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why aren't porro prisms more often cemented?

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#26 marktd

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Posted 26 May 2016 - 10:03 AM

Probably not necessary to illustrate, but here's some pictures that show exactly what I was describing, regarding inability to adjust prism rotation once prism sub-assembly is installed in housing.

 

 

Attached Thumbnails

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  • 2.jpg
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#27 Rich V.

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Posted 26 May 2016 - 10:20 AM

From the venerable Peter Abrahams' Binocular List (http://home.europa.c.../binoc_list.txt):

 

 

Bureau of Naval Personnel. Opticalman 3 & 2. 1966. (Reprinted as Basic Optics &
Optical Instruments, Dover, 1969.) The US Navy’s standards are: Vertical alignment,
2 minutes “step” (a horizontal line can have a misalignment measuring two minutes
of arc.)  Horizontal, for the instrument’s optical axes, 4 minutes of divergence, 2
minutes of convergence.  Image tilt, one degree (viewing a distant vertical line,
the two images can be misaligned by one degree). 
These last two specs are far
looser than I would expect.

 

 

I assume this applies to low mag. naval binos; higher mag binos would need more stringent standards...

 

Rich

 

 



#28 GlennLeDrew

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Posted 26 May 2016 - 11:37 AM

Rich,

Those numbers on offset (vertically and horizontally) take into account the magnification for the particular bino, representing the permissible limits as seen at the output. And so a 2' offset for a 7X bino is the same to the observer as a 2' offset for a 25X bino. If the eyepiece f.l. is the same in both instruments, the precision in alignment for their prisms is also about the same (depending also on optical path length between prism and focus/field stop.) If one's eyepiece f.l. is half that of the other, its prism alignment tolerance is about halved.

 

The 1 degree rotational error is independent of magnification. However, its effects are worse toward the edge of a wide AFoV.

 

Mark,

Indeed, the rotation of the prisms is performed independently of other adjustments for collimation. Unless knocked out of proper rotational position, this is done only the once. If the range of rotation is small (and it usually is), a prism having any notable angle error on the 45-90-45 faces must be matched with another having a suitable pyramidal error.


Edited by GlennLeDrew, 26 May 2016 - 09:28 PM.

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#29 marktd

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Posted 26 May 2016 - 12:13 PM

Interesting.  One degree is 0.017" radially for a 2" hypotenuse prism.  That tolerance seems pretty easy to hit without adjustability.  For example, in a mass production operation, +/- .002" in machining of prism holder and grinding of prism would probably keep one safely in the target zone.  I'm not sure about glass grinding, but that's not a particularly difficult tolerance in mass manufacture machining or casting (note here I'm only referring to the tolerance for prism external surface for registration in mount; the tolerance requirements of the prism faces themselves are a different calculation)  

 

The SARD components appear to be produced to slightly better tolerances than that, which presumably explains why they have no provision for adjustment. 

 

On the other hand, my Sears binos have looser tolerances -- for example, width of prisms varies by a few thou -- so the adjustment mechanism is required.

 

My super cheapies have both low tolerance components and no adjustment provisions.

 

And of course at the higher end, adjustability is mandatory.  I would guess high-end, higher mag glass strive for tolerance more like 0.1 degree or less, which is impractical to achieve by even high-precision manufacturing steps alone.



#30 Gordon Rayner

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Posted 26 May 2016 - 12:17 PM

A 2 minute   step  (up-down   displacement of   a horizontal  line  in the target),  as seen by   the observer after   passage through the binocular:

 

A 7 X  magnification   implies that   , at  the internal images  in the focal planes, before  7X magnification by the  eyepieces, the  angular  up-down   difference   between the sight lines   should be    2 minutes  divided  by   7,  not   7x2=14.

 

Commentary/ education/  ????



#31 Gordon Rayner

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Posted 26 May 2016 - 12:23 PM

"  1/10  degree   impractical ....."     ?????         That seems   pessimistic.     Good support tooling  for a block of prisms,  then  onto   a Blanchard   or similar grinder?      But  I am  shooting from the  hip  here, without    personal experience   , and without   any research.



#32 marktd

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Posted 26 May 2016 - 01:55 PM

Gordon, 1/10 degree means positioning the prism to +/- 0.0008" accuracy.  

 

This level of precision is not hard to achieve, but it's not cheap.  In manufacturing terms, especially for small quantity niche markets, it's probably more practical (ie, cost-effective) to design something with adjustability than to design something that has such close tolerance requirements that it doesn't need adjustability.  

 

There's no magic precision practicality threshold, but complexity and cost goes up exponentially as the tolerances go down.   Once you get roughly into the sub-thousandth territory, things get more finicky quickly.  For example, a rule of thumb in measurement is that a measurement tool needs calibrated precision 10x the measurement tolerance.  So to measure 2 thou tolerances, standard micrometers suffice.   To measure .0008" reliably requires more sensitive equipment.

 

Simple things like temperature becomes important.  That aluminum prism cage will shrink by half the total tolerance (0.004") with a mere 10 degree temperature change, whereas the glass will shrink by only 50 millionths of an inch in the same temp delta.

 

If you making millions of iPhones, you can invest billions (literally) in tooling to churn out infinite quantities of parts to +/- 10 microns, but if you're making a few thousand high end binos, building in adjustment and tolerating less component precision is more practical.


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#33 Gordon Rayner

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Posted 26 May 2016 - 04:08 PM

I was  thinking about   only  the prism  glass  element,  not   the  metal and glass  assembly.


Edited by Gordon Rayner, 26 May 2016 - 04:13 PM.


#34 MartinPond

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Posted 26 May 2016 - 04:17 PM

A 2 minute   step  (up-down   displacement of   a horizontal  line  in the target),  as seen by   the observer after   passage through the binocular:

 

A 7 X  magnification   implies that   , at  the internal images  in the focal planes, before  7X magnification by the  eyepieces, the  angular  up-down   difference   between the sight lines   should be    2 minutes  divided  by   7,  not   7x2=14.

 

Commentary/ education/  ????

 

They usually state the requirement as "at the eyepiece", so yes..... divided by 7, or 10, for the outside world.



#35 MartinPond

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Posted 26 May 2016 - 04:18 PM

"  1/10  degree   impractical ....."     ?????         That seems   pessimistic.     Good support tooling  for a block of prisms,  then  onto   a Blanchard   or similar grinder?      But  I am  shooting from the  hip  here, without    personal experience   , and without   any research.

 

Quite possible, but not affordably....



#36 Rich V.

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Posted 26 May 2016 - 04:19 PM

Rich,

Those numbers on offset (vertically and horizontally) take into account the magnification for the particular bino, representing the permissible limits as seen at the output. And so a 2' offset for a 7X bino is really an internal offset of 14'.

 

The 1 degree rotational error is independent of magnification. However, its effects are worse toward the edge of a wide AFoV.

 

 

 

A quote from Bill Cook:

 

" Alignment that is within the original JTII standards can be considered to function as “perfect” in that the eyes can easily accommodate the error without introducing noticeable eyestrain. For example, an 8 power instrument should have errors equal to or less than 4’ Step, 10’ Divergence and 6’ convergence, with a 16 power having 2’, 6’ and 3’ respectively."

 

I read this as saying the magnification is not accounted for and the spec must be tightened for higher mags...

 

For example, the 7x bino with a relatively small 1' deviation between barrels has a 7' apparent offset at the eyepieces; likely not enough to be noticed.  If I have the same 1' deviation between barrels of my Miyauchis, at 150x, the apparent offset between images would be 150' which is a whopping 2.5°!  I really need a tighter standard than 1' deviation between barrels with them.  I have to align them to arc second precision, not arc minutes.

 

Rich


Edited by Rich V., 26 May 2016 - 05:42 PM.


#37 GlennLeDrew

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Posted 26 May 2016 - 09:56 PM

A 2 minute   step  (up-down   displacement of   a horizontal  line  in the target),  as seen by   the observer after   passage through the binocular:

 

A 7 X  magnification   implies that   , at  the internal images  in the focal planes, before  7X magnification by the  eyepieces, the  angular  up-down   difference   between the sight lines   should be    2 minutes  divided  by   7,  not   7x2=14.

 

Commentary/ education/  ????

 

Gordon,

I don't know where my brain went on vacation there. I was up all night and must have been sleepier than I thought! I've edited that post; here's the relevant bit:

 

Assuming the permissible image offset applies after the eyepiece, as perceived by the observer... The degree of precision in prism dimensioning or positioning does not necessarily scale with the magnification. Rather, it scales with eyepiece focal length and optical path length between the relevant prism surface and the focus/field stop.

 

This is exactly analogous to binoviewers. The 'fulcrum' for the geometry is not the objective but instead is the relevant prism surface which imparts the deviation in path. This causes an offset on the focal surface which depends on the angle of deflection and the distance over which that deflection operates.

 

If a large bino uses the be identical prisms and eyepieces of a small bino, and they are spaced identically, the tolerance on prism dimensioning/positioning is identical, even if the bigger bino's magnification is 2X or 3X higher.

 

If one bino uses eyepieces having 1/2 the f.l. of another, its tolerance on prism dimensioning/positioning is twice as stringent (assuming the same distance from prism to the focus.)

 

If one bino uses the same prisms and eyepiece, but has its eyepiece field stop twice as far from the *relevant* prism surface, the tolerance on prism dimensioning/positioning is twice as stringent.

 

In that last paragraph I stressed "relevant" because a prism system has a number of surfaces at differing distance from the focus. The first reflective surface is pretty distant from the focus, and so the impact of its angle error is not so large for a given longitudinal relocation of the focus. But the rearmost reflective surface is much nearer to the focus, and so the impact of its angle error is more significant for given longitudinal relocation of the focus.

 

The corollary of the foregoing is that the more forward reflective surfaces must (or at least should) have smaller errors of angle. But as I noted earlier, errors for one surface can be compensated for another or others.



#38 marktd

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Posted 26 May 2016 - 11:17 PM

 

For example, the 7x bino with a relatively small 1' deviation between barrels has a 7' apparent offset at the eyepieces; likely not enough to be noticed.  If I have the same 1' deviation between barrels of my Miyauchis, at 150x, the apparent offset between images would be 150' which is a whopping 2.5°!  I really need a tighter standard than 1' deviation between barrels with them.  I have to align them to arc second precision, not arc minutes.

 

Rich

 

 

Working backwards, if 10' is the tolerance, then at 150x you need alignment to 4 arc seconds.

 

Edmunds Optics standard prisms have +/- 2 arcmin angle tolerance, and their "high tolerance" prisms are +/- 15 arcsec.

 

I'm not making a direct comparison, just broadly observing the precision of off-the-shelf components with potential bino needs.

 

Here's another interesting dimensional factoid: to rotate a 2" hypotenuse prism through 4 arc seconds is a radial displacement of 1.2 microns.   One can't do that with an ordinary set screw!



#39 GlennLeDrew

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Posted 27 May 2016 - 01:22 AM

Angle error at the prism is not multiplied directly as the magnification; this would imply that the *objective* is the 'fulcrum'. The 'fulcrum' is the relevant prism surface, and the geometry to consider is the triangle defined by this 'fulcrum' and the physical separation at the focal surface resulting from the angular offset. The angle subtended on the retina by this physical offset depends directly on the eyepiece f.l.

 

Working backwards:

 

Suppose we have an offset of 2', or 0.0333° as subtended on the retina, and an eyepiece of focal length 22mm. The physical offset on the focal surface is thus

 

TAN(0.0333) * 22 = 0.0128mm.

 

Suppose the relevant reflective surface is 60mm from the focus. To displace a beam 0.0128mm at a distance of 60mm, the angle of rotation for that surface is

 

0.5 * ARCTAN(0.0128 / 60) = 0.0061°, or 0.367'

 

(The 0.5 comes from the fact of doubling of the angle upon reflection.)

 

If the adjustment screw is, say, 25mm from the intersection of beam and reflective surface, the distance by which to move the screw in order to effect a rotation of 0.0061° is

 

TAN(0.0061) * 25 =  0.0027mm

 

This would be the same whether an objective of short or long f.l. is in use.

 

Such miniscule distances do not seem correct to me, for my own home-made (and crude) alignment mechanisms have required/permitted far larger adjustment for given effect than suggested here....



#40 marktd

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Posted 27 May 2016 - 10:08 AM

I'm obviously no authority on the optical alignment requirements of 150x binos, but I know enough about mechanical engineering to know that there is no way a portable binocular, even of the highest quality, is holding micron-scale tolerances.  

 

Even the couple order of magnitude larger tolerances of your calcs (0.0027mm) seems unrealistic, like you say.  Just consider the assembly to make this adjustment -- that's about 1 degree of rotation on an ordinary micrometer thread.



#41 Rich V.

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Posted 27 May 2016 - 10:50 AM

I'm obviously no authority on the optical alignment requirements of 150x binos, but I know enough about mechanical engineering to know that there is no way a portable binocular, even of the highest quality, is holding micron-scale tolerances.  

 

Even the couple order of magnitude larger tolerances of your calcs (0.0027mm) seems unrealistic, like you say.  Just consider the assembly to make this adjustment -- that's about 1 degree of rotation on an ordinary micrometer thread.

 

I'll leave the math and mechanical engineering to you, Marktd, but I can say with certainty that a binocular, even one operating at 150x, can be aligned to the accepted industry standards relative to the image space using the provided push/pull trisets on the prism mounting flange or by turning eccentric objective mounting rings, whichever convention is provided by the designer.  Our instruments would be useless if we couldn't.

 

I'm sure we're not requiring the level of precision needed to align the CERN LHC.    ;)

 

Rich


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#42 Jon Isaacs

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Posted 27 May 2016 - 11:07 AM

Simple things like temperature becomes important.  That aluminum prism cage will shrink by half the total tolerance (0.004") with a mere 10 degree temperature change, whereas the glass will shrink by only 50 millionths of an inch in the same temp delta.

 

 

The CTE of aluminum is 12.5 x 10-6 /F.  A 10 degree F temperature change would result in a 0.00012" change in a 1 inch part.

 

:shrug:

 

Jon



#43 marktd

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Posted 27 May 2016 - 12:54 PM

 

Simple things like temperature becomes important.  That aluminum prism cage will shrink by half the total tolerance (0.004") with a mere 10 degree temperature change, whereas the glass will shrink by only 50 millionths of an inch in the same temp delta.

 

 

The CTE of aluminum is 12.5 x 10-6 /F.  A 10 degree F temperature change would result in a 0.00012" change in a 1 inch part.

 

:shrug:

 

Jon

 

 

Thanks for correction.  That was a double error -- typo, meant to type .0004; and I doubled the radius.  The number I was after was 0.00025 (10° F change over two inches)

 

But my point wasn't in the exact values, it was just that manufacturing gets much more complicated and expensive as the tolerances get smaller.     



#44 marktd

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Posted 27 May 2016 - 03:21 PM

Here's a possibly interesting empirical datapoint.  I measured the divergence on some microscope binocular heads. 

 

I have one that I "feel" is not well collimated.  It's usable, but not great.  It diverges by 30 arcmin.

 

I measured three other identical model Leitz binocular heads and they ranged from 5-10 arcmin divergence.

 

I'm not sure exactly how translatable this is to astronomical requirements, but the microscopes would commonly be used up to mags way higher than telescopes, let alone binoculars.

 

PS. my measurements are probably +/- 25% at best. 



#45 GlennLeDrew

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Posted 27 May 2016 - 04:29 PM

Image offset in binoviewers is most definitely dependent on eyepiece f.l. A pair of, say, 20mm f.l. oculars will present the very same offset whether the objective f.l. is 400mm or 4,000mm. Halve the eyepiece f.l., double the angular offset.



#46 Rich V.

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Posted 27 May 2016 - 04:34 PM

Divergence is much harder for our eyes to accommodate than convergence since our eyes are used to converging when looking at close up objects.  We don't do "wall eyed" well.

 

Alignment error is easier to quantify when related to the image space; this factors magnification into the discussion.

 

Posted March 2005 by Claudio:

The tolerated apparent alignment errors (= referred to image space, i.e. the images seen through the eyepieces, i.e. magnified by the binocular under test) I have more often found are:

 

Vertical step: 15 arc minutes
Divergence: 20 arc minutes
Convergence: 60 arc minutes

 

 

Your 30' divergent error is beyond Claudio's 20' tolerance; I can see why you feel it isn't quite right.  Your other bino heads are within tolerance.  His full post is quite illustrative, IMO.  His other posts in the thread are good reading as well.  I wish he came around the bino forum these days; I miss his clear explanations.

 

Claudio's alignment tolerances relative to the image space

 

 

Rich



#47 Gordon Rayner

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Posted 27 May 2016 - 06:05 PM

I  now recall    a discussion   of    parallelism  of the sight lines   in a classic  post -WW II   British  book,  Pitman  published,  IIRC, whose author  was L. C.  Martin,   IIRC.   His equations   included  magnification  ,   and, IIRC,  were  simple, but   more precise   than  what appears above in  my   # 30,  then in  #34 and # 37.  

 

I have  that book,   maybe nearby,   maybe not.     Perhaps somebody  else has it, or is near   a  library which  does.

Google,  Amazon, ??

 

ADDENDUM:

 

BINGO !    Google   shows   free downloads  of  Voumes  I and II.    I searched via    "L.C.  Martin   optics  book,  Pitman" , or something very close.    

 

1948.   Do Pitman  and /or Martin yet exist ?    Or their heirs or assignees?  Or, is that book now in the public domain?

 

I  here posted  pics  from  hard-to-find   references , older than that,  public domain  government material, .

 several  years  ago,   but    they  were   removed .

 

Music from the '20 's   and '30's   have been  removed from YouTube  in  some  instances which I saw.  I liked

"Parlez-moi  d'Amour "    original  female  artist's  version , now gone.    


Edited by Gordon Rayner, 27 May 2016 - 06:37 PM.


#48 GlennLeDrew

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Posted 27 May 2016 - 08:26 PM

Perhaps I'm misinterpreting the meaning of "relative to image space" when *magnification* factors into it. For myself, magnification can be--and is--completely ignored.

 

When I assess and adjust a bino's collimation, such as with a comparator like the one I built last summer, I can only rely on my own resolving power. This renders the instrument's magnification superfluous. Whether 2X or 200X, the same 1-2 arcminute limit applies. My eyes don't care what the magnification is; all that matters is the divergence from parallel of the two light paths for some particular image point *in air behind the eyepieces.*

 

If my eyes demand a limit of 4' in departure from parallelism, why would I express this as a limit of 0.4' when the magnification is 10X, or 0.04' when the magnification is 100X? This requires to know the magnification and multiply it by the stated error, in order to compare to the unit magnification of the unaided eye. Far simpler to merely regard the behind-the-eyepiece angular divergence, which is quite independent of magnification.

 

Again, the eyes care not about magnification. The only relevant factor is the perceived angular offset of the two images they're attempting to fuse. To the eyes, the same 2' limit in vertical offset applies whether the images are magnified 2X or 200X, whether the instrument be a binocular microscope or telescope, or whether the two images be supplied by a complete system for each eye or one system with a binoviewer. An angle is an angle is an angle. That most relevant angle is *external* to the instrument, behind the eyepieces, and thus is de-coupled from magnification as far as the eyes are concerned.

 

I now wonder; in what way does my consideration of the matter differ from the "relative to image space" scheme?



#49 GlennLeDrew

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Posted 27 May 2016 - 08:36 PM

To buttress my thesis, in which magnification is irrelevant, consider a binoviewer. If a unit has a certain degree of mis-collimation for a certain eyepiece focal length, that same offset seen with that eyepiece pair will be observed for *any* telescope the BV/eyepiece pair is attached to. Whether it be a small scope working at 30X, or a huge scope working at 500X, the perceived image offset will be identical in angle. Magnification is utterly irrelevant.

 

And in the same way for a true binocular can magnification be ignored; it's a redundant variable that invokes unnecessary calculation.



#50 Rich V.

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Posted 28 May 2016 - 12:29 AM

Glenn, maybe I have the wrong impression but I've always interpreted the deviations stated as "collimation standards" as being before the eyepiece, not after.  The actual deviation from parallelism between binocular barrels...

 

Bill C stated two different standards for two different magnifications.

 

I'll quote him again:

 

"Alignment that is within the original JTII standards can be considered to function as “perfect” in that the eyes can easily accommodate the error without introducing noticeable eyestrain. For example, an 8 power instrument should have errors equal to or less than 4’ Step, 10’ Divergence and 6’ convergence, with a 16 power having 2’, 6’ and 3’ respectively."

 

He's saying that a 16x bino can only have half the alignment error that can be tolerated in an 8x bino.

 

That's why I found Claudio's absolute standards more easy to relate to:

 

--quote--

 

"The tolerated apparent alignment errors (= referred to image space, i.e. the images seen through the eyepieces, i.e. magnified by the binocular under test) I have more often found are:

 

Vertical step: 15 arc minutes
Divergence: 20 arc minutes
Convergence: 60 arc minutes

 

But Bill, Cory and anyone who overhauls seriously binoculars would stay well inside these limits. “Tolerances are for those who can’t get it right”, isn’t that so, Bill?

 

A reason more to adopt apparent alignment errors, i.e. data referred to the image space: they are what the eye see through the eyepieces, so they indicate (or SHOULD INDICATE, but let me say again that they are too permissive) the threshold that says what eyes sense. So, in your 16x the axes step of 3’ doesn’t give me an immediate, graphic idea of how much the misalignment is detected by eyes, on the contrary the resultant apparent step (= the step detected on the image space = 3’ x 16 = 48’) make me instantly think that your glass would benefit a lot from an overhaul of Bill or Cory. That vertical step at 100 m is about 9 cm, negligible at most for a 5x, but not for a 16x.

 

The data reported by Seyfried are too “tolerant”. Moreover,they give the same maximum axes errors for too wide ranges of magnification. For instance, in those tables a 5x and a 10x can have the same allowed axes errors, which cannot be."

 

--end quote--

 

You're saying all this is incorrect?    :confused:

 

Rich




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