几何光学101:近轴光线追迹计算.docx
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1、Geometrical Optics 101: Paraxial Ray TracingCalculationsRay tracing is the primary method used by optical engineer to determine optical system performance. Ray tracing is the act of manually tracing a ray of light through a system by calculating the angle of refraction/reflection at each surface. Th
2、is method is extremely useful in systems with many surfaces, where Gaussian and Newtonian imaging equations are unsuitable given the degree of complexity.Today, ray tracing software such as ZEMAX or CODE V enable optical engineers to quickly simulate the performance of very complicated systems. Para
3、xial ray tracing involves small ray angles and heights. To understand the basic principles of paraxial ray tracing, consider the necessary calculations and ray tracing tables employed in manually tracing rays of light through a system. This will in turn highlight the usefulness of modern computing s
4、oftware.PARAXIAL RAY TRACING STEPS: CALCULATING BFL OF A PCXLENSParaxial ray tracing by hand is typically done with the aid of a ray tracing sheet (Figure 1). The number of optical lens surfaces is indicated horizontally and the key lens parameters vertically. There are also sections to differentiat
5、e the marginal and chief ray. Table 1 explains the key optical lens parameters.To illustrate the steps in paraxial ray tracing by hand, consider a plano-convex (PCX) lens. For this example, #49-849 25.4mm Diameter x 50.8mm FL lens is used for simplicity. This particular calculation is used to calcul
6、ate the back focal length (BFL) of the PCX lens, but it should be noted that ray tracing can be used to calculate a wide variety of system parameters ranging from cardinal points to pupil size and location.Figure 1: Sample Ray Tracing SheetTable 1: Optical Lens Parameters forRay TracingVariable Desc
7、riptionCCurvaturetThicknessnIndex of Refraction由Surface PoweryRay HeightuRay AngleStep 1: Enter Known ValuesTo begin, enter the known dimensional values of #49-849 into the ray tracing sheet (Figure 2). Surface 0 is the object plane, Surface 1 is the convex surface of the lens, Surface 2 is the plan
8、o surface of the lens, and Surface 3 is the image plane (Figure 3).Remember that the curvature (C) is equivalent to 1 divided by the radius of curvature (R).The first thickness value (t) (25mm in this example) is the distance from the object to the first surface of the lens. This value is arbitrary
9、for incident collimated light (i.e. light parallel to the optical axis of the optical lens). The index of refraction (n) can be approximated as 1 in air and as 1.517 for the N-BK7 substrate of the lens.In Figure 2, the red box is the value to be calculated because it is the distance from the second
10、surface to the point of focus (BFL). The power (中)of the individual surfaces is given by the fourth line and is calculated using Equation 1Note: A negative sign isadded to this line to make further calculationseasier. In this example, Surface 1 is the only surface with power as it is the only curved
11、 surface in the system.中=(n2 - nJFigure 2: Entering Known Lens Parameter Values into Ray Tracing SheetSurface 0Figure 3: Surfaces of a Plano-Convex (PCX) LensStep 2: Add a Marginal Ray to the SystemThe next step is to add a marginal ray to the system. Since the PCX lens is spherical with a constant
12、radius of curvature and a collimated input beam is used, the ray height (y) is arbitrary. To simplify calculations, use a height of 1mm.A collimated beam also means the initial ray angle (u) is 0 degrees. In the ray tracing sheet, nu is simply the angle of the ray multiplied by the refractive index
13、of that medium. Both variables are included to make subsequent calculations simpler (Figure 4).Surface234LOCO1.ODDOOFigure 4: Adding a Marginal Ray to the Ray Tracing SheetStep 3: Calculate BFL with Equations and the Ray Tracing SheetRay tracing involves two primary equations in addition to the one
14、for calculating power. Equations 2 - 3 are necessary for any ray tracing calculations.(2)where an apostrophe denotes the subsequent surface, angle, thickness, etc. In this example, to find the ray height at Surface 2 (y), take the ray height at Surface 1 (y) and add it to -0.0197 multiplied by 3.296
15、:yr = y + ut.=y + ; n u 7tmiw一(2.1)Performing this for ray angle yields the following value. The entire process is repeated until the ray trace is complete (Figure 5).7tU = TttA 夺-二匚,川妲5扬匚2- Ml幻(3.1)Surface-012340.00000-0.01970401970Figure 5: Propagating the Ray through the SystemNow, solve for the
16、BFL by either adjusting the thickness value until the final ray height is 0 (Figure 6) or by backwards calculating the BFL for a ray height of 0. Fo#49-849, the final BFL value is 47.48mm. This is very close to the 47.50mm listed in the lens, specifications. The difference is attributed to the round
17、ing error of using an index of refraction of 1.517 instead of a slightly more accurate value that was used when the lens was initially designed.Surface-QD3B10251颇5.001.5172t/n-0.0196952380047.477715481.00040o.(woi 0.00000硕加Until the Ray Height al the Image Plane k 0Figure 6: Calculating Back Focal L
18、ength of a Plano-Convex (PCX) Lens using a Ray Tracing SheetDECIPHERING A TWO LENS RAY TRACING SHEETTo completely understand a ray tracing sheet, consider a two lens system consisting of a double-concave (DCV) lens, an iris, and adouble-convex (DCX) lens (Figures 7 - 8). To learn more about DCV and
19、DCX lenses, please readUnderstanding Optical Lens GeometriesFigure 7: Double-Concave (DCV) and Double-Convex (DCX) Lens SystemSurface0123456oiao0.01000.00M-0.025055.&025.00J5.00E.OO115.Wn1.K01.517l.flOQ1.0001.517 LOCO-中0.00520.00530.0000-0.01M-0.0129t/n5.00003濒25.00W25.00005.373i115.48?7MARGINAL RAr
20、0.00000 OJ17O31.1 烦45.。枷S.S0M& M09150.000000.142410.1 W 0.152260.1 W O.Q38I1-0.07801CA11.512.510.030.030.0CA/(y ty)皿Z湖2.000Figure 8: Sample Double-Concave (DCV) and Double-Convex (DCX) Ray Tracing SystemThe aperture stop is the limiting aperture and defines how much light is allowed through the syst
21、em. The aperture stop can be an optical lens surface or an iris, but it is always a physical surface. The entrance pupil is the image of the aperture stop when it is imaged through the preceding lens elements into object space. The exit pupil is the image of the aperture stop when it is imaged throu
22、gh the following lens elements into image space.In an optical system, the aperture stop and the pupils are used to define two very important rays. The chief ray is one that begins at the edge of the object and goes through the center of the entrance pupil, exit pupil, and the stop (in other words, i
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