A Realistic Camera Model for Computer GraphicsCraig KolbComputer Science DepartmentPrinceton UniversityDon MitchellAdvanced Technology DivisionMicrosoftPat HanrahanComputer Science DepartmentStanford UniversityAbstractMost recent rendering research has concentrated on two subprob-lems: modeling the reflection of light from materials, and calculat-ing the direct and indirect illumination from light sources and othersurfaces. Another key component of a rendering system is the cam-era model. Unfortunately, current camera models are not geometri-cally or radiometrically correct and thus are not sufficient for syn-thesizing images from physically-based rendering programs.In this paper we describe a physically-based camera model forcomputer graphics. More precisely, a physically-based cameramodel accurately computes the irradiance on the film given the in-coming radiance from the scene. In our model a camera is describedas a lens system and film backplane. The lens system consists of asequence of simple lens elements, stops and apertures. The camerasimulation module computes the irradiance on the backplane fromthe scene radiances using distributed ray tracing. This is accom-plished by a detailed simulation of the geometry of ray paths throughthe lens system, and by sampling the lens system such that the ra-diometry is computed accurately and efficiently. Because even themost complicated lenses have a relatively small number of elements,the simulation only increases the total rendering time slightly.CR Categories and SubjectDescriptors: I.3.3 [Computer Graph-ics]: Picture/Image Generation; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism.Additional Key Words and Phrases: ray tracing, camera model-ing, lens simulation, sampling.1 IntroductionThe challenge of producing realistic images of 3d scenes is oftenbroken into three subproblems: modeling reflection to account forthe interaction of light with different materials, deriving illumina-tion algorithms to simulate the transport of light throughout the en-vironment, and modeling a camera that simulates the process of im-age formation and recording. In the last several years the majorityof the research in image synthesis has been concentrated on reflec-tion models and illumination algorithms. Since the pioneering workby Cook et al.[2] on simulating depth of field and motion blur, therehas been very little work on camera simulation.Although current camera models are usually adequate for pro-ducing an image containing photographic-like effects, in generalthey are not suitable for approximating the behavior of a particularphysical camera and lens system. For instance, current models usu-ally do not correctly simulate the geometry of image formation, donot properly model the changes in geometry that occur during fo-cusing, use an improper aperture in depth of field calculations, andassume ideal lens behavior. Current techniques also do not computeexposure correctly; in particular, exposure levels and variation of ir-radiance across the backplane are not accounted for.There are many situations where accurate camera models are im-portant:One trend in realistic computer graphics is towards physically-based rendering algorithms that quantitatively model thetransport of light. Theoutput of these programs is typically theradiance on each surface. A physically-based camera model isneeded to simulate the process of image formation if accuratecomparisons with empirical data are to be made.In many applications (special effects, augmented reality) itis necessary to seamlessly merge acquired imagery with syn-thetic imagery. In these situations it is important that the syn-thetic imagery be computed using a camera model similar tothe real camera.In some machine vision and scientific applications it is neces-sary to simulate cameras and sensors accurately. For example,a vision system may want to test whether its internal model ofthe world matches what is being observed.Many users of 3d graphics systemsare very familiar with cam-eras and how to use them. By using a camera metaphor thegraphics system may be easier to use. Also, pedagogically itis helpful when explaining the principles of 3d graphics to beable to relate them to real cameras.Perhaps the earliest introduction of a camera model in computergraphics was the synthetic camera model proposed in the COREsystem[3]. This and later work used a camera metaphor to describethe process of synthesizing an image, but did not intend to repro-duce photographic effects or provide photographic-like control overimage formation. The next major breakthrough in camera model-ing was the simulation of depth of field and motion blur[10][2][12].Current methods for simulating these effects use idealized lens sys-tems and thus cannot be used to simulate the behavior of a partic-ular physical system. A number of researchers have shown how toperform non-linear camera projections, such as those for fisheye orOMNIMAX lenses[7][5]. These methods derive a transformationthat maps image points to directions in 3D, and have the disadvan-tage that effectssuchasdepth of fieldcannot be combined with thesespecial-purpose projections.radius thickndV-no ap58.950 7.520 1.670 47.1 50.4169.6600.240 50.438.5508.050 1.670 47.1 46.081.5406.550 1.699 30.1 46.025.50011.410 36.09.000 34.2-28.9902.360 1.603 38.0 34.081.54012.130 1.658 57.3 40.0-40.7700.380 40.0874.1306.440 1.717 48.0 40.0-79.46072.228 40.0Figure 1: A tabular description and profile view of a double-Gauss lens. [14, page 312]. Each row in the table describes a surface of alens element. Surfaces are listed in order from the front (nearest object space) to rear (nearest image space), with linear measurementsgiven in millimeters. The first column gives the signed radius of curvature of a spherical element; if none is given, the surface is planar.A positive radius of curvature indicates a surface that is convex when viewed from the front of the lens, while a negative radius ofcurvature is concave. The next entry is thickness, which measures the distance from this surface to the next surface along the centralaxis. Following that is the index of refraction at the sodiumdline (587.6 nm) of the material on the far side of the surface (if none isgiven, the material is assumed to be air). Next is the V-number of the material, characterizing the change of index of refraction withwavelength. The last entry is the diameter, or aperture, of each lens element. The row
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