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.

内容概要:本书《Deep Reinforcement Learning with Guaranteed Performance》探讨了基于李雅普诺夫方法的深度强化学习及其在非线性系统最优控制中的应用。书中提出了一种近似最优自适应控制方法,结合泰勒展开、神经网络、估计器设计及滑模控制思想,解决了不同场景下的跟踪控制问题。该方法不仅保证了性能指标的渐近收敛,还确保了跟踪误差的渐近收敛至零。此外,书中还涉及了执行器饱和、冗余解析等问题,并提出了新的冗余解析方法,验证了所提方法的有效性和优越性。 适合人群:研究生及以上学历的研究人员,特别是从事自适应/最优控制、机器人学和动态神经网络领域的学术界和工业界研究人员。 使用场景及目标:①研究非线性系统的最优控制问题,特别是在存在输入约束和系统动力学的情况下;②解决带有参数不确定性的线性和非线性系统的跟踪控制问题;③探索基于李雅普诺夫方法的深度强化学习在非线性系统控制中的应用;④设计和验证针对冗余机械臂的新型冗余解析方法。 其他说明:本书分为七章,每章内容相对独立,便于读者理解。书中不仅提供了理论分析,还通过实际应用(如欠驱动船舶、冗余机械臂)验证了所提方法的有效性。此外,作者鼓励读者通过仿真和实验进一步验证书中提出的理论和技术。
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