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光作为植物生长发育过程中最重要的生态因子,对提高植物生长空间内光均匀度具有重要意义。传统植物工厂采用的阵列型LED光源结构未能与LED发光单色性强和方向性强的特点相适应,造成受照空间内光强差异较大、局部光谱成分单一等混光不均匀问题,导致同一批次植物在主要生理过程和形态建成上差异较大,严重影响了植物工厂的生产效益。因此,寻求合理的植物光源系统结构对提高受照空间照明均匀度具有重要意义。
在植物照明领域光均匀度优化方面,早期的植物照明设计往往借鉴传统室内照明经验,只关注培养架底部种植面照明效果的均匀性。而随着植物生长过程的推进,依据传统经典研究方法则需研究若干不同高度下的参考面的照明情况,如图1所示。因此,为与植物整个生长过程相适应,在植物照明设计中应将整个三维参考空间的照明效果作为参考并进行优化。实验过程中可通过测量培养架种植面和竖直方向参考面的光强和光谱分布均匀度对三维参考空间内照明效果进行表征。
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所设计并研究的立体化植物光源结构如图2所示,以植物工厂培养架为整体框架,采用倒置光源模块与侧置光源模块相结合的立体照明结构。如图1所示,培养架的底面为种植位面,培养架底部设置梯形底面直四棱柱的光源支架,培养架侧壁装有直三棱柱光源支架,光源支架侧面贴附有红蓝相间的LED,培养架上顶面和侧壁光源支架两侧装有漫反射板。通过调整棱柱二面角可实现对光线出射角度的初步调整,并且顶面和侧壁的漫反射板可以很好地与倒置和侧置光源相配合,在平行于种植面和垂直于种植面两个方向上均能提高光线的耦合程度,进一步提高了受照空间的空间照明均匀度。此外,倒置光源和侧置光源相结合的设计可以减少植物生长过程中对光线的遮挡,有望在植物整个生长阶段提供均匀的照明环境。
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在植物光度学领域,植物对光的响应主要包括光量子通量密度(PPFD)和光谱组成两部分[8]。因此,若培养架内不同位置PPFD或光谱分布差异较大,会导致同批次植物品质上的参差不齐。
根据笔者课题组之前的报道,可知PPFD与照度
${E_{\rm{V}}}\left( {{\rm{lx}}} \right)$ 之间有如下关系[9]:$$\begin{split} \alpha =& \dfrac{{\displaystyle\sum\limits_{x = 1}^X {\sum\limits_{y = 1}^Y {\sum\limits_{n = 1}^N {{K_{{\rm{PPFD}}}}/\left( {X \cdot Y \cdot N} \right)} } } }}{{{K_{{\rm{PPFDmax}}}}}} =\\ & \dfrac{{\dfrac{{\rm{1}}}{{{k_{{\rm{rb}}}}}}\displaystyle\sum\limits_{x = 1}^X {\sum\limits_{y = 1}^Y {\sum\limits_{n = 1}^N {E_{\rm{V}} /\left( {X \cdot Y \cdot N} \right)} } } }}{{\dfrac{{\rm{1}}}{{{k_{{\rm{rb}}}}}} \cdot {E_{\rm{V}}}_{{\rm{max}}}}} \\ \end{split} $$ (1) 式中:
$\alpha $ 为目标平面上的均匀度;$X$ 和$Y$ 分别为待测平面的长和宽;$N$ 为待测平面上单位面积的取点数;${k_{{\rm{rb}}}}$ 为反映${E_{\rm{V}}}$ 和PPFD之间关系的常量。由公式(1)可以看出,为简化实验过程,PPFD的测量可以由测量照度值代替。此外,由光度-色度转换关系可知,混色均匀度可用来表征培养架内光谱分布均匀度。在CIE1976色度体系下,混色均匀度计算公式如下[10]:
$${\rm{\Delta }}{u^{'}}{\nu ^{'}}_{{\rm{rms}}} = \sqrt {\frac{{\rm{1}}}{M}\sum\limits_i^M {\left[ {{{\left( {u_i^{'} - u_{{\rm{avg}}}^{'}} \right)}^2} + {{\left( {v_i^{'} - v_{{\rm{avg}}}^{'}} \right)}^2}} \right]} } $$ (2) $${U_{{\rm{color}}}} = \frac{{100}}{{1 + k\Delta {u^{'}}{\nu ^{'}}_{{\rm{rms}}}}}\left( {\text{%}} \right)$$ (3) 式中:M为样本点的数目;k对应
$\Delta {u^{'}}{\nu ^{'}}_{{\rm{rms}}}$ 取最小;${U_{{\rm{color}}}}$ 为90%时算出来的数值。综上,后续实验过程中可通过测量培养架种植面和竖直方向参照面的照度均匀度和混色均匀度来反映三维受照空间内PPFD和光谱分布的均匀情况,并以两个参照面照度均匀度和混色均匀度均达到75%为优化目标。
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进一步对上述方案进行理论分析,如图3所示,该方案所涉及的参量主要有:顶部漫反射板到底部种植面的高度
$H$ (实验过程中保持$H$ 恒定值300 mm),种植面宽度$D$ ,梯形底面直四棱柱光源支架高为$h$ ,下底${d_1}$ 恒为50 mm,上底${d_2}$ 恒为20 mm,倒置光源部分相邻LED间距${l_2}$ 恒为10 mm,长度方向上,每个培养架结构单元长$L$ ,直三棱柱光源支架底面高宽比$a = {h_2}/{d_3}$ (实验过程保持${d_3}$ 恒定值50 mm),侧置光源相邻LED间距$l$ 。根据光源系统中LED位置和对受照空间的主要贡献光线类型,可将系统内LED分为三类,分别为图3中LED-A、LED-B和LED-C。
LED-A和LED-B贡献以反射光为主,两者的分析过程类似,祝振敏等[11-12]得出,入射至高漫反射面的光源可看作次朗伯光源,现以LED-B在顶部反射面的次朗伯光源为例进行分析。光线照射至漫反射板上任一点P,P点的照度为:
$$E({x_1}) = \frac{{{I_0}{{\cos }^3}\varepsilon }}{{{{(H - y)}^2}}}$$ (4) 式中:
$ {I}_{0} $ 为朗伯光源的中心光强;$\varepsilon = \arctan \dfrac{{{x_1}}}{{H - y}}$ ;$y = \dfrac{{{d_1} - {d_2}}}{{2 n}}\tan \varphi $ ,$\varphi = \arctan \dfrac{{2h}}{{{d_1} - {d_2}}}$ , n为常数。P点的照度与次朗伯光源法向发光强度${I_f}$ 成正比,照射至种植位点的光强为:$$ E(\varepsilon ) = \int_{}^D {\frac{{{I_f}{{\cos }^3}\omega }}{{{H^2}}}} {\rm{d}}x $$ (5) 式中:
$\omega $ 为次朗伯光源出射光线与法线夹角。对于LED-C,反射光和直射光贡献相当,分析其直射部分,光线直接照射到种植面任一点R,R点照度为:
$$E({x_3}) = \frac{{{I_0}{{\cos }^3}\gamma }}{{{H_1}^2}}$$ (6) 式中:
$\gamma = \arctan \dfrac{{{x_2}}}{{{H_1}}}$ 。R点照度直接与朗伯光源中心光强${I_0}$ 成正比,则照射到种植位点光强为:$$E(\gamma ) = \int_{}^D {\frac{{{I_0}{{\cos }^3}{\omega _0}}}{{{H_1}^2}}} {\rm{d}}x$$ (7) 式中:
${\omega _0}$ 为次朗伯光源出射光线与法线夹角。对于LED-C的反射部分,与LED-B的分析过程类似,光线照射至漫反射板上任一点Q,Q点的照度为:
$$E(x_2) = \dfrac{{{I_0}{{\cos }^3}\beta }}{{({H -{H_1}} )}^2}$$ (8) 式中:
${I_0}$ 为朗伯光源的中心光强;$\; \beta = \arctan \dfrac{{{x_2}}}{{H - {H_1}}}$ 。Q点的照度与次朗伯光源法向发光强度${I_{f1}}$ 成正比,照射至种植位点的光强为:$$E(\alpha ) = \int_{}^D {\frac{{{I_{f1}}{{\cos }^3}{\omega _1}}}{{{H^2}}}} {\rm{d}}x$$ (9) 式中:
${\omega _1}$ 为次朗伯光源出射光线与法线夹角。由公式(5)、(7)、(9)可以看出,植物培养架结构参数
$D$ 、$h$ 、$L$ 和$a$ 均对种植位点所受照度有所影响,而由色度光度关系可知,受照面的光谱分布和色度分布也将受到上述结构参数的影响。对于竖直方向上的均匀度,则可以认为是不同培养架高度对应不同参考面均匀度的变化,同样主要受这些因素影响。此外,光源支架上红蓝LED间距将影响照度圆和LED光色的耦合程度,从而导致照度和混色均匀度的变化,因此侧置光源LED的间距$l$ 也被纳入实验考察变量中。 -
通过1.4的理论分析可知,实验中设定了五个影响因子,每个影响因子在实际照明工程合理取值范围内各取四个水准值,若采取单一变量法,则需设置
${4^5}$ 组实验,为在不影响实验结果的基础上简化实验过程,采用Taguchi方法,通过正交表和计算方差值,选取${{{L}}_{16}}({4^5})$ 正交矩阵,即分为16组实验进行研究。每个方案所选定的水平及因子如表1所示。表 1 植物培养架影响因子及其控制标准
Table 1. Effect of factors and its control levels of plant culture shelf
Code name Factor name Number of levels Level 1 Level 2 Level 3 Level 4 A D/mm 4 400 450 500 550 B h/mm 4 10 15 20 25 C L/mm 4 100 150 200 250 D a 4 0.2 0.4 0.6 0.8 E l/mm 4 10 15 20 25 在各种波长的光中,红光(610~720 nm)和蓝光(400~510 nm)在植物的生长发育和形态构建过程中占有显著影响地位,具体影响到植物的光合作用、代谢酶的含量和活性、细胞分化表达和生物节律等众多方面[13]。因此,红光和蓝光在人工补光和植物照明设计中得到了广泛应用。同样地,实验过程中选用640 nm的红光LED和460 nm的蓝光LED作为系统光源进行研究。
实验过程借助Trace Pro进行模拟,根据CIE的基本标准和度量程序[14],并结合不同波长光线明视函数差异,在模拟过程中,设置460 nm蓝光LED芯片为45 lm/W,640 nm红光LED芯片为90 lm/W。功率均分别设定为2 W和1 W,每个芯片发出10000条光线。
S/N值(信噪比)用于表征品质特性[6],且实验中照明均匀度为望大特性,对应S/N值的公式为[5]:
$${L_{{\rm{TB}}}}\left( {\dfrac{S}{N}} \right) = - 10\lg \dfrac{{\displaystyle\sum\limits_{i = 1}^n {\dfrac{1}{{y_i^2}}} }}{n}$$ (10) 式中:
${y_i}$ 表示第$i$ 个品质特性;$n$ 为实验次数。将实验的影响因子及水平代入$ {{L}}_{\rm{1}{6}}{(}{\rm{4}}^{\rm{5}}{)} $ 正交矩阵。利用Trace Pro模拟仿真并计算,采用九点取样法测出照度及色度,计算出水平和竖直方向参考面照度均匀度以及混色均匀度,并根据公式(10)计算出参考面照度均匀度的S/N值及色度均匀度的S/N值,如表2所示。表 2
${{{L}}_{16}}({4^5})$ 直角表实验设计Table 2.
${{{L}}_{16}}({4^5})$ orthogonal arrayExperiment
numberA B C D E Horizontal/
VerticalIllumination
uniformityColor-mixed
uniformityS/N of illumination
uniformityS/N of color-mixed
uniformity1 1 1 1 1 1 Horizontal 76.9008% 74.6193% 37.7186 37.4570 Vertical 91.3002% 71.8227% 39.2094 37.1252 2 1 2 2 2 2 Horizontal 87.6265% 86.6183% 38.8527 38.7522 Vertical 90.2956% 90.0000% 39.1133 39.0849 3 1 3 3 3 3 Horizontal 73.3094% 74.4289% 37.3032 37.4348 Vertical 76.5618% 80.6504% 37.6802 38.1321 4 1 4 4 4 4 Horizontal 59.3363% 90.0000% 35.4664 39.0849 Vertical 70.6207% 81.5623% 36.9786 38.2298 5 2 1 2 3 4 Horizontal 75.7509% 76.8971% 37.5878 37.7182 Vertical 79.1110% 81.4826% 37.9647 38.2213 6 2 2 1 4 3 Horizontal 69.5528% 68.8260% 36.8463 36.7551 Vertical 84.8666% 80.6880% 38.5747 38.1362 7 2 3 4 1 2 Horizontal 73.3071% 79.2486% 37.3029 37.9798 Vertical 90.4582% 87.8421% 39.1290 38.8741 8 2 4 3 2 1 Horizontal 80.3125% 61.3495% 38.0957 35.7562 Vertical 93.6031% 76.3883% 39.4258 37.6605 9 3 1 3 4 2 Horizontal 74.3324% 87.2168% 37.4236 38.8120 Vertical 83.2272% 84.2542% 38.4053 38.5118 10 3 2 4 3 1 Horizontal 82.8161% 72.4249% 38.3623 37.1978 Vertical 91.6616% 81.2238% 39.2437 38.1937 11 3 3 1 2 4 Horizontal 68.5804% 88.9663% 36.7240 38.9845 Vertical 93.1065% 80.3089% 39.3796 38.0953 12 3 4 2 1 3 Horizontal 70.2089% 86.0483% 36.9278 38.6948 Vertical 93.1065% 84.9398% 39.3796 38.5822 13 4 1 4 2 3 Horizontal 86.8233% 80.8601% 38.7727 38.1547 Vertical 93.4749% 76.9877% 39.4139 37.7284 14 4 2 3 1 4 Horizontal 81.4725% 83.0723% 38.2202 38.3891 Vertical 94.5569% 84.9398% 39.5139 38.5822 15 4 3 2 4 1 Horizontal 73.4857% 61.5852% 37.3241 35.7895 Vertical 90.9310% 80.8429% 39.1742 38.1528 16 4 4 1 3 2 Horizontal 69.5711% 79.7158% 36.8486 38.0309 Vertical 80.0277% 75.6580% 38.0648 37.5771 为了获得最优解,将各因子的S/N值进行计算统计并绘图,结果如图4所示,并根据望大特性选取各因子中S/N值最大的水准组合形成初步最优解。
观察对比图4各因素水准对应的S/N值可知,水平面照度均匀度、竖直面照度均匀度、水平面混色均匀度和竖直面混色均匀度四项测试指标对应的最优因素组合分别为A4B2C3D2E1、A3B2C2D2E1、A3B1C4D1E4、A3B2C2D1E2,而最优解应使四项属性尽可能多地取高。权衡方案一每个因子在水平面竖直面的照度均匀度和混色均匀度上S/N值的变化,可初步认定系统最优解组合为A3B2C2D2E1,对应培养架具体结构参数:培养架宽度
$D$ 为500 mm,倒置光源支架底面高$h$ 为15 mm,长度方向相邻结构单元距离L为150 mm,侧置光源支架高宽比$a$ 为0.40,相邻LED间距$l$ 为10 mm。模拟仿真后结果如图5所示,水平面照度均匀度为88.25%,混色均匀度为85.90%,竖直面照度均匀度为92.23%,混色均匀度为87.71%。 -
ANOVA法即方差分析法,即通过比较各影响因子在实验偏差中的占比来评估各影响因子的贡献率,即对实验结果的影响程度。贡献率大的因子被选出进一步研究,而贡献度较小的因子则被当作偶然事件处理,影响程度的强弱程度通过参量
$\rho $ 来表示[4]:$$\rho = \dfrac{{{S_{{{sd}}}}}}{{{S_{{{st}}}}}}, \;{S_{{{st}}}} = {S^{'}}_{{{sd}}} + {S_{{{se}}}}$$ (11) 式中:
${S_{sd}}$ 和$S{'_{sd}}$ 表示方差和;${S_{se}}$ 为错误方差和(由于实验的重复性,可近似认为${S_{se}}$ 为0)。${S_{sd}}$ 由S/N比的方差和可表示为[15-16]:$${S_{{{sd}}}} = {\sum\limits_{i = 1}^m {\left( {{\eta _i} - \overline \eta } \right)} ^2}$$ (12) 式中:
$m$ 为实验次数;${\eta _i}$ 为每个因子第$i$ 次实验的S/N比;$\overline \eta $ 为每个因子S/N的平均值,实验中,$\eta = $ $ {L_{{\rm{TB}}}}\left( {S/N} \right)$ 。计算得出各影响因子对品质的贡献度如表3所示。表 3 各因子对照度均匀度和混色均匀度的贡献率
Table 3. Contribution of different factors to illumination uniformity and mixed-color uniformity
Impact factor Contribution to horizontal plane illumination uniformity Contribution to vertical plane illumination uniformity Contribution to horizontal plane color-mixed uniformity Contribution to vertical plane color-mixed uniformity A 4.7638% 21.0976% 27.9095% 6.4361% B 36.6491% 9.9159% 3.1440% 24.6564% C 11.2826% 1.1566% 3.3579% 34.1685% D 32.8398% 51.8429% 4.8867% 4.5342% E 14.4647% 15.9870% 60.7020% 30.2049% 对水平面和竖直面的照度、混色均匀度贡献大的影响因子为D、E,在保持A取A3、B取B2、C取C2的情况下,对D、E因子进一步进行微调优化。先保持A、B、C、E的值为A3B2C2E1不变,对D因子进行细分取0.15、0.20、0.25、0.30、0.35、0.40、0.45、0.50八个水准,依次命名为水准1~水准8。利用Trace Pro模拟仿真,测量计算水平面照度均匀度和混色均匀度(k=53.4167),以及竖直面照度均匀度和混色均匀度(k=44.7583)。
从图6中得出D因子在取0.35时系统综合属性最优,具体为水平面照度均匀度87.01%,竖直面照度均匀度91.82%,水平面混色均匀度87.59%,竖直面混色均匀度89.29%。所以取A=500 mm、B=15 mm、C=150 mm、D=0.35,然后继续细分E因子。分别取8、10、12、14、16、18、20 mm七个水准,依次命名为水准1~水准7并进行测试。
分析比较图7培养架各项属性,可知E因子在取12 mm时系统综合属性最优,因此该植物培养架的最优组合为A=500 mm、B=15 mm、C=150 mm、D=0.35、E=12 mm,对应培养架具体结构参数为培养架宽度
$D$ 为500 mm,倒置光源支架底面高$h$ 为15 mm,长度方向相邻结构单元距离$L$ 为150 mm,侧置光源支架高宽比$a$ 为0.35,相邻LED间距$l$ 为12 mm。仿真结果如图8所示,测得其各属性为水平面照度均匀度为87.22%,混色均匀度为90.11%;竖直面照度均匀度93.02%,混色均匀度91.43%。 -
进一步,在最优解的基础上研究培养架各均匀度属性受灯珠形状的影响情况。灯珠的形状和尺寸(
$n \times m$ ,其中$n$ 为与LED灯列平行方向长度,$m$ 为与LED灯列垂直方向长度)为:5×5正方形、4×6矩形-1、6×4矩形-2、R=2.5圆形。用Trace Pro软件对这四种不同形状的灯珠模型进行模拟仿真,测得培养架的水平面和竖直面的照度和色度均匀度,如图9所示。图 9 各项属性随灯珠发光面形状和尺寸的变化曲线
Figure 9. Variation curves of various attributes with the shape and size of light-emitting surface of the lamp bead
可以看出,采用发光面为正方形的灯珠时,培养架水平面的照度均匀度和混色均匀度为最大值,在竖直面照度均匀度方面4×6的矩形LED灯珠最佳,在竖直面混色均匀度方面则是圆形LED灯珠最佳,正方形灯珠稍次之。综合考虑四项属性,该培养架采用发光面为正方形的灯珠更合理。
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在培养架照明质量评价过程中,在植株育苗期,由于植株矮小,对光源系统遮挡很弱,可将种植面照明均匀度作为培养架内照明效果的主要评价标准。但随着植物生长,植株对光线的遮挡作用增强,需考虑植物在各个高度下培养架内照明情况,即需要在最优模型的基础上对植物生长过程中的植物表面的照度和光谱分布进行测试,研究植物不同生长阶段的照明效果。研究过程的简化模型如图10所示。通过倒三棱柱的顶面和侧面分别模拟植物的顶面和侧面,通过增加模型的高度来模拟植株的生长过程。并测试植物高度在25、50、75、100、125、150、175 mm时种植面(k=53.4167)、倒三棱柱顶面(代表植物体正上方的受照情况,k=31.3263)、侧面(代表植物体侧面叶片的受照情况,k=31.6157)的照明均匀度,测量结果如图11(a)~(c)所示。
从图11中分析可得,三个参考面的色度均匀度基本不随植株高度的增加而明显变化,总体上维持在较高水准。在照度均匀度方面,种植面和植株顶面照度始终处于较高水平,只在小范围内波动,植株侧面的照度均匀度则整体呈下降趋势,并在150 mm后明显下降。这是由于随植株高度的增加,植株顶部面积变大,培养架内光线主要被植株顶部吸收,导致侧面吸收光线较少,无法得到很充分的混合,故均匀度有所下降。但侧面的混色均匀度始终保持较高的水平,且侧面对光照需求较低,因而不会对植物的生长带来较大的影响。
图 11 植物不同高度时的照度均匀度、混色均匀度
Figure 11. Illumination uniformity, color uniformity at different heights of plants
综上,在植株高度0~150 mm范围内植株顶部、植株侧面和种植面的照度均匀度和混色均匀度均可保持在较高的水准。因此,该植物光源系统在植株的育苗阶段和生长阶段均能提供均匀的空间照明环境,具有较高的实用价值。
Design of LED plant light source system with high spatial illumination uniformity
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摘要: 传统的植物照明设计只针对单一参考面均匀度进行评价,难以满足植物在整个生长过程中对均匀光照环境的需求。针对这一问题,首先提出了空间照明均匀度评价体系,并基于该体系设计了一种复合光源模块的立体化照明系统,以期构建照明均匀的植物生长空间。进一步利用Taguchi方法优化实验过程,在结合ANOVA分析的基础上,获得了最优结构参数。最后对所得最优解进行灯珠形状分析和植物生长过程中的照明效果测试。实验结果表明:最优结构可提供一个水平参考面照度均匀度为87.22%,混色均匀度为90.11%;竖直参考面照度均匀度93.02%,混色均匀度91.43%的均匀照明空间。该植物光源系统可满足植物生长过程中对均匀空间照明环境的需求。Abstract: The traditional plant lighting design only evaluates the uniformity of a single reference surface, and it is difficult to meet the light intensity and light quality requirements of different stages of plant growth. Aiming at this problem, first, a space lighting uniformity evaluation system was proposed, and based on this system, a three-dimensional lighting system with a composite light source module was proposed, in order to construct a plant lighting space with uniform lighting. Further, the Taguchi method was used to optimize the experimental process, and the optimal structural parameters were obtained on the basis of ANOVA analysis. Finally, the lamp beads shape analysis and the lighting effect test during the plant growth process were performed on the obtained optimal solution. The experimental results show that the optimal structure can provide a uniform illumination space with horizontal reference plane illumination uniformity of 87.22%, color mixing uniformity of 90.11%; vertical reference plane illumination uniformity of 93.02%, and color mixing uniformity of 91.43%. The plant light source system can meet the requirement of a uniform space lighting environment during plant growth.
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Key words:
- applied optics /
- spatial illumination uniformity /
- Taguchi /
- plant light source /
- optics design
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表 1 植物培养架影响因子及其控制标准
Table 1. Effect of factors and its control levels of plant culture shelf
Code name Factor name Number of levels Level 1 Level 2 Level 3 Level 4 A D/mm 4 400 450 500 550 B h/mm 4 10 15 20 25 C L/mm 4 100 150 200 250 D a 4 0.2 0.4 0.6 0.8 E l/mm 4 10 15 20 25 表 2
${{{L}}_{16}}({4^5})$ 直角表实验设计Table 2.
${{{L}}_{16}}({4^5})$ orthogonal arrayExperiment
numberA B C D E Horizontal/
VerticalIllumination
uniformityColor-mixed
uniformityS/N of illumination
uniformityS/N of color-mixed
uniformity1 1 1 1 1 1 Horizontal 76.9008% 74.6193% 37.7186 37.4570 Vertical 91.3002% 71.8227% 39.2094 37.1252 2 1 2 2 2 2 Horizontal 87.6265% 86.6183% 38.8527 38.7522 Vertical 90.2956% 90.0000% 39.1133 39.0849 3 1 3 3 3 3 Horizontal 73.3094% 74.4289% 37.3032 37.4348 Vertical 76.5618% 80.6504% 37.6802 38.1321 4 1 4 4 4 4 Horizontal 59.3363% 90.0000% 35.4664 39.0849 Vertical 70.6207% 81.5623% 36.9786 38.2298 5 2 1 2 3 4 Horizontal 75.7509% 76.8971% 37.5878 37.7182 Vertical 79.1110% 81.4826% 37.9647 38.2213 6 2 2 1 4 3 Horizontal 69.5528% 68.8260% 36.8463 36.7551 Vertical 84.8666% 80.6880% 38.5747 38.1362 7 2 3 4 1 2 Horizontal 73.3071% 79.2486% 37.3029 37.9798 Vertical 90.4582% 87.8421% 39.1290 38.8741 8 2 4 3 2 1 Horizontal 80.3125% 61.3495% 38.0957 35.7562 Vertical 93.6031% 76.3883% 39.4258 37.6605 9 3 1 3 4 2 Horizontal 74.3324% 87.2168% 37.4236 38.8120 Vertical 83.2272% 84.2542% 38.4053 38.5118 10 3 2 4 3 1 Horizontal 82.8161% 72.4249% 38.3623 37.1978 Vertical 91.6616% 81.2238% 39.2437 38.1937 11 3 3 1 2 4 Horizontal 68.5804% 88.9663% 36.7240 38.9845 Vertical 93.1065% 80.3089% 39.3796 38.0953 12 3 4 2 1 3 Horizontal 70.2089% 86.0483% 36.9278 38.6948 Vertical 93.1065% 84.9398% 39.3796 38.5822 13 4 1 4 2 3 Horizontal 86.8233% 80.8601% 38.7727 38.1547 Vertical 93.4749% 76.9877% 39.4139 37.7284 14 4 2 3 1 4 Horizontal 81.4725% 83.0723% 38.2202 38.3891 Vertical 94.5569% 84.9398% 39.5139 38.5822 15 4 3 2 4 1 Horizontal 73.4857% 61.5852% 37.3241 35.7895 Vertical 90.9310% 80.8429% 39.1742 38.1528 16 4 4 1 3 2 Horizontal 69.5711% 79.7158% 36.8486 38.0309 Vertical 80.0277% 75.6580% 38.0648 37.5771 表 3 各因子对照度均匀度和混色均匀度的贡献率
Table 3. Contribution of different factors to illumination uniformity and mixed-color uniformity
Impact factor Contribution to horizontal plane illumination uniformity Contribution to vertical plane illumination uniformity Contribution to horizontal plane color-mixed uniformity Contribution to vertical plane color-mixed uniformity A 4.7638% 21.0976% 27.9095% 6.4361% B 36.6491% 9.9159% 3.1440% 24.6564% C 11.2826% 1.1566% 3.3579% 34.1685% D 32.8398% 51.8429% 4.8867% 4.5342% E 14.4647% 15.9870% 60.7020% 30.2049% -
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