Dependences of Judd-Ofelt (JO) intensity parameters Ω_t (t = 2,4,6) and their relative ratios (Ω₄/Ω₂ and Ω₆/Ω₂) on overall changing factor (q) of integrated absorption bands of Er³⁺ have been studied theoretically. These dependences can help us to use relevant method to correctly extract Ω_t of a powder material. The study was done by exemplifying the widely studied Er³⁺ system, which is doped into Gd₃Ga₅O₁₂, LiNbO₃ and SrGdGa₃O₇ bulk single-crystals and β-NaYF₄ crystalline powder. The results show that the Ω_t changes linearly with the overall changing factor q: Ω_t = γ_tq + ξ_t. The linear feature changes from one material to another. The magnetic-dipole oscillator of the 1.5 μm transition results in non-zero nodal increment ξ_t and hence dramatical changes of the relative ratios Ω₄/Ω₂ and Ω₆/Ω₂ (with q) in smaller q region. The dramatical feature limits application of the relevant method for Ω_t calibration of a luminescent powder. To get the precise Ω_t values using the relevant method, the q value must be large enough. This can be realized by adopting a thin powder plate with a low Er³⁺ concentration for spectral measurement.

Judd-Ofelt (JO) 强度参数 Ω _t (t = 2,4,6) 及其相对比率（Ω ₄ /Ω ₂和Ω ₆ /Ω ₂）对积分吸收带的整体变化因子（q）的依赖性Er ³⁺已经在理论上进行了研究。这些相关性可以帮助我们使用相关方法正确提取粉末材料的Ω _t。该研究以广泛研究的 Er ³⁺系统为例，该系统掺杂到 Gd ₃ Ga ₅ O ₁₂、LiNbO ₃和 SrGd​​Ga ₃ O _{7 中}块状单晶和β-NaYF ₄结晶粉末。结果表明，Ω _t随整体变化因子q呈线性变化：Ω _t  = γ _t q  + ξ _t。线性特征从一种材料变为另一种材料。1.5 μm 跃迁的磁偶极子振荡器导致非零节点增量 ξ _t，因此在较小的q区域中Ω ₄ /Ω ₂和 Ω ₆ /Ω ₂（与q）的相对比率发生显着变化。戏剧性的特征限制了相关方法对Ω _{t 的应用}荧光粉的校准。要使用相关方法获得精确的Ω _t值，q值必须足够大。这可以通过采用具有低Er ³⁺浓度的薄粉板进行光谱测量来实现。