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摄像机标定原理1、像素坐标系UOV以像素为单位，原点在图像左上角，向左为u+,向下为v-。
2、成像平面坐标系X I O I Y I成像平面坐标系建立在成像平面上，对于数字摄像机来说，成像平面即为相机CCD（或CMOS）感应元件平面，成像平面与光轴的交点即为原点，单位为mm。
假设成像平面坐标系原点O I在像素坐标系UOV中的坐标为（u0，v0）,对于图像平面坐标系中的点(u,v)，成像平面坐标系中的点（x1 ,y1）,它们之间的关系如下：u=x1dx+u0v=y1dy+v0其中， dx和dy表示图像中每一个像素在成像平面上对应的物理尺寸，通俗地讲，面积为dx∗dy（单位为mm2）的小单元在图像中表现为一个像素。
我们将上面两个等式改写为矩阵形式为：[uv 1]=[1dx 0u 001dy v 001][x 1y 11] 3、相机坐标系O c −X c Y c Z c相机坐标系O C 建立在摄像机上，坐标原点与投影中心(光心)重合，Z C 轴与成像透镜光轴重合，X C 和 Y C 分别与成像平面坐标系的X I 和 Y I 平行，图中O C O I 的距离即为相机焦距f 。
由透视投影模型可得，摄像机坐标系下的物点P(x c ,y c ,z c )与成像平面坐标系中的点(x 1,y 1)之间的变换关系为：x 1=f x cz cy 1=f y cz c写成矩阵形式为：z c [x 1y 11]=[f 00 0f 0 001 000][x cyc z c1]内部参数矩阵[uv 1]=[1dx 0u 001dy v 0001][x 1y 11]两边同时乘以z c 得 z c [u v 1]=[1dx 0u 001dyv 001]z c [x 1y 11]=[1dxu 01dyv 0001][f 00 0f 0 001 000][x cy c z c 1]=M 1[x cy cz c 1] 其中 M 1=[1dxu 01dyv 001][f 00 0f 0 001 000]=[fdxu 00f dyv 0001]，M 1只与相机的内部参数结构有关，称为相机的内部参数矩阵。
Important question•Why is this toy so expensive–EF 70-200mm f/2.8L IS USM•Why is it better than this toy?–EF 70-300mm f/4-5.6 IS USM•Why is it so complicated?•What do these buzzwords and acronyms mean?Affected by sensor size24mm 50mm 135mmLens quality varies!source: the luminous landscapesource: the luminous landscape•/equipment/canon/70-300do_2/Image corners are often sacrificed •/equipment/canon/70-300do_2/•/equipment/canon/70-300do_2/Gets better when stopped down •/equipment/canon/70-300do_2//equipment/canon/70-300do_2/Again, better when stopped down •/equipment/canon/70-300do_2/Power of lenses•(full aperture, 135mm)source: canon red bookWhy are lenses so complex?•It’s not so easy to send light where it should gosource: canon red bookFrom Ray's Applied Photographic OpticsFrom Ray's Applied Photographic Optics•Wave optics: diffraction problemsFrom Optical System Design by Fisher and TadicGeeky jokeAt first God saidand there was light(interestingly, the jokehas a higher Googlerating than the actualbook of Genesis)Equations from /physics/MaxwellEquations.htmlFrom Hecht's OpticsLots of things get linearizedIncoming coherent plane wave, apertureFourier transformsame path length in bluephase differencemono-chromaticplanewaveIntegral ofshifted/scaledwaveDCAbsolute limit on lensFrom Hecht's Optics Lens diffraction •http://luminous-/tutorials/understanding-series/u-diffraction.shtml(heavily cropped)Lens diffraction•http://luminous-/tutorials/understanding-series/u-diffraction.shtml(heavily cropped)•See alsohttp://www.cambridg/tutorials/diffraction-photography.htmPhoto by Eric Chansource: Hecht Optics will become spherical)From Optical System Design by Fisher and TadicAspherical lensessource: canon red booksource: canon red booksource: canon red bookFrom Hecht's OpticsAstigmatism source: canon red bookDefects source: canon red bookCurvature of fieldsource: canon red bookChromatic aberration•The previous aberrations depend on wavelength(because of varying index of refraction)source: canon red book/optics/chromatic.htmlFrom Hecht's Opticsexpensive and usually not used for cheaper heavily so the effect is often downgraded to a lens will always feature two or more of these special http://www.photozone.de/3Technology/lenstec8.Fluorite•Low dispersionsource: canon red bookDiffractive optics (DO)source: canon red bookFrom Optical System Design by Fisher and Tadicsource: canon red bookEnables smaller lenseserrationUse this instead of normal projectionsource digital outbackGeneral principle•Calibrate lens•Perform image warp•Perform different warps for various color channelsFrom the luminous landscape /reviews/chromatic.shtmlCorrected with Picture Window 3.1From DXOFlareFrom "The Manual of Photography" Jacobson et alOptimized for one wavelengthFrom "The Manual of Photography" Jacobson et alFrom Ray's Applied Photographic Opticssource: canon red bookAdapted from Ray's Applied Photographic Optics Hood is to shortFlare rayGood hoodFlareFighting reflectionssource: canon red book From Optical System Design by Fisher and TadicFlare/ghosting special to digital source: canon red bookCoating for digital source: canon red booksource: canon red book Vignetting•http://www.photozone.de/3Technology/lenstec3.htm •/Pdf_files/how_to_measure_mtf.pdfInputAfter lens /docs/sharpness.htmlSharpness MTF•ModulationTransferFunction•Preety muchFouriertransform oflens response•Complexbecauseneeds to bemeasured atmultiplelocationsource: canon red book Here the x axis is image location Blur index based on Photoshop!Optimization software•Has revolutionized lens design• E.g. zooms are good nowFrom Hecht's OpticsLens design, ray tracing source: canon red book(but are not responsible for focusing) source: canon red bookImage stabilizationsource: canon red bookImage stabilization source: canon red bookImage stabilization source: canon red book1000mm, 1/100s, monopod, IS•/articles2/rubinar/500mm vivitar($100)500mm Canon (5k)References。
