Calculating effective f-number when using teleconverters

Would anyone care to comment on the following proposition?

When using teleconverters, effective f-number can be calculated using the following formula

effective f-number = nominal f-number *

( 1 + magnification / (pupil magnification * teleconverter power ) )

where nominal f-number is the f-number set on the camera/lens, and teleconverter power is defined as 1.4 for a 1.4X teleconverter, 2.8 for a 1.4X and 2X teleconverter used together, etc (and is defined as 1 if no teleconverter is used).

If anyone can confirm this as an established formula the rest of this post becomes moot. (I haven't ever come across it, which is why I am asking.)

I am unable to contribute to discussion of any theoretical aspects which might support or contradict the proposition, but I present below evidence from two practical exercises which appear to me to be strongly consistent with the proposition.

The "usual formula" referred to below is:

effective f-number = nominal f-number * ( 1 + magnification / pupil magnification )

With the teleconverters used in the exercises below, the cameras reported f-numbers taking account of the use of teleconverters, so for example the f/2.8 to f/16 MPE-65 was shown as f/4 to f/22 with a 1.4X teleconverter in use, and the f/2.8 to f/22 Laowa 100mm macro was shown as f/11 to f/90 with a pair of 2X teleconverters in use.

First exercise

I used a Canon MPE-65 lens on a Canon 70D dSLR, and captured five images with 1X, 2X, 3X, 4X and 5X magnification set on the MPE-65, with all five using the same settings of f/11, 1/10 sec, ISO 3200. I photographed a light area on my computer screen and held the lens against the screen so there would not be an issue with the lightness changing because of different working distances from shot to shot. (The fact it would be out of focus would not matter as it is the lightness of the shots that matters here).

I then added a 1.4X teleconverter and captured another five images with the same magnifications set on the MPE-65 and the same settings for aperture, shutter speed and ISO. Then the same again with a 2X teleconverter and lastly with both of the teleconverters together.

Before I did this, I did some calculations, to see what the proposed formula would predict I would see. Not knowing what the pupil magnification of the MPE-65 is I took the usual approach of assuming it to be 1.

As shown in last but one column of the table below, the proposed formula predicted that with 1X magnification on the MPE-65 the four images using no teleconverter, 1.4X, 2X and 2.8X should all have the same effective aperture, so they should all be the same lightness. And it predicted the same would be the case for 2X, 3X, 4X and 5X magnification.

Those predictions are very different from what the usual formula predicts, as shown in the last column in the table below. It predicted that the images with 1X set on the MPE-65 would have a larger effective f-number and so would get darker when I added the 1.4X teleconverter, darker again with 2X and darker still with 2.8X. And it predicted the same would be true with 2X, 3X, 4X and 5X magnification set on the MPE-65. (It also predicted some pairs of images, shown by the colours in the table, where the brightness would match between images that had a different magnification set on the MPE-65 but which had the same overall magnification once the teleconverters were taken into account.)



Here are the 20 images. They are consistent with the predictions of matched lightnesses derived from the proposed formula.



Second exercise

With the Laowa 100mm macro on a Sony A7ii I captured images at 1X, 2X and 4X magnification, once with one 2X teleconverter and again with two 2X teleconverters. This time the magnification was the actual, overall magnification, so for example for the 1X magnification shot I set the magnification on the lens to 1:2 when using the 2X teleconverter and 1:4 when using both teleconverters. And similarly for the 2X and 4X shots.

Assuming once more that a pupil magnification of 1, using the usual formula so the effective aperture depends only on the magnification, then both 1X magnification shots should have the same effective aperture and therefore the same lightness, and the same for the pair of 2X magnification shots and the pair of 4X magnification shots. (The Laowa 100mm macro goes to 2:1, allowing it to reach 4:1 with a 2X teleconverter.)

In contrast, the table below shows calculations using the proposed formula that takes the teleconverters into account. As shown by the colours, it predicts that the effective f-number, and hence the lightness, should match between the 1X magnification using the 2X teleconverter and the 2X magnification using 4X teleconversion, and also between 2X magnification using the 2X teleconverter and 4X magnification using 4X teleconversion.

In this table "Pupil magnification" refers to an assumed lens pupil magnification of 1 multiplied by the teleconversion power.



This is what the images looked like. They match in the way predicted by the proposed formula that takes teleconverters into account.



Histograms from Raw Digger show that the two matches were in very close indeed.



--
Nick
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I had noticed this thread but didn't post.

Optically adding a teleconverter (TC) is no different than adding a close-up lens; they both change the optical prescription for the overall lens.

In the case of the TC the entrance pupil is unchanged but the exit pupil changes in size (and probably position) and, of course, the focal length changes.

The usual equation

(1 + m / p)

is simplfied from

((p + m) * f) / (p * f)

where p and f on the top are at magnification and p and f on the bottom are at infinity

The usual equation is an approximation that assumes the p's and the f's match

But it will work properly is we don't "simplify" it.

so f# * ((pm + m) * fm) / (pi * fi)

where pm and fm are p and f at magnification and pi and fi are p and m at infinity.

bclaff said:

I had noticed this thread but didn't post.

Optically adding a teleconverter (TC) is no different than adding a close-up lens; they both change the optical prescription for the overall lens.

In the case of the TC the entrance pupil is unchanged but the exit pupil changes in size (and probably position) and, of course, the focal length changes.

The usual equation

(1 + m / p)

is simplfied from

((p + m) * f) / (p * f)

where p and f on the top are at magnification and p and f on the bottom are at infinity

The usual equation is an approximation that assumes the p's and the f's match

But it will work properly is we don't "simplify" it.

so f# * ((pm + m) * fm) / (pi * fi)

where pm and fm are p and f at magnification and pi and fi are p and m at infinity.

Click to expand...

Thanks Bill. Fascinating to see that (1 + m/p) is itself a simplification.

I would welcome any thoughts you have on the proposition I put forward, which does seem to me to be strongly consistent with the two exercises I did. I can't see a way of applying the full formula above to the exercises I did as I don't know the values of any of the parameters apart from m (and possibly fi) for any of the options I tested.

There must surely be some underlying principle in operation here; the regularities are striking. Here is another one. Is there some sort of clue in this? I have no idea. I'm currently just trying to sort out the practical implications of all this. But I would be happy to have some sort of intuitive grasp of what is causing these (to me at least) unexpected results.





--
Nick
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gardenersassistant said:

There must surely be some underlying principle in operation here; the regularities are striking. Here is another one. Is there some sort of clue in this? I have no idea. I'm currently just trying to sort out the practical implications of all this. But I would be happy to have some sort of intuitive grasp of what is causing these (to me at least) unexpected results.

Click to expand...

I don't know what the y-axis is on that chart.

Remember to take the focal length after attaching the TC into account.
I suspect that's what you're missing.

--
Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

bclaff said:

gardenersassistant said:

There must surely be some underlying principle in operation here; the regularities are striking. Here is another one. Is there some sort of clue in this? I have no idea. I'm currently just trying to sort out the practical implications of all this. But I would be happy to have some sort of intuitive grasp of what is causing these (to me at least) unexpected results.

Click to expand...

I don't know what the y-axis is on that chart.

Click to expand...

The y axis is "effective f-number " as calculated with the two formulas set out above the chart. Namely:

The red line uses (nominal f-number * ( 1 + magnification )).

The other lines use (nominal f-number * ( 1 + magnification/amount of teleconversion))

where amount of teleconversion is 1.4 for a 1.4X teleconverter, 2.8 for a 1.4X and a 2X used together, etc.

The second of those formulas correctly predicted the results of the two exercises I described in the top post, for which the simplified usual formula made incorrect predictions.

bclaff said:

Remember to take the focal length after attaching the TC into account.
I suspect that's what you're missing.

Click to expand...

Focal length does not appear in the formulas I used.

It does in the full formula that you set out, but as I noted here I don't have the information needed to use that formula.

--
Nick
Summary of photo activity since 2007 https://fliesandflowers.blogspot.com/2019/01/when-i-retired-in-2006-i-had-it-in-mind.html
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gardenersassistant said:

bclaff said:

gardenersassistant said:

There must surely be some underlying principle in operation here; the regularities are striking. Here is another one. Is there some sort of clue in this? I have no idea. I'm currently just trying to sort out the practical implications of all this. But I would be happy to have some sort of intuitive grasp of what is causing these (to me at least) unexpected results.

Click to expand...

I don't know what the y-axis is on that chart.

Click to expand...

The y axis is "effective f-number " as calculated with the two formulas set out above the chart. Namely:

The red line uses (nominal f-number * ( 1 + magnification )).

The other lines use (nominal f-number * ( 1 + magnification/amount of teleconversion))

where amount of teleconversion is 1.4 for a 1.4X teleconverter, 2.8 for a 1.4X and a 2X used together, etc.

The second of those formulas correctly predicted the results of the two exercises I described in the top post, for which the simplified usual formula made incorrect predictions.

gardenersassistant said:

Remember to take the focal length after attaching the TC into account.
I suspect that's what you're missing.

Click to expand...

Focal length does not appear in the formulas I used.

It does in the full formula that you set out, but as I noted here I don't have the information needed to use that formula.

Click to expand...

Effective f-number between 50 and 300 ? Huh?

And ... your formulas don't make sense to me.

--
Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

I have read your posts here and in the macro forum several times trying to make sure I understand your data. I don’t use teleconvertors with macro lenses often, but I noticed something very interesting in your data and in the data I have for my new Laowa 65. The interesting thing is how well simplifications work. In my case, effective f-number (as measured by relative exposure) tracks exactly at all magnifications with the overly simplistic Av * (1 + M). In your case, the teleconvertor is a complication, but once dealing with that with an over simplification, your data appears to correlate just as well. Simplifications work, but they shouldn’t. In my case, my data implies a pupil magnification of one throughout the focus range and I am certain that is very wrong. You assume the same lens pupil magnification of one which probably isn’t true for either of your lenses, either.

If we go to bclaff’s optical bench, we can find a couple of popular macro lenses (although none of the ones of interest to you or me). I pulled up the Sigma 70 A and the Canon 100 L. The nice thing is that bclaff has the focus sliders working for these and these two lenses are quite different in the way they focus. Throughout their focus ranges, focal length and pupil magnification vary. Bclaff’s model shows aperture diameter remaining constant, a modeling element I would question, but if true, and focal length changes, then aperture ratio as we dial it is not some reliable constant (it becomes aperture diameter at infinity or worse, some rounding of that value). Everything is dynamic as we move through focus in complex lenses, yet my data and your data match simplifications. Perhaps these simplifications are actually design goals of the designer. Or perhaps Mother Nature just delivers us unavoidable offsets in pupil magnification and focal length to keep her own balance. She sometimes seems to work that way.

It is really difficult to know what happens with focal length, pupil magnification, and even aperture ratio as we change focus distance and magnification, but magnification and relative exposure are easy to measure and perhaps tell us all we need to know. In my case, I think I can simply use the old 1 + magnification approximation and in your case, it looks reliable to use your teleconvertors as the only source of pupil magnification even though that is likely not even close to 100% accurate. The thing that takes up the slack in this dynamic situation is simply distance which is a highly technical matter, but not one of practical interest. We focus but we don’t really measure how far we are from any relevant plane. To us, we either want more or are satisfied with the distance (usually working distance), even if we have no idea of the actual technical realities of distance in an optical formula.

From what I see, you and I have everything we need to know about our specific lenses, but we know very little about our specific lenses. I only wish I was more confident that this idea of effective aperture as measured by relative exposure translated to diffraction and DOF as reliably. I can measure diffraction directly, but not for 2:1 macro as I don’t currently have a test chart that is only 7.5mm tall. I can probably answer my diffraction and DOF concerns through experience, but I prefer data and math and it is really hard to do any calculations if I don’t know distance, focal length, pupil magnification, or even perhaps pupil diameter. The good news is that it looks like simplifications work very reliably.

bclaff said:

gardenersassistant said:

bclaff said:

gardenersassistant said:

There must surely be some underlying principle in operation here; the regularities are striking. Here is another one. Is there some sort of clue in this? I have no idea. I'm currently just trying to sort out the practical implications of all this. But I would be happy to have some sort of intuitive grasp of what is causing these (to me at least) unexpected results.

Click to expand...

I don't know what the y-axis is on that chart.

Click to expand...

The y axis is "effective f-number " as calculated with the two formulas set out above the chart. Namely:

The red line uses (nominal f-number * ( 1 + magnification )).

The other lines use (nominal f-number * ( 1 + magnification/amount of teleconversion))

where amount of teleconversion is 1.4 for a 1.4X teleconverter, 2.8 for a 1.4X and a 2X used together, etc.

The second of those formulas correctly predicted the results of the two exercises I described in the top post, for which the simplified usual formula made incorrect predictions.

bclaff said:

Remember to take the focal length after attaching the TC into account.
I suspect that's what you're missing.

Click to expand...

Focal length does not appear in the formulas I used.

It does in the full formula that you set out, but as I noted here I don't have the information needed to use that formula.

Click to expand...

Effective f-number between 50 and 300 ? Huh?

Click to expand...

Using the usual simplification, with nominal f/32 and 8X magnification

effective f-number = 32 * ( 1 + 8 ) = 288

And yes, if you are wondering, I do use apertures like this. I have been using nominal f/45 at up to 8X magnification, although mostly around 6X, which at f/45 nominal is f/315 effective using the usual formula. This sort of thing (probably around 2mm long, in motion).

bclaff said:

And ... your formulas don't make sense to me.

Click to expand...

They don't make sense to me either, but they predicted the results of the two exercises I did whereas the usual formula got it badly wrong. That's why I'm asking for those who understand these things to explain what is going on.

--
Nick
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AKRover said:

I have read your posts here and in the macro forum several times trying to make sure I understand your data. I don’t use teleconvertors with macro lenses often, but I noticed something very interesting in your data and in the data I have for my new Laowa 65. The interesting thing is how well simplifications work. In my case, effective f-number (as measured by relative exposure) tracks exactly at all magnifications with the overly simplistic Av * (1 + M). In your case, the teleconvertor is a complication, but once dealing with that with an over simplification, your data appears to correlate just as well. Simplifications work, but they shouldn’t. In my case, my data implies a pupil magnification of one throughout the focus range and I am certain that is very wrong. You assume the same lens pupil magnification of one which probably isn’t true for either of your lenses, either.

If we go to bclaff’s optical bench, we can find a couple of popular macro lenses (although none of the ones of interest to you or me). I pulled up the Sigma 70 A and the Canon 100 L. The nice thing is that bclaff has the focus sliders working for these and these two lenses are quite different in the way they focus. Throughout their focus ranges, focal length and pupil magnification vary. Bclaff’s model shows aperture diameter remaining constant, a modeling element I would question, but if true, and focal length changes, then aperture ratio as we dial it is not some reliable constant (it becomes aperture diameter at infinity or worse, some rounding of that value). Everything is dynamic as we move through focus in complex lenses, yet my data and your data match simplifications. Perhaps these simplifications are actually design goals of the designer. Or perhaps Mother Nature just delivers us unavoidable offsets in pupil magnification and focal length to keep her own balance. She sometimes seems to work that way.

It is really difficult to know what happens with focal length, pupil magnification, and even aperture ratio as we change focus distance and magnification, but magnification and relative exposure are easy to measure and perhaps tell us all we need to know. In my case, I think I can simply use the old 1 + magnification approximation and in your case, it looks reliable to use your teleconvertors as the only source of pupil magnification even though that is likely not even close to 100% accurate. The thing that takes up the slack in this dynamic situation is simply distance which is a highly technical matter, but not one of practical interest. We focus but we don’t really measure how far we are from any relevant plane. To us, we either want more or are satisfied with the distance (usually working distance), even if we have no idea of the actual technical realities of distance in an optical formula.

From what I see, you and I have everything we need to know about our specific lenses, but we know very little about our specific lenses. I only wish I was more confident that this idea of effective aperture as measured by relative exposure translated to diffraction and DOF as reliably. I can measure diffraction directly, but not for 2:1 macro as I don’t currently have a test chart that is only 7.5mm tall. I can probably answer my diffraction and DOF concerns through experience, but I prefer data and math and it is really hard to do any calculations if I don’t know distance, focal length, pupil magnification, or even perhaps pupil diameter. The good news is that it looks like simplifications work very reliably.

Click to expand...

Thanks very much for setting all this down, and so clearly too. I am reassured that I'm not going off my rocker.

As you say, from a practical perspective we have all we need. I wanted greater depth of field than I could get with my previous setups, I wanted to be able to handle smaller subjects more effectively, and for those smaller subjects I wanted working distances I could handle. My strange double TC setup has given me all of this. For example, I'm ok with the working distance of around 72mm that I get at 8:1 (compared for example to around 40mm with the MPE-65 at 5:1).

You are right about what is readily measurable: magnification and relative exposure, and not much else.

The amount of diffraction I don't have a clue about in measurable terms. I just know (well, believe) that I shouldn't get anything usable out of the effective apertures that I'm apparently using. And of course the usual formula says I am using even smaller effective apertures than the strangely modified formula that I have come up with which, as you say, exactly tracks effective f-number as measured by relative exposure. I did a third exercise today with a third sensor size and a third macro lens and once again the strangely modified formula correctly predicted what I would see and the usual formula didn't.

As to the amount of DOF, I don't have measurements there either. But I do have a decade's experience of photographing certain types of subject and I am confident I am getting significantly more DOF that I was previously. Exactly how much more, i don't know. Since DOF apparently roughly doubles for each two stops reduction in effective aperture, the usual formula would suggest that in some cases I'm getting something over 8 times the amount of DOF than I was previously. The strangely modified formula suggests that in those cases it may be more like 3 times as much. 3 times feels reasonable to me from what I'm seeing. 8 times feels less credible.

I can see what is going on, and I can work with it. As to why it works the way it does, I don't have a clue. I'd like to know, but it's more out of interest than anything else. I suspect that knowing why wouldn't make much practical difference to me.

--
Nick
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AKRover said:

...

If we go to bclaff’s optical bench, we can find a couple of popular macro lenses (although none of the ones of interest to you or me). I pulled up the Sigma 70 A and the Canon 100 L. The nice thing is that bclaff has the focus sliders working for these and these two lenses are quite different in the way they focus. ...

Click to expand...

FWIW, since f# (NA) and magnification (and everything else) are measured you can note them as you move the focus slider. (If you use the arrow keys instead of a mouse the slider moves by fixed amount per key press.)

The normal simpler formulas do work "OK" especially when focal length doesn't drop too much and pupil magnification doesn't get far from unity.

For example, the Sigma 70mm F2.8 DG Macro Art only drops from 67.95mm to 60.06mm, not much my macro standards. And pupil magnification ranges from 1.26 to 1.10, not far from unity and not much of a change.

--

Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

gardenersassistant said:

gardenersassistant said:

..

Click to expand...

Using the usual simplification, with nominal f/32 ...

Click to expand...

I missed that you were starting at f/32

bclaff said:

And ... your formulas don't make sense to me.

Click to expand...

Nor me. I've been thinking some more about this.

This is all about how to calculate effective f-number when using teleconversion. We have three formulas, as defined in the illustration below.

• The "Simplified Formula" gave answers which are not consistent with observations made when teleconversion was used with three different cameras, sensor sizes and macro lenses. (I have done a third exercise since my previous posts.)
• The "Full Formula" that you provided can't be used in this case because there are unknown parameter values.
• The seemingly nonsensical "TC Modified Formula" gave answers which were consistent with observations made in the three exercises but no one has so far suggested how this could be the case.

Presumably the Full Formula has been derived from the laws of optics and is solidly established, correct and covers all eventualities, That means that in order to produce results which are consistent with the observations made in the three exercises there must be some parameter values which when inserted into the Full Formula give the same results as those produced by the TC Modified Formula. I therefore attempted to find some parameter values which do this, to see if this would give a clue as to what is going on here.

The two parameters shown in red below, t and m, are known and fixed for each calculation. The two parameters shown in orange below, pi and fi, are not known, but they are fixed for a particular combination of lens and teleconverter. This leave the three parameters shown in green as candidates for varying, singly or in combination, in such a way as to produce the results we are looking for. I made various simplifying assumptions, and I looked at varying each of the three parameters on its own. Obviously there must be many combinations that could also be used, but varying them one at a time was more tractable and hopefully can provide some clue.

Part of the simplification was to look at a single teleconversion factor and a single nominal f-number. I chose the values for these that I used for the whole of a session yesterday so as to provide some sort of "anchor" into reality: nominal f/45 and magnifications from 1:1 to 8:1 using two 2X teleconverters with a maximum 2:1 macro lens.



Cases 3, 4 and 5 in the illustration show, in the green areas, what values of f#, pm and fm respectively are need to get results which match the results from the TC Modified formula.

In the case of f#, the nominal f-number, to get matching results this would have to decline from around f/28 at 1X magnification to around f/15 at 8X magnification, while being reported as f/45 by the camera at all the used magnifications.

In the case of pupil magnification, this would have to decline in equal steps of -0.75 from 0.25 at 1X magnification to -5 at 8X magnification.

In the case of focal length, this would have to decline from 250mm at 1X magnification to 133mm at 8X magnification while being reported as 400mm by the camera at all magnifications.

Is parameter variation of this type and scale credible for any of the three parameters?

If so, would the variation be independent of sensor size and lens used?

--
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gardenersassistant said:

bclaff said:

And ... your formulas don't make sense to me.

Click to expand...

Nor me. I've been thinking some more about this.

This is all about how to calculate effective f-number when using teleconversion. ...

Click to expand...

Honestly, I didn't read the entire post as I'm busy on something else at the moment.

But my intuition tells me that you shouldn't be thinking of the tele-converter as a special case.
Once you attach it you have a different lens with a different optical prescription.
That lens has an increased focal length, the exit pupil got smaller, and the exit pupil location shifted (toward the rear I believe).

Are you trying to calculate something useful to you or just trying to understand the concept better?

If I get a chance I'll try to construct an example for you in the Optical Bench.
For now compare Fujifilm Fujinon XF200mm F2 R LM OIS WR to Fujifilm Fujinon XF200mm F2 R LM OIS WR with Fujifilm Fujinon XF1.4X TC F2 WR to see what I'm talking about.

bclaff said:

gardenersassistant said:

bclaff said:

And ... your formulas don't make sense to me.

Click to expand...

Nor me. I've been thinking some more about this.

This is all about how to calculate effective f-number when using teleconversion. ...

Click to expand...

Honestly, I didn't read the entire post as I'm busy on something else at the moment.

But my intuition tells me that you shouldn't be thinking of the tele-converter as a special case.
Once you attach it you have a different lens with a different optical prescription.
That lens has an increased focal length, the exit pupil got smaller, and the exit pupil location shifted (toward the rear I believe).

Are you trying to calculate something useful to you or just trying to understand the concept better?

Click to expand...

I am trying to better understand the way my kit performs, in particular the way depth of field and diffraction softening vary with magnification, so as to be able to better manage the amounts of and trade-offs between depth of field and diffraction softening. My handle on depth of field and diffraction softening is effective aperture.

bclaff said:

If I get a chance I'll try to construct an example for you in the Optical Bench.
For now compare Fujifilm Fujinon XF200mm F2 R LM OIS WR to Fujifilm Fujinon XF200mm F2 R LM OIS WR with Fujifilm Fujinon XF1.4X TC F2 WR to see what I'm talking about.

Click to expand...

Please don't take the time doing that because I don't understand how the example you kindly provided above relates to the issue I have, which is that when using teleconverters the effective aperture appears to vary in a way which differs significantly from the usually used formula for calculating it.

I have just done another example of this, in this case an extremely simple one.

I took a photograph of a light area of my computer screen with my MPE-65 at 4:1, using f/11, and then with a Sigma 105 macro at 1:1 using two 2X teleconverters, so at 4:1 overall.

The usual formula says that these should produce the same effective aperture, namely f/55. However, the Sigma produced an image that was over two stops lighter than the MPE-65.

The TC modified formula predicted that at f/28 the Sigma with TCs would produce the same lightness as the MPE-65 at f/11. I had to set a slightly smaller f/29, and as you can see below it produced an image of lightness very close to that of the MPE-65 at f/11, just a bit darker, which is consistent with the slightly smaller f/29 in place of f/28. Once again, the TC modified formula correctly predicted the outcome, which the normal formula got wrong.

As it stands it looks like I should use the TC modified formula for practical, day to day calculations in the field. However, this seems so unlikely that I can't help feeling I'm making a mistake and the usual formula is fine. So I'm offering up these examples to give people who know infinitely more about all this than I do to show that I am in error, and that I should use the usual formula.



--
Nick
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The learning experience for me in following this was the effect of a teleconvertor on pupil magnification . When I read that in bclaff's first response, the algebra, perhaps wrong, jumped out at me and the full formula in his post that we often simplify to 1 + m or maybe 1 + m/p does algebraically reduce to your 1 + m/(p*tc) but only if the effect on p is p*tc which the example bclaff pointed us to (the Fuji 200) doesn't actually support. Still, if I can algebraically manipulate that full formula to get to your deduced formula based on an assumption that somehow teleconvertors mathematically alter the pupil magnification and that deduced formula works well with field data, I think we are on to something. Unfortunately without going through the painstaking efforts of full thick lens analysis of a real world example, the reasons why this works might not ever be clear to me. I keep thinking that there are offsetting realities in practical lens design that keep us constrained to this reliability in our results even though individual lenses can be dramatically different in design.

AKRover said:

The learning experience for me in following this was the effect of a teleconvertor on pupil magnification . When I read that in bclaff's first response, the algebra, perhaps wrong, jumped out at me and the full formula in his post that we often simplify to 1 + m or maybe 1 + m/p does algebraically reduce to your 1 + m/(p*tc) but only if the effect on p is p*tc which the example bclaff pointed us to (the Fuji 200) doesn't actually support. Still, if I can algebraically manipulate that full formula to get to your deduced formula based on an assumption that somehow teleconvertors mathematically alter the pupil magnification and that deduced formula works well with field data, I think we are on to something.

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I wondered about algebraic manipulation, but I couldn't get my head around what would be involved, hence the one-parameter-varying, reverse-figuring numerical approach to see if that pointed us to what we should be looking at algebraically in the Full Formula to get it to reduce to the observation-consistent TC Modified Formula, at least for the circumstances of the tests I have done.

Thanks for interpreting Bill's example for me. So is our only route forward something that isn't possible? Nowhere else to go now? Impasse?

Given the results of the now four practical exercises I have done, and with no indication yet of errors in the conduct of or observations from those exercises, or of errors in the deductions in terms of effective apertures, I don't see that I have any rational choice but to assume provisionally, for the kit I'm using, that the TC Modified Formula is the one I should be using, as that formula is consistent with all my TC test observations while the Simplified Formula is consistent with none of them, and the Full Formula has too many unknown (to me) parameters to be useful, and would in any case have to produce the same results as the TC Modified Formula, at least for my test cases, in order to be consistent with observations. I note too that my test case exercises match my real world use of teleconverters so the results do matter to me in practical terms out in the field.

AKRover said:

Unfortunately without going through the painstaking efforts of full thick lens analysis of a real world example, the reasons why this works might not ever be clear to me. I keep thinking that there are offsetting realities in practical lens design that keep us constrained to this reliability in our results even though individual lenses can be dramatically different in design.

Click to expand...

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Nick
Summary of photo activity since 2007 https://fliesandflowers.blogspot.com/2019/01/when-i-retired-in-2006-i-had-it-in-mind.html
Flickr image collections http://www.flickr.com/photos/gardenersassistant/collections/
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gardenersassistant said:

So is our only route forward something that isn't possible? Nowhere else to go now? Impasse?

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The one thing that has guided my journey through the technical side of photography is never-ending curiosity. There are times like this where I have to admit that I don’t have the answer and that I am not finding people who do have the answer (at least not in terms I am capable of understanding), but that is never the end of it. My curiosity over the last six months has really focused on this thick lens model. There have been a couple good threads on DOF and pupil magnification that left me with more questions than answers. I revisit bclaff’s optical bench about once a week and sooner or later he will have data on a lens that I actually own and I can perhaps do a full analysis throughout the range of focus to see how the math really works out and to compare it to real world test results. I assure you that I will one day fully understand this, but that could take a few years. It is a fun journey, though.

Until then, I am a far more interested in photography than technology. Experience matters often more than the technical understanding. I hate starting from what seems like square one on experience when buying a new lens, but if I screw up a few images of insects this year by not hitting the best settings, it isn’t the end of the world. My feeling is that your experience level in macro is something you can better rely on, even if you have to operate for a while with a less than perfect technical guide. It makes me laugh that my fundamental belief is that we don’t have to be optical experts to be photographers, but when we get to more technical aspects of photography, I think we have to be well-versed in optical design in order to be able to convince ourselves that we don’t need to understand optical design when doing photography. The way modern lenses operate through their range of focus leaves me uncomfortable in all of my understandings of how to do photography. I miss the joys of the simple thin lens model. I now find myself doubting the most basic of assumptions like the f-number I just dialed on my camera. I don’t even know what that means anymore, and my problem is far more than just in the macro realm. I am pretty sure I am dealing with errors due to assumptions about f-number that are greater than one stop. I know how much I pay for one stop of performance in a wildlife lens so an error of one stop is quite disturbing. Macro takes that issue to a very concentrated form and may actually be the better place for me to study my questions. If nothing else, your threads gave me some intriguing clues about the role of teleconvertors which I do use for wildlife, just not often in the macro realm. Thanks for making me think.

AKRover said:

gardenersassistant said:

So is our only route forward something that isn't possible? Nowhere else to go now? Impasse?

Click to expand...

The one thing that has guided my journey through the technical side of photography is never-ending curiosity. There are times like this where I have to admit that I don’t have the answer and that I am not finding people who do have the answer (at least not in terms I am capable of understanding), but that is never the end of it. My curiosity over the last six months has really focused on this thick lens model. There have been a couple good threads on DOF and pupil magnification that left me with more questions than answers. I revisit bclaff’s optical bench about once a week and sooner or later he will have data on a lens that I actually own and I can perhaps do a full analysis throughout the range of focus to see how the math really works out and to compare it to real world test results. I assure you that I will one day fully understand this, but that could take a few years. It is a fun journey, though.

Click to expand...

Interesting. We have different approaches. Mine is very biased towards heuristics rather than analysis.

AKRover said:

Until then, I am a far more interested in photography than technology. Experience matters often more than the technical understanding. I hate starting from what seems like square one on experience when buying a new lens, but if I screw up a few images of insects this year by not hitting the best settings, it isn’t the end of the world. My feeling is that your experience level in macro is something you can better rely on, even if you have to operate for a while with a less than perfect technical guide. It makes me laugh that my fundamental belief is that we don’t have to be optical experts to be photographers, but when we get to more technical aspects of photography, I think we have to be well-versed in optical design in order to be able to convince ourselves that we don’t need to understand optical design when doing photography.

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:-D

AKRover said:

The way modern lenses operate through their range of focus leaves me uncomfortable in all of my understandings of how to do photography. I miss the joys of the simple thin lens model. I now find myself doubting the most basic of assumptions like the f-number I just dialed on my camera. I don’t even know what that means anymore, and my problem is far more than just in the macro realm. I am pretty sure I am dealing with errors due to assumptions about f-number that are greater than one stop.

Click to expand...

That seems like a lot. Up to now, teleconverters aside, I've never noticed an inconsistency that I've found troublesome. Mind you, that is on a very, very shallow basis of understanding. Even the word "understanding" seems a bit strong tbh. I operate mainly on impressions, feelings, hunches, guesses, assumptions and the like.

AKRover said:

I know how much I pay for one stop of performance in a wildlife lens so an error of one stop is quite disturbing. Macro takes that issue to a very concentrated form and may actually be the better place for me to study my questions. If nothing else, your threads gave me some intriguing clues about the role of teleconvertors which I do use for wildlife, just not often in the macro realm. Thanks for making me think.

Click to expand...

I find this sort of discussion works both ways, so thank you too for your input.

AKRover said:

AKRover wrote:

... I revisit bclaff’s optical bench about once a week and sooner or later he will have data on a lens that I actually own and I can perhaps do a full analysis throughout the range of focus to see how the math really works out and to compare it to real world test results. ...

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FWIW, you might want to subscribe to this thread.
I typically note any lens that I add to the Optical Bench Hub there.