植被遥感常用反射特征表达

Figure:

在这里插入图片描述

HDRF

Let Ω′\Omega'Ω be the incident solid angle, Ω\OmegaΩ is leaving solid angle. Consider the BRDF of a Lamvertian target is 1π\frac{1}{\pi}π1, the BRF is 1. The HDRF of a target is defined as:
Rhem(Ω)=ΦrΦrlam=LrLrlam=∫2π−fr(Ω′,Ω)dE′∫2π−1πdE′=∫2π−fr(Ω′,Ω)∣μ∣I′dΩ′1π∫2π−I′∣μ′∣dΩ′=I1π∫2π−I′∣μ′∣dΩ′,  μ>0. \begin{aligned} R^{hem}(\Omega)&=\frac{\Phi_r}{\Phi_r^{lam}}=\frac{L_r}{L_r^{lam}}\\&=\frac{\int_{2\pi-}f_r(\Omega',\Omega)dE'}{\int_{2\pi-}\frac{1}{\pi}dE'}=\frac{\int_{2\pi-}f_r(\Omega',\Omega)|\mu| I'd\Omega'}{\frac{1}{\pi}\int_{2\pi-}I'|\mu'| d\Omega'}\\ &= \frac{I}{\frac{1}{\pi}\int_{2\pi-}I'|\mu'| d\Omega'}, \ \ \mu>0. \end{aligned} Rhem(Ω)=ΦrlamΦr=LrlamLr=2ππ1dE2πfr(Ω,Ω)dE=π12πIμdΩ2πfr(Ω,Ω)μIdΩ=π12πIμdΩI,  μ>0.
This is equivelent to:
HDRF=<I(Ω)>01π∫2π−<I(Ω′)>0∣Ω′⋅n1∣dΩ′ HDRF=\frac{<I(\Omega)>_0}{\frac{1}{\pi}\int_{2\pi-}<I(\Omega')>_0 |\Omega'\cdot n_1|d\Omega'} HDRF=π12π<I(Ω)>0Ωn1dΩ<I(Ω)>0

Here,n1n_1n1 is the outward normal, <⋅><\cdot><> denotes mean over upper surface δVt\delta V_tδVt​ , and we will ignore this notion for a simplification in remaining part of the blog. HDRF depends on atmosphere conditions. HDRF is the ratio of real radiance to the radiance reflected from a lambertian target of canopy upper surface .

HDRF has no unit.

BRF

If no atmosphere, *i.e.,*incident solar radiation at upper canopy boundary δVt\delta V_tδVt is a parallel beam of light, the HDRF become BRF:
BRF=I(Ω)1πI(Ω′)∣Ω′⋅n1∣=I(Ω)ILam BRF=\frac{I(\Omega)}{\frac{1}{\pi}I(\Omega')|\Omega'\cdot n_1|}=\frac{I(\Omega)}{I_{Lam}} BRF=π1I(Ω)Ωn1I(Ω)=ILamI(Ω)
Here, ILamI_{Lam}ILam​​ is the radiance over upper surface of the canopy from a Lambertian target under the same illumination.

BRF does not depend on atmosphere conditions, only varies with Ω\OmegaΩ and Ω′\Omega'Ω​.

BRF has no unit.

BRDF

BRDF describes the scattering of a parallel beam of incident radiation from one direction into another direction. However, the denominator of BRDF is the incident flux, not the radiance.
BRDF=I(Ω)∫2π+ILam∣μ∣dΩ=I(Ω)ILamπ=I(Ω)ELam BRDF=\frac{I(\Omega)}{\int_{2\pi+}I_{Lam}|\mu| d\Omega}=\frac{I(\Omega)}{I_{Lam}\pi}=\frac{I(\Omega)}{E_{Lam}} BRDF=2π+ILamμdΩI(Ω)=ILamπI(Ω)=ELamI(Ω)
From the second equality, we could get that π⋅BRDF=BRF\pi \cdot BRDF=BRFπBRDF=BRF​.

BRDF has unit sr−1sr^{-1}sr1.

BHR

The BHR is defined as mean irradiance exitance to incident irradiance:
A=∫2π+I(Ω)∣μ∣dΩ∫2π−I(Ω′)∣μ′∣dΩ′ A=\frac{\int_{2\pi+}I(\Omega)|\mu|d\Omega}{\int_{2\pi-}I(\Omega')|\mu'|d\Omega'} A=2πI(Ω)μdΩ2π+I(Ω)μdΩ
BHR has no unit.

DHR

If no atomophere, BHR become DHR:
DHR=∫2π+I(Ω)∣μ∣dΩILam∣μ′∣ DHR=\frac{\int_{2\pi+}I(\Omega)|\mu|d\Omega}{I_{Lam}|\mu'|} DHR=ILamμ2π+I(Ω)μdΩ
DHR has no unit.

For Lambertian Surface and no atmosphere

HDRF becomes:
HDRF=<I(Ω)>01π∫2π−<I(Ω′)>0∣Ω′⋅n1∣dΩ′=πIM HDRF=\frac{<I(\Omega)>_0}{\frac{1}{\pi}\int_{2\pi-}<I(\Omega')>_0 |\Omega'\cdot n_1|d\Omega'}=\frac{\pi I}{M} HDRF=π12π<I(Ω)>0Ωn1dΩ<I(Ω)>0=MπI
DHR becomes
DHR=∫2π+I(Ω)∣μ∣dΩILam∣μ′∣=πIM DHR=\frac{\int_{2\pi+}I(\Omega)|\mu|d\Omega}{I_{Lam}|\mu'|}=\frac{\pi I}{M} DHR=ILamμ2π+I(Ω)μdΩ=MπI
BHR becomes
A=I∫2π+∣μ∣dΩ∫2π−I(Ω′)∣μ′∣dΩ′=IπM A=\frac{I\int_{2\pi+}|\mu|d\Omega}{\int_{2\pi-}I(\Omega')|\mu'|d\Omega'}=\frac{I\pi}{M} A=2πI(Ω)μdΩI2π+μdΩ=MIπ
BRF becomes:
BRF=I(Ω)1πI(Ω′)∣Ω′⋅n1∣=πIM BRF=\frac{I(\Omega)}{\frac{1}{\pi}I(\Omega')|\Omega'\cdot n_1|}=\frac{\pi I}{M } BRF=π1I(Ω)Ωn1I(Ω)=MπI
So they are the same.

评论
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值