Lecture 006

Assumptions:

There are: Light sources, reflectance spectra, sensor sensitivity modeled separately at each wavelength
Geometric/ray optics
No polarization
No fluorescence, phosphorescence

Basic Quantities:

flux $\Phi$
irradiance $E$
radiosity $B$
intensity $I$
radiance $L$

Flux (Radiant Flux, Power): total amount of radiant energy passing through surface or space per unit time

number of photons hitting a wall per second ( $W = J/s$ )
number of photons leaving a lightbulb per second

Irradiance: flux per unit area ( $W/m^2$ ) arriving at a surface

Radiosity (Radiant Exitance): same as Irradiance, but leaving a surface

Radiant Intensity: flux per solid angle $W/\text{solid angle}$

Angle vs Solid Angle: Solid angle is just angle but in 3 dimension. You can think of it as surfaces but independent of radius

Radiance: flux density per unit solid angle, per perpendicular unit area

Cameras measure integrals of radiance (after a one-time radiometric calibration). So RAW pixel values are proportional to (integrals of) radiance.

also processed images are not linear radiance measurements.

Photometry

Photometry: radiometric but accounts for response of human visual system

We generally solve two problems:

given 3 types of sensor, what range and weight of frequency of lights should contribute to sensor output
how to arrange mosaic to express spectrons with only 3 colors

Luminance ( $Y$ ): radiance but weighted by eye's luminous efficacy curve

Eye's Curve under different lighting condition

Vignetting

Vignetting: pixels far off the center receive less light

Cause and types of vignetting

mechanical: light blocked by filters, hoods
lens: light block by lens
natural: due to cosine fourth falloff
pixel: angle-dependent sensitivity of sensors (photodiodes)

Cosine Fourth Falloff (the first cosine come from radiance, the second is change of variable from hole to sensor)

BRDF

Property of BRDF:

conservation of energy: no generation of energy
Helmholtz reciprocity: forward is the same as backward
isotropic (often): BRDF is the same when you rotate with normal axis

Some resources I promised today.

(Unrelated to today's lecture) This is a good resource for standard meshes and other scene assets: https://casual-effects.com/data/

Below are the three most-commonly used measured BRDF datasets, one being the MERL dataset I mentioned in class: https://www.merl.com/brdf/, https://rgl.epfl.ch/publications/Dupuy2018Adaptive, http://www.ivlab.org/brdf-btf.html

This paper is a great summary of microfacet models for both reflection and refraction: https://www.cs.cornell.edu/~srm/publications/EGSR07-btdf.html

This paper describes the energy loss issue associated with microfacet BRDFs that we discussed today; note also the notes the page includes on using ensemble averaging to validate statistical models: https://eheitzresearch.wordpress.com/240-2/

This is a representative paper on rendering of layered materials: https://belcour.github.io/blog/research/publication/2018/05/05/brdf-realtime-layered.html

This page is a good summary of work on modeling and rendering fabrics (some of the renderings are stunning, even by SIGGRAPH standards): https://www.cs.cornell.edu/projects/ctcloth/

This is a representative paper on rendering hair: http://www.cs.cornell.edu/~pramook/papers/elliptical-hair.pdf

Actually, some more notes.

This is the paper I mentioned that uses microfacet theory to design and fabricate surfaces with microgeometry that results in very unusual BRDFs (e.g., anti-specular). It also discusses in a lot of detail why we do not care about wave effects such as speckle and diffraction when rendering under the assumptions of radiometry. It's a pretty useful read in general: https://dl.acm.org/doi/abs/10.1145/2461912.2461981

This is sort of the opposite of the above paper. It uses a microscope to measure the microgeometry of a real surface, and then uses microfacet theory to produce a BRDF that predicts the surface's BRDF: https://dl.acm.org/doi/abs/10.1145/2815618

This is a paper on modeling diffraction wave effects using a generalization of the BRDF: https://dl.acm.org/doi/abs/10.1145/2231816.2231820

This is a paper on modeling speckle wave effects using a generalization of the BRDF: https://dl.acm.org/doi/abs/10.1145/3472293 Lastly, as we are wrapping up our discussion of radiometry and we'll move on to Monte Carlo, I wanted to post some notes on a few more general topics that have come up during the past 3-4 lectures.

This is a nice classical textbook on radiometry and how it is derived from first principles in applied physics: https://www.wiley.com/en-us/Radiometry+and+the+Detection+of+Optical+Radiation-p-9780471861881

Eric Veach's thesis has an incredibly thorough discussion of radiometry and light transport, including its axiomatization through measure theory, detailed proofs of BRDF properties such as energy conservation and reciprocity (we skipped the latter in class), and so on. It is my go-to reference whenever in doubt about something. See chapter 3: https://www.proquest.com/docview/304456010?pq-origsite=gscholar&fromopenview=true

We briefly mentioned spectral rendering a few times, here is a recent review that should have pointers to related literature: https://dl.acm.org/doi/10.1145/3450508.3464582

We briefly mentioned polarization rendering, here is another recent review that should have pointers to related literature: https://dl.acm.org/doi/10.1145/3415263.3419172

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