概述
德国物理学家M.普朗克在量子论基础上建立的关于黑体辐射的正确公式。19世纪末,经典统计物理学在研究黑体辐射时遇到了巨大的困难:由经典的能量均分定理导出的瑞利-金斯公式在短波方面得出同黑体辐射光谱实验结果相违背的结论。同时,维恩公式则仅适用于黑体辐射光谱能量分布的短波部分。也就是说,当时还未能找到一个能够成功描述整个实验曲线的黑体辐射公式。
The Planck Function (convert from temperature and wavelength to spectral radiance)
The Planck Function:
L(λ,t)=λ5(ec2/λt−1)c1
Where:
L(λ,t)=blackbody radiance (W/m2⋅sr⋅um)
c1=1.191042∗108(W/m2⋅sr⋅um−4)
c2=1.4387752∗104
λ=wavelength(um)
t=blackbody temperature(K)
The Planck Function (convert from temperature and wavenumber to spectral radiance)
The Planck Function:
L(v,t)=ec2v/t−1c1v3
Where:
L(v,t)= blackbody radiance (mW/m2⋅sr⋅cm−1)
c1=1.191042∗105(mW/m2⋅sr⋅cm−4)
c2=1.4387752(K cm)
v= wavenumber(cm−1)
t= blackbody temperature (K)
The Inverse Planck Function (convert from spectral radiance and wavelength to temperature)
The Inverse Planck Function:
t(λ,L)=λln(c1/λ5L+1)c2
Where:
t= blackbody temperature (K)
L= blackbody radiance (W/m2⋅sr⋅um)
c1=1.191042∗108(W/m2⋅sr⋅um−4)
c2=1.4387752∗104(K um)
λ= wavelength (um)
The Inverse Planck Function (convert from spectral radiance and wavenumber to temperature)
The Inverse Planck Function:
t(v,L)=ln(c1v3/L+1)c2v
Where:
t= blackbody temperature (K)
L= blackbody radiance (mW/m2⋅sr⋅cm−1)
c1=1.191042∗105(mW/m2⋅sr⋅cm−4)
c2=1.4387752(K cm)
v= wavenumber (cm−1)