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Archive 2013 · Why m43 over full frame in two pictures

  
 
RustyBug
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p.17 #1 · p.17 #1 · Why m43 over full frame in two pictures


Thank again guys ... I'm still not there (as others groan yet again) @ where I want to be, but as always I appreciate the respectful spirit of help from fellow FM'ers.

I just feel like there is an illusive formulaic Sasquatch out there that provides the missing link that would formulaic connect us to the image circle as an area with an amount of photons falling on it to yield our derived formula from a root formulaic perspective.

Okay, so the light falls on our subject at a given concentration, it is reflected from our subject into a direction that can be captured by our lens. That will put an X amount of photons at our lens (for a given time @ component of flow), with our entrance pupil having a given area. Through the refractive properties of the lens elements, that same amount of photons will be "condensed" to the size of our max aperture which would yield a given amount/area.

After passing through (flow ) the physical (orifice ) aperture (which when stopped down reduces the amount "passing through", i.e. cross-section area iaw the area reduction), that same amount of photons would be "re-expanded" by the refractive properties of the lens elements to the area of the image circle. For a max aperture WO, the amount of light at our entrance pupil should be the same as the amount of light at our image circle

If our lens FL is 50mm at f/1, then our entrance pupil is also 50mm diameter (25mm radius). As such, no orifice is (smaller physical aperture) in place to restrict the amount/flow of photons below that which is available at our entrance pupil. The amount of photons available at our entrance pupil is the same amount available to be projected onto our image circle. If our image circle is the same area as our entrance pupil and our amount of light at our image circle is the same as the amount of light "passing through" our entrance pupil, then the amount/area will be the same for each ... i.e. 1:1 proportion, hence f/1.

If we stop down our physical aperture, we are then reducing the cross-section area of our ability to pass through (flow) photons. This reduction in cross section area, yields a reduction in the amount of photons that can flow (per unit time). Thus a 1/2 reduction in diameter/radius yields a 1/4 reduction in the cross-section area to reduce the amount of photons that can pass through to the image circle area. Now that we have a a reduced amount (without an offsetting change in time) photons reaching our image circle, a 1/4 reduction in amount will yield an amount/area(unit) 1/4 that of our entrance pupil. And, of course, this is why we increase the time by a corresponding two stops (2 x 2 = 4) to allow the total amount of photons reaching our film/sensor to accumulate iaw with Q=Av.

As it turns out, our FF film area is 24X36 for, then the distance to our furthest corner is 43.3 mm, so a "perfectly fitting" image circle would be one of the same size. But for convenience we call 50mm "normal" when it is actually a very, very short tele compared to the format size image circle @ 43.3 mm. Note here that our "normal lens" between formats are correlated to our image circle size (see other sizes in link below).

http://en.wikipedia.org/wiki/Normal_lens

While it is highly doubtful that I've convinced anyone of the proportional relationship to the image circle or to the role of flow relative to the amount/area (unit) ... and have yet to fully derive the formulaic connection ... I'm good.

I'll leave (for now ) the remaining deductions and correlations regarding format size equivalencies for each to resolve in the manner of their choosing. I highly recommend using formulaic, dimensions and proper units to accurately make those equivalencies. However, most photographers are not interested in the fully developed math, but instead lean heavily on the pragmatic reduced/derive equations ... i.e. FL/aperture = f/stop (proportion).

As it turns out, I aspire to understand this proportion in terms of area rather than length (given our significance to exposure @ amount/area(unit). However, since area is derived from length, the proportions of area vs. area can retain the same resultant as length vs. length, and our image circle is defined by length of its radius, similar to how the diameter and area of our entrance pupil are resultant of its radius, thus proportions are retained ... even if not the far easier conventional way that we make the calculation using length to assess the proportion.

But, I would suggest that once you start trying to make certain equivalency comparisons, it is very easy to grab one portion of the underlying math while omitting another aspect of it as we aspire to present our position to one another ... hence the enormity of confusion that abounds on the subject of equivalency as people are mixing/matching area vs. length @ r^2 (i.e. linear vs. exponential).

I still believe that if you consider the amount/area(unit) as key, you must consider the image circle area relative to the entrance pupil area (sans physical aperture restriction) as a proportion, which is what an f-stop is (i.e. proportion) even if we have found an easier way to calculate that proportion via length rather than area ... i.e. saying the same thing in a different way.

Thanks again for the indulgence, assistance and patience ... FM'ers rock !!!

FWIW ... feel free to ignore the ramblings of a brain damaged individual. It's just the way things have to work for me sometimes in a post-TBI reality. In case you didn't already know or forgot, I got whacked. So if you ever thought I was whack (or a little slow sometimes) ...

Thus, my appreciation for the indulgence is genuine.

Edited on Oct 29, 2013 at 10:58 AM · View previous versions



Oct 29, 2013 at 08:57 AM
JimUe
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p.17 #2 · p.17 #2 · Why m43 over full frame in two pictures


not too long ago the alt forum was pretty much exclusively a zeiss fanboy club..


Oct 29, 2013 at 09:12 AM
JonPB
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p.17 #3 · p.17 #3 · Why m43 over full frame in two pictures


Rusty,

From my perpsective, taking area works well--but using subject area, not image circle.

For example:

A 50mm lens at f/2 has an aperture of 25mm in diameter or about 1963 mm^2 in area.
A 25mm lens at f/2 has an aperture of 12.5mm in diameter or about 491 mm^2 in area, exactly one-quarter of the 50mm lens' aperture area.

Field of view for a rectilinear lens is 2 * arctan([format diameter]/2*[focal length]).

Let's take 135 format's 43.3mm diameter and our 50mm & 25mm lenses. Plugging that in, I get 46.825 degrees and 81.785 degrees, respectively.

To get subject area diameter, I'll take half those angles and find the opposite side of the right angle triangle at an arbitrary distance of 1 meter, then double it to get the full flat plane diameter at that distance. (tan (A/2))*2. This gives me diameters of 0.866m and 1.732m, respectively.

The area is, of course, pi * r^2. Therefore, the 50mm lens' subject area is about 0.589 square meters and the 25mm lens' is about 2.36 square meters--a difference of exactly four times.

So even though the aperture lets through four times less light per subject area, it has four times more subject to work with, keeping overall exposure constant.

I hadn't done that math before--and, yes, I found brushing up on my trig to be quite fun.

Cheers,
Jon



Oct 30, 2013 at 06:47 PM
RustyBug
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p.17 #4 · p.17 #4 · Why m43 over full frame in two pictures


Thanks Jon, glad you enjoyed dusting off the trig cobwebs. Sorry for the uber-convoluted way it took me to get there.


Well, if you think about it subject area and image circle SHOULD work equally as well.

If we stay on a 43mm image circle (math of 24mmx36mm FF), a 43mm focal length would yield a 1:1 image magnification @ equal triangles/equal area based on the opposites @ intersection (image below). Which is why on a given format, with a different image circle size, the definition of a "normal" lens varies.

e.g. ... 6 x 6 film area has an image circle of 60mm * 2^.5 (1.414) = 84.9mm, thus a "normal" lens on MF is routinely established as the 80mm lens, while the normal on FF is routinely accepted as the 45mm-50mm.
http://en.wikipedia.org/wiki/Normal_lens

For aperture or f/1 (proportion), our entrance pupil would be 43mm using our FL/f-stop formula that we commonly agree to. A 43mm entrance pupil will be receiving a given amount of light X, and projecting/passing that same X amount of light onto our image circle. Thus the same amount of light over the same area will yield the same amount/area(unit), or 1:1 proportion.

If we double our FL to 86mm and aspire for the same f/1 aperture, and have an 86mm entrance pupil the reduction in FOV and the increase in area are offsetting to the retain the same amount of light at the entrance pupil. If the same amount of light is projected onto the same 43mm image circle as that which came from our 43mm f/1, then our proportion of light @ the entrance pupil to light the image circle remains 1:1.

If we were to retain only a 43mm entrance pupil from an 86mm focal length fov, then we would have a 1:2 proportion, which provides us with an f/2 f-stop ... pi*r^2 yielding factors of 4X.

Long story short ... image circle is really where it all begins (lens design follow), we just have learned it is much quicker to go FL/entrance pupil = f-stop or FL/f-stop = entrance pupil. But, the math derived from the image circle trig to the entrance pupil to the subject is not incongruous to our common formula as f-stop is a proportion.






Edited on Oct 31, 2013 at 08:12 AM · View previous versions



Oct 31, 2013 at 07:36 AM
Makten
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p.17 #5 · p.17 #5 · Why m43 over full frame in two pictures


RustyBug wrote:
Long story short ... image circle is really where it all begins (lens design follow), we just have learned it is much quicker to go FL/entrance pupil = f-stop or FL/f-stop = entrance pupil. But, the math derived from the image circle trig to the entrance pupil to the subject is not incongruous to our common formula as f-stop is a proportion.


I think you still haven't understood a word of what's been written in this thread.



Oct 31, 2013 at 08:04 AM
RustyBug
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p.17 #6 · p.17 #6 · Why m43 over full frame in two pictures


Lee Saxon wrote:
The meaningful one, light per mm2, is the same.


To which you replied ...

Makten wrote:
To be fair, you have no clue of what you are talking about. Light per area is meaningless without taking total area into account.


This is what I didn't understand ^ ... the rest was set in motion from there and I grappled with piecing it together from root to derivative. Despite the fact that I took a very unorthodox approach, does not mean I didn't understand. I simply was trying to relate to that which I did understand ... even if that seemed incomprehensible along the way.

I wasn't joking about the TBI ... I have to rebuild certain things predicated upon that which didn't get fragmented into oblivion by a 10G - 40G (estimates vary) impact. On a visceral level, I know I know what I used to know ... however, finding the pieces can be incredibly tough (pseudo impossible) sometimes for me. And, some of those pieces have literally been destroyed. Explaining it, even tougher at times. The indulgence and assistance that comes from our fellow FM'ers is genuinely appreciated.


Simple ... f-stop is a proportion.
Length vs. length can yield a proportion. Area vs. area can yield the same proportion, since area is a function of length. BOTH can be correctly calculated to derive the proportion. Sorry it took such a long route for me to connect the dots.

Makten wrote:
I think you still haven't understood a word of what's been written in this thread.


Coming from someone who (likely) has never incurred a TBI ... I can understand why you might feel that way. If you think it has been frustrating for you ... you can't begin to image how frustrating the last 8 years have been for me. With 100% earnestness, you guys have been a part of my recovery at rebuilding things. You guys are a tough crowd, it forces me to give my best effort ... sometimes it comes across well, other times not so much. From that incessant effort, the incredibly slow process of brain healing/restoration/remapping continues at its sub-glacial pace.

I realize that at times you likely think poorly of me regarding why I won't let something go and or why I just "don't get it". Unlike for some, where this is just fun (and it is ), for me it is earnestly therapeutic via the challenges presented both in physics/photographic terms, but also in communicative and logic terms (portions damaged).

Also, if you've ever noticed ... a vast majority of my threads are lengthy and or revised. Expediency, conciseness and completion of thought are a challenge that I've not yet resolved (areas of damage), but I carry on giving that which I can. Damage to the Corpus Callosum has essentially reduced me from 128 bit to 4 bit file transfer speed. Combine that with a couple of fragmented storage areas ... and yup, it takes longer to find things, to process them and to properly save them. The save function for new information doesn't work very well and the filing system is a disorganized mess ... thus the dependency on association to old information from which to correlate and associate proper restorative understanding (even if highly unorthodox).


Anyway ... I get that I come across poorly at times. My apologies for that. But, thanks for the head's up, I never knew.


Thanks to all for the assistance along the way. My appreciation is genuine. FM Rocks !!!



Oct 31, 2013 at 08:18 AM
jcolwell
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p.17 #7 · p.17 #7 · Why m43 over full frame in two pictures





Oct 31, 2013 at 09:47 AM
JonPB
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p.17 #8 · p.17 #8 · Why m43 over full frame in two pictures


To me, the magic of the f-stop is its format independence. Whether I'm working with a sensor that has dozens of square millimeters or thousands, the same f-stop, shutter, and sensitivity combination produces the same exposures. This allows compact digital snapshot cameras to turn into extremely reliable exposure meters for larger film cameras. However, the field of view argument I made did rely upon image circle size, so if that's the starting point that works for you I see no real difference in using it to show that exposure remains constant despite varying aperture sizes.

As far as brain injuries go, I have a family member who designed some of the first consumer applications for lasers and LEDs--he was on the cutting edge of that in the eighties. An infection led to heart troubles that led to brain damage, and he lost the ability to read, write, and a large portion of his vocabulary. Becoming an engineer again took a tremendous amount of effort, but the brain is a wonderfully malleable thing. Memories, knowledge, and skills can all come back, at least in part, though in unpredictable cascades of varying size. He found that, while he isn't at his previous level in some ways, other attributes--such as abstract creativity--are better than before. It is a tough road to walk, though, and I wish you all the best.

As far as off-kilter ideas go, I enjoy reading ethical, philosophical or political rants by people I disagree with. If I can't understand their arguments and debunk them intelligently, then I can't have confidence in the opposing viewpoint I hold. Often my own ideas are improved in that process. With optics, that much moreso because I have little understanding to begin with. So, never hesitate to float an idea that might not have wide acceptance, at least don't hesitate on my account.


... a vast majority of my threads are lengthy and or revised. Expediency, conciseness and completion of thought are a challenge ...


I wish more people cared about expressing ideas rather than just kicking out their initial reactions and knocking down anyone who seems to disagree. This thread is a bit bipolar in that respect, but there's still more intelligence floating around here than most of the social interwebs. So,

Cheers!

[Edit for UBB code error.]



Oct 31, 2013 at 12:06 PM
Makten
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p.17 #9 · p.17 #9 · Why m43 over full frame in two pictures


RustyBug wrote:
Coming from someone who (likely) has never incurred a TBI ... I can understand why you might feel that way.


I have no idea of what TBI is, but I apologize if it has something with all this to do. The reason I'm acting a bit rude is because this question has been discussed to death many times before, and since you use a sort of stilted language that doesn't at all match the content, I just got a bit fed up with all the repeating. I'm sorry.

If you really want to learn, I suggest that you try not to draw conclusions from your own reasoning built on what you don't know, if you see what I mean.



Oct 31, 2013 at 01:05 PM
ulrikft2
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p.17 #10 · p.17 #10 · Why m43 over full frame in two pictures


Makten wrote:
I have no idea of what TBI is, but I apologize if it has something with all this to do. The reason I'm acting a bit rude is because this question has been discussed to death many times before, and since you use a sort of stilted language that doesn't at all match the content, I just got a bit fed up with all the repeating. I'm sorry.

If you really want to learn, I suggest that you try not to draw conclusions from your own reasoning built on what you don't know, if you see what I mean.


TBI = traumatic brain injury ( I assume)



Oct 31, 2013 at 01:07 PM
RustyBug
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p.17 #11 · p.17 #11 · Why m43 over full frame in two pictures


Jon,

Thanks for sharing and understanding. Your point at different and levels attainable is well noted. It's kinda like going from racing Muscle Cars with a Big Blocks to Mini-Cross for ten year olds and still trying to race competitively. The strategies you employ aren't the same as the setup options are rather different ... then you start to climb through the classes all over again.

Starting over from a slow performing, scrambled mess was a pity party for a long while coupled with an untold volume of exercises in frustration. Learning to race in the kiddy league wasn't exactly anything that welled up ones self-esteem or confidence that they'd ever return to even a portion of their former self. Sometimes you just longed for a frontal labotomy so that you might forget who you once were and relieve the comparative anguish it presented.

A few years ago, I had set my benchmark goal to be able to produce one quality photographic image starting from RAW with actually having "command & control" over what I was doing. I had never processed from RAW, didn't own Photoshop, had no clue what Layers or color theory of CMYK or RGB were (now there's a couple challenges to embark upon.) Well, it has taken me a few years to arrive at a level that others figure out in a few days, weeks or months and take for granted as "easy".

Some here may recall my angst with what color is green in RGB.

Suffice to say that what I lost in processing ... I've since come to learn that unbridled tenacity can still get you there, eventually, if your heart and will to do so are undaunted.

No worries @ apology to me, I understand how it can look. But I think Lee is the one that really deserves an apology here.

As to me, I simply go about applying what I do know about energy, vector forces, photons, math, trig and physics toward the application of derivative photographic explanation as building on what I do know. Apologies for the angst its repetition causes.

Case in point ... I've got a Graflex Century Graphic that I've never shot. Stemming from this dialogue, I've come to realize that all I have to do is calculate the size of the image circle for the format as follows:

2 1/4 in x 3 1/4 in >
52.15mm x 82.55mm>
100.4mm image circle

Thus, the 101mm lens for that format renders a "normal" 1:1 magnification, and the corresponding f/4.5 max aperture yields an entrance pupil of 22.22mm a 1:4.5 proportion to both the normal FL and to that of the image circle (which defines what normal is for a given format). Given that I like the perspective of my 24mm on FF, I can realize that in order to achieve a corresponding "equivalent" perspective for the different format can be accomplished with a lens calculated by 24mm * 100.4mm/43.3mm = 55.9mm.

Meanwhile, if I wanted to have an f/1 normal lens on 2 1/4 x 3 1/4, it would be a 101mm focal length with a 101mm entrance pupil. Whereas an f/1 normal lens on FF would be 43mm focal length with a 43mm entrance pupil; and a normal f/1 on 4:3 would be 21.6mm focal length with a 21.6mm entrance pupil.

I think I get it now.

Thanks to all.



Oct 31, 2013 at 01:21 PM
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