upcoming graphics courses: light and cameras

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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

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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!!!

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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)

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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


[Heidrich97]Rendering of a thick lens approximation is similar to rendering a thin lens, exceptthat an additional displacement of the ray is necessary.

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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.


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!


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 +

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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.

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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)


I = illuminance, E = irradiance, L = illuminancefrom scene,

θπ

τ 42 cos

4)(

nLxIi =′ )(xE ′=


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)

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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

print

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.

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Summary

Light Units

Radiometric / Photometric

Camera Geometry Radiometry

Next time: Color

upcoming graphics courses: light and cameras

Documents