Finding the focal plane

mathbias

TPF Noob!
I'm trying to find the focal plane of my camera (Sony a7 iii, with FE 28-70mm F3.5-5.6 OSS). The camera has the location of the sensor plane marked, but all focus math requires the location of the focal plane.

A hypothetical single element lens would have the focal plane ahead of the sensor plane by the focal length. I thought that separation would be lower for a real lens. My test results (below) make no sense. Please explain what I'm doing wrong and/or tell me what I should do instead and/or which product stats to disbelieve.

Camera on tripod with center of view aimed EXACTLY (11.7x digital zoom assisted) at one end of 4-foot "yardstick), with sensor plane 70 inches from that centered tip of the stick. I take a photo, then zoom within the edge of that image to get a precise measure of half the subject width, which is 41.125 inches at the 28 end of the zoom and 16.25 at the 70 end.

I looked up the sensor width and found 36mm.
Using H = half the subject width and D=distance subject to focal plane and F=focal length, I'm pretty sure the right formula is:
D = (2*H)*F/36
Notice D and H are in the same units as each other, while F and 36 are in the same units as each other, so D,H don't need to be in the same units as F.

The distance from the center of the subject to the focal plane is then 63.2 inches for F=70 and 64 inches for F=28. But that puts the focal plane 6 to 6.8 inches ahead of the sensor plane. But that is further away than the front of the lens. I don't understand how the focal plane could be entirely outside the physical structure.
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Before posting, I searched this forum and elsewhere for similar subjects. I found many threads that describe the sensor plane symbol on the camera and say that it is the "sensor plane" but then treat it (in all the related instructions) as if it were the focal plane. I don't think I misunderstood. But please correct me if you think I did and/or point to a discussion that has correct focal math given a sensor plane marking and no focal plane marking.
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On a related subject, the bundle I bought included a Vivitar 55mm 2.2x Professional Telephoto Lens HD4. All the online info I could find claims it multiplies focal length by 2.2. With testing similar to what I described above, I'm pretty sure I measured that it multiplies focal length by about 1.4; I checked the product name on the product, not just on the box. Both say 2.2

Is it not really the product it is labeled as? Does it interact with my Sony lens to produce less magnification than it would with a different lens? Is there some misleading standard whereby 2.2x means it multiplies focal length by 1.4?

If I later buy some other lens for multiplying focal length, how can I translate before purchase from what it says the multiple is to what the multiple actually is?

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Jeff15

Photographizing junkie!
Supporting Member
Hello and welcome, your question is too complicated for my simple mind. With luck, someone will be here soon to cast some light on your problems....... Ysarex

Been spending a lot of time on here!
I'm trying to find the focal plane of my camera (Sony a7 iii, with FE 28-70mm F3.5-5.6 OSS). The camera has the location of the sensor plane marked, but all focus math requires the location of the focal plane.

A hypothetical single element lens would have the focal plane ahead of the sensor plane by the focal length. I thought that separation would be lower for a real lens. My test results (below) make no sense. Please explain what I'm doing wrong and/or tell me what I should do instead and/or which product stats to disbelieve.

Camera on tripod with center of view aimed EXACTLY (11.7x digital zoom assisted) at one end of 4-foot "yardstick), with sensor plane 70 inches from that centered tip of the stick. I take a photo, then zoom within the edge of that image to get a precise measure of half the subject width, which is 41.125 inches at the 28 end of the zoom and 16.25 at the 70 end.

I looked up the sensor width and found 36mm.
Using H = half the subject width and D=distance subject to focal plane and F=focal length, I'm pretty sure the right formula is:
D = (2*H)*F/36
Notice D and H are in the same units as each other, while F and 36 are in the same units as each other, so D,H don't need to be in the same units as F.

The distance from the center of the subject to the focal plane is then 63.2 inches for F=70 and 64 inches for F=28. But that puts the focal plane 6 to 6.8 inches ahead of the sensor plane. But that is further away than the front of the lens. I don't understand how the focal plane could be entirely outside the physical structure.
-------
Before posting, I searched this forum and elsewhere for similar subjects. I found many threads that describe the sensor plane symbol on the camera and say that it is the "sensor plane" but then treat it (in all the related instructions) as if it were the focal plane. I don't think I misunderstood. But please correct me if you think I did and/or point to a discussion that has correct focal math given a sensor plane marking and no focal plane marking.
------
On a related subject, the bundle I bought included a Vivitar 55mm 2.2x Professional Telephoto Lens HD4. All the online info I could find claims it multiplies focal length by 2.2. With testing similar to what I described above, I'm pretty sure I measured that it multiplies focal length by about 1.4; I checked the product name on the product, not just on the box. Both say 2.2

Is it not really the product it is labeled as? Does it interact with my Sony lens to produce less magnification than it would with a different lens? Is there some misleading standard whereby 2.2x means it multiplies focal length by 1.4?

If I later buy some other lens for multiplying focal length, how can I translate before purchase from what it says the multiple is to what the multiple actually is?
Focal plane and sensor plane are the same thing. The marking on your camera for sensor plane indicates the focal plane.

Many modern lenses, wide angles, zooms, telephotos, employ designs that shift the nodal point away from the center of the lens. Retrofocus - Camera-wiki.org - The free camera encyclopedia Add to that the lens/camera makers aren't especially fussy about labeling a lens focal length with precision -- they'll round off to the nearest commonly used value. So the lens may be labeled 135mm but it's really 131.6 or really 140.3.

Can't help with the Vivitar HD4.

• Lez325

Grandpa Ron

No longer a newbie, moving up!
My canon T6 Rebel has an O with a horizontal line -- through it, on the top of the camera body that is supposed to show the location of the sensor.

I believe that is the focal plane.

Lez325

Wildlife Photographer
Supporting Member
Focal plane and sensor plane are the same thing. The marking on your camera for sensor plane indicates the focal plane.
I shoot only Sony and you hit his particular nail on the head Sir - I was about to type the self same comment

Les Last edited:

weepete

TPF Supporters
Supporting Member
Seems pretty complicated, what is it you are trying to achieve?

• Lez325
OP
M

mathbias

TPF Noob!
I hope someone who knows the answer will see this thread and post.
I'm still quite sure focal plane and sensor plane are not the same thing.

But if this is a terminology problem, rather than a technical issue, please correct my terminology:

By "focal plane" I mean the plane that in a theoretical ultra simple camera would be in front of the sensor plane by exactly the focal length.

lens/camera makers aren't especially fussy about labeling a lens focal length with precision -- they'll round off to the nearest commonly used value.
That could easily explain a significant part of my confusion. But no alternate values for the 70 and 28 could fit the measurements I've already made.
Seems pretty complicated, what is it you are trying to achieve?
There were even more complicated aspects of the camera I actually wanted to test, in order to get information to improve my ability to take good pictures.

I have very poor visual memory and other visual issues, so seeing through the viewfinder whether settings look better/worse good/bad etc. doesn't work for me. I never know what picture I've taken until I get it onto a computer with a large display, by which time I've lost too much information to easily learn from my mistakes.

But I am more comfortable working with numbers than most people are. So if I can quantify certain things when taking photos and then see the impact later when evaluating my photos, I can learn.

As I tried to measure aspects of the camera behavior, I realized that working with a guess at the location of the focal plane wasn't good enough. I can't measure the things I want to measure without first finding the focal plane.

So I used the 70 inch and 53 inch subject distances (to sensor plane) setups I had been trying to use for other measurements and tried to measure location of the focal plane. In hindsight, those were poor choices. They magnify several kinds of error, especially the error if the manufacturer were approximating the 70 and 28 specs on the lens.

So next step is to select three different close distances and repeat the test at each of those three distances. If focus doesn't have much impact on the position of the focal plane, that should allow independently solving for both the true F (in place of the labeled 70 and 28) and the position of the focal plane.

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wfooshee

No longer a newbie, moving up!
this is the first I have EVER heard of someone trying to define the focal plane as the focal length in front of the sensor plane, and I've been shooting for over 40 years.

The sensor plane IS the focal plane. Focal plane is that plane on which the image is focused by the lens, and has nothing to do with the lens's focal length.

That's the only distance you need to worry about, not matter what lens is in use.

I just simplified your life immensely. You're welcome.

I think you're confusing focal plane with focal length, and I say that because of your initial definition of the focal plane as being how far in front of the image plane a single element lens is. That is actually the definition of focal length. A single element lens with a 50mm focal length will produce an image when placed 50mm in front of the image plane. The focal plane is the plane on which the image is produced.

• Lez325
OP
M

mathbias

TPF Noob!
What I'm really asking is the relationship between subject width and subject distance from the sensor plane.
D = subject distance from sensor plane
W = subject width
F = focal length
I'll assume sensor width of 36

D = W * F/36 + some_adjustment
So I'm looking for that some_adjustment part.

Many online diagrams of the topic are showing the light path of a pinhole camera, even though they talk about real cameras. In a pinhole camera:
D = W * F/36 + F

Sorry for the ugly algebra, but for one aspect of this I need a rearranged formula:
then we have the effective definition of F, which is that in the limit as D approaches infinity
W/D = 36/F

But over the distances of real photographs, the adjust in that formula does matter. So I'd like to get some idea what it is. With a multiple element lens, I'd expect the value to depend on F, but not simply be F (as it would in a pinhole camera). I don't yet understand the optics of focusing (as opposed to zooming) so I'd expect the adjust to slightly depend on D. But the camera would be hard to use if it depended a lot on D, so hopefully I can ignore that.

My tests so far have all given values greater than 5 inches and less than 7 inches for the adjustment. Possibly, the adjustment is a fixed amount, and all the rest is measurement error (I doubt it, but maybe). If the sensor plane were the theoretical focal plane (as I think I understand the replies here) then the adjustment would be zero. There is absolutely no way I made measurement errors that large. One inch in the computed result is the absolute max of what could result from the scale of measurement error I might have made.

I see I confused matters with the term "focal plane". In all the simplified diagrams I see online, there is some marked plane (different from the sensor plane) where the distance from the subject is exactly
D = W * F/36
I even saw online discussions of professional movie camera lenses having a mark at that point in addition to the mark at the sensor plane. So I thought asking where that plane was would get the answer, which is equivalent to asking the amount that
D=W * F/36
is wrong by when talking about the sensor plane.

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Ysarex

Been spending a lot of time on here!
I hope someone who knows the answer will see this thread and post.
I'm still quite sure focal plane and sensor plane are not the same thing.

But if this is a terminology problem, rather than a technical issue, please correct my terminology:

By "focal plane" I mean the plane that in a theoretical ultra simple camera would be in front of the sensor plane by exactly the focal length.
That's the nodal point. Focal plane and sensor plane are the same thing.

• Lez325
OP
M

mathbias

TPF Noob!
That's the nodal point.
Thankyou for the terminology correction. I'll see if that helps in my online info searches.

Meanwhile, any comments or help on the questions I was trying to ask?

And, is it still called the "nodal point" with what I was really trying to refer to: the point at which the formula D = W * F/36 would be exactly correct?

For those that don't like algebra, what I'm talking about is the place where the viewing angle reaches a point. The first diagram I found online explaining "nodal point" showed exactly that for "first nodal point". But I can't tell if it really meant exactly that, because it shows the lines straight through the first lens element rather than bent by the lens element, but the text seems to contradict the picture. Straight through is what I mean: Where the sight lines would converge if the lens hadn't bent them, not where they actually do converge after being bent.

To the best I can mentally visualize, the way I mean would fit the described use of nodal point: Correct construction of a panorama should require rotating the camera around the point where the sight lines would have converged, rather than where inside the camera they actually do converge.

Panorama construction was another purpose for which I originally wanted to know the location of this point.
Please correct me if I'm visualizing the geometry wrong, but I'm pretty sure the rotation point for a panorama should be the point at which the viewing angle reaches a point, which (by the definition of viewing angle) is where D = W * F/36 is exactly correct.

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Ysarex

Been spending a lot of time on here!
What I'm really asking is the relationship between subject width and subject distance from the sensor plane.
D = subject distance from sensor plane
W = subject width
F = focal length
I'll assume sensor width of 36

D = W * F/36 + some_adjustment
So I'm looking for that some_adjustment part.

Many online diagrams of the topic are showing the light path of a pinhole camera, even though they talk about real cameras. In a pinhole camera:
D = W * F/36 + F

Sorry for the ugly algebra, but for one aspect of this I need a rearranged formula:
then we have the effective definition of F, which is that in the limit as D approaches infinity
W/D = 36/F

But over the distances of real photographs, the adjust in that formula does matter. So I'd like to get some idea what it is. With a multiple element lens, I'd expect the value to depend on F, but not simply be F (as it would in a pinhole camera). I don't yet understand the optics of focusing (as opposed to zooming) so I'd expect the adjust to slightly depend on D. But the camera would be hard to use if it depended a lot on D, so hopefully I can ignore that.

My tests so far have all given values greater than 5 inches and less than 7 inches for the adjustment. Possibly, the adjustment is a fixed amount, and all the rest is measurement error (I doubt it, but maybe). If the sensor plane were the theoretical focal plane (as I think I understand the replies here) then the adjustment would be zero. There is absolutely no way I made measurement errors that large. One inch in the computed result is the absolute max of what could result from the scale of measurement error I might have made.

I see I confused matters with the term "focal plane". In all the simplified diagrams I see online, there is some marked plane (different from the sensor plane) where the distance from the subject is exactly
D = W * F/36
I even saw online discussions of professional movie camera lenses having a mark at that point in addition to the mark at the sensor plane. So I thought asking where that plane was would get the answer, which is equivalent to asking the amount that
D=W * F/36
is wrong by when talking about the sensor plane.
You're talking about the nodal point in the lens and your formula's variable D is to the sensor (focal) plane. F is measured from the nodal point (center of the lens where light rays converge) to the sensor plane when the lens is focused at infinity (the distant horizon).

This is theoretical at best in that so many lenses are designed with a shifted nodal point. I have a 21mm lens designed to work on a FF Nikon. If the nodal point really was at the center of that lens then to focus the lens at infinity using a Nikon DSLR I'd have to smash the mirror in the camera as I shoved the back of the lens through the mirror.

As you focus a lens on nearer subjects the lens moves away from the sensor plane. Watch most lenses as you turn the focus ring. When a camera is focused on a subject at life-size magnification the lens will have moved forward to double it's focal length and the nodal point will be halfway between the subject and sensor plane. Four times F is the closest the subject can physically be to the camera (sensor/focal plane) and be in focus. But again it's all theory as modern lens designs will screwup your measurements.

You earlier posted this formula: D = W * F/36 + F -- that + F on the end is your "some adjustment."

This may help: Focal length inscribed on a lens is the focal length when the lens is focused at infinity. When you focus on nearer objects and the lens moves forward away from the sensor then it's focal length is increasing. Maybe you need to use that value for F in your formula.

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OP
M

mathbias

TPF Noob!
In a pinhole camera D = W * F/36 + F
Lots of diagrams explaining this for real cameras show exactly that pinhole camera geometry.
But a real camera does not have that same relationship between the sensor and the apex of the viewing angle. Some other value (or function of F) goes in place of the +F in that formula.

Ysarex

Been spending a lot of time on here!
In a pinhole camera D = W * F/36 + F
Lots of diagrams explaining this for real cameras show exactly that pinhole camera geometry.
But a real camera does not have that same relationship between the sensor and the apex of the viewing angle. Some other value (or function of F) goes in place of the +F in that formula.
In a pinhole camera the nodal point is the pinhole. With normal-design modern lenses I believe they make an effort to place the aperture at the nodal point.

OP
M

mathbias

TPF Noob!
As I continue to search/read online, I have now reached a better understanding of the behavior of a theoretical single ideal lens camera.

There, focus is achieved by the ratio between the actual distance lens to sensor distance and the focal length of the lens. When that ratio is 1 the camera is focused on infinity. The viewing angle is determined by the actual distance from lens to sensor, not by the len's focal length.

So in that idea single lens camera, the distance you focus at affects the viewing angle. That seems to be less true of modern cameras. To what extent is it untrue, and why, especially with a zoom lens?

In other words, to what extent is the viewing angle stable for a lens focal length (as set or reported for the zoom lens)?

I tried the simple experiment: at the max zoom, focus far away, point without refocusing at something just a few feet away and try to see the edges of the blurred image, then refocus, seeing those edges go slightly out of the field of view. So at a fixed lens focal length, the viewing angle is reduced by focusing on a nearer object.

So I need to take that effect into account as well, as I try to understand the relationship between lens focal length, object distance (from sensor) and object width.

I hope/expect that effect is smaller than it would be in a theoretical single lens camera. But I'll need a lot of measurement to find out if that is true. I'm trying to figure out what experiments would measure such things without much error. Any suggestion?

I still want to know where the apex of the viewing angle is. Finding both the viewing angle and its apex (given both unknown) requires test photos at two different distances. If those distances are large and not very different from each other, then the change in viewing angle would be trivial, but any measurement error would be magnified in the process of converting to location of the viewing angle apex. If those distances were both small, then ordinary measurement error has little impact on finding the apex, if the angle were either constant or known. But the angle isn't constant when focusing at a short distance.

BTW, in that single element lens, the apex of the viewing angle is the center of the lens. My testing hasn't yet been far off from the theory that the apex of viewing angle in my camera is the center of the frontmost (furthest from the sensor) element of the lens. That certainly was not near true of my previous camera. But if it works as a decent approximation for this one, that will simplify a lot of what I'm trying to figure out.

I think I did the algebra right for a single element lens and got a surprisingly complicated result, computing subject distance from sensor (rather than the simpler distance from lens) and using the lens focal length rather than the focused length from lens to sensor:
D = W * F/36 + 2F + 36F/W
in the limit where D,W are very large that still reaches D = W * F/36. But it is further from that than a pinhole camera is.
I expect I could find that formula via google if I had a bit more correct terminology.
But I think my testing shows my camera isn't behaving at all like a single lens element camera in the way that formula diverges for short distance, from the long distance approximation. I got that ugly equation using the simple relationships of the two parts of D:
D = A + B
A = distance from sensor to lens
B = distance from lens to subject
F = focal length of lens
W = width of the subject that fills the full width of the sensor
The amount of zoom is described by
A/36 = B/W
The fact that the subject is in focus is:
(A-F)/36 = F/W
Notice in that last relationship that when W is super large, we get the basic approximation A=F.
Also, notice that the units don't cancel well in that last equation (as they did in some equations I gave earlier) so the fact that the 36 is in mm means all the other values must also be in mm. So D and W are numerically large because they are in mm.

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