The primary goal of physically-based rendering (PBR) is to create a simulation that accurately reproduces the imaging process of electro-magnetic spectrum radiation incident to an observer. This simulation should be indistinguishable from reality for a similar observer.
Because a camera is not sensitive to incident light the same way than a human observer, the images it captures are transformed to be colorimetric. A project might require infrared imaging simulation, a portion of the electro-magnetic spectrum that is invisible to us. Radically different observers might image the same scene but the act of observing does not change the intrinsic properties of the objects being imaged. Consequently, the physical modelling of the virtual scene should be independent of the observer.
While the human eye has red, green, and blue-sensing cones, those cones are cross-wired in the retina to produce a luminance channel plus a red-green and a blue-yellow channel, and it’s data in that color space (known technically as “LAB”) that goes to the brain. That’s why we can’t perceive a reddish-green or a yellowish-blue, whereas such colors can be represented in the RGB color space used by digital cameras.
The back of the retina is covered in light-sensitive neurons known as cone cells and rod cells. There are three types of cone cells, each sensitive to different ranges of light. These ranges overlap, but for convenience the cones are referred to as blue (short-wavelength), green (medium-wavelength), and red (long-wavelength). The rod cells are primarily used in low-light situations, so we’ll ignore those for now.
When light enters the eye and hits the cone cells, the cones get excited and send signals to the brain through the visual cortex. Different wavelengths of light excite different combinations of cones to varying levels, which generates our perception of color. You can see that the red cones are most sensitive to light, and the blue cones are least sensitive. The sensitivity of green and red cones overlaps for most of the visible spectrum.
Here’s how your brain takes the signals of light intensity from the cones and turns it into color information. To see red or green, your brain finds the difference between the levels of excitement in your red and green cones. This is the red-green channel.
To get “brightness,” your brain combines the excitement of your red and green cones. This creates the luminance, or black-white, channel. To see yellow or blue, your brain then finds the difference between this luminance signal and the excitement of your blue cones. This is the yellow-blue channel.
From the calculations made in the brain along those three channels, we get four basic colors: blue, green, yellow, and red. Seeing blue is what you experience when low-wavelength light excites the blue cones more than the green and red.
Seeing green happens when light excites the green cones more than the red cones. Seeing red happens when only the red cones are excited by high-wavelength light.
Here’s where it gets interesting. Seeing yellow is what happens when BOTH the green AND red cones are highly excited near their peak sensitivity. This is the biggest collective excitement that your cones ever have, aside from seeing pure white.
Notice that yellow occurs at peak intensity in the graph to the right. Further, the lens and cornea of the eye happen to block shorter wavelengths, reducing sensitivity to blue and violet light.
By stimulating specific cells in the retina, the participants claim to have witnessed a blue-green colour that scientists have called “olo”, but some experts have said the existence of a new colour is “open to argument”.
The findings, published in the journal Science Advances on Friday, have been described by the study’s co-author, Prof Ren Ng from the University of California, as “remarkable”.
(A) System inputs. (i) Retina map of 103 cone cells preclassified by spectral type (7). (ii) Target visual percept (here, a video of a child, see movie S1 at 1:04). (iii) Infrared cellular-scale imaging of the retina with 60-frames-per-second rolling shutter. Fixational eye movement is visible over the three frames shown.
(B) System outputs. (iv) Real-time per-cone target activation levels to reproduce the target percept, computed by: extracting eye motion from the input video relative to the retina map; identifying the spectral type of every cone in the field of view; computing the per-cone activation the target percept would have produced. (v) Intensities of visible-wavelength 488-nm laser microdoses at each cone required to achieve its target activation level.
(C) Infrared imaging and visible-wavelength stimulation are physically accomplished in a raster scan across the retinal region using AOSLO. By modulating the visible-wavelength beam’s intensity, the laser microdoses shown in (v) are delivered. Drawing adapted with permission [Harmening and Sincich (54)].
(D) Examples of target percepts with corresponding cone activations and laser microdoses, ranging from colored squares to complex imagery. Teal-striped regions represent the color “olo” of stimulating only M cones.
This paper presents an introduction to the color pipelines behind modern feature-film visual-effects and animation.
Authored by Jeremy Selan, and reviewed by the members of the VES Technology Committee including Rob Bredow, Dan Candela, Nick Cannon, Paul Debevec, Ray Feeney, Andy Hendrickson, Gautham Krishnamurti, Sam Richards, Jordan Soles, and Sebastian Sylwan.
“Fix your gaze on the black dot on the left side of this image. But wait! Finish reading this paragraph first. As you gaze at the left dot, try to answer this question: In what direction is the object on the right moving? Is it drifting diagonally, or is it moving up and down?”
We introduce a principle, Oz, for displaying color imagery: directly controlling the human eye’s photoreceptor activity via cell-by-cell light delivery. Theoretically, novel colors are possible through bypassing the constraints set by the cone spectral sensitivities and activating M cone cells exclusively. In practice, we confirm a partial expansion of colorspace toward that theoretical ideal. Attempting to activate M cones exclusively is shown to elicit a color beyond the natural human gamut, formally measured with color matching by human subjects. They describe the color as blue-green of unprecedented saturation. Further experiments show that subjects perceive Oz colors in image and video form. The prototype targets laser microdoses to thousands of spectrally classified cones under fixational eye motion. These results are proof-of-principle for programmable control over individual photoreceptors at population scale.
A measure of how large the object appears to an observer looking from that point. Thus. A measure for objects in the sky. Useful to retuen the size of the sun and moon… and in perspective, how much of their contribution to lighting. Solid angle can be represented in ‘angular diameter’ as well.
A solid angle is expressed in a dimensionless unit called a steradian (symbol: sr). By default in terms of the total celestial sphere and before atmospheric’s scattering, the Sun and the Moon subtend fractional areas of 0.000546% (Sun) and 0.000531% (Moon).
On earth the sun is likely closer to 0.00011 solid angle after athmospheric scattering. The sun as perceived from earth has a diameter of 0.53 degrees. This is about 0.000064 solid angle.
The mean angular diameter of the full moon is 2q = 0.52° (it varies with time around that average, by about 0.009°). This translates into a solid angle of 0.0000647 sr, which means that the whole night sky covers a solid angle roughly one hundred thousand times greater than the full moon.
The apparent size of an object as seen by an observer; expressed in units of degrees (of arc), arc minutes, or arc seconds. The moon, as viewed from the Earth, has an angular diameter of one-half a degree.
The angle covered by the diameter of the full moon is about 31 arcmin or 1/2°, so astronomers would say the Moon’s angular diameter is 31 arcmin, or the Moon subtends an angle of 31 arcmin.
In the retina, photoreceptors, bipolar cells, and horizontal cells work together to process visual information before it reaches the brain. Here’s how each cell type contributes to vision:
import math,sys
def Exposure2Intensity(exposure):
exp = float(exposure)
result = math.pow(2,exp)
print(result)
Exposure2Intensity(0)
def Intensity2Exposure(intensity):
inarg = float(intensity)
if inarg == 0:
print("Exposure of zero intensity is undefined.")
return
if inarg < 1e-323:
inarg = max(inarg, 1e-323)
print("Exposure of negative intensities is undefined. Clamping to a very small value instead (1e-323)")
result = math.log(inarg, 2)
print(result)
Intensity2Exposure(0.1)
Why Exposure?
Exposure is a stop value that multiplies the intensity by 2 to the power of the stop. Increasing exposure by 1 results in double the amount of light.
Artists think in “stops.” Doubling or halving brightness is easy math and common in grading and look-dev. Exposure counts doublings in whole stops:
+1 stop = ×2 brightness
−1 stop = ×0.5 brightness
This gives perceptually even controls across both bright and dark values.
Why Intensity?
Intensity is linear. It’s what render engines and compositors expect when:
Summing values
Averaging pixels
Multiplying or filtering pixel data
Use intensity when you need the actual math on pixel/light data.
Formulas (from your Python)
Intensity from exposure: intensity = 2**exposure
Exposure from intensity: exposure = log₂(intensity)
Guardrails:
Intensity must be > 0 to compute exposure.
If intensity = 0 → exposure is undefined.
Clamp tiny values (e.g. 1e−323) before using log₂.
Use Exposure (stops) when…
You want artist-friendly sliders (−5…+5 stops)
Adjusting look-dev or grading in even stops
Matching plates with quick ±1 stop tweaks
Tweening brightness changes smoothly across ranges
Use Intensity (linear) when…
Storing raw pixel/light values
Multiplying textures or lights by a gain
Performing sums, averages, and filters
Feeding values to render engines expecting linear data
Examples
+2 stops → 2**2 = 4.0 (×4)
+1 stop → 2**1 = 2.0 (×2)
0 stop → 2**0 = 1.0 (×1)
−1 stop → 2**(−1) = 0.5 (×0.5)
−2 stops → 2**(−2) = 0.25 (×0.25)
Intensity 0.1 → exposure = log₂(0.1) ≈ −3.32
Rule of thumb
Think in stops (exposure) for controls and matching. Compute in linear (intensity) for rendering and math.
The dynamic range is a ratio between the maximum and minimum values of a physical measurement. Its definition depends on what the dynamic range refers to.
For a scene: Dynamic range is the ratio between the brightest and darkest parts of the scene.
For a camera: Dynamic range is the ratio of saturation to noise. More specifically, the ratio of the intensity that just saturates the camera to the intensity that just lifts the camera response one standard deviation above camera noise.
For a display: Dynamic range is the ratio between the maximum and minimum intensities emitted from the screen.
The Dynamic Range of real-world scenes can be quite high — ratios of 100,000:1 are common in the natural world. An HDR (High Dynamic Range) image stores pixel values that span the whole tonal range of real-world scenes. Therefore, an HDR image is encoded in a format that allows the largest range of values, e.g. floating-point values stored with 32 bits per color channel. Another characteristics of an HDR image is that it stores linear values. This means that the value of a pixel from an HDR image is proportional to the amount of light measured by the camera.
For TVs HDR is great, but it’s not the only new TV feature worth discussing.
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![[gamma correction test]](http://www.madore.org/~david/misc/color/gammatest.png "sRGB gamma correction test")
