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Near out-of-focus point, program to determine

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#51 j.gardavsky

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Posted 24 May 2021 - 08:14 AM

I changed the 2-stage-lens program

   so it will accept the focal length of the objective directly

   (instead of assuming FL = 4 *diam for binoculars).

 

I have a nice Keplerian spyglass with an achromat

    and a fine Plossl EP. It makes you woozy to hold the

    fully-inverted and reversed image steady, but the clarity is amazing.

Anyway, it is longer than a 30mm binocular would be.

 

When I put an objective FL of 186mm (F6) and a power of 10 into the

    2-stage lens program, I come up with an infinity-focused near range

    distance of:  122 feet.

    Testing this out the window, I come up with an observed near-edge of range

      of :   130 ft. (the object is at 130, couldn't pick exact distances to trunks).

 

So.....the range modeling looks very good at F6 and various powers of F4...still great. 

I can add other long-barrel range tests now..

Hello Martin,

 

this sounds like your formulas are working well.

Thank you for the good news,

JG
 



#52 Henry Link

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Posted 24 May 2021 - 08:35 AM

Henry,

 

I assume when you say that "The iris cannot correct the aberrations of the binoculars" that you mean any iris placed behind the eyepiece, not just the eye's iris. You can test that. Since you are equipped to boost the magnification of your 7x50 to 56x you can precisely evaluate its aberration levels directly using a star test rather than indirectly inferring them from the subjective appearance of the image at 56x.

 

I used an artificial star in subdued light, but a glitter point of the sun outside should work equally well for observations at 56x, but perhaps not so well at 7x since your eye, if it responds like mine, will be closed to about 2mm. That's so close to the stopped down apertures I'm going to suggest that it may interfere with the results.

 

Make two stop-down masks, one about 14mm in diameter for the front of objective lens and one about 2mm in diameter for the back of the eyepiece. For lack of something better I made my 2mm mask by carefully poking a hole in a piece of aluminum foil with a ballpoint pen and then stretching the foil over the eyepiece eyecup with the hole centered over the eyelens and hopefully standing out at about the eye relief distance.

 

With the binocular at full aperture bring the star to best focus at 56x in one side,  In every 7x50 I've ever tested the focused star is a big mess, with plenty of chromatic aberration and enough spherical aberration to prevent a clean Airy disk from forming. There could be (probably are) other defects like astigmatism, pinching, coma, etc. Those will likely vary from one side to the other, so it's best to carry out the test on only the "better" side.

 

Now position the objective stopdown mask and see how the the aberrations are reduced. In the binocular I testing I could see  a pretty clean Airy disk with one diffraction ring. Remove the objective mask, position the eyepiece mask and place your eye as close as possible to the opening. What I saw was exactly the same clean Airy disk with one diffraction ring. Whether the stop was applied in front of the objective or behind the eyepiece made no difference.

 

Henry


Edited by Henry Link, 24 May 2021 - 09:07 AM.


#53 MartinPond

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Posted 24 May 2021 - 09:14 AM

Looks like more observers are discovering things with masking, in various places.

  (your eyes have to be keen to profit, of course)   Awesome.  

Even masking the EP eye lens affects aberrations most?  Fascinating.

When I blow up the final image to check it out, I have a nice 6x16 monocular to help.

 

 

My next stop for testing the 2-stage lens program is the 

   70x600 scope I retain because of its uncanny contrast and quality..

 

I set up the simulation for a 30mm EP, (20x), got the number

   (near-limit for 1/20th EP FL fuzzing), and went to check.

   The "squared rule" for range has been exceeded, but it's just an approximation...

   With a focus at infinity, I am supposed to see the image get fuzzy at.... 

     240 meters (790 feet).

    The setup won't work out my window, since my 'far' target is ~240 meters.

     SO...I jaunted down the the hilltop office park and focused on a cloud

      miles away for infinity.   What was the near distance where things got 

      fuzzy?   With the laser rangefinder, I got    760 feet.

      Not bad compared to the predicted 790 feet.   Still....crazy distant.

 

   One thing this sort of shows is how terrible the range becomes at

      high objective FL and power.   Looking up at the heavens, it is

      all close enough to infinity, of course. 


Edited by MartinPond, 24 May 2021 - 02:38 PM.


#54 Henry Link

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Posted 24 May 2021 - 10:26 AM

Sigh...Reading the above leaves me feeling that the situation in this thread is hopeless. So, I'm signing off again, this time for good. I don't have the time or patience for this.



#55 MartinPond

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Posted 24 May 2021 - 02:37 PM

The observations of what happens to a point are very interesting, though.

There are multiple layers of image affliction...you have explored at least a few

   finer ones with a sensitive technique.   

 

In ordinary binocular operation, you can see abberations affecting the edges

   of a real focused object, especially when you blow up the object.

If you move the focus wheel a little, the image becomes very fuzzy.

At that point, you can't see the aberrations any more, the blurring is so bad. 

Being out of focus is simply in a bigger ballpark, orders of magnitude worse.  


Edited by MartinPond, 24 May 2021 - 08:48 PM.


#56 ECP M42

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Posted 25 May 2021 - 01:24 PM

I assume when you say that "The iris cannot correct the aberrations of the binoculars" that you mean any iris placed behind the eyepiece, not just the eye's iris.

I have done all the necessary tests. Even during the day, but I still don't see any improvement, as the mask can. What I see with your experiment of masking the eye is an improvement in the defects of my eye (astigmatism, etc.). What I see is that in part, but mostly in appearance, it seems to improve the performance of the binoculars, but only improves the eye.

 

I also tried to blur the light point slightly, up to the size of the aberrations of my eye. In this case the mask on the eye slightly reduces the diameter of the disc, but just as it reduces the aberrations of the eye, how perfectly it is in focus. Nothing more.

If instead I put the 2mm mask in front of the lens, then yes I can clearly see the typical diffraction pattern (but with only the first clear ring).

 

If your test is done during the day, with the addition of the 8x multiplier (i.e. with an 8x2 binoculars as a magnification multiplier), I can see even better that the image improvement refers only to the eye and not to the binoculars under examination. (the 7x50), which continues to present the same exaggerated volume of aberrations that it is endowed with. But it is sufficient to mask it at 20mm (7x20), because the image acquires a fabulous sharpness, impossible to obtain with the masked eye.

 

But all this also seems very logical to me: how can the iris affect the aberrations in the image that has already been formed by the lenses of the binoculars?

 

It is not possible!

 

 

 

During the last century, in my country there was a character who drank a lot, nicknamed Stopàj (cork, bottle cap - now there is also a wine with that name) and who said so many funny things.

One night, a policeman on horseback saw him bent over looking at the ground under the light of a street lamp. He came up and asked him, "Are you okay? What are you doing here?"

"I'm looking for the watch I lost"

"but where did you lose it, exactly?"

"I lost it down there"

"so why are you looking for him here?"

"because there is more light here!" 

 

lol.gif lol.gif lol.gif  ... wink.gif



#57 MartinPond

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Posted 25 May 2021 - 10:24 PM

Not possible?    Anything's possible, if you look just right!  ;-)

 

ECP M42:  You are looking at images of things.

        H.Lnk is looking at artificial stars....points, not lines or curves.

        I can see the different results, but I prefer to look at

        real, distributed things and rank them.  And the edges wash away

        very quickly when I de-focus,  aberrations and all.

        So....what matters more?

 

In range-figuring, you are concerned with the crumpling of

   the body of a train-wrecked car,   not the cracks in its tail-light.


Edited by MartinPond, 25 May 2021 - 10:26 PM.


#58 ECP M42

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Posted 26 May 2021 - 04:28 AM

Sorry, Martin. I went into your thread and moved the needle of the speech by involving Henry Link on the pending DOF topic.

I don't know if it is right to interrupt here or continue, but you continue ... I follow.



#59 Henry Link

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Posted 26 May 2021 - 07:13 AM

 

 

But all this also seems very logical to me: how can the iris affect the aberrations in the image that has already been formed by the lenses of the binoculars?

 

It is not possible!

 

 

 

 

The sirens' song comes again. Next time I'm putting wax in my ears! 

 

The impossible is made possible because the image that forms at the exit pupil and falls on the iris of the eye is a focused image of the objective lens itself, not a focused image of the the objective lens's focal plane. Therefore, the only rays from the objective that can enter the eye are those from whatever central part of the objective the iris can accept. If the iris is open to 7mm it can accept the full ray bundle from the 50mm aperture of a 7x50 with all its aberrations. If the iris is open to 2mm it can only accept a ray bundle corresponding to the central 14mm of the the objective lens, a bundle with much lower chromatic and spherical aberrations than the full aperture. The final image of the objective's focal plane (the one we actually "see") doesn't form until the light reaches the retina.

 

Throw me overboard if I come back again.


Edited by Henry Link, 26 May 2021 - 07:22 AM.

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#60 MartinPond

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Posted 26 May 2021 - 08:04 AM

Henry's core assumption concept is, I think, that 

    aberrations are the cause of limited range, not

    plain defocusing.  That becomes clearer each time..

 

As such, using aberrations as the one or main determinant of 

   in-focus range is outside the topic of this thread.  

That's why I have honed in on the problem.  It has

  propagated for many years.

 

I might try an aperture at the eye, but perhaps in its own thread.

 Focusing in on the tests and factors, as it were, helps clarify things.

 

-----------------

Ah.....just put a little trial in this thread..

---I put a 35mm EP into my 800x400 scope (forest daylight)

---then focused at 200 yards

---then swung to the tree trunk at 65 feet

    --- it was pretty blurry

----I found a spacer that was about the eye relief length,

           and put foil with a 1.5mm hole over that

    ----it did improve image

    ---but my eye was 2 ERs away.

         ...I put my eye right next to the foil...very close.

            ..more like the real iris.   Things went pretty fuzzy again.

       If the foil were where my actual pupil was....meh, I can't see

      how the focus would be better. Far back, sure, but tiny afov.


Edited by MartinPond, 26 May 2021 - 10:12 AM.


#61 Henry Link

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Posted 26 May 2021 - 10:04 AM

It’s just the opposite, Martin. I abandoned the use of extended objects for evaluating DOF in favor of highly defocused artificial stars in order to completely isolate defocus from everything else, like aberrations and accommodation.

 

Throw me overboard.



#62 MartinPond

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Posted 26 May 2021 - 10:17 AM

Defocused artificial star....it's hard to figure how that compares.

The source is still a point..

 

I got a 1.5mm foil iris foil to clean up the defocused view a bit,

but it got fuzzy again as I moved my eye very close.

The foil was about at the ER point.

So the foil hole that improved things was at roughly 2*ER.



#63 Henry Link

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Posted 26 May 2021 - 10:58 AM

Yes, the source is a point, but when that point is highly defocused by simply moving it much closer and examining it through two telescopes of the same magnification and effective apertures (both focused at the original distance to the point), then the point forms a diffraction disk and the eye will see it as exactly the same size in both scopes, indicating the same amount of defocus, even if one telescope has very high aberrations and the other very low aberrations.

 

Toss me back again


Edited by Henry Link, 26 May 2021 - 12:50 PM.


#64 MartinPond

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Posted 26 May 2021 - 11:39 AM

It is interesting to note that it has an effect, period...

   ...so "I can see it".  It is a thing.

And..I saw it with a real object.

    

And....it is similar to the effect of a teeny mask way out front.

This is interesting....the cone-portion effect, at front and at back.

 

Given my cases with 12.5% moon filter and dusk,

    I'm not sure it fits into normal use of the binoculars.

    So a shift: you are saying it's diffraction, not aberration?

 

I was experiencing small-camera effects, though...I think.

Untill I put my ey at the ER....and then it was fuzzy again. 


Edited by MartinPond, 26 May 2021 - 11:50 AM.


#65 Henry Link

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Posted 26 May 2021 - 12:42 PM

It doesn't appear to me that we are talking about the same subject at all, maybe not even living on the same planet. So, this time I'm really going to leave this to you and the other Henry to work out. If I have any objections I'll just keep quiet.



#66 KBHornblower

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Posted 26 May 2021 - 01:28 PM

Out of curiosity I did some calculations with the formula 1/Fo + 1/Fi = 1/F, with hypothetical telescopes of the same aperture and magnification, but different objective focal lengths F.  They were focused at infinity and looking at a hypothetical point source at the same distance Fo.  I found that the blur circles as seen through the eyepieces had nearly the same angular diameter, and that the same amount of accommodation by the eye would bring it into sharp focus.  The greater the ratio of Fo to F, the more nearly exact the result was.  Of course, this is thin lens approximation textbook optics, but it should work well for typical bird watching range.



#67 MartinPond

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Posted 26 May 2021 - 01:35 PM

Not sure whay you are seeking a point sources again

 

Out of curiosity I did some calculations with the formula 1/Fo + 1/Fi = 1/F, with hypothetical telescopes of the same aperture and magnification, but different objective focal lengths F.  They were focused at infinity and looking at a hypothetical point source at the same distance Fo.  I found that the blur circles as seen through the eyepieces had nearly the same angular diameter, and that the same amount of accommodation by the eye would bring it into sharp focus.  The greater the ratio of Fo to F, the more nearly exact the result was.  Of course, this is thin lens approximation textbook optics, but it should work well for typical bird watching range.

Not sure why you are looking at a point source instead of looking out your window   at birds.   

  It is a very common experience people have that a 7x35 has a wider in-focus

  range than  a 10x50.  The 10x50 binoculars always have a longer FL//objective.

 

How did you calculate blur circles with 1/Fo + 1/Fi = 1/F?


Edited by MartinPond, 26 May 2021 - 02:54 PM.


#68 MartinPond

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Posted 26 May 2021 - 01:41 PM

It doesn't appear to me that we are talking about the same subject at all, maybe not even living on the same planet. So, this time I'm really going to leave this to you and the other Henry to work out. If I have any objections I'll just keep quiet.

I realized what was probably happening when looking through

   a small mask out front or a pinhole out back.

 

I was looking through a pinhole camera.

A pinhole camera doesn't really care what the lenses are.



#69 ECP M42

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Posted 26 May 2021 - 07:47 PM

The sirens' song comes again. Next time I'm putting wax in my ears! 

You do not hear what I say, you do not read what I write, you do not answer my questions, you do not do the tests I do, you offer me tests that do not explain anything or rather prove the opposite, you do everything to escape from here, but then you come back always (and I'm glad) ... 

 

How should I do to bring the speech to a resolution consistent with reality? 

 

 

Here you state that: "the image that forms at the exit pupil and falls on the iris of the eye is a focused image of the objective lens itself, not a focused image of the the objective lens's focal plane.

 

For me it is obvious that if you start from an incorrect precept, you have no chance of arriving at a thesis consistent with reality. What you see only has the round shape of the aperture, but the focused plane that is actually printed on the retina, is decided by the eyepiece based on the focus within the three-dimensional image space formed by the lens. In other words, you are not looking at the lens glass, but a slice-section of the image that it produced by converging the light of the object space. 


Edited by ECP M42, 26 May 2021 - 07:49 PM.

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#70 KBHornblower

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Posted 26 May 2021 - 08:49 PM

Not sure whay you are seeking a point sources again

 

Not sure why you are looking at a point source instead of looking out your window   at birds.   

  It is a very common experience people have that a 7x35 has a wider in-focus

  range than  a 10x50.  The 10x50 binoculars always have a longer FL//objective.

 

How did you calculate blur circles with 1/Fo + 1/Fi = 1/F?

If a nearby point source is accurately focused, it follows that a bird at the same distance will be accurately focused.  After all, the light reflected from the bird or any other extended object is coming from a multitude of points on the bird.

 

You are comparing binoculars with different apertures and magnification, and there is no doubt that the smaller glass will have far greater depth of field.  Your assertion that the difference in focal length is responsible for this does not necessarily follow.  I am challenging your assertion by properly controlling the variables, that is, keeping the aperture and magnification the same while changing only the focal lengths of the objectives and eyepieces in hypothetical instruments.  I will not be bothered with finding such instruments for this purpose, let alone buying or borrowing them.

 

Now I will show you the number crunching in excruciating detail.  Suppose we have a 10x50 f/5 glass consisting of objective F = 250mm, and a 25mm eyepiece accurately focused for infinity.  The object is at 25m.

 

I am confident the following work refutes your assertion.

 

1/Fo + 1/Fi = 1/F

 

            1/Fi = 1/F - 1/Fo

 

Plug in given numbers in mm.

 

1/Fi = 1/250 - 1/25000 = 0.004 - 0.00004 = 0.00396

 

Fi = 252.5252525mm  (precision limit of my calculator)

 

The focal point from the nearby object is pushed back 2.5252525 mm.  Bear with me on these empty figures.  They will give me a cushion for further work.  In this sort of thought exercise we can take the given measurements as exact. 

 

Let blur circle diameter d be the diameter of the Fi light cone at distance F from the objective.  An exercise in similar triangles gives

 

d = a(Fi - F)/Fi, where a is the aperture of the objective.

 

d = 50(252.5252525 - 2.50)/252.5252525

 

If this is truly a repeating decimal the result is exactly 0.5mm.  If not, it will not be off by more than about one part in a million.  The angular size of this blur pattern as seen through the eyepiece is 0.02 radian, a little over a degree.  This is assuming no accommodation by the eye, and my rebuilt eyes are incapable of accommodation.

 

Now consider a 10x50 f/10 scope, meaning F = 500mm with a 50mm eyepiece.  To make the same angular blur we need d = 1mm.  We can work back to find what Fo is needed for this condition.  Again, d = a(Fi - F)/Fi.  Solving for Fi,

 

Fi = [a/(a - d)]*F

 

1/Fi = [(a -d)/a]*1/F

 

1/Fo = 1/F -1/Fi  = 1/F - [(a - d)/a]*1/F = {1 - [(a-d)/a]}*1/F

 

Plugging in numbers for a and d,

 

1/Fo = {1 - [(50 - 1)/50]}*1/F = (1 - 49/50)*1/F = 0.02/F

 

Fo = 50F = 25000mm  = 25m

 

Same view as the other scope.



#71 MartinPond

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Posted 26 May 2021 - 11:44 PM

I actually follow you 2/3rds of the way! Awesome.

I'll have to return later to pick through this 'blur-diameter',

   but you based it it entirely on the lens equation, so I have to love that..

   intriguing.   "I''ll be back", as Arnold would say...

 

To clarify:

"

You are comparing binoculars with different apertures and magnification, and there is no doubt that the smaller glass will have far greater depth of field.  Your assertion that the difference in focal length is responsible for this does not necessarily follow.

"

 

You share my assertion  that a 6x30 , for example , has a greater depth of  field than a 10x50.

How can I refuse what many witnessses see....when I hand them the binocs?

 

No.....actually: wait, you are comparing a   10x30 to a 10x50?

"controlling the power"? ..... There is a chance we are both right,

   but that does leave my hanging on proving FLobj.

 

You are assuming the same power,

  but I am assuming marching objectives and marching powers,

   because that's what's available to buy.....what we can buy.

   It's very hard to buy a 10x30 pair, for example.

    I do happen to have a long 10x30 spyglass I made ..... interesting for tests.

    Has a long fl objective, Keplerian set-up.

 

The detail wasn't excrutiating...cool.   Not yet, anyway.

 

The tendency can be tested.  Easier to test obervation than equation, of course,

   but I will try to understand the 'blur diameter'.   I have been relying on the 

    standard of the  the "push" on the image (we share that term!)

    being off by something like 5% of the focal length of the eyepiece.

    Is that not quite right?  If you say why in a satisfying way....I won't even 

    have to grind theough all of the above.....maybe I can alter the "off-by" standard

    and my program can grind on, corrected.

 

I am close...


Edited by MartinPond, 26 May 2021 - 11:54 PM.


#72 MartinPond

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Posted 27 May 2021 - 07:24 AM

Empirical test of the assertion:

"If you keep the power the same,
  the depth of focus for a long barrel and
  a short barrel of the same aperture
  will be the same.

So, the players:
   set#1----a 80x400 telescope
            with a 17mm eyepiece (23.5x)
   set#2----a 80x720 telescope
            with a 30mm eyepiece (24.0x)
The actions:
   ---adjust to focus at 200 yards
   ---swing telescope to objects at 125 , 85 , 65 , 45 feet 

Results for set#1:
       focus at 200yds,just sharp at 125ft , quite blurry at 85ft

Results for set#2:
       focus at 200yds  .... a bit blurry at 125ft , quite blurry at 85ft

Conclusion:
    It looks like the longer barrel, with the same power,
             comes out of focus at a greater distance.
     The focuser travel for the 720mm barrel
              to achieve focus again is about 4mm.
     For the 400mm barrel, it takes 1.5mm of travel.
     The results lean against the same-range hypothesis, to my eye.
     However, the difference in focuser travel is small.

     Power closer to regular binoculars would be handy..



#73 MartinPond

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Posted 27 May 2021 - 02:44 PM

OK....I understand what you say about the 'blur,,
which is the diameter the light occupies
instead of the zero of perfect focus.

So,   with a 250mm prime FL, assuming focus for
     infinity to start, and then looking at a target
          25000 millimeters away (25 meters)
"
1/Fi = 1/250 - 1/25000 = 0.004 - 0.00004 = 0.00396
     Fi = 252.5252525mm 
"
...that all checks out, and is just what I would do.

So, assuming things "spread in"  from a 50mm diameter,
  the eyepiece ends up seeing a fuzzy cone slice that is
  (2.5252/250) * 50(the diam of the objective wide)
     =  0.5mm diameter.  
            ...and this is seen by a 25mmFL eyepiece

----------------------------------  

And, you do it again for 500mm fl // 50mm fl
   ...oops....no, you insert the number from part#1.

I am going to do part1 over, as 500mm // 50mm, to avoid
    contaminating one example with products of another example.
    SO:
     1/500 - 1/25000 = .002 - .00004 =  .00196
     AND:   Fi =  1/.00196 =  510.204mm
     So the blur becomes:  (10.204/500) * 50 = 1.0204 <--blur diameter
    
So....a 1mm blur, as seen by a 50mmFL eyepiece.
    Seems the same, angularly.....

------------------------------------------

So...I get it.  Mathematically..

This is based on a model of a disk of light, though,
  assuming it is the same as the light falling on a ground glass screen.

  It is a real thing to be refocused beyond.

But that is different than the actual rays passing through that disk area,
   arriving from different places on a bird, or Jupiter.
I feel like we need a ray-tracing type to follow things home, to the retina.
It isn't focusing anymore, so it comes down to rays.

The way the objective diameter works into your story defies
actual observations, too.   I looked at masking from 50mm
  to 35 to 25, and it only mattered (brought the near target into focus)
   at 12mm...

 

 

 

Hmmmm...
I don't think either of us has it right.

My model seems to work, but maybe by coincidence.

Calling all ray-tracers! You need to walk all the way to the retina.


Edited by MartinPond, 27 May 2021 - 02:45 PM.


#74 KBHornblower

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Posted 27 May 2021 - 10:45 PM

I thought of the possibility that a ground glass view and a direct view might make different sized spots on the retina.  My preliminary approximate ray tracing indicates that they do not do so.  Sometime tomorrow, when I am fresh, I will do it precisely with the calculator to look for the possibility of minor differences.  I do not expect anything remotely approaching the difference between a 10x50 and a 7x35.


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#75 MartinPond

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Posted 28 May 2021 - 09:22 AM

"

the difference between a 10x50 and a 7x35.

"

Excellent!

   Now you are on a practical page,

    with real, commonly manufactured products.

 

 

And as such, you must consider that the 

7x35 has an Fobj of 4*35 = 140mm (give or take)

and the

10x50 has an Fobj of 4-50 = 200mm

 

But we need to re-do the 1st image location...

 

So...starting with each focused at infinity.....

    and looking at a target at 25 meters  =  25000 millimeters

 

1/140 - 1/25000 = 1/(i)

 

.007142857 -  0.00004  =   .007102578

  so, i = 140.788418   (7x35 case)

 

and 

 

1/200 - 1/25000 = .005 - .00004 =  .00496

so, i = 201.6  (10x50 case)


Edited by MartinPond, 28 May 2021 - 10:09 AM.



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