Paper Summaries Any takers? Advanced Cameras Models Assignments - - PDF document

1 Advanced Cameras Models

Paper Summaries

• Any takers?

Assignments

• Checkpoint 1

– Most should have received e-mail

• Checkpoint 2

– Due Wednesday after break – Any questions?

Plan for today

• Advanced Camera Models

– How real cameras do it – How this is simulated in Computer Graphics

Photographic Pipeline

• Follow the path of light from scene to photo to

viewer!

scene camera film enlarger print viewer

Step 1: 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)

2

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

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

Terminology

• Focal point is the location at

which rays parallel to the optical axis 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 after passing though the lens.

Aperture Model - Focal Length The Aperture

• Circular region that light passes through.
• Contains a lens used to focus the light
• Measured as an F-Stop = focal length /

diameter of opening

3 The THIN Lens Aperture Model

• Focus

f s s 1 1 1 = ′ +

[Heidrich97]

S = object (Q) distance; S’ is image (Q’) distance; F is the focal length; F’ is the focal point in image space.

The THIN Lens Aperture Model

• Thin lens applet

Lens and Magnification

• Both the distance from the lens an object and the

curvature of the lens will affect object magnification in final image.

• http://www.rit.edu/~visualiz/lenses.html

The Aperture Model - Depth of Field

• Depth range at which the scene will appear in

focus in the resulting image.

• Points outside this range will appear as blurry

circles on the image (circle of confusion)

Depth of Field Example Circle of Confusion

No Lens Ray Focused using Lens Focused Point in back of film Ray Focused in front of film

4

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 is dependent upon the lens diameter The integral of the intensity distribution over the area of a pixel is the contribution of the sample point to the intensity of the pixel – a convolution.

The THICK Lens Aperture Model

• The thin lens model assumes that the lens is

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, except that an additional displacement of the ray is necessary.

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 of individual lens elements packaged together to achieve a given effect.

5

A Geometric Model

• Accurately accounts for the geometry of the

elements in a lens system

• The thick and thin lens aperture models are

approximations of effects due to the actual geometry of the lenses.

• Lens Ray Tracing Applet

Geometric Model

• A typical lens system (from Lens handbook)

[Kolb95] front back Index of refraction Change index of refraction wrt wavelength 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 trace rays

through the system.

The Kolb Geometric Model [1995]

• Brute force ray tracing solution using lens

specifications

• Accurately calculates geometry and

radiometry

• Framework also allows for thin and thick

model approximations

The Kolb Geometric Model

• Ray tracing

– Ray direction modified using

• Curvature of lens surface
• Refraction using Snell’s Law

– Supersampling - Multiple rays cast per pixel.

The Kolb Geometric Model

• Pixel values are determined relative to

accurately calculated irradiance on surface.

• Note that depth of field effects come for

free since accurately modeling lens effect.

• Getting close to photography!

6 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 film surface.
• Recall that light incident on a surface is given by

irradiance / 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 denoted as E

Radiometry

• Irradiance - flux density in

dA d E Φ =

dA

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 values over 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 as

viewed from image space.

7

Radiometry

A d x x x x L x E

D x

′ ′ ′ − ′ ′ ′ ′ ′ ′ ′ ′ = ′

∫ ∈

′ ′ 2

cos cos ) , ( ) ( θ θ

[Kolb95] Aperture opening

Radiometry

• Some simplifying assumptions give rise to

formula on following slide

– Aperture (D) is parallel to film plane – The solid angle subtended by exit pupil is small

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

θ π

4 2 cos

4 ) ( n L x E = ′

Radiometry - Vignetting

• Characterized by the fact that a uniformly

illuminated scene will actually look brighter in the center than on the picture edges. Luminance decreases towards picture edges.

• Notice the cos term here

– irradiance depends upon location on film plane

θ π

4 2 cos

4 ) ( n L x E = ′

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]

8 Radiometry - Lens Transmittance

• So far we assumed 100% transmittance

through the lens

– In reality, this isn’t the case – Transmission lost due to refraction – Therefore, introduce a transmittance factor, τ

θ π τ

4 2 cos

4 ) ( n L x E = ′

Radiometry - Transmittance

• Estimate by

where k = number of glass-air surfaces

• May be more if lens are coated

k

) 95 . ( = τ

Radiometry - Flair

• Additional light hitting film surface not

caused 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.

Radiometry - Flare

• Model with

where

E - total irradiance Ei - irradiance due to scene Ef - irradiance due to flare f i

E E E + =

Radiometry - Flare

• Depends not only on camera and lens

system but also on type of scene photographed.

• As a result, it is very difficult to model in a

general fashion.

Radiometry - Exposure

• Photographic measurements are made in

response to exposure.

• Photographic science uses photometric

quantities to measure light.

• Exposure = Iluminance x time (lux-sec)

9

Radiometry - Exposure

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

θ π τ

4 2 cos

4 ) ( n L x Ii = ′ ) (x E ′ =

Radiometry - Exposure

t x I x Exposure ) ( ) ( ′ = ′

scene from e illuminanc scaled time flare 4 2

) cos 4 ( ) ( t I n L x Exposure

f

+ = ′ θ π τ

Radiometry - Camera Shutters

• Most CG camera models (even Kolb’s)

assume shutters open and close instantaneously.

• In reality, this is not the case which leads to

a decrease in exposure values.

• Must introduce a shutter efficiency constant

to exposure equation (η)

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 . 5 . (

3 2 1 3 2 1 rated actual

t t t t t t t t + + + + = = η

t1 t2 t3

10

Radiometry - Exposure

Final model time shutter eff. flare scene from e illuminanc 4 2

) cos 4 ( ) ( t I n L x Exposure

f

η θ π τ + = ′

We now know how much exposure is present on each 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.

Summary

• Modeling of light through a real camera

– Geometry

• Aperture Model
• Geometric Model

– Radiometry

• Questions?

Next time

• Start rendering

– Material properties – How light interacts with different materials