?_> .%l!\FRayHelp1982 - presentBrowseButtons()ZmainRay HelpUZpopupK8  ray.cnt /&;)z4 y |CONTEXT|CTXOMAP|FONT |KWBTREE|KWDATA>|KWMAPs|SYSTEM|TOPICm|TTLBTREE|bm0%|bm1+" > J1[ JHelp Contents7 & "Help ContentsJ_U xfp~,lRay is a program that traces of ray through an optical system to evaluate aberrations via spot diagrams and spot statistics. A number of surface types (conic, aconic, diffraction grating, central obscuration, etc.) can be specified. There is also a method for doing some optimization of the optical system.ContentsGeneral DescriptionMain WindowPrescription Parametersb"@ PDPllWindowSurfaces TypesE_. ,.PJTrace Parameters GM. ,2P㼛Parameter Variation(u% P; M. ,POutputsFu. ,0P㙪kNote on dimensions(% PEc. ,.PpkRayTrace Tutorial(% PCc. ,*PwProgram History> ) "*XRevision History(4% XwL + &XnꉂThis help file was created with the free trial version of HelpScribble.D41F General DescriptionW$F3 6H-i General DescriptionContents&l# Fo ; D!Aa%RAY is a general ray-trace program that will trace rays through a specified optical system and generate spot diagrams as well as RMS statistics and focal shift information. Conic and aconic surfaces of revolution are allowed as are cylindrical conic sections, toroidal surfaces, diffraction gratings, prisms, aperture stops and obscurations. All of these surfaces can be tipped and/or offset from the optical axis. Real co-ordinate transformations (both displacements and rotations) are allowed to ease the specification of "bent" systems such as spectrometers. A total of 30 surfaces are permitted including all optical elements and dummy surfaces inserted for obscurations and coordinate transformations.o5l : Bk!Aa%Although RAY does not perform optimizations in the manner of commercial ray-trace programs, automated variation of parameters for optical elements is possible and several different metrics can be tabulated vs. the varied parameters. This allows for a fairly straightforward and easy optimization process. <o  9 B!Aa%< V 9 B!Aa%L ? N!Aa%nꉂThis help file was created with the free trial version of HelpScribble.@V ! 1O! v Program HistoryU" v 3 6D-i Program History Contents&! # Z v : BA!Aa1RAY was originally written by Jim Houck to run under CP/M machine in the early 1980s. Terry Herter ported the program to the PC. Since then both authors have made changes to improve capabilities of RAY. Although not a full-scale professional ray tracing program, RAY is very capable. > 4; F!Aa1^ ; F!Aa1In 2002 the program was converted to run under Windows. Before then it ran under MS-DOS.<4 9 B!Aa1L? N!Aa1nꉂThis help file was created with the free trial version of HelpScribble.< 1.@BMain Windowf@W ~-i @J ,l 㼛 Main Window Contents Trace window Prescription window Variation window Bg /J ,l 㼛  "nꉂA snapshot of the main window for Ray is shown below. This window enables reading and writing of prescription (.ray) files, display system and illumination plots, and data output. In addition, the trace, prescription, and variation windows are made visible here. Click on a location for more information.This help file was created with the free trial version of HelpScribble.8@B1BqDFile IOhBqD; DnꉂFile I/OOptions are:New - Start a new prescription (clears the current prescription).Load - Read in a prescription from disk. The default file extension is "ray".Save - Save current prescription to disk. If this is a new prescription then a file name will be requested.This help file was created with the free trial version of HelpScribble.IBD1D0HSpot Diagram/System PlotqDFZ s J  J  Spot Diagram/System PlotSpot Diagram:Perform a spot diagram for the current prescription using the parameters set up in the trace parameters window.System Plot:Traces a limited set of rays through the system and shows their path along with sketches of the optical elements. The settings for the system plot can be changed in the trace parameters window. Notes: 1. System plots typically do spot diagrams as well.c3D0H0 .gnꉂ2. When coordinate transformations are present, system plots will not work properly (or at be easily intelligible).3. Use the "magnification" factor if the either the vertical or horzontal dimension of the system are off scale.This help file was created with the free trial version of HelpScribble.EFuH1suHLMatrix/Variation Run_0H K7 <㼛 Matrix/Variation RunStep through a set of specified parameter values (such as a change in radius of curvature of a surface and the off-axis distance of a source together). Parameters are set in the variation parameters window. A "list" of outputs must be specified. These are listed on the "Output" tab of the main window. This allows parameters to be varied in a systematic way.A variation table is 4 columns by 9 rows in size. Each table entry can change any parameter in the prescription or a trace parameter. There are two ways to then "vary" parameters while performing spot diagrams.XuHL@ N  nꉂVariation run: Step through each line (up to 9 lines) with up to 4 parameters changing on each line, e.g. 1, 2, 3, 4 change together (line by line)Matrix run: Step through each line of columns 1 and 2 for every line of columns 3 and 4, e.g. (1,2) x (3,4)This help file was created with the free trial version of HelpScribble.: KL1LNPlot AreaLNL f)J ,l nꉂPlot AreaSpot diagrams and surface illumination plots appear in this area. Spot diagrams are the default. To view the illumination of a surface either set the "View Surface" in the trace parameters window to the surface number (a non-zero value) or use the "View Illumination" button in the prescriptions window.This help file was created with the free trial version of HelpScribble.ALN1SNRefocus/RecenterN6 :nꉂRefocus/RecenterWhen a spot diagram is present, this will refocus to the best average focus of the spots. When viewing a surface illumination, this will center the surface.Note: There are times wheNNn this can go astray, particularly when there are coordinate transformations, tips, and decenters. As a safety precaution you should save your work before trying this - RAY has no undo command!This help file was created with the free trial version of HelpScribble.AN]1 ]Meridional Trace]4 6nꉂMeridional TraceThis will trace a set of rays in the meridional plane giving estimates for spherical aberration (L - l), astigmatism, and coma by comparing a paraxial ray and marginal ray. Right now this doesn't work if the first element of the system is decentered.This help file was created with the free trial version of HelpScribble.< ]*1 *Color Trace6 :)nꉂColor TraceWill successively the three different wavelength codes (which in general have different indices of refraction) through the system. These will appear as different colors.The biggest mistake here is forgetting to update all the wavelength codes (e.g. for a mirror all three wavelength codes must be changed). This help file was created with the free trial version of HelpScribble.A*51P 5DWindow Show/HideDX ~o,l J 㼛 nꉂWindow Show/HideShow or hide the prescription, trace parameter, and/or variation windows.This help file was created with the free trial version of HelpScribble.< 51K @Trace ParmsODK f-i ,l 㼛 Trace Parms Contents Prescription parms Variation parms<V% /The trace window is used for setting the parameters for the ray trace not specified with the optical elements. These include the location of the object field (and distance), the number of rays to trace, the type of pattern, etc. Fields in the trace window are listed below.3 ( ( Startup)V W |SP}~     Object Field:Near or far field for the for the object. Distance:Distance to the object. Applies only to the near field case.dx,dy:Off-axis location of the object. Measured in degrees for the far field case and in linear dimensions for the near field case.Starting Index:The starting index of refraction (before the first surface, usually 1)Wvlngth Code:The wavelength code to study chromatic aberrations. A value of 1 selects the following index for each surface. While 2 selects the short index and 3 selects the long index.bkG \7P}~   Back Focal Dist.The distance from the last element to the focal plane. It follows all of the usual sign conventions for thickness values.Spot DiagramsNo. of Panels:The number of panels (spot diagrams) to perform. This allows several sets of bundles of rays to be traced through the system at one time, e.g. the four corners of a camera's field-of-view. Typical numbers are 1, 4, 9, 16, etc. Spot diagrams are traced starting at -|DX| to |DX| and |DY| to -|DY| with increments appropriate for the number of panels chosen.T @ N)P}~  No. of Rays:The minimum number of rays that will be followed all the way to the focal plane. If there is a lot of obscuration then things will slow down as a large number of rays must be tried before the required number reach the focal plane.View Surface:View illumination of the selected surface. Normally this is set to 0 for a standard spot diagram. Setting it equal to the number of the focal plane will show spot diagrams within the context of the entire focal plane area, not just the area about the chief ray. Ck@ NP}~  DPlot Scale:Sets the full scale of size of a spot diagram. A scale (per tic) will be listed below the plot. This will usually be 10 to 20 times smaller than the full scale value (10 or 20 tics per plot). For instance, this might be set to some fraction (or factor) of the pixel size.Ray Pattern:Selects from list of available input ray patterns. This is the llumination pattern of the first optical element. Options include: inscribed square, circumscribed square, bull's eye, random, and "plus" signIS tP}~    Refocus:Causes the best focus to be plotted for each pixel. This does not change the output data.Recenter Colors:Recenters plots for each color, otherwise plots are centered on the following index.Overlay Colors:Combines stats and plots for all wavelengths. For instance this would give an estimate of the total aberration of a lens.List Central Ray:List the intersection coordinates of the central ray with each surface. There are three options which are labelled 0, 1, and 2. These produce the following for each element (Cx = direction cosine in x, etc) :PT vP}~   0:x, y, z, Cx, Cy, Cz, path1:x, y, z, atan(Cx/Cz), atan(Cy/Cz), abs(z)2:x, y, z, 90-acos(Cx), 90-acos(Cy), acos(Cz), abs(z)System PlotsStart Surface:Surface where system plot starts. For instance, if you have a telescope in front of an instrument, you can start the system plot at the element where the instrument starts rather than the telescope.No. of Rays:This is the number of rays used for the system plot. Typically reasonably small number (~10) to avoid a confusing plot.QR rP}~    Magnification:Set the vertical to horizontal scale ratio. This allows adjustment for "thin" or "fat" systems.Off Axis Tolerance:For asymmetric systems, this sets the tolerance for graphing only one-half of an optical element. Axis Select:Change the view of the optical system, e.g. x,z or -z,x or -y,z. Any combination and signs are allowable, except the two axes cannot be the same and one must be the z-axis.1-D rays:System plot rays are only in one direction. This works well for most cases but you aren't seeing the full illumination try turning this feature off.S9I `P}~   Element ListsThe locations of the elements are listed on the Elements tab of the main window. For each element the x, y, z coordinates of the vertex are listed along with the tip of the element (alpha, beta, and gamma). There are two options.z start:Adds this offset to the z position of the element list. This can be handy to cause the coordinates to center about a given element.Extended Listing:Gives more info on the elements that the standard listing. Also included are surface type, radius of curvature, eccentricity, aperture, following distance, and following index.1j. ,Pm~-9* $-j* $|L@0 0nꉂThis help file was created with the free trial version of HelpScribble.= }1 }DOptimizationp@DW ~-i J ,l 㼛 Parameter Optimization Contents Trace window Prescription window Variation windowQ}0 0nꉂThis help file was created with the free trial version of HelpScribble.@D1" MVariation Parms p -i ኯa vxW D ,l J Variation Parms Contents Parm Codes Save Codes Command Codes Prescription parms Trace parms + $The variation function in Ray provides the ability to change a parameter or set of parameters and view the results (such as the change in rms spot size or the location of the spot). For instance, the input offsets can be varied or wavelengths (and indices of refraction) can be changed over a wider range than possible with just the trace and prescription parameters. It also provides a somewhat primitive capability to do optimization, but one which works well if there are only a few parameters to vary. This is especially useful since plots can easily be done between the varied parameters and the outputs (such as rms spot size, minimum rms spot size, focus shift, etc. Parameters changed by the variation table take effect before the start of the trace. For instance, if an entry changes the radius of curvature for surface 2, this will override the previous value in the prescription. All parameters are returned to their previous values when a variation (or matrix) run is complete.2 O. * You can either step through 9 different configurations while changing up to 4 parameters in each, or you can do a matrix run of up to 9 configurations by 9 configurations while changing two parameters in each. There are 10 different "variation planes" you can set up (each of which can be assigned a name for ease of recalling its purpose). Selection of the "cell" to edit is done via the arrow keys (or selecting with the mouse).Some example commands are given below (assuming upper left region is selected):-|* $l.O> J]Py~vary ec 2 0.8 1.2Vary the eccentricity of surface 2 from 0.8 to 1.2 in current columnvary dx -0.1 0.1Vary the x-offset from -0.1 to 0.1 in the current column (for far-field this is in degrees)ra 3 510.2Change the radius of curvature of surface 3 to 510.2.npChange to next variation plane (up to 10, will wrap at 10)vpName focus testSet name of current variation plane to "focus test"mrDo a "matrix" runvrDo a "variation" run (line by line)You must also specify the parameters you want to appear on the "Outputs" tab of the main window, e.g.1| . ,Py~ 3 4P|list ec 2 raycnt avg_x rms sm_rms delta_zList eccentricity of surface 2, the ray count, average x position, rms spot size, smallest rms spot size, and the delta z (distance) between the two.list dx dy raycnt avg_x avg_y rms sm_rms delta_zList x and y offsets, the ray count, average x and y positions, rms spot size, smallest rms spot size, and the delta z (distance) between the two.5   , &You will notice that after a command is executed it is stays in the command line but is highlighted. This makes it easy to type to execute the command again or start typing to write over it. There is no command recall (such as using the up arrow key).1 9 . ,P}~  + $1Here are a listing of the various options for the command line. "n" refers to a surface number (1, 2, 3, ...) and "v" to a value (1.23, 56.3, etc.):E9 A 5 : P}~ Parm Codes  aM hPQAll these are of the form RA n v which sets the radius of curvature of surface n to value vRA n vRadius of curvatureEC n vEccentricityAP n vAperture (currently you can not change the second aperture value)FT n vFollowing ThicknessFI n vFollowing IndexSI n vShort IndexLI n vLong indexFA n vFourth order aconicSA n vSixth order aconicEA n vEighth order aconicAT n vAlpha TipBT n vBeta TipGT n vGamma TipXD n vx decenterYD n vy decenterA q@4 6PQZS n vz shiftSS n vchange type of surface (presently disabled)S1 n vchange special coefficient for suaq@rface, e.g. focus for perfect lens. The meaning of this coefficient will depend upon surface typeaBb YPQecentral obs.x-size (diameter if y-axis = 0) perfect lensfocal lengthdiff. gratingwavelengthbranchelement to jump totoroid:x-radiusronchi grat.blocking factorS2 n vLike s1 but applies to the following surface typescentral obs.y-sizediff. gratingordertoroid:y-radiusS3 n vLike s1 but applies toaconic:convergence criteriadiff. grating:groove spacingtoroid:convergence criteria5q@B0 0 PQeQ BDD VPQ CU n vCurvatureBE n1 n2 dvBend surfaces n1 and n2 together by curvature amount dvDXstarting x-offsetDYstarting y-offsetWCwavelength codeBFback focal distanceSave CodesValue you can save (in addition to those above that are sent to the output window.B#FF ZPrmsrms spot sizesm_rmssmallest rms spot sizedelta_zfocus shift from current focus position to smallest spot sizerms_x, sm_rms_x, delta_xsame as above but for x-directionrms_y, sm_rms_y, delta_ysame as above but for y-directionRayCntnumber of rays actually tracedavg_x, avg_y,avg_zaverage position of spotabs_zabsolute z position of spotavg-c_x, avg-c_yaverage direction cosines in x and yL-lspherical aberration estimate (from meridional trace)qDGH ^PD-dDNpath change (from MT)d-dDnMaxmax path change (from MT)CRHChief ray heightRTFRadius tangent fieldAstigastigmatism (from MT)Comacoma (from MT)x_c, y_c, z_cposition of central rayat(Cx/Cz), at(Cy/Cz)angular slope of central ray90-ac(Cx), 90-ac(Cy)90-slope of central ray in x or y (from direction cosine)ac(Cz)angle of z-direction cosineH#F$H5 :&PQ Command Codes-GQJ= HPList parm1 parm2Parameters to save in output window (see examples above)FillFill column with a constant valueVary parm strt stopVary a parameter over start to stop range (see examples above)Delta parm valueVaries parameter over range current_value+-value (value is +- total range)Incr parm valueVaries parameter over range current_value+-4*value (value is step between rows)helpBring up help for variation window - same as "help" buttonPRMove to previous row (same as up arrow)!$HrLL fPNRMove to next row (same as down arrow)PCMove to previous column (same as left arrow)NCMove to next column (same as right arrow)ClrClear current positionClrAllClears all positions (rows and columns)DefSurf nSpecifies default surface (doesn't look for surface number on Parm Codes)VP nSet variation plane to nNPNext variation planePPPrevious variation planeCopy p1 p2Copy variation plane p1 to p2vpName stringSet name of variation planeQJ3M> JP MPGo to modify prescription windowSDSpot diagramVRVariation runMRMatrix runESExit variation window (and close it)+rL^M(  zL3MM. ,nꉂThis help file was created with the free trial version of HelpScribble.8^MN1SNNOutputs^MNW ~-i #, - ̠ Outputs Contents Num Panels = 1 Num Panels > 1 Meridional Trace3N+ $ Following an SD command you will get a list of numbers in the "Spot Listing" tab of the main window. When the number of panels (NP) = 1, you will get a page showing the results of the trace like that below. It will lis the file name and the prescription name (that you'NMve entered through the Edit|Prescription Name menu option. The top row of numbers gives the average position of the rays in the focal plane.File : HBO-EX.RAY Name: HBO Telescope Average Spot Position: X = 0.721171 Y = 0.475973N3 4  Central Ray Values: X = 0.720872 Y = 0.475775 Z = 0.000000 Cx = 0.002179 Cy = 0.001438 Cz= 0.999997 Spot Statistics: ( 486 rays traced in 547 tries) RMS = 0.000287 Sm_RMS = 0.000259 Delta_Z = -0.004268 RMS_x = 0.000219 Sm_RMS_x = 0.000197 Delta_Zx = -0.004711 RMS_y = 0.000185 Sm_RMS_y = 0.000168 Delta_Zy = -0.003825 Bull's Eye pattern traced.The central ray data lists the coordinates of the central ray (the one going through the center of the first surface) in the focal plane relative to the geometric axis of the system. Note: the focal plane can be tipped, curved, etc. just like any other surface. Note too: central rays have the ability to go through an obscuration. The spots on the spot diagram are plotted relative to the location of the central ray. The direction cosines are also listed for the central ray.sd3 4l A line giving the number of rays reaching the focal plane and the number of rays tried is displayed next. You can get a rough idea if one or more of the elements is too small by looking at these statistics. A better way to do this is to view the illumination of the surfaces (see the prescription window).Next come three lines each listing the RMS spot size, the smallest RMS spot size (assuming you refocus the system) and the required shift in focus to reach the smallest spot size. You can refocus by manually changing the back focal distance in trace window or by using the refocus button on the main window. m/ , When NP > 1 a different statistical display appears. In this case a summary is given for each set of rays traced. An example for NP = 9 is shown below. The columns are pretty much self-explanatory in that they follow the description given above for NP = 1.File : HBO-EX.RAY Name: HBO Telescope Panel Mode: 9 panels computed 547 rays attempted in bull's eye pattern.Avg x,y,dz = 0.000000 0.000000 -0.002818alpha and beta tilts = -0.03 0.00 degJ d* "A DX DY NumRays Avg. X Avg. Y Z-Center RMS sm_RMS Delta_Z 1 -0.05000 0.03300 486 -0.72117 0.47597 0.00000 2.87e-04 2.59e-04 -0.00427 2 0.00000 0.03300 486 0.00000 0.47597 0.00000 1.46e-04 1.42e-04 -0.00124 3 0.05000 0.03300 486 0.72117 0.47597 0.00000 2.87e-04 2.59e-04 -0.00427 4 -0.05000 0.00000 486 -0.72117 0.00000 0.00000 2.32e-04 2.16e-04 -0.00295 5 0.00000 0.00000 486 0.00000 0.00000 0.00000 2.42e-06 5.05e-07 8.20e-05$mۍ- (  6 0.05000 0.00000 486 0.72117 0.00000 0.00000 2.32e-04 2.16e-04 -0.00295 7 -0.05000 -0.03300 486 -0.72117 -0.47597 0.00000 2.87e-04 2.59e-04 -0.00427 8 0.00000 -0.03300 486 0.00000 -0.47597 0.00000 1.46e-04 1.42e-04 -0.00124 9 0.05000 -0.03300 486 0.72117 -0.47597 0.00000 2.87e-04 2.59e-04 -0.00427 A sample meridional trace output for the on-axis case is shown below. This will give information on spherical and chromatic aberration.&# ۍΎ+ $E Miridional Ray Trace On-axis aberations: L - l = -0.00007101 D - d delta n = 0.00000000 D - d delta n Max = 0.00000000h^( When an off-axis meridional trace is performed, the off-axis aberration coefficients are included.yΎ1 0@ Miridional Ray Trace On-axis aberations: L - l = -0.00007101 D - d delta n = 0.^M00000000 D - d delta n Max = 0.00000000Off-axis aberations: Offaxis distance/angle = 0.05000 Chief ray height = 0.72087 Radius tan field = -115.69326 Astigmatism = -0.00157 Coma = 0.00036S^2 4nꉂThis help file was created with the free trial version of HelpScribble.C14 Note on dimensionsX%43 6J-i Note on dimensions Contents 4 6EnꉂYou are free to use any type of linear dimensions you like i.e. cm or inches but you must be consistent. In the special case of diffraction gratings you must use the same linear dimensions for the wavelength and the groove spacing but these need not be the same units as for thicknesses etc. All angular measures must be in degrees. This help file was created with the free trial version of HelpScribble.B4L1+SL RayTrace TutorialW$ 3 6H-i RayTrace Tutorial ContentsL& This is a step-by-step guide to entering and analyzing a simple prescription using the ray trace program. The user should follow it as he or she sits at the computer. For more detailed information on operation and options with ray, see the other sections of this file.This example examines the 24-inch Hartung-Boothroyd Observatory on Mt. Pleasant. In the following, all distances are in centimeters, and the rays travel primarily along the z-axis.k#) "Starting the programThere are two basic ways to start the program -1) Open a "command prompt" windowp6: BmH Go the directory you would like to run the program and type ray(this assume that ray can be found in the directory path)2) Make a window short cut to ray and use itThis way you can set up the path to find "ray" andthe start up directoryNote: Ray will save its startup parameter (window locations, path to .ray files, etc.) in the start up directory. It will also try to retrieve this information from the start up directory when ray is executed (if an init file is not found ray will look in the directory where the ray executable is located). #I `H    Entering the Presciption:Use the Edit|Prescription Name command to set the prescription name to HBO Telescope.Use the Edit|Prescription command or the "view presciption parms" button to show the prescription windowThen enter the following presciption values (do not use the key or the program will try to do a ray trace which may not work properly at this point - you values will be retained as you move to another field or surface).(% H: , (Pu~HSurface 1:h Pu~      NamePrimaryname of surfaceRadius-500.8negative because center of curvature is negative z-distance from vertexEccentricity1.0eccentricity of a parabolaAperture62.224-inch circular aperture (leave second field as 0.0)Following Dist.-177.96negative z-distance to vertex of next surfaceFollowing Index-1.0refractive index changes sign on reflectionSurface 2:- $* $Pu~;l WPu~       NameSecondaryRadius-207.9Eccentricity1.87Aperture20.0Following Dist.238.97Following Index1.0another reflectionSurface 3:NameFocal Plane$' WNote: Nearly all of the parameters for the last surface (the focal plane) can be left at their default values - it is only necessary to set the following ind; ex to zero.-;F* $Pu~3 4  This is a good time to save the prescription to disk by selecting the File|Save command or using the Save button in the main window.JFN1 22Pu~Start-up Parameters)w& lN2 4  Use the Edit|Trace Parms command or the "view trace parms" button to show the trace parameters window)w>& pJ& Enter the following trace parameters (again don't use the key):>k Pq~       Object FieldFar Fieldincoming ray are parallelStarting Index1.0starting index of refractionNo. of rays500number of rays to traceNo. of panels1just one panel for nowPlot Scale0.002525 microns, the size of one pixel in the (direct) imaging cameraPatternbull's eyedoes a series of concentric circlesWavelength code1we are tracing only one wavelengthm4 6?  Now you are ready to trace rays. To trace rays through the system and look at a "spot diagram" (a plot of the ray intersections with the last surface), use the Run|Spot Diagram command in the main window or use the spot diagram button in any of the windows. A spot diagram will appear on the "spot diagram" tab and statistics of the spot will appear on the spot listing menu. The statistics are show belowR,& X File : HBO-EX.RAY Name: HBO Telescope*m&  c=L& z Average Spot Position: X = 0.000000 Y = 0.000000*v&  <L& , Central Ray Values:c=v& z X = 0.000000 Y = 0.000000 Z = 0.000000c=x& z Cx = 0.000000 Cy = 0.000000 Cz= 1.000000*&  [5x& j Spot Statistics: ( 547 rays traced in 547 tries)iCf &  RMS = 0.000166 Sm_RMS = 0.000000 Delta_Z = 0.006083iC &  RMS_x = 0.000118 Sm_RMS_x = 0.000000 Delta_Zx = 0.006083iCf 8 &  RMS_y = 0.000118 Sm_RMS_y = 0.000000 Delta_Zy = 0.006083* b &  C8  & : Bull's Eye pattern traced.*b  ' p m . * Comparing the rms spot size with the smallest possible rms shows that focusing is necessary. Refocusing can be done with the refocus botton at the bottom right of the main window (refocusing the back focal distance, really the following thickness for surface 2). The spot should now be a well-focused point (and the rms stats will all be zero, as will delta_z).m9  4 6s  To get an idea of what the optical system looks like, do a system plot using the Run|System Plot command in the main window or using the system plot button in any of the windows. The by default system plot displays a view of the rays with the z-axis running horizontally and the y-axis running vertically.:m ) ""Off-axis rays0 P@: B   A common use of RayTrace is to evaluate off-axis aberrations. An example is finding the aberrations at the edge of the HBO CCD camera. This instrument has a field of view of 4 arcmin by 6 arcmin, so to put in a ray at the longest edge, in the trace window set x-offset = 0.05 degrees (which is 3 arcmin). Now do a Spot Diagram again. You should see the fan-like shape characteristic of coma -- but note that it is much smalleP@ r than one pixel (the extent of the plot, as set by plot scale).MA9 @)   To trace rays to all four corners of the array, set y-offset = 0.033 (2 arcmin) and No. of Panels = 9. This will trace rays incoming at angles of +2, 0, and -2 arcmin in the y-direction and +3, 0, and -3 along x. Now a Spot Diagram will produce an interesting plot.)P@A& I AB) "@Adding a Central ObscurationAC. * In a real Cassegrain telescope, the secondary mirror obscures part of the primary. We can simulate this effect by adding a new surface. Enter the prescription window. and make the following additions/changes.B"Eo ?P~        Up/DownMove to the first surfaceInsInsert a surface before the primaryNameSecondary ObscurationName of surfaceAperture62.2 0.0Again a circular aperture (size of primary)Foll. Dist.177.96Distance from second to primary (now in +z-direction)Foll. Index1.0Surface is virtual (no index change)SurfaceCentral ObscurationSelect special type of surfacex-size20.0Size of secondaryT!CvE3 6BP~ y-size0.0Make is circularG"EHH ^    Now do a Spot Diagram (the number of panels is still 9). You won't notice much of a difference in the spot diagrams or statistics, except the number of rays trace will be reduced (from 547 above to 486. A System Plot will now show rays proceeding from the Secondary Obscuration surface to the primary mirror.Viewing the Illumination of an ElementWe can look at the illumination of various elements in the prescription. The simplest way is to go the the presciption window and go to the desired element. Now use the View Illumination button to look at the surface. You can also change the view surface number to a non-zero value in the trace parameters window. Be sure to set it back to zero again when you are done if you use this latter method.JvEI- *:Introducing AsymmetriesCHK@ N    Thus far the prescription is completely symmetric about the z-axis. A real telescope may suffer from misalignment, or one of the optical elements may be purposely tipped. To simulate misalignment of the secondary, we can rotate this surface about the x-axis by changing alpha tip for the secondary to some non-zero value. Try setting alpha tip = 0.0167 (1 arcmin) for the secondary mirror in the prescription modification menu and do a spot diagram with x-offset = y-offset = 0, and No. of Panels = 1. The coma caused by this small misalignment should be evident.~IBN: B   In some situations, it may be desirable to the secondary to bring a different part of the sky onto a fixed detector. Moreover, the point about which the secondary is rotated may not be its vertex. To simulate a tip about another axis, we want to tip the secondary about its vertex, then decenter it. For example, the optimum point in a classical Cassegrain about which to tip the secondary is the focal point of the primary. Set alpha tip = 0.0167 and y-decenter = 0.021 to simulate such a rotation. A spot diagram with x-offset =y-offset = 0 should be much improved -- but this no longer hits the center of the focal plane.K.O- (Can you find y-offset such the spot diagram for the tip, decentered secondary hits the center of the focal plane? (Hint - look at average spot position in the spot diagram statistics).-BN[O* $Pq~).OO& xL[O , (nꉂThis help file was created with the free trial version of HelpScribble.O  COO1 O.Prescription Parms| .c -i l l J 㼛 Prescription Parms Contents Prescript Window Surface Types Trace window Variation windowGOu( ? The prescription (optical parameters) of each surface need to be specified. This is done via the Prescription Window. Below are a list of parameters that must be set for each surface. Note: The last surface (focal surface) is specified by setting the index of refraction to zero..X ~}P9   Name:Specify a convenient name for the surface, e.g. Primary, Secondary, Lyot Stop, etc. Radius:Radius of curvature - double click on "Radius" to change to curvaturera < 0= )center of curvature is to the left of the vertexra = 0= |flat surfacera > 0= (center of curvature is to the right of the vertexAperture:Size of optical elementLet ap[1] and ap[2] represent the two fields which specify the aperture sizeu@ NP9 ap[2] = 0circular with the diameter of element = ap[1]ap[2]<>0rectangular with width = ap[1], height = ap[2]Eccentricity:eccentricity - double click on "Ecc" to change to conic constant (-ecc^2)d aP9 ec = 0sphere0 < ec < 1ellipse,ecc = sqrt(a^2 + b^2)/aec = 1parabolaec > 1hyperbola,ecc = sqrt(a^2 - b^2)/a cY^2The equation of a conic section is: x = -------------------------------- 1 + (1 - c^2 Y^2(1-e^2))Fol. Dist.Following distance - The distance along the optical axis from the vertex of the current surface to the vertex of the next. fd > 0ray going from left to rightY Z P9  fd < 0ray going from right to leftFol. Index:The index of refraction following the surface. If the ray is to be reflected at a particular surface, the sign of the index changes at that surface.fi > 0ray going to the left to rightfi < 0ray going to the right to leftfi = 0surface is the focal planeShort/Long:Short and long refractive indices (corresponding to wavelength codes 2 & 3). This is used for evaluating chromatic aberrations. All spot diagrams are centered on the position of the central ray corresponding to the refractive indices given by the following index. Therefore, any lateral shift for the other colors corresponds to lateral chromatic aberration. A shift in focus corresponds to longitudinal chromatic aberration.F ZP9  Decenters:These are translations in the x, y and z coordinates. They are applied and removed in the same way as rotations. Translations are applied after rotations. Note that the z coordinate is set to 0.0 at the vertex of each surface.Tips:Rotations about the x, y, and z axes, performed in this order. The coordinate system is maintained by rotating the ray before it reaches the surface and de-rotating it after the ray is refracted or reflected.d ` P9  l Aconics:The Fourth, Sixth, Eight, and Tenth order coefficients for Aconic surfaces, e.,g. Schmidt plates. The aconic coefficients are cY^2 x = -------------------------------- + a4*Y^4 + a6*Y^6 + a8*Y^8 + a10*Y^10 1 + (1 - c^2 Y^2(1-e^2))Surface:Specify the type of surface. The default is a conic surface.0- *9L3 69nꉂThis help file was created with the free trial version of HelpScribble.DՏ1ՏPrescription Windowd -iՏ ,l l J 㼛 Prescription Window Contents Prescription Parms Surface Types Trace window Variation windowՏo%  This window allows the optical prescriptions of the various optical elements to be specified. It can be activated with either the Edit|Prescription command or with the prescription button on the main window. A snapshot of this window is shown below. Regions of the image are clickable for more info. The entrance fields that specify the parameters of a surface are described below.0, (  "o6 : nꉂNote - After updating a parameter, you must use or click out of the field for the change to take effect.This help file was created with the free trial version of HelpScribble.> 1O uSurface TypesSuK f-i ,l ,l Surface TypesContents Prescription Parms Prescription Window_ yPF< ,*  'V  Conic:Surface is a conic section with a given eccentricity or conic constant.Aconic:Surface is an aconic (with nominally non-zero aconic coefficients).The convergence limit for surface intersection must be specified. There is a maximum of 10 iterations. The criteria should be ~ 1/4 to 1/20 of the wavelength depending if the surface is refractive or reflective. It must always be greater than 0.Central Obscuration:/u@ NPF<Ul This serves as an inner limit to the surface element. An example is the shadow caused by the secondary of a Cassegrain telescope. The indices before and after the obscuration should be the same. The radius of curvature, eccentricity, etc. have no meaning.The sizes are specified like those for the aperture (outer size) of an optical element - Let co[1] and co[2] represent the two fields which specify the obscuration size co[2] = 0circular with the diameter of element = co[1]EGC TPF<  co[2]<>0rectangular with width = ap[1], height = co[2]Coordinate Transformation:Normally a rotation or tip of an element is offset or tipped. In the case of a coordinate transformation, an actual transformation to a new coordinate system occurs. This can be handy if you want to change to a new system for entering element information (but can be confusing to interpret).Perfect Lens:The puts in a perfect lens, which will focus light perfectly in the absence aberrations. This is handy to check the performance of collimated light at any given point in a design.YL fPF< J  Diffraction Grating:The groove spacing and ruling direction are specified. The default is for rulings are along the x direction. The dispersion is along the +/- y direction. Checking the GD box causes the ruling to be in the y-direction.Up to three wavelengths and their respective order can be specified. The again correspond to the wavelength codes on in the trace parameter window.Branch Point:Jump to some other element. A branch point can be enabled or disabled to change the flow of the optical system. (Such as due to a mirror which flips in and out of the optical path.)S GKG \PF<   Cylindrical:The cylinder is flat along the +/- Y direction. For other orientations use Gamma Tip to rotate the element about the optical axis. Radius is the radius of the cylinder and the eccentricity can be non-zero.Toroidal:Like a piece cut out of an inner tube. Cuts along the two major axes of the torus are segments of circles. Noncircular curves are not allowed. The convergence criteria needs to be specified too.Knife Edge:The knife eKdge is in the (x, y) plane. It allows rays to pass for x < 0.t2 4PF< Ronchi Grating:Blocks for x*blocking < 0.25 and x*blocking > 0.75, where "blocking" is supplied by the user.*K' <yL- *<nꉂThis help file was created with the free trial version of HelpScribble.= 1;Element Name6&  Element NameY0 0P9Specify a convenient name for the surface, e.g. Primary, Secondary, Lyot Stop, etc. .+ &9}L;1 29nꉂThis help file was created with the free trial version of HelpScribble.D1 GRadius of Curvature?;' 0Radius of Curvatureb: ( t<Radius of curvature or vertex curvature, where c = 1/r.6 :7<ra < 0= )center of curvature is to the left of the vertexra = 0= |flat surfacera > 0= (center of curvature is to the right of the vertexlD ]( <Double click on the name to change to toggle between entry type: E) "8<radius or conic constant+]( <zLG. ,<nꉂThis help file was created with the free trial version of HelpScribble.91cAperture4 G' Aperture 1 0<Size of optical element - ap[1] and ap[2] represent the two fields which specify the aperture size ap[2] = 0circular with the diameter of element = ap[1]ap[2]<>0rectangular with width = ap[1], height = ap[2]*' <yLc- *<nꉂThis help file was created with the free trial version of HelpScribble.= 1 EccentricityG c' @Eccentricity/Conic Constant<k H ^yL9Eccentricity or conic constant of the conic section, where cc = -ecc^2.ec = 0sphere0 < ec < 1ellipse,ecc = sqrt(a^2 + b^2)/aec = 1parabolaec > 1hyperbola,ecc = sqrt(a^2 - b^2)/a cY^2The equation of a conic section is: x = -------------------------------- 1 + (1 - c^2 Y^2(1-e^2)). + &L9oDk  + &L9Double click on the name to change to toggle between entry type: O) W & RHeccentricity or conic constant entry.(  % HwLW  + &HnꉂThis help file was created with the free trial version of HelpScribble.C 9 19  Following Distance> w ' .Following Distance9 _ 4 6i<The distance along the optical axis from the vertex of the current surface to the vertex of the next. fd > 0ray going from left to rightfd < 0ray going from right to left/w  , (<~L_  2 4<nꉂThis help file was created with the free trial version of HelpScribble.@ L1L@Following Index; ' (Following Index@ L7 <<The index of refraction following the surface. If the ray is to be reflected at a particular surface, the sign of the index changes at that surface.fi > 0ray going to the left to rightfi < 0ray going to the right to leftfi = 0surface is the focal plane/ @, (< @ ~L@2 4<nꉂThis help file was created with the free trial version of HelpScribble.A @@15@CShort/Long Index<@A' *Short/Long Index @C= H9JShort and long refractive indices (corresponding to wavelength codes 2 & 3 in the trace parameters). This is used for evaluating chromatic aberrations. All spot diagrams are centered on the position of the central ray corresponding to the refractive indices given by the following index. Therefore, any lateral shift for the other colors corresponds to lateral chromatic aberration. A shift in focus corresponds to longitudinal chromatic aberration.0A@C- *9LCC3 69nꉂThis help file was created with the free trial version of HelpScribble.: @CC16CEDecenters5C.D' DecentersCFE1 09These are translations in the x, y and z coordinates. They are applied and removed in the same way as rotations. Translations are applied after rotations. Note that the z coordinate is set to 0.0 at the vertex of each surface.0.DvE- *9LFEE3 69nꉂThis help file was created with the free trial version of HelpScribble.5vE*F1G*F is typed an autocalculation of the specified type will be performed. These include: spot diagram, system plot, variation run, matrix run, color trace, and meridional trace.This help file was created with the free trial version of HelpScribble.@@ф1t$фTranslate First44 6nꉂTranslate FirstWhen this is checked translations will be applied before rotations for the current optical element. The default is for rotations to occur before translations.This help file was created with the free trial version of HelpScribble.?фD1%DChange SurfaceT9 @7nꉂChange SurfaceMove to the previous or next surface. Note - two control commands help move through the prescription^B - moves to the previous surface (back)^F - moved to the next surface (forward)This help file was created with the free trial version of HelpScribble.FDއ1&އgInsert/Delete SurfaceA' 4Insert/Delete Surface\އ) "\Ins - Insert a "blank" surface before the current oneDel- Delete the current surface.(̈% \(% \sK̈g( nThis help file was created with the free trial version of HelpScribble.= 1 'HelpScribbleg0 . HelpScribble - The Complete Help Authoring ToolThis help file was created with the free evaluation version of HelpScribble. This ad and the little footers below each topic will be automatically removed when the author recompiles this help file with the full version of HelpScribble. HelpScribble can be purchased securely online and is covered by a risk-free 90-day unconditional money-back guarantee. See http://www.helpscribble.com/ for more information.+ $aAbout HelpScribbleHelpScribble is a full-featured, easy-to-use help authoring tool for creating help files from start to finish. You can create WinHelp (.hlp) files, HTML Help (.chm) files, a printed manual and online documentation (on a web site) all from the same HelpScribble project.If you have previously used another help authoring tool, you can reuse your work by importing the HPJ+RTF files created with the other tool or by a decompiler.You can use the help files you make with HelpScribble to provide context-sensitive help with your Window applications, no matter which development tool you use. You can also use HelpScribble to create stand-alone portable documents.E. */Write Perfect Help Files for Your SoftwareYou need HelpScribble to create a top quality help file for your software. Windows users expect to receive detailed documentation at a quick press of the F1 button. You will sell more copies of your software if a thoughtful help file flattens the learning curve for prospects trying theg evaluation version of your product.No matter which development tool you are using, you can always use a help file created with HelpScribble to provide context-sensitive help for your application.o@B/ ,If you know how to use a word processor, you can build a help file with HelpScribble. Creating new topics and adding links to them cannot be easier. No experience required.Portable Documents with HyperlinksWith HelpScribble you can easily create hyperlinked documents that can be read on any computer running Windows.The WinHelp files that you create with HelpScribble are a collection of linked pages, just like a web site. But unlike a web site, you only need to distribute one file. This file can be read on any Windows computer. No other software is needed.f/ ,You need absolutely no programming experience to use HelpScribble. Many word processors and HTML editors are more complicated than HelpScribble.The Complete Help Authoring ToolHelpScribble is a full-featured stand-alone help authoring tool. It is not an add-on for MS Word like so many other help writing products. You can create the entire help file right within HelpScribble.With HelpScribble you can even provide your documentation in several forms, all from the same source. You can add context-sensitive help to your application, print a manual and provide online documentation on your web site.RBW. *WinHelpWinHelp is the help file format supported by all versions of Windows. It is fast, compact and supported by Windows 3.x, NT 3.x, 95, 98, ME, NT4, 2000 and XP. All Windows users are familiar with it. With any Windows development tool you can use WinHelp files to add context-sensitive help to your applications.With HelpScribble you have all the functionality you need to build a complete help file, including table of contents, index, browse sequences, etc. With HelpScribble's SHG (image map) editor, you can make your pictures (screen shots) say more than a thousand words.Z3 4Printed ManualReading from paper is a lot easier than reading from a screen. A printed manual or, for downloadable software, a printable manual in PDF format, adds greatly to the value of your product.You can use your HelpScribble project as the basis for your printed manual. You can export your help text to one large RTF or HTML file that you or your DTP professional can turn into a finished manual using a word processor or DTP program.HTML HelpSW/ ,With Windows 98, Microsoft introduced a new help file format called HTML Help. Using HelpScribble, you can build classic WinHelp .hlp files and new HTML Help .chm files from the same source. You decide whether you want maximum compatibility with older computers, or if you want to offer a state of the art help system.Web HelpIf you want to provide online documentation, you can create one large HTML file or a collection of HTML files from your HelpScribble project and upload those to your web site. Your customers will have instant access to the latest documentation at any time.Z7 <Cross-Platform HelpIf you are developing platforms such as Linux, where there is no standard help format, you can provide your documentation as HTML files. The user can easily view those files in a browser. If you use Kylix, you can even easily integrate them into your application.Number 1 Help Tool for Delphi & C++BuilderYou can use HelpScribble no matter which development tool you use. Even if you use no development tool at all. (Stand-alone help files can be very useful.) But if you are a Delphi or C++Builder developer, you will certainly appreciate the way HelpScribble integrates with your favorite development tool.J%% KHelpScribble's HelpContext property editor takes most of the gtedious job of assigning Topic IDs to HelpContext properties out of your hands. Adding context-sensitive help to your application could not be easier. Simply click on the corresponding controls and help topics to link them.Delphi developers like HelpScribble so much that it won the Delphi Informant Readers Choice awards three years in a row. In 1999, 2000 and 2001, HelpScribble was chosing the Best Help Authoring Package, beating well-known tools such as RoboHelp and ForeHelp.5 8 Do Not Take My Word For ItI could rattle on all day about how great HelpScribble is. But do not take my word for it!Find out what the people say about HelpScribble before you decide to buy.Chris Kryza "Just wanted to let you folks know that you have created a very, very, verynice product! The last time I had to generate a context sensitive help fileI used Doc-To-Help and I remember it took me weeks to get it right. WithHelpScribble I was able to put together a complete help system in under 2days and I then created a web-help deployment of same in seconds. I usedyour demo version to create the entire project and then purchased yourproduct online after I saw how good it all looked. Great stuff!"3 4 Roj Ash "I just felt I had to compliment you on this product. I have no experienceof producing Help files, and having evaluated a number of products, I wasbeginning to believe that a mere programmer had no chance whatever!"I am not only making good progress in producing the Help for our product(which is usually used by **very** inexperienced users), but I'm actuallyenjoying it!"Thanks for a great product."Try the Free Evaluation Version TodayHelpScribble is an excellent help authoring tool. But do not take my word for it! Take a look at the self-running online demos or download the free evaluation version and see for yourself. Convinced? Buy HelpScribble now at http://www.helpscribble.com/11(cZhArialCourier NewSymbol    C:'d, 6] X> S>HR{\=f pz4| [ N{ Ni *L5,/&;)F24  aperturedecentereccentricityHelpScribble index of refractionprescriptionprescription,apertureprescription,curvatureprescription,radius radius$tip(/&;)Lz))Help ContentsGeneral Description Program History Main WindowFile IOSpot Diagram/System PlotMatrix/Variation RunPlot Area6Refocus/RecenterMeridional Trace]Color TraceWindow Show/HideTrace Parms>OptimizationVariation ParmsOutputsSNote on dimensionsRayTrace TutorialPrescription Parms[ Prescription WindowNSurface TypesElement Name{Radius of CurvatureApertureNEccentricityiFollowing DistanceFollowing IndexLShort/Long Index|DecentersTipsAconic Coefficients{Toggle Radius/Curvature=Toggle Eccentricity/Conic Constant Surface OptionsView IlluminationAuto CalculateTranslate FirstChange Surface Insert/Delete SurfaceHelpScribble/&;)L42h2Ne"pkkSlӞll{)l=Tl ll՟ll+l|l l[ lNl*l{UllNlillL,lvxW]-J}ɛn,*-ifpw }}}~,~6W~~]~~ J>̠a 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