectors). A linear backlight design with similar specifications:

*θ*= 8°,

*d*= 0.5

_{min}*mm*,

*d*= 2.89

_{max}*mm*,

*p*= 1

*mm*is also modeled.

## 5. Three-dimensional designs

*z*-axis of both the beam slicer and collimator sections. We have selected this simple symmetry to ease the prototype manufacturing (see Section 6). The LEDs will not be glued to the collimators, which will have a flat entry surface. Therefore, the light after the refraction will form an angle with the

*x*-axis smaller than the critical angle. Note that due to the linear symmetry of the collimators, the light exiting the backlight towards the LCD plane will be collimated only in the

*x-y*plane, but not in the

*z-y*. Collimation in both directions can be obtained using cross-CPC type collimators (which collimate in both dimensions) and the same linear-symmetric beam slicer.

^{®}, using 7 equally spaced LEDs with dimensions 0.6x1.9

*mm*(the same dimensions as OSRAM microside LEDs). Beside the collimation, the collimator’s function is to mix the rays coming from different LEDs, so that the irradiance at the entrance of the slicer is uniform. This provides an equal etendue supply for the ejectors.

^{®}simulation gives 92.0% of geometric efficiency and 79.9% of total efficiency (including Fresnel and absorption losses) for the conical backlight, and 82.0% of geometric efficiency and 71.4% of total efficiency for the linear backlight.

## 6. Simulations and experimental results for a linear backlight prototype

## 7. Summary

## Acknowledgments

## References and links

1. | J. C. Miñano, P. Benítez, J. Chaves, M. Hernández, O. Dross, and A. Santamaría, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE |

2. | D. Feng, G. Jin, Y. Yan, and S. Fan, “High quality light guide plates that can control the illumination angle based on microprism structures,” Appl. Phys. Lett. |

3. | D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light-guide plate for liquid crystal display backlight,” J. Opt. A, Pure Appl. Opt. |

4. | H. Tanase, J. Mamiya, and M. Suzuki, “A new backlighting system using a polarizing light pipe,” IBM J. Res. Develop. |

5. | N. Guselnikov, P. Lazarev, M. Paukshto, and P. Yeh, “Translucent LCDs,” J. Soc. Inf. Disp. |

6. | S. R. Park, O. J. Kwon, D. Shin, S. H. Song, H. S. Lee, and H. Y. Choi, “Grating micro-dot patterned light guide plates for LED backlights,” Opt. Express |

7. | W. J. Cassarly, “Backlight pattern optimization,” Proc. SPIE |

8. | K. Imai and I. Fujieda, “Illumination uniformity of an edge-lit backlight with emission angle control,” Opt. Express |

9. | R. Winston, J. C. Miñano, and P. Benítez, with contributions of N. Shatz and J. Bortz, |

**OCIS Codes**

(220.2945) Optical design and fabrication : Illumination design

(080.4298) Geometric optics : Nonimaging optics

**ToC Category:**

Illumination Design

**History**

Original Manuscript: September 30, 2011

Revised Manuscript: November 7, 2011

Manuscript Accepted: November 18, 2011

Published: December 6, 2011

**Citation**

Dejan Grabovičkić, Pablo Benítez, Juan C. Miñano, and Julio Chaves, "LED backlight designs with the flow-line method," Opt. Express **20**, A62-A68 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-S1-A62

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### References

- J. C. Miñano, P. Benítez, J. Chaves, M. Hernández, O. Dross, and A. Santamaría, “High-efficiency LED backlight optics designed with the flow-line method,” Proc. SPIE5942, 594202, 594202-12 (2005). [CrossRef]
- D. Feng, G. Jin, Y. Yan, and S. Fan, “High quality light guide plates that can control the illumination angle based on microprism structures,” Appl. Phys. Lett.85(24), 6016–6018 (2004). [CrossRef]
- D. Feng, Y. Yan, X. Yang, G. Jin, and S. Fan, “Novel integrated light-guide plate for liquid crystal display backlight,” J. Opt. A, Pure Appl. Opt.7(3), 111–117 (2005). [CrossRef]
- H. Tanase, J. Mamiya, and M. Suzuki, “A new backlighting system using a polarizing light pipe,” IBM J. Res. Develop.42(3), 527–536 (1998). [CrossRef]
- N. Guselnikov, P. Lazarev, M. Paukshto, and P. Yeh, “Translucent LCDs,” J. Soc. Inf. Disp.13(4), 339–348 (2005). [CrossRef]
- S. R. Park, O. J. Kwon, D. Shin, S. H. Song, H. S. Lee, and H. Y. Choi, “Grating micro-dot patterned light guide plates for LED backlights,” Opt. Express15(6), 2888–2899 (2007). [CrossRef] [PubMed]
- W. J. Cassarly, “Backlight pattern optimization,” Proc. SPIE6834, 683407, 683407-12 (2007). [CrossRef]
- K. Imai and I. Fujieda, “Illumination uniformity of an edge-lit backlight with emission angle control,” Opt. Express16(16), 11969–11974 (2008). [CrossRef] [PubMed]
- R. Winston, J. C. Miñano, and P. Benítez, with contributions of N. Shatz and J. Bortz, Nonimaging Optics (Elsevier, Academic Press, 2004).

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