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

Paper Summaries • Any takers? Advanced Cameras Models Assignments Plan for today • Checkpoint 1 • Advanced Camera Models – Most should have received e-mail – How real cameras do it – How this is simulated in Computer Graphics • Checkpoint 2 – Due Wednesday after break – Any questions? Photographic Pipeline Step 1: Camera captures light from scene • Follow the path of light from scene to photo to • How do cameras capture light from a scene? viewer! – How are rays of light focused onto the film plane? enlarger ( Geometry ) film • How much light do cameras actually collect? – What physical quality of light actually gets through? ( Radiometry ) print viewer camera scene 1

How do cameras capture light from a scene? How do real cameras do this? • However, generally cameras have openings, • CG traditionally uses the pinhole camera model 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 Terminology • Focal point is the location at • Lens opening is no longer a pinhole which rays parallel to the optical • Can move the lens away from or toward the axis converges to a point. film plane to achieve “focussing” • focal length – the distance between the focal point and the middle of the lens. • Modeling – distance from the lens that lights rays from – Aperture Model an infinite far away object converge to after passing though the lens. – Geometric Model 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 2

The THIN Lens Aperture Model The THIN Lens Aperture Model • Focus • Thin lens applet 1 1 1 + = ′ s s f S = object (Q) distance; S’ is image (Q’) distance; F is the focal length; F’ is the focal point in image space. [Heidrich97] Lens and Magnification The Aperture Model - Depth of Field • Both the distance from the lens an object and the • Depth range at which the scene will appear in curvature of the lens will affect object focus in the resulting image. magnification in final image. • Points outside this range will appear as blurry circles on the image ( circle of confusion ) • http://www.rit.edu/~visualiz/lenses.html Circle of Confusion Depth of Field Example No Lens Ray Focused using Lens Ray Focused in front of film Focused Point in back of film 3

The Aperture Model The Aperture Model Amplitude is • Simulating depth of field effects [Potmesil81] dependent upon the lens diameter – Postprocess the image to simulate additional light resulting from circle of confusion. – Filter based on the physics of lens optics 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. [Potmesil81] The THICK Lens Aperture Model The THICK Lens Aperture Model • The thin lens model assumes that the lens is infinitesimally narrow • In reality, lens system have a thickness Rendering of a thick lens approximation is similar to rendering a thin lens, except [Heidrich97] that an additional displacement of the ray is necessary. The THICK Lens Aperture Model Aperture Model Issues • Ray tracing using the thick lens model • 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. [Kolb95] 4

A Geometric Model Geometric Model • Accurately accounts for the geometry of the • A typical lens system (from Lens handbook) elements in a lens system Aperture front • The thick and thin lens aperture models are approximations of effects due to the actual geometry of the lenses. back • Lens Ray Tracing Applet Change index of Index of refraction wrt refraction wavelength [Kolb95] The Kolb Geometric Model A Geometric Model [1995] • For each element: • Brute force ray tracing solution using lens – Radius of curvature specifications – Thickness • Accurately calculates geometry and – Index of refraction radiometry – Change of index of refraction • Framework also allows for thin and thick – Diameter model approximations • This specification can be used to trace rays through the system. The Kolb Geometric Model The Kolb Geometric Model • Ray tracing • Pixel values are determined relative to accurately calculated irradiance on surface. – Ray direction modified using • Curvature of lens surface • Note that depth of field effects come for • Refraction using Snell’s Law free since accurately modeling lens effect. – Supersampling - Multiple rays cast per pixel. • Getting close to photography! 5

CG Camera Models The Kolb Geometric Model • Summary – Looked at the geometry of CG camera models – Pinhole model (basic perspective projection) – Aperture Models (depth of field/thin, thick model) 35mm wide-angle 200mm telephoto – Geometric model (for full geometric effects) – Break 50mm double-Gauss 16mm fisheye How much light do cameras actually collect? Radiometry (Radiometry) • Irradiance - flux density in • Determining amount of light reaching the film surface. • Recall that light incident on a surface is given by Φ d irradiance / illuminance = E • Ultimately, we would like to calculate exposure: dA – Exposure = I*t (illuminance x time) dA – Note: I’ve chosen to spell exposure because we are talking about Irradiance as well which is also denoted as E Radiometry Radiometry • Things to consider when figuring out exposure. • To get irradiance at a given point on the film plane, we must integrate radiance values over a – Irradiance from scene radiance circle representing the exit pupil.* – Vignetting – Transmittance (formerly called transmission) – Radiance – light hitting a surface from a given direction (light traveling along a ray) – Flare – Irradiance – light hitting a surface from all directions – Shutter efficiency – Illuminance – photometric equivalent of irradiance (irradiance scaled by luminous efficiency curve) • A bit more than the basic pinhole camera! * The exit pupil is defined to be the image of the aperture stop as viewed from image space. 6

Radiometry 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 θ ′ θ ′ ′ cos cos ∫ ∈ ′ ′ ′ ′ ′ ′ = E ( x ) L ( x , x ) d A ′ ′ ′ ′ ′ − 2 x D x x Aperture opening [Kolb95] Radiometry Radiometry - Vignetting π • L = illuminance from scene ′ = θ 4 – E.g., from global illumination model E ( x ) L 2 cos • n = F-stop ( focal length / diameter of opening) 4 n • θ = angle from center of lens to point on film • Characterized by the fact that a uniformly surface illuminated scene will actually look brighter in π the center than on the picture edges. Luminance ′ = θ 4 decreases towards picture edges. E ( x ) L 2 cos 4 n • Notice the cos term here – irradiance depends upon location on film plane 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] 7

Radiometry - Transmittance Radiometry - Lens Transmittance • So far we assumed 100% transmittance • Estimate by through the lens τ = k ( 0 . 95 ) – In reality, this isn’t the case – Transmission lost due to refraction where k = number of glass-air surfaces – Therefore, introduce a transmittance factor, τ • May be more if lens are coated π ′ = τ θ 4 E ( x ) L 2 cos 4 n Radiometry - Flair Radiometry - Flare • Additional light hitting film surface not • Model with caused by light in scene. = + E E E – E.g., light reflected back from lens system due i f to flaws, dust, fingerprints where – Usually a small fraction of scene illuminance E - total irradiance – Affects shadow regions of final image. E i - irradiance due to scene E f - irradiance due to flare Radiometry - Flare Radiometry - Exposure • Depends not only on camera and lens • Photographic measurements are made in system but also on type of scene response to exposure. photographed. • Photographic science uses photometric • As a result, it is very difficult to model in a quantities to measure light. general fashion. • Exposure = Iluminance x time (lux-sec) 8