Calculating effective f-number when using teleconverters

[gardenersassistant]

Nick, I was shocked by the impossibly high F numbers until I realized that they were calculated for the image side. But aside from my culture shock, I wanted to figure out what was going on. You've done about as well as you can as a practical matter, and I don't think your calculations are wrong -- but maybe not as general as they could be. I also think there are some other insights to be gained here.

...The first observation is that by using teleconverters I have been able to achieve greater depth of field than I have previously achieved. ...the consensus seems to be that the depth of field is unusually large for non-stacked shots. Now, I can't prove that this is more than I could get for the same shots without using teleconverters, but in my own mind I'm sure that I am getting greater depth of field than I did previously.

Yes, the depth of field is remarkable, and better than what I would have thought possible.

ThrillaMozilla, post: 65156943, member: 826238"]
It tells you the size of the diffraction blur on the image. It does tell you whether the uncropped image -- the whole picture -- is going to be sharp. It doesn't tell you directly whether the bug is fuzzy or sharp.

Here is the cropping for those two images, cropped version on the left, uncropped image (resized raw file embedded JPEG) on the right. As you can see, the cropping of the first was slight, and for the second miniscule. In this context I don't understand why what the formula tells me about the sharpness of the whole image isn't what I really want to know.

These are cropped almost identically. I think if you filled the frame with one shot but cropped out a small part of the center with another shot, I think the approach might fail you.
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I think it is more a case of "would" than "might".

As you know, depth of field depends to a great extent on the size of the displayed image, and therefore also on cropping. That's probably the main reason that microscopists calculate resolution not of the image, but at the subject. If you don't do major cropping like that, you probably don't need to worry about calculating resolution.

OK. Good.

I captured two shots of a rule which was set at an acute angle to the plane of focus. I used a Canon 70D. For the first shot used a Canon MPE-65 at 1X magnification, set to minimum aperture of f/16. For the second shot I used a Kenko 1.4X teleconverter and 2X teleconverter with the MPE-65. ...For the second shot I used minimum aperture of f/45, with a magnification of a bit under 3X (presumably quite close to 2.8X).

...It looks to me as though the teleconverter image is softer than the bare lens image in the area of best focus but has larger depth of field. This is consistent with the teleconverter image having a smaller effective aperture.

I agree. You have traded depth of field for resolution. Alas, the two are inseparable except with composite images. They both depend entirely on the angle of acceptance by the lens.

For me, I believe using teleconverters does make a difference because they let me use effective apertures smaller than I can use without them, and hence get greater depth of field at the cost of the images being softer. For me, I believe using the formula I mentioned does help guide me in my experiments with different f-numbers to explore the impact, for my images, on the depth of field and associated image softening.

In the other thread you wrote: "With a teleconverter(s) you can either have the same magnification/framing with greater working distance or greater magnification with the same working distance." That confirms everything. I think what's going on here is that the teleconverters allow you to move further from the subject while still getting adequate magnification. Moving further from the subject is how you get that great depth of field -- and not incidentally, good working distance.

Yes, 72mm working distance at 8:1 is quite good compared to, for example, around 40mm at 5:1 with the MPE-65.

In principle you could the same result at the same distance with a longer lens instead of the teleconverters, if you could get the same aperture (diameter). But a longer lens would probably have a larger minimum aperture.

Indeed so. f/32 is the smallest I recall seeing for any focal length lens, and most are f/22. The MPE-65 is f/16.

I think that's why the teleconverters work so well for you. It's a brilliant solution. Well done.

I think there's one crucial point for anyone else attempting this. If the image is large enough for the sensor (i.e., that the pixel size is not the limiting factor) the teleconverters cannot further improve the resolution over what you could get without them.

Thank you so much for taking the time to discuss and explain. This sort of discussion is so useful for me (and hopefully for some lurkers too). It forces me to think very carefully when I'm trying to explain what I'm having problems with, and it is wonderful to have such high quality (and patient!) input from experts in the field to learn from,

 

[gardenersassistant]

I don't understand the practical implications of this for my use case. In particular, does this mean the formula for effective aperture that I thought Alan and I had agreed on is incorrect after all? This is the formula in question:

effective f-number = Lens_f-number x teleconverter_power * ( 1 + lens_magnification/p)

where p = pupil magnification.

It means the formula doesn't quite apply to what you really want to know. It tells you the size of the diffraction blur on the image. It does tell you whether the uncropped image -- the whole picture -- is going to be sharp. It doesn't tell you directly whether the bug is fuzzy or sharp.

You need to know the resolution and depth of field at the subject plane -- and that is determined by the lens entrance pupil diameter and the distance to the subject. That's how microscopists do it. (They actually use the numerical aperture, which is written on the objective. But never mind that.)

There are some implications.

1. The bottom line is that for this calculation the teleconverters don't make any difference. They don't change the resolution or depth of field! (Remember, we're now measuring these at the bug, not on the image.)

2. If you attempted to calculate the resolution or from any of the formulas above, you calculated the resolution at the image. To get the resolution at the bug, divide by the magnification.)

I think we may be talking at cross purposes.

<snip>

I captured two shots of a rule which was set at an acute angle to the plane of focus. I used a Canon 70D. For the first shot used a Canon MPE-65 at 1X magnification, set to minimum aperture of f/16. For the second shot I used a Kenko 1.4X teleconverter and 2X teleconverter with the MPE-65. (I found it really difficult to get the images aligned with complete precision. This was the best I could do after 30 minutes or so of trying.) For the second shot I used minimum aperture of f/45, with a magnification of a bit under 3X (presumably quite close to 2.8X).

The two images have very similar magnification. Presumably the magnification without TC would have been 1/2.8 x (rather than 2.8x) to get 1x net magnification.

Oh! My mistake. I got the lens magnifications the wrong way round. It was 1X with the teleconverters and around 2.8X with the lens alone. Thanks for spotting that.

Two comparisons are shown below, one showing the central portion of the images, the other showing the whole frame. The bare lens shot is on the left and the teleconverter shot on the right.

It looks to me as though the teleconverter image is softer than the bare lens image in the area of best focus but has larger depth of field. This is consistent with the teleconverter image having a smaller effective aperture.

Agreed.

With the 2.8x teleconverter attached your effective focal length is increased by the same factor. To get unit magnification you now need to increase the distance between subject and lens entrance pupil, compared to the case with no TC and 1:1 magnification. This reduces the object-space NA, so the depth of field increases and the image plane luminance decreases.

Assuming similar lighting conditions, exposure time with 2.8x TC was 1.3 seconds, compared with 0.6 seconds without TC. This is a factor 2.2x different, consistent with a smaller effective f-number with the TC.

The precise difference in effective f-number will depend on the extent to which any internal focussing in your macro lens changes the object space and image-space numerical apertures, but I do not see a huge discrepancy.

For me, I believe using teleconverters does make a difference because they let me use effective apertures smaller than I can use without them, and hence get greater depth of field at the cost of the images being softer. For me, I believe using the formula I mentioned does help guide me in my experiments with different f-numbers to explore the impact, for my images, on the depth of field and associated image softening.

If you can't set the MPE-65 to a smaller aperture than f/16,

Yes, that is minimum aperture with the MPE-65. (Not that I use the MPE-65. I don't like its handling characteristics, which is one of the reasons I stumbled upon the combination of a lower magnification lens with teleconverters.)

then the teleconverter will certainly allow you to achieve smaller effective f-number, both image-space and object-space, at the image magnifications you are interested in.

ThrillaMozilla is saying that the object-space depth of field and diffractive blur depend only on object-space NA. At a given image magnification, M, this is directly linked to your image-space effective f-number, fe, (which is not necessarily the same as the number reported by the camera)

Yes, with those teleconverters and the cameras I use them with what is reported is Lens_f-number * teleconverter_power rather than fe.

.

NA_obj = 1 / (2 N_obj) = M / (2 fe)

You have exceeded my comprehension with this. But no matter, I think I know what I need to from a practical standpoint. I'll go back to my photos now!

Thanks again for having the patience and taking the time to explain all this. It has been very helpful and educational.