Focusing for Smooth Transition Between EP and Camera

[Scorpius]

Greetings Fellow Stargazers,

Have been experimenting with solar system imaging using Celestron 8" OTA and Neximage 5. Main two issues have been, 1) Keeping target centered in the frame on laptop and 2) Achieving initial eyepiece focus equivalent to the camera focus necessary for imaging. I've decided issue #1 is due to my mount, which I plan to upgrade in the near future, but issue #2 appears to have more to do with technique. Good pre-focus would seem to be a critical part of the process because if you're not very close to camera focus when you switch over, the object may not even appear on the PC screen at all! Then you start wondering if it's because you're out of focus (only takes a slight difference to cause an object not to appear) but then if you spend much time at all adjusting the focus in order to "find" the target, you soon realize the object is no longer centered and that means you have to go back and start the process all over again.

So here's what I'm currently doing and also what I'd like to achieve in terms of focusing - To start off, I center the target in my 20mm reticle EP then switch to an 8mm EP and adjust the focus. I'm using an 8mm EP because Celestron's literature says the Neximmage 5 CCD is equivalent to a 7mm EP however, as you might know the Celestron EP kit I have came with a 6 and 8 but no 7. So anyway - Since I've heard you want to keep as much glass as possible out of the light path for imaging, and since my current diagonal seems to throw off the focus more than a simple difference between an 8 and 7mm EP, I've been inserting the EP directly into the barlow (attached to the visual back) without using the diagonal at all. Of course the disadvantage is having to crouch down to get a "straight through" view of the object in order to achieve good pre-focus before switching over.

What I'd much rather be doing is using the diagonal along with the EP and then removing them together as a single unit which would allow me to just pop the camera into the barlow for a quick transition with no unnecessary glass in the optics path. I recently ordered a Televue 2.5X Powermate and a Televue Everbrite diagonal hoping that combination will be parfocal between the EP and camera and if so, I may pick up a 7mm eyepiece to find out if that combination would be consistently accurate enough to switch from EP to camera with no significant change in focus.

Anyone have any thoughts on this theory or suggestions for a different approach which would yield the same results?

Thanks in advance for your interest in my predicament and for your time...

Scorpius

[Leveye]

I use a Celestron 8" SCT and sometimes get the object centered with noeyepiece just looking thu the scope. Sounds weird but it works. Also a well adjusted  beforehand guidescope does wonders.

[Steve Ward]

When they say it's "the equivalent of a 6mm EP" they mean the FOV captured by the camera is an approximation of what can be seen with the naked eye through that EP , it doesn't mean you can swap one for the other and still be in focus.

I would practice focus in daylight on a long-distant object , Moon is ideal , and make a note of where focus is reached with both the EP and camera set-ups , a mark on the drawtube in Sharpie or similar will help you get pretty close to start with and save a lot of guesswork in the dark later.

As Leveye says , make sure your finderscope is aligned spot on to start with using your shortest EP , and a good polar-alignment will stop the target drifting from the FOV while you are setting up.

Then centre the target in the EP as accurately as you can before switching to the camera.

When you connect the camera , turn all the Gain , Exposure and Brightness setting to maximum in order to give yourself an easier task of spotting an out of focus disc.

You should now just need to rack the focuser to the appropriate point and the planet should appear on screen , adjust the camera settings to suit , nail focus and you're all set.

Personally I always focus on a bright star near the intended target using a Bahtinov mask , lock focus , and then slew back to planet .

[ronin]

What you can do is make an attachment that locates the camera at the same focal plane as the eyepiece focal plane, simple piece of tube. Although it may need to be an extention for the eyepiece I would suspect rather then for the camera.

That way when you view and get the object in focus you can swap and have the object in good focus on the camera.

[JRWASTRO]

What you can do is make an attachment that locates the camera at the same focal plane as the eyepiece focal plane, simple piece of tube. Although it may need to be an extention for the eyepiece I would suspect rather then for the camera.

That way when you view and get the object in focus you can swap and have the object in good focus on the camera.

Yes good idea and also this is what I attempt to do. First set up the camera to be in excellent focus with a focusing mask and fix the distance. Next use a "suitable" eyepiece in an extension piece and jiggle it back and forth for a perfect focus. Finally a couple of parfocal rings will fix the distance for good.

What is a suitable eyepiece? Choose an eyepiece with a field stop diameter equal to or as close as possible to the diagonal of the imaging CCD. This selection will ensure thet the camera FoV and Eyepiece FoV will be the same. what isimportant here is the field stop diameter as it determines the real field of view. What about magnification? Well you get what you get as we are interested only in FoV.

Jeremy.

Jeremy.

[Scorpius]

When they say it's "the equivalent of a 6mm EP" they mean the FOV captured by the camera is an approximation of what can be seen with the naked eye through that EP , it doesn't mean you can swap one for the other and still be in focus.

I would practice focus in daylight on a long-distant object , Moon is ideal , and make a note of where focus is reached with both the EP and camera set-ups , a mark on the drawtube in Sharpie or similar will help you get pretty close to start with and save a lot of guesswork in the dark later.

As Leveye says , make sure your finderscope is aligned spot on to start with using your shortest EP , and a good polar-alignment will stop the target drifting from the FOV while you are setting up.

Then centre the target in the EP as accurately as you can before switching to the camera.

When you connect the camera , turn all the Gain , Exposure and Brightness setting to maximum in order to give yourself an easier task of spotting an out of focus disc.

You should now just need to rack the focuser to the appropriate point and the planet should appear on screen , adjust the camera settings to suit , nail focus and you're all set.

Personally I always focus on a bright star near the intended target using a Bahtinov mask , lock focus , and then slew back to planet .

Don't think I could make a reference mark on the Celestron 8" OTA because it doesn't have a drawtube type focuser - just a knob that rotates clockwise or counter clockwise. I did order a Bahtinov mask at the same time I ordered the Powermate & new diagonal so when you say focus with the mask - then lock focus - then slew back to the planet, is that with the camera or the eyepiece in the scope? If it's with the camera, I'm just wondering if the stock Alt/Az mount would be accurate enough to put the target back in view on the PC when going from the focus star back to the planet. I've had no luck at all centering up objects on the PC if they're not at least visible on the screen when I switch from eyepiece to camera.

[Scorpius]

Yes good idea and also this is what I attempt to do. First set up the camera to be in excellent focus with a focusing mask and fix the distance. Next use a "suitable" eyepiece in an extension piece and jiggle it back and forth for a perfect focus. Finally a couple of parfocal rings will fix the distance for good.

What is a suitable eyepiece? Choose an eyepiece with a field stop diameter equal to or as close as possible to the diagonal of the imaging CCD. This selection will ensure thet the camera FoV and Eyepiece FoV will be the same. what isimportant here is the field stop diameter as it determines the real field of view. What about magnification? Well you get what you get as we are interested only in FoV.

Jeremy.

Jeremy.

This sounds like a good way to accomplish what I'm trying to do. Sounds like you would basically be "calibrating" the eyepiece to match the camera's focus point by installing the parfocal rings on the eyepiece tube so it stays calibrated to match the camera. It looks like the rings don't cost that much so I'll order some and give this method a try. Great idea and thanks for making this suggestion! Only thing I don't understand is what you mean by choosing an eyepiece with a field stop diameter equal to that of the camera in order to have the same FOV?

[JRWASTRO]

This sounds like a good way to accomplish what I'm trying to do. Sounds like you would basically be "calibrating" the eyepiece to match the camera's focus point by installing the parfocal rings on the eyepiece tube so it stays calibrated to match the camera. It looks like the rings don't cost that much so I'll order some and give this method a try. Great idea and thanks for making this suggestion! Only thing I don't understand is what you mean by choosing an eyepiece with a field stop diameter equal to that of the camera in order to have the same FOV?

OK . Field Stops ?

The attached picture (Field_Stops)   shows 3 different  eyepieces. two with 50 mm Barrels and one with a 31 mm barrel.  The 2" eyepieces have focal lengths of 30 and 40 mm but notice one (30mm) has an opening of about 35mm and the other (40mm) has an opening of about 48mm. This "opening" is the eyepiece field stop. Compare these field stops with the 31mm barrel. Notice that the field stop is only about 12 mm for the eyepiece has a focal length of 15 mm.

To calculate the field of view do the following sums:

 Divide the eyepiece focal length by the telescope focal length.

EXample : for the 30mm focal length eyepiece the field stop is 28mm and a 'scope with a focal length of 820mm gives a field of view of 28 / 820 Radians = 0.0341 radians. To convert this number to degrees multiply this answer by 57.3 so the field of view is 0.0341 x 57.3 = 1.96 degrees.  For the 15 mm focal length eyepiece the field stop is 12mm so the FoV is 0.84 degrees.

Here are a couple of pictures to show what this arrangement looks like in real life:

Kind Regards,

Jeremy.

[JRWASTRO]

Additional Explanation:

Angles are easily calculated using circular measure. To cut a long story short one may estimate the field of view by simply dividing a length of the arc of a circle by the radius of the said circle. If the angle is small then the arc may be approximated by a straight line. So if we have a focal length much larger than a ccd dimension or an eyepiece field stop then the angle subtended by the , say, ccd then the angle (fov) will be simply:

FoV angle = CCD dimension / focal length ... This angle is in Radians. Now there are pi radians = 180 degrees so 1 radian = 180 / pi degrees . For school boys pi= 22/7 an excellent approximation is pi = 355 / 113 so 1 Rad = 57.3 degrees.

Example:

A "full frame" CCD measures 36 x 24 mm with a diagonal of 43 mm

If the telescope has a focal length of , say, 820mm then the CCD "sees" a field of view of 2.5 x 1.7 degrees with the diagonal FoV of 3 degrees..

Now an eyepiece with a field stop of 43 mm will have a FoV of 3 degrees which is the same as the CCD diagonal FoV. So a 2" 30 to 40mm eyepiece will do a good job to be a good view finder.

Jeremy.

[Scorpius]

Jeremy,

Thanks for your great explanation of this somewhat confusing concept! It took me some time and further research to wrap my mind around the math but I think I understand it now (except for the length of the arc of a circle part and school boy pi's)  

Here's what I came up with to determine which eyepiece in my collection would make the best "view finder" for my Neximage 5 based on its diagonal FOV.

Given the Celestron 8" OTA focal length of 2032mm and the Neximage 5's  CCD dimensions of 5.7mm x 4.28mm = 7mm diagonal:

5.7/2032=0.0028x57.3=0.16

and

4.28/2032=0.0021x57.3=0.12

and

7/2032=0.0034x57.3=0.197

Then regarding the EP, since Celestron doesn't provide field stop diameters for their plossl eyepieces, I cheated a little bit and used the following formula to determine the True FOV of the 8mm eyepiece - AFOV/Magnification = True FOV

So given an 8mm eyepiece having a 52 degree AFOV:

2032/8 = 254 X magnification

and

52/254 = 0.2 degree True FOV

This would seem to indicate the Neximage 5 "sees" a 0.197 degree diagonal FOV and the eyepiece has a 0.2 degree FOV, therefore assuming my math is correct, this should be "close enough for government work" as it were.

I do have another question though. If it's necessary to install a parfocal ring on the eyepiece tube to achieve a focal point equal to that of the camera, how will that affect the eyepiece FOV if would affect it at all?

Thanks again for a great explanation and your patience with my newbie questions...

Scorpius

[gitchnz]

I use a Celestron 8" SCT and sometimes get the object centered with noeyepiece just looking thu the scope. Sounds weird but it works. Also a well adjusted  beforehand guidescope does wonders.

Thanks to you, I was able to pretty quickly locate both Mars and Saturn last night. Before that, I'd been having some real issues locating planets with my webcam using only a generic finderscope. Sure, pre-focusing the eyepiece is a must, but after that, it's really good to know the target is at least visible through the barlow before you go hunting it down with the webcam. 

[Scorpius]

gitchnz, thanks for adding to the thread. I definitely want to try the "bore sighting" technique Leveye described next time I get out. Far be it from me to start offering much advice, but have you considered getting a reticle eyepiece to help you hit the target more often when switching from EP to camera?

I have the Agena 20mm dual illuminated crosshair version and it does a great job. I think my main problem right now is the less than precise tracking performance of the SE Alt/Az mount but I hope to remedy that situation in the near future. However, when I do have to go back and start over right now, I put the 20mm back in and don't even re-focus but just center the out of focus "doughnut" on the crosshairs and that way when I put the 8mm back in, my focus is still in the ballpark.

Anyway, glad you're having good success and it just goes to show that even us newbies will eventually get there...

[JRWASTRO]

Greetings Scorpius,

First things first. When we were first taught, in school, about circles and euclidian geometry the value value of pi was always taken to be 22/7 as I found later this (3.142) is a terrible approximation but good for doing integer arithmetic in high school hence me referring sarcastically to my school days. An excellent approximation good to 7 places is 355 / 113 .

arc of a circle = part of a circle. 90 degrees = 1/4 of a circle = pi / 2 radians , in a circle are 2pi radians.

Ok on your calcs. Good stuff!

Those fields of view are narrow. Now the 7mm diagonal on the CCD says choose an ep with a field stop of 6 to 8 mm and the visible fov will be 0.2 degrees ( narrow isn't it? ) now you have pointed out that with the AFoV of 52 degrees the magnification is x 254 . Pretty good that you did the sums ... Now you have a "real" feel for the numbers ... Terrific.

About the AFov this is purely a function of the eyepiece so it is fixed by the eyepiece design itself, all the spacers do is bring the image into focus.

It is easy to find the field stop diameter ... Measure it with calipers or a ruler. BUT DO NOT SCRATCH THE FIELD LENS !

Generally for eyepieces with AFoV of less than or equal to 57 degrees ( 1 radian) take the field stop to be equal to the focal length as an approximation.

Close enough for Government work? I'm sure Uncle Sam would take issue with that!!

Jeremy.

[Scorpius]

Jeremy,

Thanks for your response. OK, I see what you mean - I've always used 3.14 as pi which would seem to be adequate for general calcs like the area of a circle = pi x (radius squared). You ever hear that joke where the little boy went to school and his dad asked when he returned home what he had learned that day? The boy said he learned that pi r squared at which time his dad proclaimed - What's wrong with those teachers boy? Everybody knows that pies are round!!! Terrible joke I know but kinda funny in a stupid sort of way...

Now, after making my last post I realized I didn't count my barlow lense when calculating EP True FOV = AFOV/Magnification. My new 2.5X Powermate arrives today so instead of refiguring based on the stock 2X barlow, I'll use a 2.5X magnification as so:

254X (8mm EP without Powermate) x 2.5 = 635 magnification with Powermate installed and 635X is way beyond Celestron's stated maximum useful magnification for the 8" OTA of 480X!!! Also, given a 52 degree AFOV/635 = 0.082 True FOV (rounded up). Based on these numbers it appears an 8mm EP is out of the question as a camera "viewfinder" with the Powermate installed and now I'm concerned I won't even be able to use my new Powermate for imaging which would be an expensive oversight on my part to say the least!

Is my math correct and do you think my concerns are justified?

Kind Regards,

Scorpius

[JRWASTRO]

Well, using x2.5 Barlow lenses have their place in obtaining images of planets but this is out of my experience or expertise. Here we are out of the scope of our original discussion. But I will pose a question and not answer it here as the answer will be quite involved. OK. However I would encourage you to find the answer.

Now when you look at images of planets under a magnifications below the "maximum" stated for the optics have you noticed that you are looking at details that are much smaller than the "resolution limit" of the optic? My question is why can one see detail much smaller than the resolution limit ?

A crazy question ( with quite a complex answer) what does an audio amplifier and our telescope imaging systems have in common?

As for your joke, My response to a comment on one of my jokes :- " We specialise in Bad jokes ! "

Jeremy.

[JRWASTRO]

Addition.

When talking about using an 8mm eyepiece as a "view finder" to simulate the view as it appears on the CCD mentioned above I would say that this holds true. The fields of view are the same. The focal length of 2032 mm is quite long and for most viewing a Barlow lens may not be required. Using a x2.5 Barlow is like ihaving a focal length of 5000mm this is "huge" and will be used for planetary imaging using " Lucky Imaging " techniques.

What one sees in the eye piece and what one sees on the screen need much explanation. We will need to discuss the issue of resolution as one sees it in the eyepiece and what is displayed on a screen. Normally what is done is one would estimate the "frequency response" of the system and use this information to estimate what one would image or view but this is rarely if ever done in our circles.

Jeremy.

[Scorpius]

Jeremy,

I think this is beginning to get way over my head in terms of technical expertise as all I was trying to determine initially was if there was an eyepiece I already had (or could purchase) that, when properly focused, would come close to matching the camera's focal point to avoid the need for major focus adjustments when switching from EP to camera. It was only after you mentioned that it would be good to choose an eyepiece with roughly the same FOV that I considered FOV through the eyepiece at all.

I did find another thread on this forum that somewhat speaks to my last question http://stargazerslounge.com/topic/213180-best-ep-for-planetary-viewing/page-2 and basically what they're saying is a Powermate doesn't reduce the AFOV but it does cut the True FOV in half. All I know for sure is the image of Saturn below was captured (after stacking) with the Neximage 5 attached to the standard Celestron 2X Barlow and (assuming the magnification of that combination would be approximately the same as the 8mm eyepiece + the same 2X Barlow) I would have already been at X508 (2032/8 = 254 x 2 = X508) which exceeds the maximum useful magnification of the 8" OTA as stated by the manufacturer. However, since the image is acceptable (at least to me) maybe that highest useful magnification figure is not chiseled in stone.

At this point, I guess the only thing to do since I've already purchased the 2.5x Powermate with imaging in mind, is to try it out and let the "proof be in the pudding" so to speak. Not sure about the "lucky imaging" technique but if a little luck makes for better results, then I'm all for applying said technique. I just wish the Neximage 5 didn't have such a tiny chip but when I made that purchase it was my intent to just "get my feet wet" with some basic solar system imaging but as is apparently often the case, I no more than got started before wanting to upgrade to something better.

I'll let you know how it all turns out and thank you very much for all the useful advice and also for your great explanation of the math...

All the best,

Scorpius

[JRWASTRO]

Very nice picture indeed Scorpius. Very good detail . These planetary images never cease to amaze me. Your sought of images gives me the incentive to have a go. Perhaps in our summer I will. As I said before, " I like it"

Jeremy.

[Scorpius]

Thanks Jeremy,

Don't mean to wear out that Saturn pic but you gotta remember - it's all I got right now because I'm new!

I stumbled over the following elsewhere on the web & will leave it at that however, I have no doubt it's accurate and it seems to confirm that focal lengths of 5000mm can work for planetary imaging under excellent seeing conditions provided a sturdy mount is used. With the 2.5x Powermate (which just arrived today) at a scope aperture of 2032, I'm at 5080mm which is pushing it I know. However, I'll bet I can make it work once I get a better mount, (which I was planning to do anyway & Celestron's AVX is on the short list). Then if I can zero in on the "right eyepiece", and add rings if necessary for a smooth transition, I believe the quality of my solar system images will improve as I continue to learn more about post-processing and the like.

For me the goal right now is not about observing but rather to capture some good video (to be processed in Registrax and Photoshop) of each solar system object which can be photographed. It's likely I'll only be trying this when seeing conditions are good to excellent as I really don't want a bunch of mediocre video to work with - but since there aren't that many good targets around right now, I'll just practice up in preparation for clearer skies this winter and more potential targets to choose from.

Best regards and thanks again for all your help...  

Scorpius

____________________________________________________________________________________

The biggest problem with imaging planets is that they appear small. For that reason you want to use a camera with small pixels and a telescope with a long focal length, things that shrink your field of view. The Barlow or Powermate will effectively give you a longer focal length. The focal reducer goes the other way, it effectively shortens your focal length.

From the posts on the Solar System Imaging forum I notice people using 5,000 mm focal lengths. You can get this with a 2,000 mm telescope and a 2.5x Barlow.

With long focal lengths / narrow field of views you need a sturdy mount. If you can't find the planet or keep it in the field of view then you would want to try shorter focal lengths by removing Barlows or adding focal reducers.

Obviously you don't want to use a focal reducer at the same time as using a Barlow.

As far as image quality, the fewer optical components the better. A single high quality Barlow or a Powermate will give you what you want with the least harm to the image quality. Sometimes you find someone stacking two Barlows though, because planets are so darn small.

_______________________________________________________________________________

 

 

[Scorpius]

Well, using x2.5 Barlow lenses have their place in obtaining images of planets but this is out of my experience or expertise. Here we are out of the scope of our original discussion. But I will pose a question and not answer it here as the answer will be quite involved. OK. However I would encourage you to find the answer.

Now when you look at images of planets under a magnifications below the "maximum" stated for the optics have you noticed that you are looking at details that are much smaller than the "resolution limit" of the optic? My question is why can one see detail much smaller than the resolution limit ?

A crazy question ( with quite a complex answer) what does an audio amplifier and our telescope imaging systems have in common?

As for your joke, My response to a comment on one of my jokes :- " We specialise in Bad jokes ! "

Jeremy.

Jeremy,

OK, I'll take a stab at answering your riddle - in layman's terms of course since I'm no engineer. So basically you asked how is an audio system like our telescope? Well, I suppose since sound and light both travel in waves that our telescope is simply an ingenious device designed to "hear" light. To further the analogy, let's consider the main lens (corrector plate in my case) of a telescope equivalent to that electronic eye gizmo in a CD player or maybe even the stylus of a phonograph designed to read those tiny little grooves on that rotating vinyl disk. In both cases (stylus and lens) these are the system components which gather the raw data from the media which could be a hit CD or even better, an astronomical wonder. Then let's go on to surmise the amplifier (in the astronomer's case) is the telescope tube (audio circuitry) which receives the raw data from the lens (stylus), then processes it and transmits it to the broadcasting device(s) which might be speakers in an audio system or the eyepiece in a telescope. If I'm right so far, then obviously we'd have to agree that are our eyes are the equivalent of our ears in terms of this comparison.

I'm sure it's far more technical than this rudimentary explanation but I'm pretty sure I'm on the right track.

Now to my question - how does the similarity between an audio system and a telescope correlate with my previous question as to why we can view and effectively image with equipment that's being pushed beyond the manufacturer's stated maximum useful magnification? Even audio equipment is limited by its dynamic range so in theory, we shouldn't be able to perceive something beyond the system's capability to produce no matter how good our hearing or how amazing our eyesight.

Inquiring minds would like to know...

Here's a couple of my favorite riddles just for fun...

If a tree falls in the forest when no one's around, does it still make a sound? (I think it definitely does)

But my all time favorite - What happens when an irresistible force meets an immovable object? (Darned if I know but I sure don't want to be around if it ever does!!!)

[JRWASTRO]

Jeremy,

OK, I'll take a stab at answering your riddle - in layman's terms of course since I'm no engineer. So basically you asked how is an audio system like our telescope? Well, I suppose since sound and light both travel in waves that our telescope is simply an ingenious device designed to "hear" light. To further the analogy, let's consider the main lens (corrector plate in my case) of a telescope equivalent to that electronic eye gizmo in a CD player or maybe even the stylus of a phonograph designed to read those tiny little grooves on that rotating vinyl disk. In both cases (stylus and lens) these are the system components which gather the raw data from the media which could be a hit CD or even better, an astronomical wonder. Then let's go on to surmise the amplifier (in the astronomer's case) is the telescope tube (audio circuitry) which receives the raw data from the lens (stylus), then processes it and transmits it to the broadcasting device(s) which might be speakers in an audio system or the eyepiece in a telescope. If I'm right so far, then obviously we'd have to agree that are our eyes are the equivalent of our ears in terms of this comparison.

I'm sure it's far more technical than this rudimentary explanation but I'm pretty sure I'm on the right track.

Now to my question - how does the similarity between an audio system and a telescope correlate with my previous question as to why we can view and effectively image with equipment that's being pushed beyond the manufacturer's stated maximum useful magnification? Even audio equipment is limited by its dynamic range so in theory, we shouldn't be able to perceive something beyond the system's capability to produce no matter how good our hearing or how amazing our eyesight.

Inquiring minds would like to know...

Here's a couple of my favorite riddles just for fun...

If a tree falls in the forest when no one's around, does it still make a sound? (I think it definitely does)

But my all time favorite - What happens when an irresistible force meets an immovable object? (Darned if I know but I sure don't want to be around if it ever does!!!) 

has gone down

Greetings Scorpius,

About the audio amplifier and the imaging system.  Hey not a bad guess. The reason that I posed the question is that as one progresses in area of astro-photography  with a camera using a CCD one tries to understand what determines the  quality of an image.  I ask the questions to interest the motivated person in obtaining the answer. The answer is not only complex but very interesting. In a forum like this I would  mention the "buzz words" to enable the reader to research the topic.

1.  The  general theory that describes and audio amplifier (1 D) is the same theory used to describe an imaging system (2 D) !!

A most important theorem that applies is " Nyquist's Sampling theorem" this is best understood when applied to audio type systems (1 D).   Both the audio system and imaging system have a " Frequency Response" . The "wider" the audio amplifier frequency response the crisper the sound one hears. The wider the frequency response of the imaging system the sharper will be the images!!  I is easier to understand "things" in !D then apply the reasoning to 2D.  

2. The answer to  " why we can view and effectively image with equipment that's being pushed beyond the manufacturer's stated maximum useful magnification? "   lies  in our understanding of the ways we can describe a system (imaging or audio) .

Quick Background:

We may describe a system response in the "Time Domain(TD)" or the "Frequency Domain ( FD) ".  In the case of an audio amplifier we mostly talk of the performance in terms  of a frequency response (ie. FD)  and rarely do we use commonly the TD. The TD, also called the impulse response  is primarily used when we wish to filter a signal. In the audio system this Impulse response is how the amp responds to an impulse (please look up "Dirac Delta Function" ) . In describing our telescope systems we commonly talk in terms of the response  of our optics to a point  source or star and one talks about resolution in terms of this "impulse response"  ... please look up " Point Spread Function" . Now rarely, in our forums,  do we discuss the frequency response of the imaging system (Please look up Modulation Transfer Function ... grand name for frequency response also called the Contrast Transfer Function). It is this Frequency response that determines the contrast of features in the image.

Example:

Audio Amplifier responds in the range, say,  20 cycles per sec to 20,000 cycles per sec ..... frequency in time (cycles per second)

Imaging system responds in the range, say, 0 line pairs per mm to 200 line pairs per mm (LpMM) ... frequency in space (cycles per mm) ... 1 cycle has 1 black line and 1 white line.

Audio amp will let you hear 30, 000 Hz at reduced volume.

Imaging system will display features at 150 LpMM with reduced contrast but with a width much smaller than estimates using magnifications etc. 

My (weak) Response to : 

"  What happens when an irresistible force meets an immovable object? (Darned if I know but I sure don't want to be around if it ever does!!!) 

has gone down"

I guess we may have to define the problem  so  that there will be a solution . Why? I guess it is the type of problem where one has a result  of the form 0/0  (0 divided by 0 ) .  Might have to define the problem where the condition  "  irresistible force meets an immovable object" is only approached as a limit but the solution breaks down when "  irresistible force meets an immovable object ". 

Re:

If a tree falls in the forest when no one's around, does it still make a sound? (I think it definitely does)

I'm not going  down that path!!  this is a kin to starting a thread as follows : I'll present $10 to the last person who posts on this thread.

Cheers and Beers,

Jeremy