[audiobomber]

I calculated actual focal lengths for some K-mount lenses, showing the effect of focus breathing at rated maximum focal length and minimum focus distance. Please feel free to add to the thread using this formula:

Effective focal length (at minimum focus distance) = Minimum focus distance [mm] / (Maximum reproduction ratio + (1/(Maximum reproduction ratio)) + 2)

Sigma 17-50mm
MFD = 279.4mm
Max reproduction ratio = .2
Focal length = 279 / (.2 + (1/(.2)) + 2) = 39mm

DA 16-85mm
MFD = 350mm
Max reproduction ratio = .26
Focal length = 350 / (.26 + (1/(.26)) + 2) = 57mm

DA 18-135mm
MFD = 400mm
Max reproduction ratio = .24
Focal length = 400 / (.24 + (1/(.24)) + 2) = 62mm

A 135mm f2.8
MFD = 1200mm
Max reproduction ratio = .15
Focal length = 1200 / (.15 + (1/(.15)) + 2) = 136mm

DA 18-270mm
MFD = 490mm
Max reproduction ratio = .26
Focal length = 490 / (.26 + (1/(.26)) + 2) = 80mm

DA*60-250mm
MFD = 1100mm
Max reproduction ratio = .15
Focal length = 1100 / (.15 + (1/(.15)) + 2) = 125mm

DA 55-300mm WR
MFD = 1400mm
Max reproduction ratio = .28
Focal length = 1400 mm / (.28 + (1/(.28)) + 2) = 239mm

DA 55-300mm PLM
MFD = 950mm
Max reproduction ratio = .3
Focal length = 950 mm / (.3 + (1/(.3)) + 2) = 169mm

DA*300
MFD = 1.4 m = 1400mm
Max reproduction ratio = 1:4 = .25
Focal length = 1400 mm / (.25 + (1/(.25)) + 2) = 224mm

DA*300mm + 1.4X RC
MFD = 1.4 m = 1400mm
Max reproduction ratio = .35
Focal length = 1400 / (1/(.35)) + 2) = 288mm

D FA 150-450mm
MFD = 2000mm
Max reproduction ratio = .22
Focal length = 2000 / (.22 + (1/(.22)) + 2) = 296mm

Sigma 150-500mm
MFD = 2.20 m = 2200mm
Max reproduction ratio = .19
Focal length = 2200 / (.19 + (1/(.19)) + 2) = 295mm

Results are subject to the veracity of the manufacturers' stated specifications. At infinity focus, the lenses should be close to the rated focal length. As the subject distance decreases, the true focal length of the lens decreases because the lens elements are shifting. This can be an advantage if you want to shoot wide, but not as welcome for telephoto. From the results above, it would appear that only the A135mm is not an internal focus lens.

I first noticed focus breathing using a DA 18-250 and DA 55-300. I did a field test and found:
- at approximately one mile, 250mm fov on the 18-250 corresponded to about 220mm on the 55-300
- at 30 feet, 250mm on the 18-250 was like 200mm on the 55-300
- at 9 feet, 250mm was like160mm on the 55-300

At the time, I thought the 55-300mm was showing true focal lengths and the superzoom was lying, but as shown above, neither reaches maximum focal length at MFD, but the superzoom fares worse.

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Last edited by audiobomber; 11-26-2016 at 09:39 AM.

[photoptimist]

Thanks for posting this!

But are you sure the numbers are correct? The f*(2 + m + 1/m) formula is only correct for thin lens optics. If the entrance and exit nodal points are not in the same location, the numbers will be different.

[beholder3]

Winners:

• FA 77mm F1.8 --> 75mm
• DA 35mm F2.8 Macro --> 35mm
• DFA 50mm F2.8 Makro --> 49mm

The loser:

• Sigma 18-250mm --> 67mm (!)

Misc:

• DA* 300mm F4 219 mm
• Tamron 70-300 Makro 211 mm
• Tamron 70-200mm F2.8 Makro 175 mm
• Sigma 70-200mm F2.8 138 mm
• DA* 60-250mm F4 125 mm
• DA* 50-135mm F2.8 124 mm
• FA*200mm F4 Makro 128 mm
• Tamron 180mm F3.5 Makro 118 mm
• Sigma 180 F2.8 Makro 118 mm
• DA 18-270mm 80 mm
• DA 18-250mm 77 mm
• DA 70 mm F2.4 67 mm
• DA 18-135mm 62 mm
• DFA 100mm F2.8 Makro 76 mm
• Tamron 90mm F2.8 Makro 73 mm
• Sigma 70mm F2.8 Makro 63 mm
• Sigma 17-70mm 42 mm
• Canon EF 100-400mm f/4.5-5.6L IS USM 250 mm
• AF-S NIKKOR 80–400 mm 1:4,5–5,6G ED VR 243 mm
• AF-S NIKKOR 200–400 mm 1:4G ED VR II 335 mm
• Sigma 150-600 mm f / 5-6.3 DG OS HSM 375 mm
• Tamron SP AF 150-600mm 5.0-6.3 VC USD 375 mm
• DA 16-85mm 57 mm
• DFA 150-450mm 296 mm
• Nikon 24-70/2.8 64 mm
• Nikon 24-70/2.8 VR 70 mm
• Canon EF 24-70/2.8 II 55 mm
• Pentax DFA 24-70/2.8 53 mm
• EF 100-400mm II 177 mm
• EF 300/4 234 mm
• Nikkor 500 mm / F 4,0 P IF-ED 446 mm
• Tamron SP 150-600mm F/5-6.3 VC USD 375 mm
• Tamron SP AF300mm f/2.8 LD(IF) 273 mm

[audiobomber]

Thanks for posting this!
But are you sure the numbers are correct? The f*(2 + m + 1/m) formula is only correct for thin lens optics. If the entrance and exit nodal points are not in the same location, the numbers will be different.

True, but I believe thin-lens optics are normally used when discussing camera lenses outside of a lab. There is a difference but it will apply somewhat to all lenses, offsetting the real world effect. Please, redo my calculations with actual modal points. Or do an empirical test I would gladly read it.

This empirical graph shows the Sigma 150-500mm focal length at about 267mm vs. 295mm calculated above. It is one of the lenses strongly affected by FB. Others would show less of a difference.
Focal Length versus Subject Distance - Sigma 150-500mm

---------- Post added 2016-11-26 at 12:27 ----------

Winners losers

Nice, where did you get these?

[beholder3]

T
Nice, where did you get these?

A spreadsheet I started some years ago to calculate the values for macros using TCs and extension tubes.

End result was and is that a DA*300 + TC + Kenko AF/SDM extension tube is the best long macro for shy things you can get (unless you really need x1):
x0,43 at 125cm distance.

[photoptimist]

True, but I believe thin-lens optics are normally used when discussing camera lenses outside of a lab. There is a difference but it will apply somewhat to all lenses, offsetting the real world effect. Please, redo my calculations with actual modal points. Or do an empirical test I would gladly read it.

This empirical graph shows the Sigma 150-500mm focal length at about 267mm vs. 295mm calculated above. It is one of the lenses strongly affected by FB. Others would show less of a difference.
Focal Length versus Subject Distance - Sigma 150-500mm

---------- Post added 2016-11-26 at 12:27 ----------



Nice, where did you get these?

I don't have any of the lenses you mention but here's one that I do have:

Tamron 18-250
MFD = 450mm
Max reproduction ratio = .3

By your formula:
Focal length = 450 mm / (.3 + (1/(.3)) + 2) = 80mm

But if you measure the angle-of-view at the MFD (using rulers at different distances), the lens is getting the same angle of view that a 146 mm thin lens would if set at m=0.3 because the front nodal point of the extended zoom is actually behind the sensor plane.

If those calculations of the Sigma_150-500mm were based on the thin lens formula rather than actual measures of angle of view, they are almost certainly wrong.

[audiobomber]

But if you measure the angle-of-view at the MFD (using rulers at different distances), the lens is getting the same angle of view that a 146 mm thin lens would if set at m=0.3 because the front nodal point of the extended zoom is actually behind the sensor plane.

I'm not sure what you mean by "different distances". The formula is intended for only one subject distance, i.e. the minimum focus distance.

[stevebrot]

But are you sure the numbers are correct? The f*(2 + m + 1/m) formula is only correct for thin lens optics. If the entrance and exit nodal points are not in the same location, the numbers will be different.

You are correct, but in previous similar threads on the topic, this important qualifier (entrance and exit pupils not coincident) was deemed unimportant despite actual measurements, the appropriate formulas, and Web examples showing otherwise.


Steve

[stevebrot]

True, but I believe thin-lens optics are normally used when discussing camera lenses outside of a lab.

Ummmm...except for when it makes a difference. E.g. when calculating FOV, dialing in the details of shooting panos and stitched images and so on. Using the thin lens formula fails miserably when doing actual FOV comparisons. Focus breathing is due to the location of the entrance and exit pupil locations being not only non-coincident, but also varying dynamically by focal length and focus distance.


Steve

[photoptimist]

I'm not sure what you mean by "different distances". The formula is intended for only one subject distance, i.e. the minimum focus distance.

The question is: what is the angle of view of the lens at MFD? Is the lens acting like a wide angle lens, a normal lens, an extreme telephoto, or what? That question affects at least two crucial photographic effects:

1. The relative magnification of foreground versus background objects. These objects may be out-of-focus but they strongly affect the composition (e.g., do you see an entire house in the background behind a close up of a person or just a window) and perspective effects (how much does the lens distort the person's face).

2. The maximum angle one can move the camera for a panorama (e.g., Brenizer Method) and still have overlap in the frames.


In turn, that angle-of-view has an equivalent focal length such that one might say that the photos taken by that lens at MFD of complex scenes have the same relative perspective effects of a simple thin lens of some focal length value.

P.S. Stevebrot and I are saying much the same thing. The thin lens formula does not provide photographically meaningful answers for complex lenses.

[stevebrot]

Using the thin lens formula fails miserably when doing actual FOV comparisons.

Example:

Tamron 70-150/3.5 (20A)
MFD = 700mm at all focal lengths
Reproduction ratio at MFD and 150mm focal length = 1:3

700/((1/0.33) + 0.33 + 2) = 131mm

Fair enough except that FOV by visual inspection at MFD and 150mm is less than at infinity for 150mm. The lens "breathes", but in the conventional direction, i.e. longer, not shorter.

Likewise, @beholder3 calculated the FA 77 Limited as 75mm at MFD. That lens also "breathes" longer, not shorter.

The formula calculates my Sigma 50/2.8 EX DG Macro at 47mm for MFD of 188mm for 1:1. That lens also "breathes" longer with 1.67 T stops more light required for correct exposure at MFD compared to infinity due to extension. I believe that calculates to a focal length of about 89mm at MFD.* Edit: bit of a red herring. Lens definitely breathes "longer" by visual inspection.


Steve

* Extension would have been greater except for presence of a floating element. FWIW, The FA 77 T value drops 2/3 stop from infinity to MFD which calculates to 98mm.

[audiobomber]

Fair enough except that FOV by visual inspection at MFD and 150mm is less than at infinity for 150mm. The lens "breathes", but in the conventional direction, i.e. longer, not shorter.

Without proof, I don't buy it.

---------- Post added 2016-11-26 at 21:37 ----------

The question is: what is the angle of view of the lens at MFD? Is the lens acting like a wide angle lens, a normal lens, an extreme telephoto, or what?

1. The relative magnification of foreground versus background objects. These objects may be out-of-focus but they strongly affect the composition (e.g., do you see an entire house in the background behind a close up of a person or just a window) and perspective effects (how much does the lens distort the person's face).

You are talking about perspective, which is strictly a function of subject distance. Filling the frame with a flower at 85mm on a16-85mm will require you to stand at the same distance as a non-IF 57mm lens. FOV and perspective for each lens, 57mm prime and 16-85mm at 85mm, will be similar.

[photoptimist]

Without proof, I don't buy it.

Steve's right and it's easy to prove that some lenses breath to longer focal lengths and some breath to shorter ones. Just point the camera and lens at a distant object (skyline, bookshelf, etc.) and watch the viewfinder as you focus in and out. For some zooms, the view does get wider as you focus down to MFD but for other lenses, the FOV on the distant view actually zooms in a little as you focus close.

You are talking about perspective, which is strictly a function of subject distance. Filling the frame with a flower at 85mm on a16-85mm will require you to stand at the same distance as a non-IF 57mm lens. FOV and perspective for each lens, 57mm prime and 16-85mm at 85mm, will be similar.

Yes, it is strictly a function of subject distance but it's the subject's distance to the front nodal point not the subject-sensor distance that matters.

That front nodal point can be virtually anywhere. There's even a category of lens (called telecentric) in which the nodal point is at minus infinity behind the sensor even if the sensor, lens, and subject are close to each other.

We all agree that some lenses can show focus breathing but disagree that the thin lens formula accurately estimates the amount of it.

[stevebrot]

Without proof, I don't buy it.

Google is our friend. That failing, see below on how to evaluate.

Steve's right and it's easy to prove that some lenses breath to longer focal lengths and some breath to shorter ones. Just point the camera and lens at a distant object (skyline, bookshelf, etc.) and watch the viewfinder as you focus in and out. For some zooms, the view does get wider as you focus down to MFD but for other lenses, the FOV on the distant view actually zooms in a little as you focus close.

That is why they call it focus "breathing". The FOV appears to "breathe" in and out as focus is racked far/near. Traditional non-internal-focus primes will breathe "long" meaning that FOV will become narrower when focusing to near objects. This is due to increased effective focal length due to extension. A decrease in effective relative aperture is a well-known side-effect that shows itself in increasingly dim viewing as magnification increases and increased exposure times for a given aperture setting.

Lenses having floating elements and/or internal focus are less predictable and may sometimes breathe "short" meaning that FOV increases as one focuses nearer. As a result, many modern zooms may produce far less magnification at maximum focal length and MFD than anticipated despite very short focus distance. The equation used in the comments above will often detect the fault, but the calculated focal length is often simply wrong even when it is in the correct direction. That being said, the actual number generally makes little difference.

I intentionally chose the three lenses I gave as examples above because I knew that all three had reasonable MFD and behaved in a conventional manner. I did not include my Sigma 17-70/2.8-4 (C). It is a complicated internal focus zoom that has severe focus breathing at 70mm. The specs tell all:

At 70mm focal length
MFD = 220mm
Reproduction ratio = 1:2.8

Addendum: At the focus distance above, I would expect closer to 1:1 for 70mm focal length.

The Tamron 70-150 in my comment above at 70mm makes 1:3 at 700mm MFD. The focal length equation for my Sigma 17-70 calculates an effective focal length of 43mm at 70mm, though I suspect the actual may be closer to 35mm. Either way, it sucks.


Steve

[stevebrot]

I have posted this before on other threads, but the linked page below is pertinent. It is on a site dedicated to panorama photography and includes a full discussion of the weaknesses of using the thin-lens formula for effective focal length calculation as well as a workable modification of the formula to model camera lenses.

How to use the Thin Lens Formula to model a thick lens -- PanoHelp.com

Long and obtuse and complicated, but eventually useful and no, I don't understand a lot of this stuff.


Steve