© Lastra/Machiraju/Möller Fundametals of Rendering - Radiometry / Photometry CIS 782 Advanced Computer Graphics Raghu Machiraju

© Lastra/Machiraju/Möller Reading Chapter 5 of “Physically Based Rendering” by Pharr&Humphreys Chapter 2 (by Hanrahan) “Radiosity and Realistic Image Synthesis,” in Cohen and Wallace. pp. 648 – 659 and Chapter 13 in “Principles of Digital Image Synthesis”, by Glassner. Radiometry FAQ faq.htm faq.htm

© Lastra/Machiraju/Möller Realistic Rendering Determination of Intensity Mechanisms –Emittance (+) –Absorption (-) –Scattering (+) (single vs. multiple) Cameras or retinas record quantity of light

© Lastra/Machiraju/Möller Pertinent Questions Nature of light and how it is: –Measured –Characterized / recorded (local) reflection of light (global) spatial distribution of light Steady state light transport?

© Lastra/Machiraju/Möller What Is Light ? Light - particle model (Newton) –Light travels in straight lines –Light can travel through a vacuum (waves need a medium to travel) Light – wave model (Huygens): electromagnetic radiation: sinusiodal wave formed coupled electric (E) and magnetic (H) fields –Diffraction / Polarization –Transmitted/reflected compoments –Pink Floyd

© Lastra/Machiraju/Möller Electromagnetic spectrum

© Lastra/Machiraju/Möller Optics Three kinds Geometrical or ray –Traditional graphics –Reflection, refraction –Optical system design Physical or wave –Dispersion, interference –Interaction of objects of size comparable to wavelength Quantum or photon optics –Interaction of light with atoms and molecules

© Lastra/Machiraju/Möller Nature of Light Wave-particle duality – Wave packets which emulate particle transport. Explain quantum phenomena. Incoherent as opposed to laser. Waves are multiple frequencies, and random in phase. Polarization – Ignore. Un-polarized light has many waves summed all with random orientation

© Lastra/Machiraju/Möller Radiometry Science of measuring light Analogous science called photometry is based on human perception.

© Lastra/Machiraju/Möller Radiometric Quantities Function of wavelength, time, position, direction, polarization. Assume wavelength independence –No phosphorescence –Incident wavelength 1 exit 2 Steady State –Light travels fast –No luminescence - Ignore it

© Lastra/Machiraju/Möller Result – five dimensions Adieu Polarization –Would likely need wave optics to simulate Two quantities –Position (3 components) –Direction (2 components)

© Lastra/Machiraju/Möller Radiometry - Quantities Energy Q Power  –Energy per time Irradiance E and Radiosity B –Power per area Intensity I –Power per solid angle Radiance L –Power per projected area and solid angle

© Lastra/Machiraju/Möller Radiant Energy - Q Think of photon as carrying quantum of energy hc/ = hf (photoelectric effect) –c is speed of light –h is Planck’s constant –f is frequency of radiation Wave packets Total energy, Q, is then energy of the total number of photons Units - joules or eV

© Lastra/Machiraju/Möller Radiation Tungsten Blackbody

© Lastra/Machiraju/Möller Consequence

© Lastra/Machiraju/Möller Fluorescent Lamps

© Lastra/Machiraju/Möller Power -  Flow of energy (important for transport) Also - radiant power or flux. Energy per unit time (joules/s = eV/s) Unit: W - watts  = dQ/dt Falls off with square of distance

© Lastra/Machiraju/Möller dA Radiant Flux Area Density Area density of flux (W/m 2 ) u = Energy arriving/leaving a surface per unit time interval dA can be any 2D surface in space E.g. sphere:

© Lastra/Machiraju/Möller Irradiance E Power per unit area incident on a surface

© Lastra/Machiraju/Möller Radiosity or Radiant Exitance B Power per unit area leaving surface Also known as Radiosity Same unit as irradiance, just direction changes

© Lastra/Machiraju/Möller Intensity I Flux density per unit solid angle Units – watts per steradian “intensity” is heavily overloaded. Why? –Power of light source –Perceived brightness

© Lastra/Machiraju/Möller Solid Angle Size of a patch, dA, is Solid angle is Angle

© Lastra/Machiraju/Möller Solid Angle (contd.) Solid angle generalizes angle! Steradian Sphere has 4  steradians! Why? Dodecahedron – 12 faces, each pentagon. One steradian approx equal to solid angle subtended by a single face of dodecahedron © Wikipedia

© Lastra/Machiraju/Möller r  Hemispherical Projection Use a hemisphere  over surface to measure incoming/outgoing flux Replace objects and points with their hemispherical projection

© Lastra/Machiraju/Möller Isotropic Point Source Even distribution over sphere How do you get this? Quiz: Warn’s spot-light ? Determine flux

© Lastra/Machiraju/Möller Other kinds of lights

© Lastra/Machiraju/Möller Other Lights

© Lastra/Machiraju/Möller x xsxs  Irradiance on Differential Patch Inverse square Law How do you determine that ? Iso-lux contours

© Lastra/Machiraju/Möller Radiance L Power per unit projected area per unit solid angle. Units – watts per (steradian m 2 ) We have now introduced projected area, a cosine term.

© Lastra/Machiraju/Möller N V V  Projected Area Ap = A (N V) = A cos 

© Lastra/Machiraju/Möller d cos  d  Why the Cosine Term? Foreshortening is by cosine of angle. Radiance gives energy by effective surface area.

© Lastra/Machiraju/Möller Incident and Exitant Radiance Incident Radiance: L i (p,  ) Exitant Radiance: L o (p,  ) In general: p - no surface, no participating media p p

© Lastra/Machiraju/Möller Irradiance from Radiance |cos  |d  is projection of a differential area We take |cos  | in order to integrate over the whole sphere r n p

© Lastra/Machiraju/Möller Radiance Fundamental quantity, everything else derived from it. Law 1: Radiance is invariant along a ray Law 2: Sensor response is proportional to radiance

© Lastra/Machiraju/Möller Total flux leaving one side = flux arriving other side, so Law1: Conservation Law !

© Lastra/Machiraju/Möller and therefore Conservation Law !

© Lastra/Machiraju/Möller so Radiance doesn’t change with distance! Conservation Law !

© Lastra/Machiraju/Möller Sensor stuff

© Lastra/Machiraju/Möller Radiance at a sensor Sensor of a fixed area sees more of a surface that is farther away. However, the solid angle is inversely proportional to distance. Response of a sensor is proportional to radiance. T depends on geometry of sensor

© Lastra/Machiraju/Möller Thus … Radiance doesn’t change with distance –Therefore it’s the quantity we want to measure in a ray tracer. Radiance proportional to what a sensor (camera, eye) measures. –Therefore it’s what we want to output.

© Lastra/Machiraju/Möller Photometry and Radiometry Photometry (begun 1700s by Bouguer) deals with how humans perceive light. Bouguer compared every light with respect to candles and formulated the inverse square law ! All measurements relative to perception of illumination Units different from radiometric but conversion is scale factor -- weighted by spectral response of eye (over about 360 to 800 nm).

© Lastra/Machiraju/Möller VioletGreenRed © CIE, 1924, many more curves available, see CIE curve Response is integral over all wavelengths

© Lastra/Machiraju/Möller Radiometry vs. Photometry

© Lastra/Machiraju/Möller Next SPD XYZ Tone Reproduction RGB  Dither Display