Improvement of the microprism distribution expression of an integrated light guide plate

Yanyan Huang; Xulin Zhang; Wei Yang; Lei Lei; Wenda Peng; Ping Xu

doi:10.1364/AO.58.006406

Applied Optics
Vol. 58,
Issue 23,
pp. 6406-6413
(2019)
•https://doi.org/10.1364/AO.58.006406

Improvement of the microprism distribution expression of an integrated light guide plate

Yanyan Huang, Xulin Zhang, Wei Yang, Lei Lei, Wenda Peng, and Ping Xu

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Yanyan Huang, Xulin Zhang, Wei Yang, Lei Lei, Wenda Peng, and Ping Xu, "Improvement of the microprism distribution expression of an integrated light guide plate," Appl. Opt. 58, 6406-6413 (2019)

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Abstract

In our lab, the coefficient relational expressions called $A (L, H)$ , $B (L, H)$ , and $C (L, H)$ between the coefficients in the microprism distribution expression and the structural parameters of the integrated light guide plate, which is to realize high luminance uniformity, have been proposed previously. Yet, there are some deficiencies in these coefficient relational expressions, such as numerical item redundancy and inconspicuous physical characterization. On this basis, the revised coefficient relational expressions of $A (L, H)$ , $B (L, H)$ , and $C (L, H)$ are further studied. As a result, the numerical items of $A (L, H)$ , $B (L, H)$ , and $C (L, H)$ are reduced by one-quarter, one-third, and one-half, respectively. The redundant high-order items are reduced, and $C (L, H)$ is no longer a piecewise function. After revision, the effect of each numerical item on the coefficient values is highlighted, and it makes the physical characterization of each numerical term clearer. Moreover, by applying the revised coefficient relational expressions to acquire the microprism distribution, the luminance uniformities of all designed integrated backlight modules of 7.0 in. or less in size are totally higher than 85%. Taking a 5.0 in. integrated backlight module as an example, the performance of the integrated backlight module designed by the revised coefficient relational expressions is also improved over that before the revision. It verifies the correctness, effectiveness, and universality of the revised coefficient relational expressions, which will save a lot of design time.

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$a_{1} = A_{1}$	$a_{2} L = A_{2}$	$a_{3} H = A_{3}$	$a_{4} H^{2} = A_{4}$	$a_{5} H^{3} = A_{5}$	$a_{6} L H = A_{6}$	$a_{7} L H^{2} = A_{7}$	$a_{8} L H^{3} = A_{8}$
$b_{1} = B_{1}$	$b_{2} L = B_{2}$	$b_{3} L^{2} = B_{3}$	$b_{4} H = B_{4}$	$b_{5} H^{2} = B_{5}$	$b_{6} H^{3} = B_{6}$	$b_{7} L H = B_{7}$	$b_{8} L H^{2} = B_{8}$	$b_{9} L H^{3} = B_{9}$

$H / mm$	Relationship between $A$ and $L$	$L / mm$	Relationship between $A$ and $H$
0.5	$A = - 0.06896 + 0.01522 L$	61.9	$A = 1.6216 - 1.9623 H + 1.0020 H^{2} - 0.1777 H^{3}$
1	$A = - 0.01573 + 0.00864 L$	100.2	$A = 2.3210 - 2.1918 H + 0.8504 H^{2} - 0.1159 H^{3}$
1.5	$A = - 6.03 \times 10^{- 5} + 0.00558 L$	137.8	$A = 3.4650 - 3.7136 H + 1.6701 H^{2} - 0.2675 H^{3}$
Summary	$A$ and $L$ are linear relationship	summary	$A$ and $H$ are cubic polynomial relationship

$H / mm$	Relationship between $B$ and $L$	$L / mm$	Relationship between $B$ and $H$
0.5	$B = - 0.01293 - 6.2 \times 10^{- 5} L$	61.9	$B = - 0.02708 + 0.02499 H - 0.00999 H^{2} + 0.00148 H^{3}$
1	$B = - 0.00997 - 2.57 \times 10^{- 6} L$	100.2	$B = - 0.03658 + 0.04652 H - 0.02432 H^{2} + 0.00437 H^{3}$
1.5	$B = - 0.00671 - 5.47 \times 10^{- 6} L$	137.8	$B = - 0.04089 + 0.05348 H - 0.0284 H^{2} + 0.00518 H^{3}$
Summary	$B$ and $L$ are linear relationship	summary	$B$ and $H$ are cubic polynomial relationship

$H / mm$	Relationship between $C$ and $L$	$L / mm$	Relationship between $C$ and $H$
0.5	$C = 7.0 \times 10^{- 5} - 1.6195 \times 10^{- 7} L$	61.9	$C = 7.272 \times 10^{- 5} - 2.105 \times 10^{- 5} H$
1	$C = 6.33 \times 10^{- 5} - 2.129 \times 10^{- 7} L$	100.2	$C = 6.331 \times 10^{- 5} - 1.937 \times 10^{- 5} H$
1.5	$C = 5.234 \times 10^{- 5} - 2.11 \times 10^{- 7} L$	137.8	$C = 5.849 \times 10^{- 5} - 2.123 \times 10^{- 5} H$
Summary	$C$ and $L$ are linear relationship	summary	$C$ and $H$ are linear relationship

Coefficient	$α_{1}$	$α_{2}$	$α_{3}$	$α_{4}$	$α_{5}$	$α_{6}$
Value	0.9869	0.01578	−2.2555	1.2894	−0.2054	−0.005695

Coefficient	$β_{1}$	$β_{2}$	$β_{3}$	$β_{4}$	$β_{5}$	$β_{6}$
Value	−0.03260	$- 4.59 \times 10^{- 5}$	0.04570	−0.02546	0.00463	$2.27 \times 10^{- 5}$

Coefficient	$γ_{1}$	$γ_{2}$	$γ_{3}$
Value	$8.19 \times 10^{- 5}$	$- 1.75 \times 10^{- 7}$	$- 2.03 \times 10^{- 5}$

No.	$L / mm$	$H / mm$	$A^{'} / mm$	$(A^{'} - A) / A$ (%)	$B^{'}$	$(B^{'} - B) / B$ (%)	$C^{'} / {mm}^{- 1}$	$(C^{'} - C) / C$	Luminance Uniformity $U / %$
1	61.9	0.5	0.9100	−4.86	−0.0172	−2.68	0.0000590	−3.10	85.15
2	61.9	0.7	0.6355	−9.16	−0.0139	4.25	0.0000600	5.57	89.14
3	61.9	1	0.4600	4.61	−0.0095	3.70	0.0000500	−1.49	86.49
4	79	0.5	1.1650	−1.07	−0.01826	0.00	0.0000579	0.00	87.46
5	79	0.7	0.9012	0.00	−0.01386	0.00	0.0000538	0.00	85.43
6	79	1	0.6200	1.27	−0.00956	0.00	0.0000477	0.00	88.47
7	79	2	0.3371	0.00	−0.00602	0.00	0.0000275	0.00	85.40
8	79	2.5	0.2700	−15.41	−0.0041	−4.36	0.0000180	3.64	94.14
9	93.6	0.5	1.3665	0.00	−0.01877	0.00	0.0000553	0.00	85.82
10	93.6	0.7	1.0734	0.00	−0.01430	0.00	0.0000513	0.00	87.51
11	93.6	1.5	0.5158	5.47	−0.0079	15.65	0.0000359	2.34	88.04
12	93.6	2.5	0.3417	0.00	−0.00409	0.00	0.0000148	0.00	87.48
13	100.2	1.5	0.5650	5.25	−0.0073	6.06	0.0000315	−7.14	90.39
14	100.2	2.5	0.3519	0.00	−0.00401	0.00	0.0000137	0.00	88.12
15	116.3	0.5	1.6600	0.00	−0.01955	0.00	0.0000514	0.00	87.40
16	116.3	0.7	1.3411	0.00	−0.01498	0.00	0.0000473	0.00	85.87
17	116.3	1.5	0.7006	7.23	−0.00707	0.00	0.0000290	−6.77	87.17
18	116.3	2.5	0.3767	0.00	−0.00384	0.00	0.0000108	0.00	90.61
19	126.8	0.6	1.6212	0.00	−0.0170	−2.49	0.0000475	0.00	86.27
20	126.8	1.5	0.7294	0.00	−0.0075	4.22	0.0000280	−4.34	85.67
21	137.8	0.5	2.0000	3.19	−0.0205	1.02	0.0000476	0.00	85.35
22	137.8	0.7	1.6125	1.11	−0.01563	0.00	0.0000464	6.53	87.00
23	137.8	1.5	0.8200	1.36	−0.0076	3.74	0.0000250	−8.58	87.39
24	137.8	2.5	0.4200	2.46	−0.0035	−2.83	0.0000080	12.99	89.27
25	155.8	0.5	2.3191	6.83	−0.02091	0.00	0.0000450	1.21	86.84

Physical Parameters	BLM with Revised Coefficient Relational Expressions	BLM with Original Coefficient Relational Expressions
Light energy utilization/%	85.49	85.29
Average luminance/nit	7044.96	6952.33
Luminance uniformity/%	87.41	84.19

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Applied Optics