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Light and Cameras
Announcement
Upcoming graphics courses: Computer Animation: Algorithms &
Techniques (Winter)
Procedural Shading (Spring) Applications in VR (Virtual Theatre)
(Fall) AI for Interactive Environments (Spring)
Logistics
Checkpoint 4 Grading 90% done
Checkpoint 5 Due Wednesday
RenderMan Due May 14 Mac problems…see me after class.
Projects Approx 26-28 projects Listing of projects now on Web Presentation schedule
Presentations (15 min max) Last 4 classes (week 9 + week 10 + finals week) Sign up
Email me with 1st , 2nd , 3rd choices First come first served.
Mid-quarter report due today Missing many!!! Drop in dropbox.
Finals date has been set Saturday, May 19th 8:00am -- 10am Room 70-1620
Project presentations.
Conflicts? Let me know.
Computer Graphics as Virtual Photography
camera(captureslight)
syntheticimage
cameramodel
(focusessimulatedlighting)
processing
photoprocessing
tonereproduction
realscene
3Dmodels
Photography:
ComputerGraphics:
Photographicprint
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Photography and Lightpho•tog•ra•phy, n., the process or art ofproducing images of objects by the action oflight on a sensitized surface, e.g., a film in acamera.
Photography = writing with light
Photographic Pipeline (back inthe day) Follow the path of light from scene to photo
to viewer!
scene camera
film enlarger
printviewer
Photographic Pipeline (for thenew millenium!) Follow the path of light from scene to photo to
viewer!
scene digitalcamera
CCDarray
printviewerPost
process
JPEG
What we’re missing Lighting values
Currently 0 - 1…what is 0? What is 1? Camera model
Current a pinhole Color
RGB…which RGB? No postprocessing
Current directly from scene to image.
Plan towards tone reproduction
Today Light (in real units) Camera and Lenses
Wednesday Color
Next Monday Tone Reproduction
Next Wednesday High Dynamic Range Images
Light -- What it is
Electromagnetic radiation
power inductionheating
radiowaves
infrared ultraviolet
x-rays gammarays
1016 1014 1010 1081012 106 102 1 10-2 10-4 10-6 10-8
Wavelength(nm)
104
visible light
secondarycosmic rays
Redorangeyellowgreenblueviolet
700 nm650 nm600 nm550 nm450 nm400 nm
3
Light Units History and definition are intertwined
(candle-power) Two sets of units
Radiometric - Standard Physics Units Photometric – Considers human perception
Defined by history - not by logic!!
Radiometric Units
Energy Light is radiant energy Measure in Joules (Q)
Radiant Flux Amount of energy / unit time Watt = Joules (Q) per second
Radiometric Units Radiance (L)
Fundamental radiometric unit defined as “the power passing through unit
area in unit solid angle about the normal tothe area
Flux arriving at or leaving from a givenpoint or surface in a given direction.
Measured in Watts / m2 / steradian The ray!!!
Radiometric Units Radiant Flux Density
(Irradiance/Radiant Exitance) Amount of flux per unit area arriving at or leaving
from a point on the surface Measured in Watts / m2
(Remember a Watt is Joules/sec.)
dA dA
Radiometric Units Radiant Intensity (I) – point source
Amount of radiant flux in a given direction Watts / steradian Point light sources
Radiometric Units Radiant Flux - energy / time - (Joules/sec) Radiant Flux Density - total flux entering
(irradiance) or leaving (radiant excitance) a pointor surface - (Watts/m2)
Radiance - total flux entering or leaving a point orsurface in a given direction - (Watts/m2/ steradian)
Radiant intensity - flux in a given direction forpoint light sources - (Watts/steradian)
All measures can vary with wavelength!!!
4
Photometric Units Photometry measures visible light according
to the sensitivity of human eye: Cones: blue – short, green – medium, red – long Rods: low illumination Eye sensitivity varies with wavelength, e.g.., green
light appears brighter than red/blue of sameintensity!
So, photometric units are radiometric unitsscaled by the luminosity function
Same concepts -> different units
Light – CIE Luminous Efficiency Curve
Created using perception matching brightness ofmonochromatic light at different wavelengths
Provides weighting curve/function used to convert fromradiometric to photometric measurements
020406080
100120
375
400
425
450
475
500
525
550
575
600
625
650
675
700
725
750
Wavelength
% E
ffici
ency
Light – Photometric Units Luminous Flux - energy / time - (lumen) Luminous Flux Density (Illuminance) - total flux
entering or leaving a point or surface - (lux =lumen/m2)
Luminance - total flux entering or leaving a point orsurface in a given direction - (nit =lumen/m2/steradian)
Luminance intensity - flux in a given direction(candela = lumen / steridian)
All scaled by CIE Luminous Efficiency Curve
Light -- How it is measured
Example The luminance at a surface due to a blue
light of a given intensity would be less thanthe luminance at the same surface due to ayellow light of the same intensity.
Why? Humans perceive yellow light to bebrighter than blue light
Lighting Units Lighting Research Center at RPI http://www.lrc.rpi.edu/education/learning/intro.asp?
mode=terminology Luminance flux (lumen) Luminance intensity (candela) Luminance (nit) Illuminance (lux or foot-candle)
Lighting Units Unit Summary:
Radiance – light hitting a surface from a givendirection (light traveling along a ray)
Luminance – photometric equivalent of radiance(radiance scaled by luminous efficiency curve)
Irradiance – light hitting a surface from alldirections
Illuminance – photometric equivalent of irradiance(irradiance scaled by luminous efficiency curve)
5
Photographic Pipeline (back inthe day) Follow the path of light from scene to photo
to viewer!
scene
(radiance /luminance)
camera
Film
(irradiance/illuminance
enlarger
printviewer
Questions?
Camera captures light from scene
How do cameras capture light from a scene? How are rays of light focused onto the film plane?
(Geometry)
How much light do cameras actually collect? What physical quality of light actually gets
through? (Radiometry)
How do cameras capture light from a scene?
CG traditionally uses the pinhole camera model
How do real cameras do this? However, generally cameras have openings,
called apertures. Light is focused through aperture using one or more lens
A lens will bend light going through it based on its geometry. Convex lens – lens thicker in the center than at the edges
and is converging Concave lens – lens thinner in center than edges and is
diverging.
Lens applet http://lectureonline.cl.msu.edu/%7Emmp/applist/optics/o.htm
Aperture
Lens opening is no longer a pinhole Can move the lens away from or toward
the film plane to achieve “focussing”
Modeling Aperture Model Geometric Model
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Terminology Focal point is the location at
which rays parallel to the opticalaxis converges to a point.
focal length the distance between the focal point
and the middle of the lens. distance from the lens that lights rays from
an infinite far away object converge to afterpassing though the lens.
Aperture Model - Focal Length
The Aperture
Circular region that light passesthrough.
Contains a lens used to focus the light Measured as an F-Stop = focal length /
diameter of opening
The THIN Lens Aperture Model
Focus
fss
111=!
+
[Heidrich97]
S = object (Q) distance;S’ is image (Q’) distance;F is the focal length;F’ is the focal point inimage space.
The THIN Lens Aperture Model
Thin lens applet http://www.physics.metu.edu.tr/%7Ebucur
gat/ntnujava/Lens/lens_e.html
The Aperture Model - Depth of Field
Depth range at which the scene willappear in focus in the resulting image.
Points outside this range will appear asblurry circles on the image (circle ofconfusion)
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Depth of Field ExampleCircle of Confusion
No Lens Ray Focused using Lens
Focused Point in back of filmRay Focused in front of film
The Aperture Model
Simulating depth of field effects [Potmesil81] Postprocess the image to simulate additional
light resulting from circle of confusion. Filter based on the physics of lens optics
The Aperture Model
[Potmesil81]
Amplitude isdependent uponthe lens diameter
The integral of the intensity distribution over the area of a pixel is the contribution ofthe sample point to the intensity of the pixel – a convolution.
The THICK Lens Aperture Model
The thin lens model assumes that the lensis infinitesimally narrow
In reality, lens system have a thickness
The THICK Lens Aperture Model
[Heidrich97]Rendering of a thick lens approximation is similar to rendering a thin lens, exceptthat an additional displacement of the ray is necessary.
8
The THICK Lens Aperture Model
Ray tracing using the thick lens model
[Kolb95]
Aperture Model Issues
Based on a perfect perspective projection Produces perfectly undistorted (geometrically)
images Assumes that every camera consists of a single
lens In reality,
All lenses introduce distortion, sometimes intentionally,e.g. fish eye lens
A professional camera lens is actually a collection ofindividual lens elements packaged together to achievea given effect.
A Geometric Model
Accurately accounts for the geometry ofthe elements in a lens system
The thick and thin lens aperture modelsare approximations of effects due to theactual geometry of the lenses.
Geometric Model A typical lens system (from Lens handbook)
[Kolb95]
front
back
Index ofrefraction
Change index ofrefraction wrtwavelength
Aperture
A Geometric Model For each element:
Radius of curvature Thickness Index of refraction Change of index of refraction Diameter
This specification can be used to tracerays through the system.
The Kolb Geometric Model[1995]
Brute force ray tracing solution usinglens specifications
Accurately calculates geometry andradiometry
Framework also allows for thin andthick model approximations
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The Kolb Geometric Model
Ray tracing Ray direction modified using
Curvature of lens surface Refraction using Snell’s Law
Supersampling - Multiple rays cast perpixel.
The Kolb Geometric Model
Pixel values are determined relative toaccurately calculated irradiance onsurface.
Note that depth of field effects come forfree since accurately modeling lenseffect.
Getting close to photography!
The Kolb Geometric Model
16mm fisheye
200mm telephoto
50mm double-Gauss
35mm wide-angle
CG Camera Models Summary
Looked at the geometry of CG camera models Pinhole model (basic perspective projection) Aperture Models (depth of field/thin, thick
model) Geometric model (for full geometric effects)
Break
How much light do cameras actually collect?(Radiometry)
Determining amount of light reaching the filmsurface.
Recall that light incident on a surface is given byirradiance / illuminance
Ultimately, we would like to calculate exposure: Exposure = I*t (illuminance x time) Note: I’ve chosen to spell exposure because we are
talking about Irradiance as well which is also denotedas E
Radiometry
Irradiance - flux density in
dA
dE
!=
dA
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Radiometry Things to consider when figuring out
exposure. Irradiance from scene radiance Vignetting Transmittance (formerly called transmission) Flare Shutter efficiency
A bit more than the basic pinhole camera!
Radiometry To get irradiance at a given point on the film
plane, we must integrate radiance valuesover a circle representing the exit pupil.* Radiance – light hitting a surface from a given
direction (light traveling along a ray) Irradiance – light hitting a surface from all
directions Illuminance – photometric equivalent of irradiance
(irradiance scaled by luminous efficiency curve)
*The exit pupil is defined to be the image of the aperture stop asviewed from image space.
Radiometry
Ad
xx
xxLxEDx
!!!"!!
!!!!!!=! # $!! 2
coscos),()(
%%
[Kolb95]Aperture opening
Radiometry Some simplifying assumptions are
generally made to simplify the equation Aperture (D) is parallel to film plane The solid angle subtended by exit pupil is
small Focus at infinity.
Radiometry L = illuminance from scene
E.g., from global illumination model
n = F-stop (focal length / diameter of opening) θ = angle from center of lens to point on film
surface
!" 4
2cos
4)(
nLxE =#
Radiometry
Note: if camera not focused at infinity. u = distance from lens of object on which
object is focus F = focal length
!
E( " x ) = Lu # F
u
$
% &
'
( )
2*
4n2cos
4 +
11
Radiometry - Vignetting
Characterized by the fact that a uniformlyilluminated scene will actually look brighterin the center than on the picture edges.Luminance decreases towards picture edges.
Notice the cos term here irradiance depends upon location on film plane
θπ 4
2 cos4
)(n
LxE =′
Vignetting - Example
Radiometry - Vignetting
Notes: This expression actually underestimates the amount
of vignetting. Vignetting can be due to blocking of light from other
lens elements
[Kolb95]
Radiometry - Lens Transmittance
So far we assumed 100% transmittancethrough the lens In reality, this isn’t the case Transmission lost due to refraction Therefore, introduce a transmittance
factor, τ
!"
# 4
2cos
4)(
nLxE =$
Radiometry - Transmittance
Estimate by
where k = number of glass-air surfaces May be more if lens are coated
k)95.0(=!
Radiometry - Flair
Additional light hitting film surface notcaused by light in scene. E.g., light reflected back from lens system
due to flaws, dust, fingerprints Usually a small fraction of scene
illuminance Affects shadow regions of final image.
12
Radiometry - Flare
Model with
whereE - total irradianceEi - irradiance due to sceneEf - irradiance due to flare
fi EEE +=
Radiometry - Flare
Depends not only on camera and lenssystem but also on type of scenephotographed.
As a result, it is very difficult to modelin a general fashion.
Radiometry - Exposure
Photographic measurements are madein response to exposure.
Photographic science uses photometricquantities to measure light.
Exposure = Iluminance x time (lux-sec)
Radiometry - Exposure
I = illuminance, E = irradiance, L = illuminancefrom scene,
θπ
τ 42 cos
4)(
nLxIi =′ )(xE ′=
Radiometry - Exposure
txIxExposure )()( ′=′
scene from eilluminanc scaled timeflare
42 )cos
4()( tI
nLxExposure f
+=′ θπ
τ
Radiometry - Camera Shutters
Most CG camera models (even Kolb’s)assume shutters open and closeinstantaneously.
In reality, this is not the case whichleads to a decrease in exposure values.
Must introduce a shutter efficiencyconstant to exposure equation (η)
13
Radiometry
shutter efficiency
Radiometry
shutter efficiency
Radiometry - Shutter Efficiency
Estimating Shutter efficiency
Note that t1 and t3 depend not only on shutter time,but also aperture opening
)(
)5.05.0(
321
321
rated
actual
ttt
ttt
t
t
++
++==!
t1 t2 t3
Radiometry - ExposureFinal model
timeshuttereff.
flarescene from eilluminanc
42 )cos
4()( tI
nLxExposure f
ηθπ
τ +=′
We now know how much exposure is present oneach point in our film plane
scene camera
film enlarger
viewer
Photographic Pipeline Photographic Pipeline
Why we need to know this Photography is based on a photographic material’s
response to light. We need to know:
Where light is coming from How much light is arriving How long is the light incident on the materal
Only then can we attempt to model the response. Which we will do when we talk about tone reproduction.
14
Summary
Light Units
Radiometric / Photometric
Camera Geometry Radiometry
Next time: Color
Recommended