Finding the focal plane

[Ysarex]

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.

We use two different terms; angle of view (infinity focus measured in degrees) and field of view (calculated for the specific object distance closer than infinity measured in width of the subject).

That seems to be less true of modern cameras.

Don't see why that would be for a fixed focal length lens.

To what extent is it untrue, and why, especially with a zoom lens?

Only with a zoom lens because a zoom lens can change it's focal length -- it zooms. In that case it would be possible to establish a fixed FOV and maintain that for different object distances by zooming the lens to change focal length.

For example a 35mm lens on a FF camera has an AOV of 54 degrees. Focused at 10 feet the FOV is 10.3 feet (width). A 50mm lens on a FF camera has an AOV of 39.6 degrees and focused at 14.3 feet the FOV is 10.3 feet (width). A 24-70mm zoom can be set to 35mm or 50mm focal lengths.

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

Angle of view changes with focal length and format size. To the extent that a zoom lens can change focal length it can change AOV.

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 close 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.

 

[mathbias]

I think you are taking away the meaning of my question through a definition of terminology. But maybe you are saying two things are equal that aren't. I'm not sure.

If it is a terminology issue, then I really need correct terminology for what I have been calling viewing angle. I don't know how else to describe that other than viewing angle, and it is a real and significant thing that must have a name.

You seem to be defining the AOV of a lens as what the viewing angle would be if a camera using that lens were focused at infinity. Then obviously a given F and sensor size determines the AOV. But I'm talking about the viewing angle when that lens (without any change to the lens's focal length) is used focused on something closer. In a single element system, focusing closer means making the distance between the lens and the sensor larger, so it means making the viewing angle smaller.

Using my meaning of viewing angle, if you cut the subject distance exactly in half and the "viewing angle" was unchanged then the subject width would be cut exactly in half. But for a fixed lens focal length, the actual subject width would be cut to lower than half, because the thing I'm calling viewing angle goes down a little, because the sensor is further from the lens.

So, when you claim the AOV doesn't change (it is just a characteristic of the non zoom lens) is that just terminology, meaning what I'm calling viewing angle has some other term? Or are you convinced that the thing I want the term for doesn't actually change (for a fixed focal length lens) when you focus?

I don't actually have a fixed focal length lens. I have manual zoom on my zoom lens, so I can leave it at a fixed lens focal length while focusing. I also understand the math for a single element lens. In both the math for a single element lens and the actual behavior of my lens, the "viewing angle" goes down a little when you focus closer. If it doesn't work that way for a prime lens, that could only mean the prime lens has some tiny internal zoom adjustment to balance out the affect of focus on zoom.

 

[Ysarex]

I think you are taking away the meaning of my question through a definition of terminology. But maybe you are saying two things are equal that aren't. I'm not sure.

If it is a terminology issue, then I really need correct terminology for what I have been calling viewing angle. I don't know how else to describe that other than viewing angle, and it is a real and significant thing that must have a name.

You seem to be defining the AOV of a lens as what the viewing angle would be if a camera using that lens were focused at infinity. Then obviously a given F and sensor size determines the AOV. But I'm talking about the viewing angle when that lens (without any change to the lens's focal length) is used focused on something closer. In a single element system, focusing closer means making the distance between the lens and the sensor larger, so it means making the viewing angle smaller.

When you focus a lens on an object closer to the camera the lens is as you note moved away from the sensor. That action is effectively increasing the lens focal length and so lens focal length increases = angle of view decreases.

When we publish stats for lenses we use the infinity focus point as a base reference. So my 100mm macro lens is 100mm focused at infinity. If I use it to photograph a US quarter life-size with a FF camera it will be 200mm from the sensor -- a 200mm lens then.

Using my meaning of viewing angle, if you cut the subject distance exactly in half and the "viewing angle" was unchanged then the subject width would be cut exactly in half. But for a fixed lens focal length, the actual subject width would be cut to lower than half, because the thing I'm calling viewing angle goes down a little, because the sensor is further from the lens.

So, when you claim the AOV doesn't change (it is just a characteristic of the non zoom lens) is that just terminology, meaning what I'm calling viewing angle has some other term? Or are you convinced that the thing I want the term for doesn't actually change (for a fixed focal length lens) when you focus?

I don't actually have a fixed focal length lens. I have manual zoom on my zoom lens, so I can leave it at a fixed lens focal length while focusing. I also understand the math for a single element lens. In both the math for a single element lens and the actual behavior of my lens, the "viewing angle" goes down a little when you focus closer. If it doesn't work that way for a prime lens, that could only mean the prime lens has some tiny internal zoom adjustment to balance out the affect of focus on zoom.

 

[wfooshee]

The lens moving away as you focus closer does increase its focal length. How much... who knows? And it will be differing amounts for a zoom lens at different focal lengths.

I'll throw something else in for you, pointlessly and with absolutely no reason other than to demonstrate what I feel to be the futility of your efforts.

Change the color of your subject. That won't do much with a modern multi-element lens, because one of the main reasons modern lenses are multi-element is because a single-element lens will have horrible chromatic aberration. Different colors focus at different points. Blue and red will not converge together at the focal plane, and a white subject will have color fringes, blue in one direction, red in the other. Even if your 28-70 lens deals well with chromatic aberration, that 2.2x adapter won't.

I say futility, because I'm completely failing to understand why it matters what the angle of view, or field of view, actually is, down to the fraction of a millimeter. I always shoot with extra space on the frame to allow for cropping, which in itself changes the effective focal length and view of what I am shooting. If I can see it in the viewfinder, I am happy. I suppose, if for some reason, you are looking to have exactly a life-size image, or a 1/4-size image, these width-of subject calculations would be useful, but are you ever actually going to post, print, or otherwise use an image at sensor size, just to say that your captures image is exactly the same size as your subject? I know that in macro photography they speak in fractions or multiples of life-size, but I don't see that being what you're looking for, or if it is I've completely missed it.

I know I'm not actually addressing your questions, and presenting you with other questions of my own, and if need be, I apologize for that. I simply don't understand why it matters so much, other than theoretically. The nodal point moves as you focus the lens. How much depends on the lens, as every lens will be different. Unless you can measure the optical properties of a lens, I don't think you can ever calculate any of these answers accurately, because you won't have the values to put into the formulas. it may come down to practical measurements.

My closest experience to this is after inheriting my dad's Voigtlander Vitessa camera, I found he had 2 close-up adapter lenses that would attach to it. Each lens came with a chart for how to set the focus, since it was a rangefinder camera, and the adapters made the rangefinder useless. it gave a table of lens-to-subject distances along with where to place the focus knob to place that distance in focus. Each lens had its own table, but while the adapters were stackable, there was no table for using them stacked. I derived one experimentally by setting up a cribbage board with a number of toothpicks, shooting through the stacked adapters at various focus settings, recording the frame number versus the focus distance used, and when the film came back, I knew what the subject distances were to the toothpicks (color coding helped there.)

I was in high school at the time, didn't have the math in me to work out how this many diopters affected one adapter, this many affected the other, and then be able to calculate the effect of stacking them. I just went out and measured it.

That may be what you end up needing to do, when all is said and done, as I don't think you can get the right numbers for your lenses into your formulas.

 

[mathbias]

A large part (not all) of the real reason is the struggle with the question of why an image is less sharp than you would like: Because it is out of focus? Because the ISO value is too high? Because the aperture is too open? Because the shutter speed it too slow for the camera shake? Because the shutter speed is too slow for the subject shake (assuming a tripod)?

Thankyou for bringing up the extra one I hadn't really understood, that may explain a lot of my worst issues with my previous camera, the color of the subject. Hopefully this new (for me) camera will improve that.

But since my own visual issues stop me from comparing photos on the camera as I take them, I need more metric data in order to get any real value from comparing photos later on a desktop computer. Since the camera puts such unhelpful metrics into the meta-data, I need information on how those unhelpful metrics (together with basic metrics of the image itself) translate into useful metrics.

I also want to construct better panoramas, for which the location of the apex of the viewing angle (relative to the sensor) really does matter. As you change settings (zoom or focus) both the viewing angle and the location of its apex shift. The field of view depends on both. So if you have measured both object distance (from the sensor) and field of view, you still need one of viewing angle or location of the apex in order to compute the other.

It may all turn into tables, not formulas, if I can't see any decent formula fit. Of course tables need even more and harder measurements: You need to pre measure the conditions you will later care about, rather than measure conditions with the lowest error impact in order to calibrate an assumed formula.

The terminology in photography is a nightmare for me. So many things seem to have two different meanings with nothing to distinguish them and in a given article used sometimes with one meaning and sometimes the other. The "lens focal length" is so often described as a physical property of the lens independent of how the lens is being used immutable for a prime lens and well defined as the theoretical lens to sensor distance when focused at infinity. But the exact same article just as often describes the "lens focal length" (not some other "focal length") as the value that depends on the distance of the target focused on. Often those articles then provide some incorrect conclusions because the authors themselves lost track of which meaning they were using.

 

[weepete]

Finding the nodal point for panoramas is useful, but doesn't need to be bang on. The way I did it was to set up two, slim objects a few feet apart, then line them up at one side of the frame. Then I'd take a shot, and rotate the camera so the objects are on the other side of the frame. I'd do this gradually siding the camera back, and when the objects line up in both shots, that's your nodal point. I think mine's around 110mm.

Here's a link to a page descibing how: Finding The Nodal Point of Your Lens - Digital Grin

Telling the difference between a lack of sharpness is usually a matter of experience more than anything else, but there's usually a few telltale signs.

Is your vision good enough to see the focus points and roughly what they are on?

 

[mathbias]

The Sony a7 iii has a focus zoom function. There seem to be (unclearly) documented settings for making focus zoom pop up automatically when you would want it. I tried those and experimented a lot and never had any idea or control of when focus zoom would pop up. Sometimes it did, but not predictably nor usefully.

Fortunately, you can also choose to dedicate one of the custom buttons to focus zoom, which I did.

My picture taking method (assuming enough time) is to select a spot I want for setting the exposure and press the custom button I selected for "AEL toggle" to lock in exposure, then select the spot I want for focus distance and use the focus zoom button together with pressing the shutter half way down to lock in focus, then frame the picture and take the shot.

My vision is only good enough to confirm the correct position of the single focus point by using focus zoom.

With less time, one must use a mode where the camera selects multiple focus points and then trust it. Even if my vision and speed were good enough to second guess the camera on that, I can't see what good that could do. When I have time to select a single focus point representing the distance I want, I get better results than using multiple points.

I wish there was a function that was the focus equivalent of AEL toggle: press/release the button and the setting is locked in. Holding the shutter half way down while framing the shot has always been difficult for me. I tend to accidentally press it the rest of the way before I intended. I think you can configure a custom button to be the focus equivalent of AEL: press and hold to lock in focus. I will experiment with that later. Dedicating another finger to that would limit my flexibility in holding the camera. But holding a button down is easier than holding one half way down.

There is a documented function for manually fine tuning the focus after auto focus. So far as I can tell, it is totally useless. It just switches you to a manual focus that is so coarse that it is useless and the onscreen report of focus distance is even coarser, so there is no way to know what you have done. For shots with a wide aperture, such a feature (together with digital zoom of the focus point) would be great. But the people who write camera firmware seem to hate the customers. With a focus lock that worked the way AEL toggle works, I would lock auto focus then move the tripod a few inches to fine tune the focus. But focus lock doesn't work that way.

Telling the difference between a lack of sharpness is usually a matter of experience more than anything else, but there's usually a few telltale signs.

Logic tells me what the signs should be. But experience tells me the logical signs don't typically work.
Most pictures I take that are affected by subject shake have independent enough physical elements that not all are shaking (for test purposes, a shrub). So there should be sharp items in the photo (for a shrub some individual leaf that wasn't shaking) and the difference between those and others at the same distance should show subject shake. But in testing it doesn't: subject shake just generally blurs the photo.
Bad focus usually should be detectable by the better focus of some nearer or further object that happens to be in frame. But even with garden photos that always have nearer ground as well as further background, no place seems to be in focus.
My Canon SX 530 has a distinctive grainy look for ISO way too high. But for ISO slightly too high the general lack of sharpness is very hard to pin down. The Sony a7 iii have far better low light performance than my Canon (large part of why I bought it) so very high ISO still doesn't approach the grainy crap I can identify as the problem. But it seems to still be a factor in sharpness.

 

[wfooshee]

I do a lot of panoramas, and the only way they work is to NOT MOVE THE CAMERA'S POSITION. A change in perspective will destroy any chance of building a panoramic scene. Pan the camera across for wide panorama, tilt the camera for vertical panorama, but do not move the camera or change the zoom or focus. You can't make a panorama that works if you shoot a building face, then walk 30 feet down the street and shoot the next building. The perspectives will never match up.

That said, it should be obvious that a panorama of something too close won't work well, as the widest areas will be severely distorted. My usual limit is four or five frames, with about a third of a frame overlap, and I build them in Photoshop, which does a rather good job with it. This picture is four frames across, with about a third of a frame overlap from one frame to the next. No calculations (other than what Photoshop does,) but no changes to the camera between frames. You can't... change... anything.

As for a button to lock focus, you're describing back-button focus. Some cameras have a dedicated button, some have a button that can be set for that in the menus.

 

[mathbias]

Rotating the camera IS moving the camera, unless the axis of rotation is the correct point within the camera. That point I am calling the apex of the viewing angle. The site linked to above that calls it the nodal point, also includes the claim that it is incorrect to call it the nodal point and also calls it the visual center of the lens. But that term also is used for other meanings in other sites.

Anyway, there is a point within the camera (likely moves when you zoom and moves a little when you focus) that is the correct axis for panorama rotation and is important for me for several other calculations.

 

[mathbias]

On the subtopic of "viewing angle" changing due to focusing:

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.

Don't see why that would be for a fixed focal length lens.

I used manual focus with my zoom lens fixed at F=70.
Focusing at infinity take photo 1 pointed at a moderately distant target (slightly blurred but that doesn't matter)
Focus manually as near as the system allows, which the camera reports is 0.4m take a very blurred photo of the same target.
Compare the field of view. If you picked a good target, that is easy despite severe blur.

The math is pretty easy for a theoretical single element lens F=70, switching from infinity to a focus distance of 400mm (0.4m) reduces the field of view by about 21%. Experimentally, it reduced the field of view by about 2%.

That is what I meant/hoped/expected about modern cameras (but actually about modern multi element lenses). The change in field of view as a result of focusing is far less than it would be in a theoretical simple single element lens camera.

I expect that is also true for (modern multi element) prime lenses, but I haven't purchased one yet.

I'd appreciate someone else trying this same test and reporting the field of view reduction. Doesn't need to be F=70 nor does the near focus distance need to be 0.4m, but I would need to know them AND the F value must be a significant fraction of the focus distance: 400mm/70mm is just 5.7; If that were a much bigger ratio, the test wouldn't mean much.

BTW, I also tried with the zoom set at F=28, switching between infinity focus and 0.3m focus. That was about a 3% drop in field of view. A bigger fraction of the theoretical value than for F=70, but bigger is still not big.

 

[weepete]

@mathbias the link was because I thought it was a good explaination of the process rather than the terminology in that particular page. That's pretty much what I do for my panos and it works well enough for me, though I do occassionally use the boundary warp feature along with the constrain crop in lightroom's merging feature.

Lack of sharpness can be down to a few things, one of the best ways of learning is to post up an example image here and ask for some feedback if you are unsure.

With focusing I'd suggest using a depth of field app or chart. Then you can use the distance to your subject to work out what your aperture should be to cover the subject and give you a fairly wide margin for acceptable sharpness. Worst comes to the worst you coud calculate hyperfocal distance and use that to give you maximum depth of field.

Older lenses used to have distance scales on the focus ring, though a lot of modern lenses have had this feature removed.

 

[mathbias]

I did appreciate that link for its content. I should do some online shopping for the tripod accessory that it assumes you have.

In mentioning the terminology glitch my point was certainly not that the article was not good. My point was that even very good articles trip over the common terminology problems.

The lens in question has a free turning focus ring that has no direct effect on the lens and only sends info to the camera, and apparently only info about the amount you moved it, not about where it ended up after moving. So a scale would not directly help anything. If there were a way to make it change the focus less per amount turned, and then especially if I found a decent way to lock focus, it would be worth my drawing a reference mark onto the ring, so that I could know how much I moved it.

As it is, I can't imagine how a skilled photographer could get any use from that focus ring and I certainly can't.

 

[RacePhoto]

Ah ha and from the first message I suspected this was something to do with panoramas and rotating the camera on the nodal point, so the focal plane didn't change. The whole thread was interesting reading, thanks for bringing up the question.

Yes, that marking on the camera ---0--- is the focal plane point. I'm surprised at how many people knew that, because, other than some of us, who really would care?

By the way, and it's no longer available, Kolor Autopano Pro was my answer. Seems that GoPro bought the company and discontinued the image software version.

 

[weepete]

@mathbias I use an indexing rotator with a levelling base, nodal slide and an L bracket

If it's just for panoramas and you are using a wide angle focal lengths (below 35mm) you can ballpark hyperfocal distance by focusing 1/3rd of the way into the image. If your aperture is around f11, anything from 6ft away from the camera should be in acceptable focus.

 

[mathbias]

As for a button to lock focus, you're describing back-button focus. Some cameras have a dedicated button, some have a button that can be set for that in the menus.

Wow! Thanks!

I didn't know that function was called that. I didn't know the various settings interacted that way. I was seriously misunderstanding results earlier when I tried changing settings one at a time.

Once I googled "back-button focus" for my camera, I easily found the instructions for setting it up.

It does seem to need to lose some other nice-to-have features in order to get that one. But I think overall it will make the camera enough easier for me to use, that you (and the author of the web page I found) have really improved this camera for me.