L7 2012 OPTI517 Ray Tracing - University Of Arizona
Ray TracingLens Design OPTI 517Prof. Jose Sasian
Prof. Jose Sasian
Use of rays In optical designIn computer graphicsIn acousticsIn artIn photographyRay tracing universeProf. Jose SasianLens design ray-tracing
Ray tracing It is important to have an understanding about how an optical designprogram works.Most calculations are done by real ray tracing to within the computerprecision.XYZ coordinates, ray fans, wave fans, spot diagrams, apertures,wavefront deformation, optimization, field curves, etc.Sequential ray tracing vs. non-sequential ray tracingProf. Jose Sasian
Ray tracing Algorithm Each coordinate system is local to a surface and it isreferenced with respect to the previous surface.We have local XYZ coordinates for a ray intersection.A surface is locally defined by a function F(x,y,z) f(x,y) - z 0Local vs. Global coordinate systemsUDS and other surface typesStandard surfaceClose form equation for ray intersection for conicsIterative approximation for aspherics and othersurfacesProf. Jose Sasian
A bit of historical perspective Graphical ray tracingParaxial ray tracingLogarithmical or Trigonometrical ray tracingMeridional rays, (L,U) Method, (Q,U) MethodSkew raysHundreds of papers on the subject of ray-tracing (efficiency andprecision)ReferencesR. Kingslake’s Chapter 2R. Shannon’s Chapter 2.1.2W. Welford, Aberrations of optical systems, “finite ray tracing.”Prof. Jose Sasian
Some early papersProf. Jose Sasian
Some early papersProf. Jose Sasian
Ray tracing algorithm x kjj x k, yj,zj j 1,l j , m j j surface, y j 1 , z j 1 j 1, l j 1 , m j 1 j 1 surfaceGiven the Xj, Yj, Zj coordinates of a ray at the (j) surfaceof an optical system with the optical direction cosines Kj, Lj, Mjof the ray in the space following that surface, we wish to find thecoordinates of the ray at the j 1 th surface and the optical directioncosines of the ray after refraction, reflection, or diffraction at that surface.Prof. Jose Sasian
Single ray trace1) Transfer to next coordinate system;account for displacements and rotations.2) Conic or aspheric intersection3) Refraction, reflection, diffraction4) Return new coordinates, directioncosines, and optical path.5) Next surfaceProf. Jose Sasian
Multiple ray trace (ray fan)1) Define field point2) Generate loop that defines fan of raysthrough range of direction cosines.3)Trace chief ray first, surface after surfacethrough image plane4) Save coordinates5) Trace other rays, subtract chief raycoordinates, plot.Prof. Jose Sasian
Zemax DLL: code efficiencyProf. Jose Sasian
Zemax DLL : code efficiencyProf. Jose Sasian
Program output Title: P RUDOLPH TESSAR USP#721240Date : TUE SEP 23 2003Units: MillimetersWavelength : 0.587562 micronsCoordinates : LocalDirection cosines are after refraction or reflection from the surface or object.Normalized X Field Coord (Hx) : 0.000000Normalized Y Field Coord (Hy) : 0.000000Normalized X Pupil Coord (Px) : 0.000000Normalized Y Pupil Coord (Py) : 1.000000Real Ray Trace Data:SurfX-coordY-coordZ-coord X-cosine Y-cosine Z-cosine X-normal Y-normal Z-normal Angle in Path lengthOBJInfinityInfinityInfinity 0.0000000 0.0000000 1.00000001 0.000000E 000 3.934634E 001 0.000000E 000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 -1.0000000 0.000000.000000E 0002 0.000000E 000 3.934634E 001 1.655511E 001 0.0000000 -0.2905639 0.9568556 0.0000000 0.7149388 -0.6991870 45.638186.155511E 0013 0.000000E 000 3.773702E 001 -2.145273E 000 0.0000000 -0.4950848 0.8688447 0.0000000 -0.1133297 -0.9935574 23.399015.538579E 0004 0.000000E 000 3.710166E 001 -1.103024E 001 0.0000000 -0.0559880 0.9984314 0.0000000 -0.5463095 -0.8375834 62.789541.283350E 0005 0.000000E 000 3.637227E 001 -2.023041E 000 0.0000000 -0.1408544 0.9900303 0.0000000 -0.1108978 -0.9938318 9.576621.302764E 0016 0.000000E 000 2.612534E 001 0.000000E 000 0.0000000 -0.1408544 0.9900303 0.0000000 0.0000000 -1.0000000 8.097297.274832E 001Paraxial Ray Trace Data:SurfX-coordY-coordZ-coord X-cosine Y-cosine Z-cosineOBJInfinityInfinityInfinity 0.0000000 0.0000000 1.00000001 0.000000E 000 3.934634E 001 0.000000E 000 0.0000000 0.0000000 1.00000002 0.000000E 000 3.934634E 001 0.000000E 000 0.0000000 -0.2278490 0.97369653 0.000000E 000 3.373024E 001 0.000000E 000 0.0000000 -0.3691049 0.92938774 0.000000E 000 2.975875E 001 0.000000E 000 0.0000000 -0.1173775 0.99308745 0.000000E 000 2.928597E 001 0.000000E 000 0.0000000 -0.2169305 0.97618716 0.000000E 000 1.373042E 001 0.000000E 000 0.0000000 -0.2169305 0.9761871Prof. Jose Sasian
Ray tracing pitfalls Total internal reflectionThe ray misses the surfaceTwo possible intersectionsRay intersection point at some asphericsurfaces may not be found with theiterative algorithmProf. Jose Sasian
Surface types SphereConicsCartesian ovals (no implemented)Even polynomialsOdd polynomialsZernike surfacesMany, many moreUser defined surfacesProf. Jose Sasian
Summary Understanding ray tracing is critical inoptical design Ray tracing pitfalls Speed and precision Skill of user defining surfaces (UDS)Prof. Jose Sasian
Sep 23, 2003 · Ray tracing It is important to have an understanding about how an optical design program works. Most calculations are done by real ray tracing to within the computer precision. XYZ coordinates, ray fans, wave fans, spot diagrams, apertures, wavefront deformation, optimization, field curves
The goal of ray tracing is to compute intersections between rays and objects. Since ray tracing often uses only triangles as its geometric representation, we focus on ray tracing triangles in this survey. The main obstacle for efficient ray tracing is that the number of rays and triangles can be extremely large. For example, using a resolution
MDC RADIOLOGY TEST LIST 5 RADIOLOGY TEST LIST - 2016 131 CONTRAST CT 3D Contrast X RAYS No. Group Modality Tests 132 HEAD & NECK X-Ray Skull 133 X-Ray Orbit 134 X-Ray Facial Bone 135 X-Ray Submentovertex (S.M.V.) 136 X-Ray Nasal Bone 137 X-Ray Paranasal Sinuses 138 X-Ray Post Nasal Space 139 X-Ray Mastoid 140 X-Ray Mandible 141 X-Ray T.M. Joint
The OptiX Ray Tracing SDK. 5 RELEASE TIMELINE Jan 2016 Summer 2016 TODAY! OptiX 3.9 Pascal Support OptiX 4.0 LLVM Pipeline NVLINK Scaling OptiX 4.1 Performance CUDA 8, VS2015 2009 OptiX 1.0 Hello World!. 6 MODERN RAY TRACING Rasterization: 7 MODERN RAY TRACING Rasterization: Ray Tracing: 8
Possibly: OptiX speeds both ray tracing and GPU devel. Not Always: Out-of-Core Support with OptiX 2.5 GPU Ray Tracing Myths 1. The only technique possible on the GPU is “path tracing” 2. You can only use (expensive) Professional GPUs 3. A GPU farm is more expensive than a CPU farm 4. A
γ-ray modulation due to inv. Compton on Wolf-Rayet photons γ-ray and X-ray modulation X-ray max inf. conj. 2011 γ-ray min not too close, not too far : recollimation shock ? matter, radiation density : is Cyg X-3 unique ? X-rays X-ray min sup. conj. γ-ray max
Ray Tracing uses packets and frustum culling Rasterization is ugly Ray Tracing is clean . NVIDIA SIGGRAPH 2008 Demo NVSG-driven animation and interaction Programmable Shading Modeled in Maya, imported via COLLADA Fully Ray Traced 2 million polygons Bump-mapping Movable light source
3.1. Ray Tracing Ray tracing is the rendering process of projecting rays through each pixel into a 3D scene to compute intensity. For a given pixel p i [x i;y i], the equation for a ray V i is given by V i C 0 t norm( ) (1) where C 0 is the camera center, and R0 A 1 [x i;y i;1] (2) where Ais the camera matrix,and Ris the camera rotation.
ASME BPV CODE, EDITION 2019 Construction Code requirements Section VIII, Div. 1, 2 a 3 ; Section IX ASME BPV Section V, Article 1, T-120(f) ASME BPV Section V, Article 1, Mandatory Appendix III ASME BPV Section V, Article 1, Mandatory Appendix II (for UT-PA, UT-TOFD, RT-DR, RT-CR only ) SNT-TC-1A:2016; ASNT CP-189:2016 ASME B31.1* Section I Section XII ASME BPV Section V, Article 1, Mandatory .
