InvRon.Exe and the Visual Basic source code from which it is compiled, as well as this help file, whether in HTML or any other format, are Copyright © 2001 by Mark D. Holm. InvRon.exe, its source code and this help file are freeware. They are licensed under the GNU General Public License.
Licensing under the GNU General Public License obligates me to make the source code available. If you really want to see the source code, warts and all, e-mail me at mdholm@telerama.com I will send it to you. You will need VB5 or higher to make much of it. If you want to discus the theory or math behind InvRon, feel free to e-mail. I'll tell you what I know.
InvRon.Exe is distributed with files which are not the author's intellectual property. In all cases, the author believes he has the right, under the licenses of those files, to distribute them, and you have the right to possess and use them. These files include:
SWIFTPRINT.OCX
Swiftprint is the work of Brodie Thiesfield. It is also distributed under the GNU General Public License. More information about Swiftprint, including files which will let you use it in your own Visual Basic programming as well as source code, are available at http://www.ecn.net.au/~brodie/swiftprint The author is most grateful to Mr. Thiesfield. Without Swiftprint, I doubt I would have been able to make InvRon work.
Microsoft Visual Basic Runtime files, Installer, etc.
The author's right to distribute these comes from the Visual Basic license, where it is explicitly granted. The author has not knowingly modified these files in any way. These files are not covered by the GNU General Public License.
As explicitly stated in the GNU General Public License, InvRon is distributed without any warrantees. I have tried to make it a useful program, and have not knowingly included anything malicious, but if it doesn't work, misleads you, crashes your computer, burns your popcorn or whatever, I'm sorry, but I can't be responsible. In particular, since InvRon is intended to help with the figuring of telescope mirrors, or other optics, I can't be responsible if your optic doesn't turn out well, even if it turns out that there is an error in InvRon. Like most of the people whom I assume will use this program, my involvement in optics is purely a hobby. I do not have any claim to professional expertise in the field.
The author of InvRon is Mark Holm. E-mail mdholm@telerama.com If you can not contact me at this address, try joining the ATM mailing list and asking for me there. The ATM list FAQ is at http://www.jacksonville.net/~dcass/atmfaq/atm-faq.htm It is mirrored at http://www.aegis1.demon.co.uk/faq/atm-faq.htm Instructions for joining the list and sending messages are in the FAQ.
The system I used to develop InvRon and upload it to the server has been scanned with a recently updated copy of McAfee VirusScan. It found no viruses. Beyond that, I cannot guarantee.
Yes. See Copyright and License and No Warrantees. You are free to possess, use, copy, distribute and modify, if you wish, InvRon so long as you adhere to the GNU General Public License. If you distribute an unmodified copy, you must distribute it intact, with all files, with the author's (my) name and copyright statement and the GNU General Public License. If you distribute a modified version, you must make it plain that you have modified it, and give references back to the original version. Any modified version must also be distributed as freeware under the GNU General Public License. Any use which does not conform to the GNU General Public License is prohibited.
Note that InvRon is distributed with several Visual Basic auxiliary files. These are not freeware and are not covered under the General Public License. So long as they are distributed as part of an unmodified distribution of InvRon, they are covered by the author's Visual Basic license, but any other use is not covered.
What files does InvRon create, delete or change on my system?
The installation package contains compressed versions of several files. (The files are listed in Readme.txt.) The installer program installs these in the directories it thinks appropriate. Most of these are standard, Microsoft provided, Visual Basic run time files, installer and uninstaller programs. One is SWIFTPRINT.OCX, a freeware printer control for Visual Basic. InvRon uses Swiftprint for all of its printer output. There is also a Readme.txt, this help file and, of course, InvRon.exe, the compiled Inverse Ronchi program.
InvRon.exe does not itself create, delete or change any files.
Does InvRon make any entries or changes in Windows Registry?
The installer program makes registry entries for the files it installs. This is the standard installer that comes with Visual Basic. I have not modified it in any way. Swiftprint makes a registry entry in which it keeps settings for its Print Preview function. InvRon does not make any registry entries of its own, nor change any preexisting entries.
What if I want to remove InvRon?
The safest way to remove InvRon is to use the uninstaller that comes with it. Using the uninstaller cleans up registry entries as well as deleting the files. If you have accidentally deleted the uninstaller, you can get it back by reinstalling InvRon from the installation package. This will reinstall the uninstaller too.
Is InvRon bug free? Can it crash or hang? Will it crash my system?
I have fixed a number of bugs before releasing a public version, but more are likely. That is the nature of programming. Please e-mail me if you find a bug or unusual behavior.
I haven't had much trouble with crashing or hanging. When I have, I ran down the causes and fixed them. I think the program is pretty stable, but I wouldn't be surprised if there are still problems lurking. Please e-mail me if you experience a crash or hang. Try to describe what you did just before the problem.
InvRon uses mostly standard Visual Basic controls and methods. I do call the Windows API routines in the Display function, and to start a browser for the help file, but this is pretty standard Windows programming practice. Swiftprint undoubtably uses many system calls. Still, I think the likelihood of system crashes is reasonably low. I haven't had any. Please e-mail me if you experience a crash or hang. Try to describe what you did just before the problem.
There are three reasons:
1. HTML has become a more universal standard than Windows help file format. Someone can read this file even if they don't have a Windows system.
2. There are now two standards for Windows help files, the original, and a new one using compiled hypertext (.chm) files. I understand that the new standard is not supported on all Windows systems yet, so using it might prevent some from reading the file. The old version will probably be supported on Windows systems for some time, but you never know. Microsoft doesn't have the greatest record for supporting legacy applications.
3. I don't know how to write either type of Windows help file.
Is there a Mac or Linux/Unix version?
No. I am sorry, but I don't have a Mac and don't know how to program for them. I have a Linux installation, but haven't learned, and don't have C++. I might have tried to do it in Java. I have some experience with Java. Event driven stuff is somewhat tricky in VB, but VB does a lot of the dirty work for you. Java requires the programmer to deal with a lot more details. I don't think Java is as portable as its creators like to think. I also suspect getting printer routines that would be reasonably portable would be difficult.
If you would like to try writing a version for another platform, I am willing to help.
InvRon.exe is a compiled Visual Basic 5 program. It should run on Windows 95, 98, ME, NT and 2000. It may run on Windows 3.1 (but don't bet on it). I have only tested it on Windows 98.
InvRon prints patterns for "inverse" Ronchi gratings, used for testing the figure of telescope mirrors. Ordinary Ronchi gratings have straight lines. When a mirror maker looks through a straight grating at a spherical mirror, she sees straight shadows projected on the surface of the mirror. She can easily judge the straightness of these shadows and thus, judge whether the surface is truly spherical. But, most telescope mirrors are not spherical. The majority are paraboloidal. With a paraboloidal mirror, a straight grating produces curved shadows. Judging the correct curvature is difficult. An inverse grating has lines which are themselves curved so that the shadows they project will appear straight on a paraboloidal mirror.
Calculating the correct curvature for inverse gratings has been challenging. Mr. Eric G.H. Mobsby published a simplified, approximate method, useful for mirrors of moderate size and f-number.1 Willman-Bell have for many years sold gratings produced with Mr. Mobsby's methods. D. Malacara and A. Cornejo2, 7 published a more rigorous mathematical approach, but the difficulty of the mathematics has placed it largely out of reach of amateurs.
InvRon takes a different mathematical approach. Instead of Mobsby's approximations or the aberration theory of Malacara and Cornejo, InvRon computes the grating shape by direct ray tracing. A pattern of straight lines is imagined to lie on the surface of the mirror. Rays are traced from a point source to points on the boundaries of the lines and, reflecting off of the mirror, to the grating position. This method is conceptually simpler, but requires even more computation than that of Malacara and Cornejo. Modern personal computers can handle the computation with ease.
An additional advantage of the ray tracing approach is that off-axis source placement is easily accommodated. The other methods assume that the light source is on axis. Amateur testers rarely have the beam splitter needed for on-axis work. Off-axis placement usually generates only small differences from results computed for the axial case, but with larger and faster mirrors these become more significant. Ray tracing directly computes the off-axis case so that there is no need to be concerned about unknown off-axis effects. InvRon has entries for source offset in all three axes.
I suggest that anyone who wants to try this test should read all of Mobsby's original article1. I have (with permission) reprinted several paragraphs below, but I think the whole article gives a more complete picture of the test. Many large public libraries will have back issues of Sky & Telescope, perhaps on microfilm. Take the information from footnote 1 to the reference desk at your library. They can probably help you. If your local library doesn't have it, they probably can get it from another. Librarians have been doing that sort of thing for a long time. Alternately, ask on the ATM e-mail list or e-mail me.
A beginner should know that the Inverse Ronchi grating method of mirror testing is, at the time I write this, not commonly in use among amateur telescope makers. I don't know about pros. Most ATMs will not be familiar with this test. This does not necessarily imply that the method is poor, just unfamiliar. The Inverse Ronchi method does not result in simpler mechanical needs. In fact, the test apparatus has to be better than the minimum needed for the two most common tests. The mechanical requirements are however similar to the next more sophisticated test apparatus which many amateurs build and use successfully. If a test rig has a micrometer or dial indicator to measure movement toward and away from the mirror, it can probably be adapted for this test. The chief advantage of the Inverse Ronchi grating method is easier interpretation. No data reduction is needed. The eye needs only to judge the straightness of shadows, something most people are fairly good at.
In addition to a computer running one of the Windows versions listed above and a copy of the InvRon installation files, you need a reasonably high resolution, Windows-compatible, printer. Most inkjet and laser printers will be suitable. Impact printers are probably not suitable. Color printing is not needed.
The printed grating pattern will not be directly usable. It will need to be reduced in size and copied onto a transparent substrate. The most obvious way to do this is photography. Mobsby described a method using a 35mm camera with 50mm focal length lens.
It may be possible to use a slide printer to print directly to film. The major question to be answered is whether the slide printer's resolution is sufficiently fine. The final grating will be only about 0.0286 inch (0.726 mm) in diameter. I expect one would want at least 100 lines of resolution across this size.
Installation notes are in the Readme.txt file. Installation should proceed similar to other Windows programs. The installer is the standard one that comes with Visual Basic.
Three option buttons allow a choice of inches, millimeters or centimeters. These will scale the calculations and printed output appropriately, but they do not convert values you enter in the input boxes. If you have an 8 inch mirror and want to enter its data in millimeters, you will have to multiply by 25.4 yourself.
According to Mobsby, the radius of curvature should be accurate to 5 mm (1/4 inch). In order to achieve this level of accuracy, and not have the ROC change too much after the grating is made, the mirror should be completely polished, and nearly spherical before ROC is measured. It might be prudent to make gratings with ROC values a little longer and a little shorter than nominal in order to be prepared for ROC changes that may happen during figuring. (Kodachrome comes in 36 exposure rolls, so you might as well make a few extras while you are at it.)
Focal Length will be calculated automatically after you enter ROC. Or, you can enter Focal Length, and ROC will be calculated.
Measure Clear Aperture to the nearest 1 mm (1/32 inch). Do not include edge bevel. For example, a 200 mm mirror with a 1 mm bevel all around has a clear aperture of 198 mm.
Two option buttons allow you to choose either a paraboloid, or another conic. If you choose a paraboloid, the Conic Constant is set to -1.
If you choose a figure other than a paraboloid, you may choose from the ordinary conic sections by specifying the Conic Constant, k. k > 0 is an oblate ellipsoid. k = 0 is a sphere. -1 < k < 0 is a prolate ellipsoid. k = -1 is a paraboloid. k < -1 is a hyperboloid. If I understand correctly, the ellipsoids which result from -1 < k < 0 are prolate. They have their foci along the axis of revolution, the axis we usually mean when we speak of the mirror's axis. Oblate ellipsoids are rarely, if ever, used in telescopes. Their foci lie along an axis perpendicular to the axis we usually speak of as the mirror's axis.
I believe I am correct to say that k is equal to -e2, where e is the eccentricity usually mentioned in analytic geometry books. Opticians seem to use k to describe conics rather than e. I really don't understand how one gets k for an oblate ellipsoid from this definition since, unless e takes on an imaginary value, -e2 must always be negative.
I suspect that amateurs are not always consistent about the sign of the conic constant. For that matter, I am not sure the pros are either. In the current version of InvRon, conic constants will always be negative except for the probably rare cases of oblate ellipsoids. Although InvRon will work for spheres, k = 0, there is little point. The computed grating for a sphere has straight lines. An ordinary Ronchi grating is easier to obtain and use.
I have also seen the conic constant called the Schwarzchild constant, with the same range of values described here.
Mirror testing mathematics and programs often assume that both the light source and test probe (grating, knife edge, wire, etc.) are located on the mirror's axis of revolution (what amateurs usually just call the mirror's axis). This assumption simplifies the math a lot. In practice, this is usually only true if a beam splitter is used. Most amateur testers do not use a beam splitter. Their light source is a little to one side of the axis. The image, and therefore the test probe, are an equal distance to the other side. In most cases, the offset introduces negligible error. InvRon uses a ray tracing method to calculate grating shape. Ray tracing makes it relatively easy to include source offset in the calculation. Image offset then follows automatically. Three text boxes allow you to enter the source offset that applies to your setup. In general it is best to keep source offsets small, but enter whatever your tester has.
For X and Y offsets, enter the distance from the axis to the source, that is 1/2 the distance from the source to the image. For the Z axis, enter 1/2 the distance from the source to the mirror's center zone null position as determined by the Foucault method. The tolerances on these measurements are probably fairly loose; measurements good to 5 or 10 mm are probably good enough for most mirrors. For really large or fast mirrors, a bit more precision may be good. Every time you move the mirror or tester, these values will change a little. Don't be paranoid, just spend a couple of minutes shifting things till you are within that 5 - 10 mm range of the numbers you used when you calculated the grating.
X and Y offsets cause the calculated grating to become slightly elliptical rather than circular. Z offsets change the band shape and calculated grating diameter, so it is good to get reasonable estimates entered for X, Y and Z. Don't ignore them completely.
Note: InvRon does not display the image offset. The image offset is subtracted from the calculated grating position, so that the pattern always displays and prints in the same place. In practice, you will have to find the correct image position by shifting the grating till it is centered in the light cone, but the numeric value (of the X and Y directions) will not be important.
The X direction is the horizontal one perpendicular to the mirror axis. It is typically the direction the Foucault knife edge moves to "cut" the light cone. In other words, left and right. If your light source is to the left of the axis, enter a negative value. For right, use positive.
The Y direction is the vertical one perpendicular to the mirror axis. In other words, up and down. If your light source is below the axis, enter a negative value. If it is above, use positive.
The Z direction is toward and away from the mirror along the mirror's axis of rotation. If your light source is nearer to the mirror than the image, enter a negative number. If the light source is farther from the mirror than the image, enter a positive number.
If your tester uses a moving source, that is, if the source and grating move together, check this box. If the source sits still while the grating moves, or vice versa, uncheck this box. The motion that is important here is Z axis motion.
This is one part of the test that requires some precision.
The grating Z axis position has to be established by measurement. Although some other method might work, a micrometer screw drive or a dial indicator is probably most convenient. First use the "knife edge" on the film to find the position of a particular mirror zone. Do this exactly as if you were taking a Foucault reading of that zone. A Couder mask, or Everest pin stick for that zone will probably be necessary.
Next add the Grating Offset value to the reading, and move the grating (usually toward the mirror) to the new value. These readings need to be precise to about 0.02 mm or 0.001 inch. Now the grating has to be centered in the light cone in the X and Y axes. Do this by moving the grating left-right and up-down it till you see the shadows centered on the mirror.
Your grating has to be calculated for a particular position, so record the Grating Offset you enter when you make the grating, and use that value when you test.
The grating cannot go in the range of positions where the Foucault test is usually made. It must be closer to the mirror than the center zone or farther than the edge zone. If not, the grating shape includes artistic loops which will probably not be informative during the test. Mobsby suggests that the grating should be placed 0.0143 R/r inch ahead (closer to the mirror) of the measured edge zone position. Since the far edge zone is difficult to measure, I have modified Mobsby's suggestion slightly. My default for the zone to measure is the 0.912 r zone. This is the same radius as the outer zone of the example Couder mask in Texerau. InvRon includes a function to calculate this value automatically. To get this automatic calculation, check the Use Default box.
For some large or fast mirrors, Mobsby's suggestion will not be far enough forward to be clear of the "forbidden" zone. You will recognize this by the strange loops in the calculated grating. Decrease (or increase if you decide to work on the "back end") the grating offset till the loops go away and the curves do not come to a point. Then record this value to use when you test.
The reference zone is used for offsetting the grating. Pick the zone that you can measure most reliably. Make a mask or pin stick for this zone. Mobsby suggests the "edge" zone. I am not quite sure what he means by that. I have suggested the 0.912r zone. This is the outermost zone of the Couder mask Texerau suggests for his "standard" mirror. My default Grating Z Offset is slightly smaller than Mobsby's 0.0143 R/r in order to compensate for not using the "edge" zone. If you change to another zone, the default Grating Z Offset will change to remain at Mobsby's suggested position. Zone can not be set greater than 1.00 for obvious reasons. It can also not be set less than 0.1. There are two reasons for the lower limit: 1. The arithmetic of one of my subroutines may fail for a smaller value. 2. Most everybody agrees that the center zone is difficult to measure accurately.
Offset toward (negative) or away from (positive) the measured zone null position at which to locate the grating. See discussion above.
Use the offset suggested by Mobsby. The default offset will change for different mirror f-ratios or zones. Uncheck to use another offset.
The number of lines on the grating. Minimum = 3. Maximum = 21. Mobsby used 3.
Width of each line as projected on the mirror. Width is specified in percent of the mirror diameter. The width of the lines on the grating varies because of the nonuniform curve shapes. Note that the width of a central line varies from top to bottom. One of Mobsby's approximations was the use of a straight central line. When projected on the mirror, his straight line must appear curved. That would be confusing. InvRon's gratings should be superior in this respect.
There are two option buttons, Linear and Area Weighted. Linear will make a grating with lines evenly spaced across the mirror. Area weighted will space the lines so that equal fractions of mirror area are between the lines. For example, with a three line, area weighted design, one line will be at the center and one each will be at 0.707 r left and right. The design just mentioned is the one Mobsby recommended.
There is an interaction between Number of Lines, Line Width and Line Spacing which you will have to manage for yourself. As Number of Lines increases, Line Width must decrease or the lines will overlap. You will see for yourself when you Display or Print Preview.
InvRon assumes that most users will print the grating at a size larger than the final grating and use some reducing method, probably photography, to produce the final grating. Enter here the reduction factor you will be using. InvRon will print the grating this many times larger than the final size. See Mobsby's method below for reducing the grating onto film using a 35mm camera with 50 mm lens.
If you use a slide printer to print the grating directly to film, ignore the Reduction factor on the main screen. Instead, use the Slide Reduction Factor in the Print To Slide section of the Print Options screen.
Click the Display button to see the grating displayed on the display pop-up form. Screen resolution is usually much poorer than printer resolution, so the curves will seem rather jagged. Sometimes the routine that blackens the lines doesn't work correctly. When that happens, portions of the grating that should be white will be black. View the grating in Print Preview. So far, Print Preview has always displayed the gratings correctly for me.
Click the Print button to bring up the printing form. On this screen, you can choose options, preview or print.
If this box is checked, a vertical line will be printed above and below the grating pattern. This line is intended to aid locating the grating during testing.
If this box is checked, scale marks will be printed on both X and Y axes. Measure these to be sure that the printed pattern is correctly sized. If the measurement units are inches, the scale marks should be 6 inches long. If the measurement units are millimeters or centimeters, the scale marks should be 150 millimeters long. (See Printer X Scale and Printer Y Scale.)
If this box is checked, a three character identification code will be printed with the grating. You can enter a code in the text box below this check box. The default code is A01. The code can contain any printing characters on your keyboard. I recommend capitol letters and digits.
In this text box you can enter the spacing of a conventional, straight line Ronchi grating. This grating can be printed to paper, or will be automatically included if you print to slide. Default spacings are 100 lines per inch, 4 lines per millimeter or 40 lines per centimeter depending on the units setting.
If the grating will be photographed with a negative film, such as the high contrast black and white films Mobsby mentions (below), the white and black portions of the pattern will need to be reversed. Reversing the whole page uses a great deal of ink. Checking this box will reverse only the portion of the page around the grating and finder line. If you use Print to Slide, both Part Negative and Full Page Negative will result in the whole slide being reversed.
Checking this box will reverse the whole page. With both part and full page cases, there will be white margins around the pattern that will need to be trimmed.
Clicking this button opens the Select Error form. In order to produce gratings which differ from a nominal grating by a known amount, the Select Error form will calculate a change in k or ROC. The change is calculated so that the edge zone of the hypothetical mirror differs (in surface height) from the nominal mirror by a specified fraction of a wavelength of light. (1 wave = 550 nanometers.) One can select positive (high) or negative (low) errors. The default is zero (produce a grating for the nominal mirror). One can also select whether the error is produced by a change in k (figure) or in ROC (Radius of Curvature or Focal Length).
The purpose of the Select Error option is to provide for a degree of quantification in the test. Normally, the Inverse Ronchi test is essentially qualitative, like the ordinary Ronchi test. By making available gratings with known deviations, I hope to give a mirror maker some sense of how large remaining errors in her own mirror may be. These error gratings are used in exactly the same way ordinary Inverse Ronchi gratings are used. In particular, I have set up the calculations so that one positions an error grating using exactly the same Zone measurement and Grating Offset as for the corresponding nominal grating. I think this use of error gratings is somewhat analogous to the "quantitative" or "matching" Ronchi test as taught by Mel Bartels.
There is one somewhat wierd property to be aware of. Gratings calculated with k errors do not have the same diameter as nominal gratings. A bit of reflection (Pardon the pun.) shows that this is indeed expected behavior. The program keeps the calculation of the circle to nominal values, so the curves may end either inside or outside of the circle. With a correctly figured mirror, the circle should correspond to the mirror edge as seen under test. Gratings calculated with ROC errors do not show such large differences between the lines and the outer circle. I am not sure why this is so.
I have not tested error gratings against any standard measurements, so I don't know for certain that the calculations are valid. I have checked that the ROC and k value changes do result in numerical changes in calculated mirror shape of the specified size.
Changes in k and ROC as implemented here, have maximum effect at the edge zone. These will probably be most helpful in quantifying edge zone mirror defects. It might be nice to produce gratings that would simulate errors in other zones, but, for the moment, I don't have any idea how to calculate those.
If this description leaves you confused, then just leave the error set to 0 waves. You will produce the nominal grating for your mirror as intended by Mobsby, Malacara and Cornejo.
If this box is checked, the Y-axis will be aligned along the long direction of the paper.
If this box is checked, the Y-axis will be aligned along the short direction of the paper. I think portrait orientation will be more useful than landscape for most people.
If the X-axis scale marks are not the correct length, change this value to adjust. (See Scale Marks.)
If the Y-axis scale marks are not the correct length, change this value to adjust. (See Scale Marks.)
Click this button to close the Print Options screen. Choices you make on the Print Options screen are preserved when you Cancel. This includes comments you enter with Edit Comments. Choices and comments are lost when you exit from InvRon.
Five option buttons let you choose which item to preview or print. Each item prints on a separate sheet of paper. You can only select one at a time.
Print the inverse grating.
Print an ordinary Ronchi grating pattern. This pattern will have the same reduction factor as the inverse grating.
Print a black (or white if negative) rectangle which can be used to form a "knife edge" on the finished slide.
Print the grating i.d. in large letters that can be photoreduced onto the finished slide.
Print Grating Data to document your grating. You will want to know the dimensions you used to make the grating. Edit Comments lets you append other information to this page.
Click this button to bring up the comments editing screen. Comments print on the same page as Grating Data.
Click this button to preview the chosen item before printing it.
Click this button to send the chosen item to the default printer.
Print to Slide puts all of the elements, except Grating Data and Comments, onto a slide, or a single sheet of paper. The controls under Grating Options work here too. Height to width ratio is automatically adjusted to 2:3, which is the ratio of height to width of a standard 35mm film frame. (The printable area of a standard 35mm film frame is 24mm by 36mm.) Print to Slide always prints in landscape format.
If Slide Reduction Factor is 1.00 and you select Use Reduction Factor, the image is adjusted to fit a 24mm by 36 mm rectangle.
If you choose Auto Adjust to Slide, the program adjusts Slide Reduction Factor to the largest size that will fit in the printable area of your paper or slide as reported by your printer. If you print on paper using Print to Slide, you will still need to reduce the image onto film, however the reduction ratio will not be as large as with Print to Paper. Reduction ratios in the range 1 to ~8.4 are possible. You may find that a copy camera allows reductions in this range. You will have to judge whether your printer has sufficient resolution.
Scale marks are adjusted to be 15mm long on a finished 35mm slide. If you print with a Slide Reduction Factor other than one, the scale marks will be scaled by that factor. (This is different behavior than the scale marks for paper printing, which have their specified size on paper regardless of the Reduction setting.)
With a grating pattern printed on paper, you will need to reduce its size and transfer it to a transparent substrate. The following description of using photography to produce a grating on film from artwork on paper is taken from Mobsby's Sky & Telescope article1.
Photographing the Grating:
Whether to blacken the bands themselves or the spaces around them depends on the method of photoreduction that will be used. A sharp dense film is essential, so many ordinary emulsions are not suitable. Kodachrome II 3 is, but cannot be processed at home. I have found it more convenient to use black-and-white film intended for line copy work. Kodak's Recordak Microfile type 5669 and Kodalith are both excellent for the purpose, but the exposure is very critical and the data sheets packed with the film must be followed carefully.
If one of the line-copy films is to be used (and developed as a negative) 4, apply ink to the spaces between the bands and leave the bands themselves white. When the ink is dry, carefully cut out the drawing along the circumscribed circle and attach it to a large black background, about four feet square and made of black cloth, paper or painted cardboard. Little pieces of double-stick tape are excellent for attaching the drawing. A strip of white adhesive tape, about 1/2" in Width should be placed vertically above and below the drawing of the inverse grating for later use as a finder line. Other helpful additions include a white rectangle (which will become a miniature knife-edge) and a series of strips of 1/2" adhesive tape with 1/2" spaces between them, for performing the regular Ronchi test.
An ordinary 35-mm. camera is convenient for achieving the necessary 100-times reduction. With a standard 50-mm. lens (about 2" focal length), the grating should be placed 201" from the camera's film plane.
After developing the film and mounting it on the usual knife-edge holder next to the pinhole light source, the problem of how to position it in the converging light cone arises. The grating is to be placed inside the focus of the mirror's edge zone by an amount a = 0.0143(R/r) inch, or 0.4004 for our 8-inch f/7 mirror. First find the mirror's edge-zone focus by means of the knife-edge on the film; then advance the carriage by the distance a toward the mirror. A micrometer adjusting screw is the surest device for accomplishing this.
Without changing the longitudinal setting, move the film laterally in its holder until the black finder line is picked up in the light cone. Then adjust the film vertically until the tiny grating is centered in the beam. If the mirror is a perfect paraboloid, three vertical straight, and parallel bands will be seen against the mirror's surface, one in the middle and the other two at the 70-percent zone on the right and left sides. 5 Any departure from straightness will be an indication of under- or over-correction or, if locally placed on a band, of a zonal error.
The optimum size for the pinhole is about 0.03 millimeter or 0.001". With a larger one, the bands are poorly seen (if at all); with a smaller, the illumination is too feeble and diffraction effects are more troublesome.
In my own experience the test is rapid, sensitive, and easy to apply. Figuring is continued until the lines show no departure from straightness. There is no ambiguity, and nothing to measure, so this test may properly be called a null test for a paraboloid. 6
5 InvRon allows more than three bands and other spacing.
6 InvRon can create gratings for conic sections other than paraboloids.
7 A web page based on the Malacara and Cornejo article2 is at http://www.fortunecity.com/marina/manatee/1879/mosby.htm
Eric G. H. Mobsby for the original idea of using inverse gratings and his methods for producing them. op cit1
Robert E. Cox for his helpful notes following Mr. Mobsby's article. op cit1
Sally MacGillivray at Sky Publishing for permission to reprint the excerpt from Mobsby's article.
James W. Burrows for the form of the general equation for conics, and its derivatives, that I ended up using. Jim got the equation from W.J. Smith, "Modern Optical Engineering", McGraw-Hill, 1966, p. 392. Jim also showed me how to normalize the equation so it would not "blow up" for values of k near -1.
James W. Burrows for help with the vector math in an improved version of the ray trace.
Michael Koch, Andrew Bell and Carl Woebcke for more help with the math.
Martin Trittlevitz for testing early versions of the program and making helpful suggestions.
Steve Lindberg, Richard Schwartz, John D. Upton, Hugues LaRoche, Michael Lindner and Roger Ceragioli for encouragement and suggestions.
Bob May for pointing out that I needed to make the program's forms fit in a VGA screen.
My wife, Cathy, for being patient with me while I expend way too much time on this project and for proofreading this help file.
My sons, Peter and Daniel, for not calling me crazy to my face, even though it is clear they think anyone who would put this much work into something as boring as this must be nuts.
Any amateur attempting to make a telescope mirror should become a member of the ATM e-mail list. Even if your only internet access is at a public terminal, you can get a free e-mail account from a source such as HotMail. To become a member of the list, read the instructions in the FAQ at http://www.jacksonville.net/~dcass/atmfaq/atm-faq.htm or at the UK mirror site http://www.aegis1.demon.co.uk/faq/atm-faq.htm
List members are usually very helpful to newcomers, and reading the various ideas others are trying, or thinking about can be very enlightening.
All the list messages are archived at http://astro.umsystem.edu/atm/ There is a search engine to help you find relevant messages.
Useful Books for Mirror Makers
This list is not exhaustive. The books are ones I have some familiarity with.
Texereau is very thorough. He aims at first time mirror and telescope makers. His mechanical designs are probably not what most ATMs would recommend anymore for beginners but his mirror making procedures are sound, if perhaps a bit too fussy in places. The book is well organized. Many consider this the best all-round book for beginners.
This book is not really aimed at beginning mirror makers. Its primary focus is telescopes too large for most beginners. However, there is a lot of practical information that has more general application. Also, two appendices are useful for beginners. One describes a modern, simple telescope design suitable for small and medium sized scopes. The other gives a good description of mirror making. The mirror making appendix is aimed at "large, thin mirrors", but its procedures and advice are applicable to smaller mirrors as well. This book is very well written, and easy to follow.
This book is a compilation of several short booklets on mirror and telescope making. I used the original booklet on mirror making when I made my first mirror. It is actually pretty sound, and quite concise. I doubt you can get it directly from Edmund any more, but Willman-Bell still carry it. (It is in their paper catalog, but is not listed on their web site.)
Copyright © 2001 Mark D. Holm mdholm@telerama.com
The GNU General Public License is the product of the Free Software Foundation, Inc.
GNU GENERAL PUBLIC LICENSE
Version 2, June 1991
Copyright (C) 1989, 1991 Free Software Foundation, Inc.
59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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How to Apply These Terms to Your New Programs
If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
convey the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
Copyright (C)
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
Also add information on how to contact you by electronic and paper mail.
If the program is interactive, make it output a short notice like this
when it starts in an interactive mode:
Gnomovision version 69, Copyright (C) year name of author
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, the commands you use may
be called something other than `show w' and `show c'; they could even be
mouse-clicks or menu items--whatever suits your program.
You should also get your employer (if you work as a programmer) or your
school, if any, to sign a "copyright disclaimer" for the program, if
necessary. Here is a sample; alter the names:
Yoyodyne, Inc., hereby disclaims all copyright interest in the program
`Gnomovision' (which makes passes at compilers) written by James Hacker.
, 1 April 1989
Ty Coon, President of Vice
This General Public License does not permit incorporating your program into
proprietary programs. If your program is a subroutine library, you may
consider it more useful to permit linking proprietary applications with the
library. If this is what you want to do, use the GNU Library General
Public License instead of this License.