RadiometryRadiometry

Computer Vision I CSE252A Lecture 5

CSE 252A RadiometryRadiometry

• Read Chapter 4 of Ponce & Forsyth

• Solid Angle • Irradiance •Radiance •BRDF • Lambertian/Phong BRDF

CSE 252A MeasuringMeasuring AngleAngle

• The solid angle subtended by an object from a point P is the area of the projection of the object onto the unit sphere centered at P. • Measured in steradians, sr • Definition is analogous to projected angle in 2D • If I’m at P, and I look out, solid angle tells me how

CSE 252A much of my view is filled with an object SolidSolid AngleAngle

• By analogy with angle (in radians), the solid angle subtended by a region at a point is the area projected on a unit sphere centered at that point

• The solid angle subtended by a patch area dA is given by dAcosθ dω = r 2

CSE 252A RadianceRadiance (θ, φ) • Power is energy per unit time dω • Radiance: Power traveling at some point in a specified direction, per unit area perpendicular to the direction x of travel, per unit solid angle dA • Symbol: L(x,θ,φ)

• Units: watts per square meter per steradian : w/(m2sr1)

CSE 252A RadianceRadiance α (θ, φ) • Power is energy per unit time dω • Radiance: Power traveling at some point in a specified direction, per unit area perpendicular to the direction x of travel, per unit solid angle dA • Symbol: L(x,θ,φ) P • Units: watts per square meter L = α per steradian : w/(m2sr1) (dAcos )dω

Power emitted from patch, but radiance in direction different from surface normal CSE 252A RadianceRadiance transfertransfer What is the power received by a small area dA2 at distance r from a small emitting area dA1?

From definition of radiance P L = θ (dAcos )dω

From definition of solid angle dAcosθ dω = r 2

P = LdA1 cosθ1dω1−>2 L θ = 2 dA1dA2 cos 1 cosθ2 CSE 252A r IrradianceIrradiance • Crucial property: • How much light is arriving at a Total Irradiance arriving at the surface? surface is given by adding • Units of irradiance: Watts/m2 irradianceθ overφ all incoming angles • This is a function of incoming angle. Total irradiance is θ ω • A surface experiencing radiance L(x, , )cos d L(x,θ,φ) coming in from solid angle ∫ hemisphere θ φ dω experiences irradiance: θ 2ππ /2 θ E(x) = L()x,θ,φ cosθdω = ∫∫L()x, , cos sin dθdφ 0 0

φ N L(x,θ,φ) θ x x

CSE 252A