VER 2.1
6/27/89
DOCUMENTATION FOR THE PROGRAM MIRROR.EXE
by Dick Suiter
MIRROR executes on an IBM compatible computer with-orwithout a coprocessor and one of these monitors: a 40 column TV
monitor as used by the oldest PCjr's; a CGA or EGA monitor (the
program uses the highest resolution monochrome CGA graphics
display --it does not take advantage of EGA graphics although
it can be operated on them); a Hercules-compatible monitor.
Since I am a rather crude programmer, it quizzes you about what
you have at the beginning. It also helps to have a printer,
although if you don't request printing operations, you will be
able to execute this program without a printer attached. There
are a number of ways to start this program. On the 40 column
or the CGA/EGA monitors, just put in:
any> a:
A> mirror2
On Hercules monitors, you must first ease the way with a
QuickBASIC module (included by permission of Microsoft):
any> a:
A> msherc
A> mirror2
The program must have an auxiliary run time file either in
the same directory or PATH'ed so it can find it. It is
copyrighted by Microsoft and appears here covered by the
license agreement. It is called BRUN45.EXE. Of course, all of
these programs can be transferred to a hard disk, in which case
the A becomes a C in the examples above.
DUMPING GRAPHICS: If you have either the 40 column or a
CGA/EGA compatible monitor, you must have executed the DOS
utility GRAPHICS.COM to enable the <Shift><PrtSc> screen dump
of a graphics display. To do this rather painlessly, add the
following line to your AUTOEXEC.BAT:
GRAPHICS
or, alternately, execute GRAPHICS before you execute MIRROR2.
1
GRAPHICS is a "terminate-but-stays-resident" (TSR) program that
knows where to find the graphics memory in your computer and
dumps it to your IBM Graphics Printer (i.e., an Epson
compatible printer) whenever you hit the keys <Shift> and
<Print Screen> at the same time. The equivalent for the
Hercules monitor is HARDCOPY, which goes when you hit
<Shift><PrtSc> and then hit <1>. HARDCOPY is not supplied with
a majority of Hercules compatible adapters, however, so I have
built in a Hercules screen dump. Whenever you are in MENU
items 1 through 4 (see explanation below) and want a hard copy
of the graphics image of the screen, hit "D" in a similar
manner to hitting "M" for the menu or "R" for remembering, and
if you have an Epson compatible printer installed (and on), you
will get a very slow screen dump. This feature is not
programmed very well. It uses a very poky 8-byte split-andpivot algorithm, but it is all I could come up with. It
doesn't work with other (namely Okidata) printers. If you have
HARDCOPY, I advise using it. If you don't, my Hercules screen
dumper is better than nothing.
MIRROR is easy and fast to use. The easiest way to learn
this program is to just sit down and diddle at the keyboard.
You can always get from a plotting screen to the menu by
hitting M. Read the help screen the first time you encounter
the menu.
REMEMBER:
You can get help from most locations by hitting H
or 8 at the MENU.
You can return to the MENU at most locations by
hitting M.
The exceptions are when the program is waiting for other
inputs.
MIRROR is a program to ease the analysis of Foucault test
readings as taken through a Couder screen (reference: How to
Make a Telescope, 2nd ed. by Jean Texereau, Willmann-Bell
1984) It is designed to come at the problem from a slightly
different angle than that in Texereau, and to take advantage of
peculiar properties of high-speed computers to perform
operations that were difficult when Texereau wrote up his
hand-calculation procedure. See my article in Telescope
Making #32, published by the same folks who publish ASTRONOMY
magazine. The article is called "Testing Paraboloidal Mirrors"
and gives an alternative description of Texereau's procedure as
well as my own.
MIRROR is not designed to compete with a nearly generic
BASIC program published in the Appendix to Texereau. That
program was written to follow the procedure of Texereau
almost precisely, and to generate a copy of Texereau's TEST
DATA SHEET. People have noted trouble using this program,
2
even with an errata sheet that was given out soon after
publication. I have examined this program, and in my
opinion, it sometimes fails because:
a) It occasionally doesn't find the proper constant that
must be subtracted in line 9 of the data sheet.
b) It searches for two maxima in the wavefront profile,
but occasionally there is only one. This happens when
the residual aberrations of inner zones are all
negative and the residual aberrations of outer zones
are all positive, i.e., the wavefront slopes up in
inner zones and slopes down in outer zones. It
doesn't search for the reference parabola underneath
the wavefront.
This program can be modified (I have sent an enhanced version
to Perry Remaklus and it has appeared in the latest printing),
but we can use computers to do so much more, and that is the
function of MIRROR.
Nor is it meant to compete with a little generic program I
wrote (and which appears in the TM32 article) called GENMIR. I
wrote it as mostly an illustration of my method of exploratory
focus.
The first thing the computer asks you is what sort
of monitor you have. The "40 column" choice is thought to be
needed only in the crudest PCjr's. Even in the late PCjr's,
you can specify CGA compatible graphics display. Few people
should ever require the crude display. Anyone with a CGA/EGA
can execute it to see what it looks like however.
MIRROR's next display is the "begging" screen. It says
this is a shareware program. That means that you are allowed
to use this program to try it out and freely copy it to give
to your mirror-testing friends. If then you find this
program to be useful, you are supposed to send me a fifteen
dollar donation to help cover the costs of making this
program available and to register for further update
information. To those who think that it costs nothing
to make this program available, I say you have never lost a
couple of weekends to a mailing list, not to mention the
hundreds of hours I spent in writing it. I have roughly $4000
worth of labor in this program. Don't I deserve a few coins to
recompense me the time saved by users? The Ohio address (116
West Union Pike, Hillsboro OH 45133) is my most non-changeable
address. I actually presently (6-89) live in Panama City FL.
Please send contributions to Ohio.
This shareware program is user-supported (i.e., if you
have trouble, don't expect me to fix it), but I do feel
responsible for bugs in the program. Please inform me of bugs,
real or imagined. I welcome correspondence about TM'ing and
3
the program in particular. Write me at the Ohio address for
the highest likelihood of your letter reaching me.
I admit that I cannot force users to pay for this
program (nor do I want to), but if you use this program ALL
THE TIME during your mirror making, and the thought of not
getting a notice of the latest update makes you weak in the
knees, perhaps you should register. Get some guilt-free sleep
for a change, you poor reprobate! The purpose served in paying
is to encourage me to write another good program that does
another useful function.
One thing I feel obligated to clear up is that I receive no
money from any computer bulletin board or shareware
redistributor. I HAVE NOT BENEFITTED FROM ANY SUCH
REDISTRIBUTION. I ask you to still consider sending me the
registration money. Another thing is that the arrangement
starts from ground zero with every new user. If you get a copy
from friend Ralph who you know HAS registered, that does not
let you off the hook. This arrangement is based on trust. I
TRUST you to pay for what you use. You TRUST me not to have
high prices or squirrely copy-protection schemes.
One of the last things the begging screen asks for is a
verification that you have completed the ASCII file
COUDER.DAT. This file contains information about the Couder
mask that typically won't change during the course of a
mirror's progress. An example file, with explanation, is
included with the diskette. Since you can stack up many
Couder masks within this file (it only reads the top one), it
is advised that you don't erase what's there, but just add
your present Couder mask to the top or use a text editor to
bring the desired mask to the top. Be sure to name the mask.
This is the present form of COUDER.DAT:
BEGINNING OF COUDER.DAT -->
4, Texereau's example
8, 7.92
0.0
1.415
2.56
3.335
3.96
6, six-inch non-equal weights
6, 6
0.0
1.0
1.5
2.0
2.5
2.98
3.00
4
**********************************************************
This is the file COUDER.DAT -- it should be filled as follows:
Number of zones <comma> label for Couder screen <-- note comma
Nominal diameter of mirror <comma> Optical diameter of mirror
Inner radius of innermost zone
--\
Outer radius of innermost zone
|
Outer radius of next zone out
|
.
|-- Number of zones + 1
.
|
entries
.
|
Outer radius of outer zone
--/
This file can be longer than necessary; you only need
shuffle the Couder screen you are using presently to the
top of the file. You can even leave these instructions
at the end to help you remember the entry order. The
6-inch example is largely meant to investigate spheres.
You can put your "real" data at the beginning, before
these examples.
The only thing you must remember about this file is
that it need be a pure ASCII file. Some word processors
don't output ASCII by default. EDLIN works well if
somewhat crudely. Some "programmer's editors" will work
fine, including the editor that comes with QuickBASIC 2.0,
with which I am writing this.
(QB4 doesn't work as easily. ds 1/18/89)
***********************************************************
<--END OF COUDER.DAT
What I am talking about in the comments at the end of
COUDER.DAT is that you must have a pure ASCII editor to edit
this file. Most word processors have an ASCII storage option,
but NOT AS THE PRIMARY DEFAULT. Any formatting information is
typically imbedded as invisible code. In addition, most word
processors store prefacing setup information to record the last
settings used in the previous editing session. One word
processor I know puts a great deal of information in the
"hyperspace" behind the <CNTL><Z> that marks the end of an
ASCII file in DOS. Read your word processor's documentation
for the method of bringing the ASCII storage method to the
foreground. You may need to "print to file" instead of "print
to printer." Be sure to watch out for margins or white spaces
that are placed automatically (a typical mistake is the 1-inch
of white space that is put at the top of a page -- good for
documents, bad for data files). Optimal editors to use include
a good programmer's editor, although the QuickBASIC 4.0 editor
now must have the syntax checking turned off and the ASCII file
storage method turned on (use Save As...), or else MIRROR
complains bitterly. QuickBASIC 2.0's editor worked fine. If
you have nothing else, use EDLIN, which comes free with DOS.
You will find that it is worth every penny.
5
By the length of this explanation, you have probably
concluded that I am doing this the hard way, but you will find
this method is as transparent as a window pane. When you find
an editing method that will work, you just pull COUDER.DAT into
your editor, add the information to the top of the file, and
exit the editor. Then you may forget about it until you finish
the mirror and start another using a different Couder screen.
The next screen asks for a title, which will later be
put at the top of the report. This title won't change until
you ask to start over. It then asks for the pathname to find
the file COUDER.DAT. It defaults to the root directory of
the A: drive, but if you've moved the files on the distribution
diskette to a hard drive, you must put the name of the
subdirectory there. A short cut and headache-saver is to have
the present directory in the subdirectory where all of the
diskette files have been tranferred anyway ... say it's called
directory C:\TM. When it prompts you for the pathname, you
don't have to reply with a laborious retyping of the full
"C:\TM" -- just type "C:" or even "." (a period). Then it will
know you mean the subdirectory that you are sitting in right
now.
Going on, it looks on the drive or in the directory
indicated for the file COUDER.DAT, and gives you a printout of
the data it found there as well as some derived quantities. It
prints zone edges as Rad( n ) and averaged zones as Rm( n ).
After this it asks for the radius of curvature, which may
change slightly during polishing, hence its location here.
Then MIRROR asks for the size of the diagonal. If you don't
know yet or don't want to use this feature, just use the
default of 0.
NOTE: All defaults appear in SQUARE brackets. To invoke them
just hit the <ENTER> or <RETURN> key with no other input
(don't put in blanks).
If you DO use this diagonal feature, it will do the
calculations in only as far as the edge of the diagonal for the
wavefront plot. This often makes a considerable difference,
particularly with holes or bumps at the center. It won't
change values calculated for the other plots, but it will
truncate their displays.
MIRROR then asks how many zone sequences you measured.
With rough figuring, this is usually only 1. (This is the
default.) But the final report may be measured over two
diameters and be the average of two zone readings -- in which
case you would input 4 for the number of sequences. Then it
asks for the measurements themselves. The parabola and
Millies-Lacroix tolerances are printed there for convenient
theoretical calculations. IMPORTANT: YOUR values can easily be
outside these limits, because they are calculated assuming the
COC constant is zero. For real measurements such as you have
6
taken, the COC constant also contains a number related to where
you had your micrometer set. Don't worry about any apparent
discrepancy between these two values.
NOTE: these are fixed source readings. If you have a moving
source tester such as appeared in my TM22 article on slitless
Foucault testers, DOUBLE the readings before inputing them.
The reason for doing this is apparent from the diagram below:
/K'
/ |
/
|
A'
|
/ |
|
/
|
|
/_____|_____|
S
A
K
FIXED SOURCE
S'_____A'____ K'
|
|
|
|
|
|
|_____|_____|
S
A
K
MOVING SOURCE
where S and S' are the initial and final positions of the
source
A and A' are the COC of zones A and A'
K and K' are the initial and final positions of the
knife
(version 2.1 will double these readings automatically)
In each case we are measuring the same difference in the center
of curvatures, A to A', but since we move only the knife edge,
we actually measure twice that distance in the FIXED SOURCE
tester. In the MOVING SOURCE tester, the points all move
together. The quantity measured by a moving source tester has
more to do with the reality of distance A to A', but standard
tests (such as that appearing in Texereau) usually have the
fixed source tester in mind. Rather than go to all of the
effort required to "translate" between fixed and moving source
tester techniques, I prefer to convert all measurements to
those of a fixed source tester and use the equations
unmodified.
END NOTE
The last thing this screen asks you is whether you want
to input the COC constant yourself. The first time through,
use the default reply of NO. It then goes ahead with an
automatic selection that minimizes wavefront error. The
next screen is MENU. You may want to input this constant
by hand, but do it later. This constant is the same as appears
in line 9 of the TEST DATA SHEET in Texereau.
The automatic selection procedure differs from that in
Texereau in that it minimizes the wavefront error rather than
the transverse aberration. It selects the COC constant so that
you are focused on that reference sphere in which the WAVEFRONT
ERROR is at a minimum. Texereau focuses at the point in which
7
TRANSVERSE ABERRATION is at a minimum. He then uses the clever
trick of the reference parabola to find the minimum wavefront
error without all of the pain involved in searching. In the
days before commonly-available computers, this wasn't mere
convenience -- it was crucial. With computers, we can let the
machines do the drudgework.
The "reference parabola" appearing in the Texereau plot is
a flat, level line in my plot. My default wavefront plot will
always be capable of either sitting levelly on two points or
seems to be hanging from two equal height points. These two
points represent a reference parabola of Y = A*X*X + C, with
A = 0.
The four plots available in the MENU are:
1) the Millies-Lacroix plot (parabola removed)
2) the transverse aberration compared with the Airy disk
radius
3) the wavefront error
4) a plot of the last four remembered COC constants, to use
in the method of exploratory focus
Note that the wavefront error graph (MENU #3) seems fairly flat
for the auto-search reference sphere. It is also a different
curve than Texereau would calculate, reflecting the difference
of the two COC constants ("line 9 constants") between his and
my techniques.
MENU #1 gives the Millies-Lacroix test with the parabola
removed. When we first look at this point, we are focused at
the same place where the wavefront is minimized. If part of
the curve extends beyond the tolerances, we no longer have
full latitude as to where we are allowed to focus.
We can move the point of focus by adding to or
subtracting from the COC constant. We do this using the up
and down arrow keys. The amount we move per step is in the
upper right corner of the plot screens. This stepsize can be
modified by hitting the "*" or "x" keys (this makes it
bigger) or the "/" key (this makes it smaller). The amount
this increment or decrement changes is by the square root of 10
each time you divide it or multiply it. Two divides or two
multiplications in a row change it a factor of 10. This was
found to be about right when you are narrowing-in on the proper
answer.
When looking at the Millies-Lacroix plot, adding or
subtracting focus position just moves the curve up and down.
It actively changes the shape of the transverse aberration and
wavefront curves.
Danjon and Couder (Lunettes et T‚lescopes (French), Paris
1935) have said that a mirror is really good if it
8
simultaneously meets two conditions:
1) If the wavefront is within 1/4 wave, i.e., meets the
Rayleigh tolerance.
2) If the system is diffraction limited, or puts most of its
light into the Airy disk, i.e., meets the M-L tolerance.
Using this program, you can map out the focus regions where
these conditions are true. You can find either end of the
1/4 wave focus region by moving the curve until it's 1/4 wave
extended first one way or the other, using the Wavefront
Plot (MENU #3). Or, you can map where the focus is
diffraction-limited by extending the curve until it sends
light first to +rho and then -rho, using the Transverse
Aberration Compared with Airy Disk Plot (MENU #2). You can
save the particular COC constant (MENU #5 or R on the first
three display screens) of any given situation, and then plot
all four of them like this, using MENU #4:
better than 1/4 wave region
|
|
diffraction-limited region
|
|
|
|
|------------------|
|
|-------------------------|
|
|
likely best focus
----- C O C
C O N S T A N T -- T H I S
A X I S --------
After you have plotted such a diagram, you can pick off
the COC constant that represents best overall focus, input it
by hand using MENU option #0, or use the cursor in MENU # 4,
and derive a report that better represents your mirror's
true performance. (Note: the upper bar isn't necessarily the
diffraction-limited region. It assigns bars depending on which
were the last two COC constants remembered.)
Since it was cumbersome to continually toggle back to the
MENU just to remember a COC constant, I now have placed a quick
memory option within the Millies-Lacroix, Transverse
Aberration, and Wavefront screens. You just hit R when you
want to remember the present COC constant. It beeps for
confirmation. (I hope that you haven't decoupled your beeper
to defend your ears from your kids' video games!) You no longer
have the option of naming this memory yourself or dumping
memory (those are still available at the menu). It take the
name of the screen and the time as the comment.
9
The execution of MENU #5 goes a little differently, too.
If you request a printer dump of remembered COC constants, it
no longer forgets all values afterwards, but IT DOESN'T
remember that particular COC constant. If you want a dump AND
a remembered constant, execute MENU #5 again after you have
remembered the constant. All you will get if you ask for a
dump is a listing of remembered COC's, with the values
undisturbed. I have done it in this slightly more difficult
manner because you won't usually want a dump, and are probably
annoyed when it always asks (I certainly am).
The normal way of remembering constants to use the method
of exploratory focus is to follow this procedure:
1) At the MENU, request screen 3. Move the wavefront until
it extends upward to give a total wavefront error (look
at the display at the top) of 1/4 wave. Hit R and hear
a beep.
2) Move the wavefront the other way until the wavefront is
distorted in the other direction by 1/4 wave. Hit R
again and hear a beep. Hit M.
3) At the MENU, request screen 2. Move the transverse
aberration, until it intersects (barely) the line +Rho
at the top of the box. Hit R and hear a beep. Move the
transverse aberration down until it barely intersects
the line -Rho at the bottom of the box. Hit R and hear
your fourth beep. You now have 4 constants remembered.
4) Hit M. At the MENU, request choice 4. It will display
the last (and only) 4 constants, and various things
remembered with them, including the wavefront error and
transverse aberration. It also displays an automatic
comment of which screen it was on and the time it was
remembered. It then asks for the ordering of the
constants. This is in case you remembered them in a
screwy order such as: one end of the wavefront chart,
then one end of the transverse aberration chart, next
back to the wavefront chart, and lastly the other end of
the aberration graph. Usually (if you are smart), you
had the good sense to remember these in pairs. You can
then use the default by hitting <ENTER> with no input.
5) On the focus screen,
cursor sticking down
left it on the other
and right arrow keys
you see two bars, with a line
from one end of one bar where you
graph. Now you can use the left
to move it to the point of most
overlap (which won't in general be at the center of
either bar) and request a report there. The perfect
mirror is given in the hatched bars below. You no
longer have to deal with this case separately and then
try to match differing scales.
10
NOTE: The transverse aberration number at the top of graph 2 is
calculated using only the MEASURED values. This is because we
are supposed to be scientific and trust only measured values.
But it is not unreasonable to expect the slopes of the M-L plot
and Transverse Aberration plot continue on TO THE EDGE. This
is the way Texereau had you plot the transverse aberration
although he had you balance the values that could be traced to
a measurement. You can perhaps derive better (and more
conservative) results by eyeballing the behavior of the
transverse aberration line continued on to the edge of the plot
and Remember that COC constant. My 6-inch Couder screen has an
artificial narrow zone at the edge of the mirror to induce
this. I had GENMIR calculate it this way, too. END NOTE
In Texereau, the difficulty of hand calculation
precluded all of this focus-changing other than as a
trial and error procedure for minimizing transverse
aberration. Consequently, Texereau got within a very close
striking range with the transverse aberration minimization
procedure, and then adjusted focus to the center of the
wavefront region using the reference parabola.
He mentioned that this was at a different focus, but he
didn't emphasize that it may move the transverse aberration out
of the diffraction-limited region. The reason that he did not
do this is because for well-figured, smooth-zoned mirrors like
the one appearing in the example, IT DOES NOT MATTER. The
diffraction-limited region and the 1/4 wave regions strongly
overlap in such a case. But it is perhaps unfortunate that he
did not mention that in early figuring, when the wavefront is
closer to the sphere or maybe is not as smooth as it should be,
the bottom-line wavefront error may be overly optimistic. The
1/4 wave regions and diffraction-limited regions may only
weakly overlap or even be mutually exclusive.
As an example of this, move the many zoned 6-inch Couder
screen to the top of the file COUDER.DAT and execute the
program 3 times using radii of curvature = 98.4", 115.2", and
123". In other words for 6-inch f/8.2, f/9.6, and f/10.25
mirrors. Put all zone measurements in as the same number (a
sphere). A value of 0 is good as all you have to do is keep
hitting the <Return> or <Enter> key.
Note that the automatic procedure finds a wavefront within
about 1/4 wave for the f/8.2 mirror, but that the transverse
aberration extends to both sides of the tolerance. In other
words, the 1/4 wave region plotted above is a point and the
diffraction-limited region does not exist.
For the f/9.6 sphere, the diffraction-limited region is a
point and the 1/4 wave region is a short bar segment, but they
DO NOT OVERLAP. Finally, for the f/10.25 sphere, both regions
are plotted as short bar segments and they have just begun to
overlap. The f/10.25 is the fastest 6-inch sphere that
11
satisfies both conditions of Danjon and Couder.
In general, the diffraction-limited region of focus is
smaller than the 1/4 wave region, and "zigzaggy" mirror
profiles have even smaller diffraction-limited regions (if
they exist at all). My method of placing the best focus at
the center of the region where the overlap occurs gives a
better estimate of what is the true wavefront error than the
method of Texereau for crudely figured mirrors. But when
a mirror is nearly finished, both methods give about the same
results. Indeed, strong overlap of the 1/4 wave and
diffraction-limited regions could be a necessary criterion of
just when a mirror is finished, since it only happens when
the wavefront is smooth and well-behaved. Please note that
the definition of "smooth" here is different than in my TM28
article. There I was discussing statistical smoothness,
where here I mean zonal smoothness of a type that has been
already statistically averaged. I am assuming that the
mirror has little primary- or micro-ripple, but broad zonal
errors can still exist. Remember, though, that if SHARP zones
exist, you really have no business running mirror measurements
through this program. Fix the zones first.
No doubt you have toyed with the program enough by now
to realize it takes as the wavefront error the total
deviation of the wavefront for the reference sphere derived
from the COC constant. This program does not use the
reference parabola.
NOTE: To get an idea of the size of the regions in the method
of exploratory focus at focus rather than at COC, divide the
COC numbers by FOUR. The resultant squished-down numbers give
you the behavior at focus, plus an estimate of the tolerable
errors in focus. Remember, the COC constant contains a
micrometer-setting constant, so its absolute value has no
significance --only the relative settings mean anything. END
NOTE
If the center of the 1/4 wave region (i.e., near the point
of minimum wave error) is well within the diffraction-limited
region, and the sizes of the regions are similar to the perfect
mirror, YOU ARE DONE FIGURING. You can either go to the center
of the overlap region and request a report there, or you can
use Texereau's slightly smaller wavefront error value. If you
choose the first, move there on MENU choice 4. If you choose
the second, let the program search for the constant
automatically. It really doesn't make any difference.
You can locate the interim calculations (and graphs) that
Texereau would have gotten by going to MENU #2 and balancing
the transverse aberration (the same as minimizing the value
printed at the top of the screen as the "Maximum Transverse
Aberration"). During this procedure, you will get a larger
value for the wavefront error than Texereau gets because
12
MIRROR2 does not look for the reference parabola.
the smallest wavefront during the autosearch.
MIRROR2 gets
Other MENU choices:
6) Start over from beginning ***
Restarts you clear at the beginning, assuming only that the
file COUDER.DAT still applies. You are asked for fresh data
input.
7) Report ***
Delivers a full report to your line printer. It asks for a
label. This is so you can distinguish between two different
reports requested at two different reference spheres (or
equivalently, two different COC constants). The label is
printed in parentheses below the title asked for at the very
beginning. A form looks like the following, with <...>
surrounding the explanation of the entry:
Texereau's example
<global title>
(automatic search)
<(label for report)>
Nominal diameter of mirror: 8 inches
<shorthand form of mirror's
size in inches>
Active diameter of mirror: 7.92
<actual optical size>
Radius of curvature: 97.06
<measured value>
Infinity focal distance: 48.53
<half the radius of curvature>
Infinity focal ratio of mirror: 6.127525
<f/number of mirror>
Radius of diffraction spot: 1.622201E-04
<"rho" or half of Airy disk>
Measurements:
ZONE
1
2
3
4
<... number of zones>
Seq 1
.573
.611
.657
.698 <sequence 1 measurements>
Seq 2
.562
.607
.658
.698 <sequence 2 meas, if any>
.
.
ZONE Radii Mean Radii Parabola M-L tol Av. Meas Res Aberr
|
|
|
|
|
|
|
<labels for zone number (line 1 Texereau),
|
|
| outer edge radius (line 2 Tex), |
|
|
|
|
radius to center of zone (line 3 Tex),
|
13
|
|
|
|
|
|
|
|
|
|
|
|
0
1
2
3
4
|
|
|
|
|
|
|
|
|
|
|
|
0
1.415
2.56
3.335
3.96
| the parabola to that mean radius (line 4 Tex),
|
| Millies-Lacroix tolerance
|
|
| (2*rho*radius of curvature |
|
| /mean radius), |
|
|
|
| measurements averaged
|
|
| over sequences (line 8
|
|
| Tex), |
|
|
|
|
| residual
|
|
|
| longitudinal
|
|
|
| aberration at
|
|
|
| COC (line 10
|
|
|
| Tex)>
|
|
|
|
|
|
0.7075
0.0052
0.0445
0.5675
-0.0034
1.9875
0.0407
0.0158
0.6090
0.0026
2.9475
0.0895
0.0107
0.6575
0.0023
3.6475
0.1371
0.0086
0.6980
-0.0048
Center of curvature constant: .5657399
<"COC constant" used in line 9
of Texereau -- NOT SAME VALUE
HOWEVER, search uses different
criterion>
Aberration with respect to Airy disk and slope:
ZONE
Trans Aberr
slope x1E6
<zone number, |
|
|
transverse aberration in units of
|
rho at focus (line 12 Tex),
|
|
slope of wavefront in millionths>
|
|
|
1
-0.0763
0.2551
2
0.1617
-0.5405
3
0.2107
-0.7043
4
-0.5574
1.8633
Wavefront in 1E-6 inches: <label: wavefront is described in
millionths of an inch>
Radius
Wavefront
0.0000
1.415
2.5600
3.3350
3.9600
0.0000
0.3610
-0.2579
-0.8037
0.3609
<radius, vertex point of wavefront graph>
.
.
.
.
Maximum Wavefront Error for THIS reference sphere: 1/18.55 wave
<note: refers to this COC constant only without use of
reference parabola>
NOTE: You can specify MENU #0 and hand input Texereau's value
for the COC constant (in line 9 of Texereau). What you will
then get in MENU choices #2 and #3 will much resemble what
appears in Texereau's TEST DATA SHEET plots. The bottom line
14
will differ, though, because this program does not use the
reference parabola. That is what the auto-search is for.
Texereau's value for the COC constant is very near the value
that minimizes the transverse aberration in MENU #2's plot. END
NOTE
Since this is one of the automatic searches, note that the
wavefront appears to be hanging from two same-height wavefront
points at the second (r = 1.415 inches) and last (r = 3.96
inches) vertex. This is what I was talking about when I was
saying how my automatic search searches for the reference
parabola that is a flat, level line. This is what Texereau's
wavefront chart would look like if we stretched it to flatten
the reference parabola.
The way you should make a logbook entry is to find the COC
constant that you feel best represents your true error. Then
go to the first three (or four) MENU choices and request a dump
of the image to the printer. Finally request a MENU #7 report
giving you the full calculation. Keep them together in a
looseleaf notebook to record your intermediate progress.
8) Help ***
This is the menu entry for the help screen. Read it the
first time you encounter it. You may notice peculiar spacing.
This is to allow 40 column monitors to present something
approaching a reasonable display. I may clean this up if I
ever stop supporting them.
9) Exit ***
This is the graceful exit for the program. It avoids
keying mistakes by asking you to hit 9 again if you REALLY want
out. Any other key will return you to the menu.
COMMENTS:
UPDATE TO VERSION 2.1 -- CHANGES
-- I fixed the wavefront plot so the wavefront moves up when
you hit the up arrow and down when you hit the down arrow.
This is formally incorrect (watch the COC constant in the
upper center of the display -- it goes the other way!), but
it makes better hand-eye sense.
-- I cleaned up the display on menu choice 4, the exploratory
focus screen. I automatically calculate the perfect mirror
results and scale relative to them. I pull the real mirror
results onto the same display, but remember, there is no
relative left-right alignment between the real and perfect
mirrors! The real mirror has the micrometer offset in it.
This is unimportant, but it means that you can't make direct
comparsons between the locations, only the sizes.
15
-- I made it so you don't have to double moving tester results
by hand.
FUTURE ENHANCEMENTS
1) automatic finding of the four COC constants (if there)
marking the edges of the exploratory focus zones during the
auto-search.
-------I hope you find this program helpful. It is certainly no
LOTUS 1-2-3, since I am a fairly unskilled programmer. My aim
is in providing a service to telescope makers everywhere. It
certainly is not making me much money. The only reason I beg
for a little is to hold my head above water on the costs of
making it available. My net profit at this time (3-89) is
about $50! Please help if you can.
-------This program uses as the default wavelength standard a
slightly different value than Texereau -- 550 nm instead of
560. Values will vary a small amount for Texereau's example.
The present version does the calculations only in inches.
Sorry about the inconvenience for foreign users. To convert
millimeter units to inches, divide the value in millimeters by
25.4 exactly.
The program is not presently trapped for boneheaded errors
very well. It requires a knowledgeable user. You can easily
generate nonsense answers using nonsense input. I will
eventually do as much internal checking as possible but it is
not presently built into the program. Nothing beats knowing
what you're doing.
The results of this program are only as good as the actual
measurements. If you take bad measurements, the results
will be wrong.
I use a kind of scattered approach in describing the above
operating procedures. Sometimes, I assume you know nothing
about DOS. Sometimes I assume you know what the PATH statement
is and what ASCII files mean. Most computer user confusion
I've seen stems from ignorance of MS-DOS, the fundamental
operating system of IBM-compatible computers. People want to
start using their applications (their WordPerfects or LOTUS
1-2-3s or even little MIRROR2s) without investing a little time
in the seemingly non-productive effort to find out how their
computer works! Let's use astronomy as our analogy. DOS is
the Universe in which these applications orbit. DOS is the
16
godhead, the only thing they can touch directly. When the
applications look up, the sky is filled with DOS. My program
doesn't know how to get information directly from the disk. It
humbly asks DOS to do it. If you get peculiar error messages
like "Can't find file" or something even more obscure, I ask
you one thing. Have you familiarized yourself with DOS?
Perhaps a little effort along these lines will clear up your
problem.
No legal liability shall be incurred by the author of this
program from misuse by users or errors in this program. It is
not guaranteed to work. Users shall proceed at their own risk.
MAY YOU MAKE A BEAUTIFUL MIRROR
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