Sigma 400mm tele macro magnification/focal length help

Have questions about the equipment used for macro- or micro- photography? Post those questions in this forum.

Moderators: rjlittlefield, ChrisR, Chris S., Pau

bbobby
Posts: 54
Joined: Sat Jan 15, 2022 12:40 pm
Location: Indianapolis, IN

Sigma 400mm tele macro magnification/focal length help

Post by bbobby »

Not sure if this is the right place to ask...
Anyway... it so happens I got 2 of these lenses, before selling one of them I was testing it for max magnification... and I think there is discrepancy which maybe somebody can help me with.
Specs for the lens in the manual are: min focusing distance of 160cm and max magnification of 1:3.
An online calculator shows that 400mm lens @ 160cm will give 1:4 magnification. For 1:3 it should go down to 120cm. Lens is internal focusing and I do know some of them are shortening the focal length of the lens to get better magnification. But according the calculator the focal length of this lens should increase to close to 500mm. I never heard of any lens doing that.
Using same calculator the same lens (on Sony A7R IV) @ 42 meters (+/- 1 meter) is measured 389mm instead of 400mm which is close enough for all practical purposes and in the margin of error.
So I mounted the lens on D800 (35.9x24mm sensor) and I took a picture of a ruler - attached - just short of 11mm. Focusing distance measured by me is 154cm - from the sensor to the ruler. Allowance for mistake here is no more than 1 cm. From the front of the lens is 123 cm (adding 26cm for the lens itself and another 4.6 for the flange distance it is 153.6 cm).
Using an online calculator at this distance I should get about 13.8cm of the ruler for a magnification 1:3.8. So maybe I made a mistake in my testing. OR I am using the calculator wrong. OR...?
Any input will be greatly appreciated.
Attachments
sigma400f56maxmag.jpg

JKT
Posts: 417
Joined: Fri Oct 28, 2011 9:29 am
Location: Finland
Contact:

Re: Sigma 400mm tele macro magnification/focal length help

Post by JKT »

One thing you are missing is the location of input and exit pupils. That distance is either added to the focus distance or subtracted from it depending on which pupil comes first. It also might make sense to design for long pupil distance and/or long focal length at minimum focus in order to justify the tele-macro designation.

rjlittlefield
Site Admin
Posts: 23543
Joined: Tue Aug 01, 2006 8:34 am
Location: Richland, Washington State, USA
Contact:

Re: Sigma 400mm tele macro magnification/focal length help

Post by rjlittlefield »

bbobby, welcome aboard.

The way to bet is that the online calculator is using some simplifying assumptions that are not valid for your lens. It's very common for calculators to use formulas that are based on the "thin lens" model of optics, when in fact real lenses are always "thick". The significance of being "thick" versus "thin" is that for thick lenses, distances have to be measured from two special locations called "principal planes", and the locations of those principal planes are never included in the specifications for the lens. The usual result is that the calculators are sort of OK at long distances and small magnifications, but become progressively inaccurate at shorter distances and higher magnifications, unless corrections are made for the locations of the principal planes. But you don't know those locations, and you don't know how to apply the corrections, so the calculators can easily provide more misdirection than insight.

So, let's start back at the beginning.

You say that the specs in the manual are minimum focusing distance of 160 cm (or is it 1.6 m?) and max magnification of 1:3. You measure 154 mm and 108.5/35.9 = 3.02X. To me those are minor differences, not indicating any issues.

Then you started plugging numbers into the online calculator and got numbers that did not make sense.

Working with thin lens model, the simplest formulas say that in general the distance behind the lens will be FL*(mag+1) and the distance in front of the lens is FL*(1/mag+1). So, to get 1:4 with a 400 mm lens would require 500 mm behind the lens and 2000 mm in front of it. (Check: 500:2000 = 1:4 and 1/500+1/2000 = 1/400.) Similarly to get 1:3 would require 533.3 behind the lens and 1600 mm in front of it. (Check: 533.3:1600 = 1:3 and 1/533.3+1/1600 = 1/400). So if your lens were thin and FL=400mm, the sensor-to-subject distance at 1:3 would be 533.3+1600 = 2133 mm, about 213 cm. But you're measuring 1:3.02 at only 154 cm. So clearly either the effective FL has become a lot less than 400 mm, or the locations of the principal planes are messing with the distances. Further measurements would be required to sort that out.

In any case, you say that the online calculator "shows that 400mm lens @ 160cm will give 1:4 magnification. For 1:3 it should go down to 120cm." I cannot make any sense of those numbers. Possibly the calculator is messed up, or possibly the numbers are labeled confusingly, or possibly the calculator is really designed for some other task and it's being misapplied here. If you can point to the exact calculator you used, maybe I can figure out what's going on.

--Rik

rjlittlefield
Site Admin
Posts: 23543
Joined: Tue Aug 01, 2006 8:34 am
Location: Richland, Washington State, USA
Contact:

Re: Sigma 400mm tele macro magnification/focal length help

Post by rjlittlefield »

JKT wrote:
Thu Jun 23, 2022 12:57 pm
One thing you are missing is the location of input and exit pupils. That distance is either added to the focus distance or subtracted from it depending on which pupil comes first.
A quibble: this should be principal planes, not input and exit pupils. For some lenses the distance between the pupils is very similar to the distance between the principal planes. But that's not always true, and when it's not, the focus distances follow the principal planes, not the pupils.

--Rik

bbobby
Posts: 54
Joined: Sat Jan 15, 2022 12:40 pm
Location: Indianapolis, IN

Re: Sigma 400mm tele macro magnification/focal length help

Post by bbobby »

Thank you for the answer. Something did not make sense and I hate to leave a question unanswered. The lens clearly goes to 1:3 or very close to that and the resolution is very good at long distances, but these calculators are giving me a headache instead of making my life easier ;-)

This is what I was using:
https://www.scantips.com/lights/fieldofview.html#top
https://www.omnicalculator.com/other/ca ... ld-of-view
minimum focusing distance of 160 cm (or is it 1.6 m?)
1.6 m
Further measurements would be required to sort that out.
What else I can do/measure to figure out the effective focal length?
Attachments
sigma400f56maxmagcalc.jpg
sigma400f56maxmagcalc2.jpg

rjlittlefield
Site Admin
Posts: 23543
Joined: Tue Aug 01, 2006 8:34 am
Location: Richland, Washington State, USA
Contact:

Re: Sigma 400mm tele macro magnification/focal length help

Post by rjlittlefield »

Thank you for the links.

You had very bad luck in finding these. I have reservations about all the online calculators I know, but these two are particularly bothersome because they present some appearance of authority and completeness, while egregiously ignoring or mishandling some important aspects of basic optics.

In particular, scantips.com manages to ignore that as a lens focuses closer, either it must move farther away from the sensor or its focal length must shorten, or some combination of both, and neither of those effects is reflected in the calculator or in most of the associated formulas at https://www.scantips.com/lights/fieldofviewmath.html . Oddly, the math page correctly quotes the thin lens equation, which it writes as 1/S1+1/S2=1/f, but then in the same paragraph it writes that
Working Distance = d = S1 (distance in front of lens)
Focal Length = f = S2 (distance behind lens)
Focus Distance = d + f
If you work through the algebra, you'll find that these statements cannot all be true. If we agree to write that d = S1 (distance in front of lens), and S2 is distance behind the lens, and we agree to use the thin lens formula, then it must be true that S2 is larger than f, by a factor of (1+m), where m=S2/S1 as correctly written elsewhere on the page. The only way that S2 can equal f is if either the focused subject is at infinity, or the subject is not focused!

If I were inclined to cut scantips.com some slack (which I'm not), I would note that the calculator page does say
The Angle of Field of View is independent of the field distance, but the angle is computed from sensor size and focal length. The Field Distance is not limited to be only the subject or focus distance. Here it means the distance to the point where you want field size calculated. It might be the background distance for example (which then would show the Field of View at the background distance). A 2nd distance can be entered for convenience, but it is the same result as simply changing the first distance.
In retrospect, with much effort, I can read that paragraph as saying "The calculator assumes infinity focus, regardless of actual distance to the subject". But that treatment is so bizarre that I cannot believe any reader of the page would read it that way without special prompting.

In comparison, the omnicalculator page is much simpler: it just ignores focus altogether! (This seemed so strange that I asked my browser to search the page for "focus". It found only one instance, at "Keep reading to discover...some focused examples", none of which address focus.)
minimum focusing distance of 160 cm (or is it 1.6 m?)
1.6 m
My question was prompted by some lens reviews that mentioned 1.6 m. So then, assuming the manufacturer did the rounding correctly, the actual value might be as small as 155.1 cm, scarcely different from your 154 cm.
Further measurements would be required to sort that out.
What else I can do/measure to figure out the effective focal length?
The trick is to add extension behind the lens, so as to change its focus point without moving any of its elements. Then you measure the optical magnification at two different measured extensions, and calculate as follows:
focal length = (extension1 - extension2) / (magnification1 - magnification2)

So for example, if you start with no added extension and your measured magnification of 0.33, then you add 100 mm of extension and measure a new magnification of 0.62, then you would calculate as
focal length = (100-0)/(0.62-0.33) = 345 mm

The origin of this formula is the thick lens equation that rear focus distance = f*(magnification+1) + K, where K is a constant that represents the distance from the rear principal plane to wherever you based your own measurement. K is unknown, but by working with the difference of two distances, K disappears and then you can recover focal length from just the ratio of the differences.

--Rik

bbobby
Posts: 54
Joined: Sat Jan 15, 2022 12:40 pm
Location: Indianapolis, IN

Re: Sigma 400mm tele macro magnification/focal length help

Post by bbobby »

You are most helpful.
I will definitely try this trick with the extensions...
Thank you!

JKT
Posts: 417
Joined: Fri Oct 28, 2011 9:29 am
Location: Finland
Contact:

Re: Sigma 400mm tele macro magnification/focal length help

Post by JKT »

rjlittlefield wrote:
Thu Jun 23, 2022 1:34 pm
JKT wrote:
Thu Jun 23, 2022 12:57 pm
One thing you are missing is the location of input and exit pupils. That distance is either added to the focus distance or subtracted from it depending on which pupil comes first.
A quibble: this should be principal planes, not input and exit pupils. For some lenses the distance between the pupils is very similar to the distance between the principal planes. But that's not always true, and when it's not, the focus distances follow the principal planes, not the pupils.
:oops:

rjlittlefield
Site Admin
Posts: 23543
Joined: Tue Aug 01, 2006 8:34 am
Location: Richland, Washington State, USA
Contact:

Re: Sigma 400mm tele macro magnification/focal length help

Post by rjlittlefield »

JKT wrote:
Thu Jun 23, 2022 11:21 pm
:oops:
No worries. I see this as a great opportunity to gain some understanding. I went looking for some striking illustrative example, using the lens models and analysis capabilities of https://www.photonstophotos.net//GeneralTopics/Lenses/OpticalBench/OpticalBench.htm . But I was surprised to find that for most of the common lenses I looked at, the distance between the pupils was not much different from the distance between principal planes. So now I wonder, how many people have used the wrong metric and gotten a decent result anyway?

--Rik

bbobby
Posts: 54
Joined: Sat Jan 15, 2022 12:40 pm
Location: Indianapolis, IN

Re: Sigma 400mm tele macro magnification/focal length help

Post by bbobby »

Working with thin lens model, the simplest formulas say that in general the distance behind the lens will be FL*(mag+1) and the distance in front of the lens is FL*(1/mag+1). So, to get 1:4 with a 400 mm lens would require 500 mm behind the lens and 2000 mm in front of it. (Check: 500:2000 = 1:4 and 1/500+1/2000 = 1/400.) Similarly to get 1:3 would require 533.3 behind the lens and 1600 mm in front of it. (Check: 533.3:1600 = 1:3 and 1/533.3+1/1600 = 1/400). So if your lens were thin and FL=400mm, the sensor-to-subject distance at 1:3 would be 533.3+1600 = 2133 mm, about 213 cm. But you're measuring 1:3.02 at only 154 cm. So clearly either the effective FL has become a lot less than 400 mm, or the locations of the principal planes are messing with the distances. Further measurements would be required to sort that out.
Using your formula: This 400 mm lens should shorten the focal length to 290 mm to get 1:3 @ 154 cm (1160 in front and 387 behind the lens). Correct?
The trick is to add extension behind the lens, so as to change its focus point without moving any of its elements. Then you measure the optical magnification at two different measured extensions, and calculate as follows:
focal length = (extension1 - extension2) / (magnification1 - magnification2)

So for example, if you start with no added extension and your measured magnification of 0.33, then you add 100 mm of extension and measure a new magnification of 0.62, then you would calculate as
focal length = (100-0)/(0.62-0.33) = 345 mm
I did that, I think, but the result is not even close.
This time I used Pen-F with sensor width 17.3 mm - it is just way lighter than D800. I am guessing only magnification plays role here, not the sensor size. I also did not measure the sensor to subject distance. Got some extension tubes together to 103.5 mm.
Without any extension: I can see 52 mm of the ruler, 52/17.3=3.01 or 0.33x - no surprise here.
With 103.5mm extension I can see 21.5 mm which is 0.81x.
Applying the formula FL=(103.5-0)/(0.81-0.33)=103.5/0.48= 215.6. So this 400mm lens shorten the focal length to 216 mm to reach 1:3 ?? This is unexpected!

rjlittlefield
Site Admin
Posts: 23543
Joined: Tue Aug 01, 2006 8:34 am
Location: Richland, Washington State, USA
Contact:

Re: Sigma 400mm tele macro magnification/focal length help

Post by rjlittlefield »

bbobby wrote:
Fri Jun 24, 2022 11:42 am
Using your formula: This 400 mm lens should shorten the focal length to 290 mm to get 1:3 @ 154 cm (1160 in front and 387 behind the lens). Correct?
Correct. But remember, that formula is for thin lens model with no space between the principal planes.
The trick is to add extension behind the lens, so as to change its focus point without moving any of its elements. Then you measure the optical magnification at two different measured extensions, and calculate as follows:
focal length = (extension1 - extension2) / (magnification1 - magnification2)

So for example, if you start with no added extension and your measured magnification of 0.33, then you add 100 mm of extension and measure a new magnification of 0.62, then you would calculate as
focal length = (100-0)/(0.62-0.33) = 345 mm
I did that, I think, but the result is not even close.
The example was mostly intended to illustrate the calculation. I plucked values out of the air, having no reason to think they would match your lens.
This time I used Pen-F with sensor width 17.3 mm - it is just way lighter than D800. I am guessing only magnification plays role here, not the sensor size.
Correct -- sensor size is not relevant except as an input to the calculation of magnification.
I also did not measure the sensor to subject distance. Got some extension tubes together to 103.5 mm.
Without any extension: I can see 52 mm of the ruler, 52/17.3=3.01 or 0.33x - no surprise here.
With 103.5mm extension I can see 21.5 mm which is 0.81x.
Applying the formula FL=(103.5-0)/(0.81-0.33)=103.5/0.48= 215.6.
I agree with your calculation, to within rounding of intermediate values. I do calculations like this in a spreadsheet, so values flow from input to output without rounding. That approach calculates 219.3.
So this 400mm lens shorten the focal length to 216 mm to reach 1:3 ?? This is unexpected!
It is shorter than I would have guessed, but not short enough to make me convinced there must be some error. I have seen other lenses that shortened by more than half, albeit at larger magnifications.

In any event, this thread nicely illustrates why I have reservations about online calculators. Except for special conditions, typically around infinity focus, calculating an accurate prediction requires much more information than is commonly available or can be easily measured. Unfortunately that fact is not well known, so people expect calculators to do a job they really cannot. :-(

--Rik

bbobby
Posts: 54
Joined: Sat Jan 15, 2022 12:40 pm
Location: Indianapolis, IN

Re: Sigma 400mm tele macro magnification/focal length help

Post by bbobby »

You are right, without rounding the number will be 219.2987776 instead of 215.6. I am not doing anything scientifically so difference between 215 and 220 (or about 2%) is not something which bothers me at all. Actually I will be perfectly happy with a tolerance +/- 5%.
On the other hand a lens which should be 400mm, simple theoretical calculation to show about 290mm at close distance and then actual measurement to show 219.3mm is a like a shock for me at this moment. If it was somewhere close to 290 mm, probably +/- 15 mm I would expected it... but still value of 219.3 mm is shocking for me right now. There was a fuss years ago with Nikon 70-200/2.8 VR II which shortened the focal length from 200 mm to about 135 mm at close distance, if my memory service me well... I assumed this was more because it was zoom and not prime lens... I will run similar test to some other lenses, I got also the smaller Sigma 300/4 introduced at the same time and also going to 1:3... then to some true macro ones going to 1:1...

Is there any other test which I can run at home to confirm this value of 219mm?

rjlittlefield
Site Admin
Posts: 23543
Joined: Tue Aug 01, 2006 8:34 am
Location: Richland, Washington State, USA
Contact:

Re: Sigma 400mm tele macro magnification/focal length help

Post by rjlittlefield »

bbobby wrote:
Fri Jun 24, 2022 7:01 pm
Is there any other test which I can run at home to confirm this value of 219mm?
I do not know of any. Once upon a time I ran into an academic publication of methods to determine focal length. (HERE, I think.) All the methods that I thought might be practical involved imaging a subject that is (virtually) at infinity, for example a pinhole or reticle viewed through a collimating lens. But for your lens turned to closest focus, the image of a subject at infinity will retreat inside the lens, quite possibly even in front of the rear element in which case I think the methods fail.

It would be nice to have another method. If you find one, please share!

--Rik

rjlittlefield
Site Admin
Posts: 23543
Joined: Tue Aug 01, 2006 8:34 am
Location: Richland, Washington State, USA
Contact:

Re: Sigma 400mm tele macro magnification/focal length help

Post by rjlittlefield »

bbobby wrote:
Fri Jun 24, 2022 7:01 pm
Is there any other test which I can run at home to confirm this value of 219mm?
As I mentioned in previous post, I do not know of a different method.

However, from personal experience I have found there is great value in taking a larger set of measurements, with varying values for added extension, and checking to be sure that all the values for extension versus magnification lie on a good straight line.

For any photo quality ordinary lens (maybe not fisheyes), theory says the association should be linear to within the limits of measurement error. I have found great reassurance in seeing that actually happen. Any significant deviations from a straight line strongly suggest that something has gone wrong with the measurement. Possibilities include miscounting tick marks on the ruler, aligning on opposite edges of tick marks, miscounting pixels in the image, transcription errors at any time, accidentally bumping the focus ring off its limit position, failing to have digital calipers properly zeroed, getting calipers hung up on a flange ring, having the camera misregistered with the ruler when measuring front distance, and so on. I have made every one of those particular mistakes on multiple occasions; probably there are others that I have momentarily forgotten.

In any case, with only two points there is no way to detect measurement error. With three points any error is likely to be detectable, and with 5 or more points the graph will show any single error as an obvious outlier.

--Rik

bbobby
Posts: 54
Joined: Sat Jan 15, 2022 12:40 pm
Location: Indianapolis, IN

Re: Sigma 400mm tele macro magnification/focal length help

Post by bbobby »

rjlittlefield wrote:
Sat Jun 25, 2022 11:24 am
bbobby wrote:
Fri Jun 24, 2022 7:01 pm
Is there any other test which I can run at home to confirm this value of 219mm?
As I mentioned in previous post, I do not know of a different method.

However, from personal experience I have found there is great value in taking a larger set of measurements, with varying values for added extension, and checking to be sure that all the values for extension versus magnification lie on a good straight line.

For any photo quality ordinary lens (maybe not fisheyes), theory says the association should be linear to within the limits of measurement error. I have found great reassurance in seeing that actually happen. Any significant deviations from a straight line strongly suggest that something has gone wrong with the measurement. Possibilities include miscounting tick marks on the ruler, aligning on opposite edges of tick marks, miscounting pixels in the image, transcription errors at any time, accidentally bumping the focus ring off its limit position, failing to have digital calipers properly zeroed, getting calipers hung up on a flange ring, having the camera misregistered with the ruler when measuring front distance, and so on. I have made every one of those particular mistakes on multiple occasions; probably there are others that I have momentarily forgotten.

In any case, with only two points there is no way to detect measurement error. With three points any error is likely to be detectable, and with 5 or more points the graph will show any single error as an obvious outlier.

--Rik
I already pondered the implication of applying only 1 method to reach a conclusion. And I got to the same point as you - will have to do a bit more comparison work. To get 4-5 measurement up to 1x if possible with more of less extension... Although I do not know if I have more extension tubes, but will find some or use a bellows... Then I was wondering if I can compare the lens with another one... all this got me thinking and I actually was gonna ask something else too ;-)

Many older macro lenses are going only to 1:2 and need extension tube to reach 1:1. For example Nikon PK-13 is 27.5mm and if I remember correctly it is for 55/2.8. 25.7 is half of 55mm - so my guess here is that for a lens to go from 1:2 to 1:1 it needs 50% extension. Is that always true? If this is a fact I can apply it here... I need to determine how much extension this Sigma needs to get to 1:1 and then double the value.

Example: to get 1:1 this Sigma will need 110 mm extension - meaning its focal length is 220 mm and voila - I got the 2nd confirmation.

My 2nd question is about shortening the effective focal length going close to the target - is this happen only with internal focusing lens? If this is the case I probably need to find lens which extends to get closer then compare it to this one and this way getting 2nd confirmation of the focal length. I am not aware of any 400mm lens going so close (Sigma also made 400/5.6 mirror lens which was going pretty close,) but if the effective focal length actually is bellow 300mm... then maybe I can get old Tamron SP 300/5.6 which I think extends when focusing and goes down to 1:3.3 and Canon FD 200/4 Macro (it can go to 1:1) which also extends... Then maybe with some calculation I can have meaningful comparison.

Using Canon FD 200/4 macro I can measure the distance from sensor to the object at 1:3.3 magnification. Assuming it is true 200mm lens (which I will try to confirm) I will get some value. Then I can to the same with the Tamron which is going only to 1:3.3. Again assuming it is true 300mm and measuring again the distance from sensor to subject I will have another value. My theory is the Sigma should be somewhere between them at the same 1:3.3x and when I know where I will know approximate focal length for this magnification.

Example: Canon measure 120mm, Tamron measure 180mm and Sigma measure 160mm for 1:3.3 magnification. This numbers are from the air of course. Then 250mm lens should have distance from sensor to subject of 150mm.

Or I can be completely wrong and this would not work like that at all... and in this case better to know it beforehand and not waste time in pointless comparisons ;-)

And again, thank you very much for your help. I learned now 2 formulas which I can apply myself in the future without the need to look at unreliable online calculators. And obviously this lens shorten the focal length to get close - which I expected, although not almost halving it - the only question now is how much indeed and if it can be confirmed by not only 1 but 2 ways.

Post Reply Previous topicNext topic