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Focal equivalent and how it relates to zoom?

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OldNikonFan2025 said:
Michael Fryd said:
Where the larger sensor helps, is in situations where you can tolerate a DoF shallower than what you can get on your crop body.
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Often the shallower DOF is desired rather than tolerated. OTOH, the most common beginner mistake moving to a larger format is not compensating for the narrower DOF at the same f-stop, and understanding equivalence is the answer to that.
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Sometimes DoF can be too shallow.

If you are shooting a group of people, you may want all the faces in focus, and they may not all be the same distance from the camera.

While this is a style choice, some photographers like having a DoF that includes the tip of the nose and the eyes.

When shooting birds in flight, I often like a DoF deep enough to span from wingtip to wingtip. It can be nice to have a little extra DoF in case the focus was not spot on.

These are aesthetic choices. Sometimes it's good to have extremely shallow DoF, sometimes it isn't.

As has been mentioned, DoF is not an inherent property of the image, how the image is displayed and viewed are important factors. Common DoF calculators make some assumptions about viewing conditions. These assumptions work reasonably well for many, but not all situations. There are situations where the DoF will be deeper or shallower than expected. For instance, print something the size of a postage stamp, and you will have greater than predicted DoF. Print something 8 feet high by 12 feet wide, and stand 18 inches from it, and your DoF will be less than predicted.

OldNikonFan2025 said:
OldNikonFan2025 said:
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camera-user said:
OK! Thank you!
Using this animation:
https://fr.wikipedia.org/wiki/Profo...ier:Profondeur_de_champ_selon_l'ouverture.gif
I think I am now clearer!

So, the f/N denotes the aperture, with f constant, the bigger N the lower the aperture is.
And, as DOF = (2u²Nc)/f², with f constant the bigger N the deeper the DOF!
It then makes sense to have a small N for portrait, since we want to have small DOF to get Bokeh!
Click to expand...
The formula DOF = (2u²Nc)/f² is an approximation that works reasonably well if the subject distance is not too small and not too large.

A more accurate formula is only slightly more complicated:

DOF = 2E/(1-D^2) if D<1 and infinity if D>1

where D = cuN/(f^2)

and E = uD

For details of how to derive this formula, see this post.
 
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Michael Fryd said:
OldNikonFan2025 said:
Michael Fryd said:
Where the larger sensor helps, is in situations where you can tolerate a DoF shallower than what you can get on your crop body.
Click to expand...
Often the shallower DOF is desired rather than tolerated. OTOH, the most common beginner mistake moving to a larger format is not compensating for the narrower DOF at the same f-stop, and understanding equivalence is the answer to that.
Click to expand...
Sometimes DoF can be too shallow.
Click to expand...
Yes, and I thought I covered that when I wrote, "OTOH, the most common beginner mistake." Implicit in that was that failing to compensate for the narrower DOF is often undesirable.
Michael Fryd said:
These are aesthetic choices. Sometimes it's good to have extremely shallow DoF, sometimes it isn't.
Click to expand...
Exactly, and that's where equivalence helps to understand where the overlap is and isn't going from one format to another. This brings the opposite wrong proposition, that a smaller format somehow offers inherently more DOF. The advantage of a larger format is that it can attain a shallower DOF with the appropriate lens, and that it is equally capable of attaining a shallower DOF with the appropriate f-stop.
Michael Fryd said:
As has been mentioned, DoF is not an inherent property of the image, how the image is displayed and viewed are important factors.
Click to expand...
Yep, and display size and viewing distance are included in any good DOF calculator – sometimes described as the CoC (circle of confusion).
 
OldNikonFan2025 said:
Michael Fryd said:
OldNikonFan2025 said:
Michael Fryd said:
...
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OldNikonFan2025 said:
These are aesthetic choices. Sometimes it's good to have extremely shallow DoF, sometimes it isn't.
Click to expand...
Exactly, and that's where equivalence helps to understand where the overlap is and isn't going from one format to another. This brings the opposite wrong proposition, that a smaller format somehow offers inherently more DOF. The advantage of a larger format is that it can attain a shallower DOF with the appropriate lens, and that it is equally capable of attaining a shallower DOF with the appropriate f-stop.
OldNikonFan2025 said:
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We agree here. It's a very common misconception that smaller formats offer more depth of field.

The truth is that a full frame camera can generally match a crop body's depth of field.

One thing to keep in mind that DoF is the range of distances where subjects appear to be in focus. At very small aperture diameters, diffraction can become enough of an issue that everything looks out of focus (nothing is sharp). In my opinion (and others will disagree), at this point the DoF is zero as nothing looks focused.

While crop bodies do generally offer smaller minimum apertures, they often bring you to the point where nothing is sharp. In my mind, this is not an advantage.
 
Michael Fryd said:
OldNikonFan2025 said:
Michael Fryd said:
These are aesthetic choices. Sometimes it's good to have extremely shallow DoF, sometimes it isn't.
Click to expand...
Exactly, and that's where equivalence helps to understand where the overlap is and isn't going from one format to another. This brings the opposite wrong proposition, that a smaller format somehow offers inherently more DOF. The advantage of a larger format is that it can attain a shallower DOF with the appropriate lens, and that it is equally capable of attaining a shallower DOF with the appropriate f-stop.
Click to expand...
We agree here.
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Hmmm, I didn't realize we were ever really in disagreement.
Michael Fryd said:
It's a very common misconception that smaller formats offer more depth of field.

The truth is that a full frame camera can generally match a crop body's depth of field.

One thing to keep in mind that DoF is the range of distances where subjects appear to be in focus. At very small aperture diameters, diffraction can become enough of an issue that everything looks out of focus (nothing is sharp). In my opinion (and others will disagree), at this point the DoF is zero as nothing looks focused.
Click to expand...
Depending on display size and viewing distance.
Michael Fryd said:
While crop bodies do generally offer smaller minimum apertures, they often bring you to the point where nothing is sharp. In my mind, this is not an advantage.
Click to expand...
I've never been a fan of designating some formats as "cropped" and others as "full frame." Other than that semantic issue, we again agree.

As this relates to the original topic of this thread, tiny formats only attain equivalence with significantly larger formats when the larger formats are stopped down quite a bit –e.g., the HX-60 used at 89mm and f/5.6 is the same as my D850 at 500mm stopped down past f/30 or my D500 at 335mm stopped down to f/21, so the HX-60's resolution is heavily affected by diffraction which will become readily visible as the display size is increased, which in turn affects any equivalence when comparing effective focal lengths between the tiny formats and the larger formats. Indeed, this is why I was able to match the resolution of the Panasonic ZS-70 at its longest focal length with my D500 using a 280mm focal length.
 
OldNikonFan2025 said:
Michael Fryd said:
OldNikonFan2025 said:
Michael Fryd said:
…
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As this relates to the original topic of this thread, tiny formats only attain equivalence with significantly larger formats when the larger formats are stopped down quite a bit –e.g., the HX-60 used at 89mm and f/5.6 is the same as my D850 at 500mm stopped down past f/30 or my D500 at 335mm stopped down to f/21, so the HX-60's resolution is heavily affected by diffraction which will become readily visible as the display size is increased, which in turn affects any equivalence when comparing effective focal lengths between the tiny formats and the larger formats. Indeed, this is why I was able to match the resolution of the Panasonic ZS-70 at its longest focal length with my D500 using a 280mm focal length.
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I’m not sure I am following you.

But in terms of equivalence, full frame does not have a diffraction advantage.

At the same angle of view and same depth of field, you get the same diffraction independent of sensor size.

If you want less diffraction on either format, you need to use a wider aperture diameter. The advantage of full frame is that you generally have the option of that wider aperture diameter.

.

The Panasonic Lumix DC-ZS70 Has a crop factor of 5.6X, and a max actual focal length of 128mm and f/6.4. You will get the same results from a full frame with a 720mm lens at f/36

You can also get the same results by using full frame with a 500mm lens at f/25, and then cropping to match the same angle of view at the Lumix.

By “same results” I mean same depth of field, and same diffraction issues. If you are shooting full frame at 500mm and cropping to match, you will get less diffraction and less DoF by opening up wider than f/25. As a full frame 500mm lens will generally open wider than f/25, you have the option of less diffraction (and less DoF) than the Lumix is capable of.
 
Michael Fryd said:
OldNikonFan2025 said:
As this relates to the original topic of this thread, tiny formats only attain equivalence with significantly larger formats when the larger formats are stopped down quite a bit –e.g., the HX-60 used at 89mm and f/5.6 is the same as my D850 at 500mm stopped down past f/30 or my D500 at 335mm stopped down to f/21, so the HX-60's resolution is heavily affected by diffraction which will become readily visible as the display size is increased, which in turn affects any equivalence when comparing effective focal lengths between the tiny formats and the larger formats. Indeed, this is why I was able to match the resolution of the Panasonic ZS-70 at its longest focal length with my D500 using a 280mm focal length.
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I’m not sure I am following you.
Click to expand...
I'll try to be more clear.
Michael Fryd said:
But in terms of equivalence, full frame does not have a diffraction advantage.
Click to expand...
When the format gets tiny then everything is adversely affected by diffraction. Also, I'm not talking about the differences of diffraction between my D850 and D500 here, but between either of them and the OP's HX-60.
Michael Fryd said:
At the same angle of view and same depth of field, you get the same diffraction independent of sensor size.
Click to expand...
Yep, but I'm not going to stop down the lenses I use on my D500 and D850 to f/13-f/22 for every shot.
Michael Fryd said:
If you want less diffraction on either format, you need to use a wider aperture diameter. The advantage of full frame is that you generally have the option of that wider aperture diameter.

The Panasonic Lumix DC-ZS70 Has a crop factor of 5.6X, and a max actual focal length of 128mm and f/6.4. You will get the same results from a full frame with a 720mm lens at f/36
Click to expand...
I suppose if I had a lens with that long a focal length and that small a minimum aperture, and wanted to use it that way, then the results would depend on the pixel density.
Michael Fryd said:
You can also get the same results by using full frame with a 500mm lens at f/25, and then cropping to match the same angle of view at the Lumix.

By “same results” I mean same depth of field, and same diffraction issues.
Click to expand...
This is where equivalence becomes absurd. I really don't want to replicate what I can do with a tiny sensor using my larger sensor camera/lens combos. It's far more useful to approach equivalency from the other direction, and that way you can figure out if it's worthwhile to upgrade to a larger format.
Michael Fryd said:
If you are shooting full frame at 500mm and cropping to match, you will get less diffraction and less DoF by opening up wider than f/25. As a full frame 500mm lens will generally open wider than f/25, you have the option of less diffraction (and less DoF) than the Lumix is capable of.
Click to expand...
As I said more than once in this thread, in actuality I got equal resolution at 280mm and I think I was at f/5.6 when I did it (repeatedly). FWIW, I always opt for the widest acceptable aperture when shooting longer focal lengths.
 
camera-user said:
So, the f/N denotes the aperture, with f constant, the bigger N the lower the aperture is.
And, as DOF = (2u²Nc)/f², with f constant the bigger N the deeper the DOF!
It then makes sense to have a small N for portrait, since we want to have small DOF to get Bokeh!
Click to expand...
Another point that you may find helpful:

If you want the maximum amount of background blur in a portrait, it is helpful to know that the maximum size of the background blur is f/N, so you want a small N and a large f.

For example, an 85mm f/1.8 lens can give more background blur than a 50mm f/1.4 lens because 85/1.8 = 47mm, which is greater than 50/1.4 = 36mm.

Of course, to get the maximum size of blur, you also need to have a background which is much further away than your subject. A background that is twice as far away as your subject will give half the maximum amount of blur.
 
OldNikonFan2025 said:
John Sheehy said:
Used the way it is here only really means restriction of the AOV, which may give the viewfinder or LCD more of a telescopic function, but does not speak directly at all to the resolution of the subject. What good would an angle of view "equivalent" to 5000mm on a FF camera be if it only had 0.5MP resolution? Yes, it may help in the viewfinder to see what your subject is doing, but that is only because the wider angles of view have to shrink each object in the viewfinder more, obscuring detail which may in fact, actually be captured with a high pixel count.
OldNikonFan2025 said:
As it so happens I have done some comparisons in the past between the Panasonic ZS-70 and my D500 and repeatedly found that I could match the Panasonic using a good 280mm lens on my D500 or D850.
Click to expand...
The only area in which larger sensors can't easily follow is the "superzoom" range. Take the Nikon P1000, for example. To duplicate what it does in capturing pixels-on-subject from a given distance at "3000mm" FF-equivalent AOV, with the D500 pixel density, you would need a 1690mm lens. The speed of the lens would not be demanding, though, as you would need only f/25 to match pixel-level total light, diffraction, and DOF. To match AOV, you'd need 2000 real mm with the D500.
Click to expand...
It's not all just about pixel density. The diffraction hit to resolution also needs to be accounted for. FWIW, I didn't arrive at 280mm being the equivalent using formulas and a calculator, although I probably could have come close. I simply made visual comparisons of shots taken at different focal lengths with the D500 to what was the best I could do with the ZS-70, and I was actually able to do it much easier with the D500 and D850 (the D500 is a bit better in this regard owing to its greater viewfinder magnification). My guess is that the Nikon P1000 resolution could be matched at less than 1200mm on a D500, but the usefulness of such narrow AOVs using a handheld camera elude me.
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I was actually talking about pixels-on-subject; not pixel density per se, IIRC.

You seem to be talking about pixel-level diffraction, rather than the more relevant subject-level diffraction. If we consider the underlying, scale-less analog image of the subject before it gets binned into pixels, its diffraction, is determined by the size of the entrance pupil of the lens and the distance from the subject. So, for any given subject from any given distance, the P1000's 67mm entrance pupil gives the same subject diffraction as any lens with a 67mm entrance pupil. Pixels-on-subject just determines the quality of sampling. If someone used a FF camera with a lens with an entrance pupil smaller than 67mm, it would have more subject diffraction than the P1000 at "3000mm" (539/8). At "3000mm", the capture, is the same as 16.7MP cropped from a FF camera with about 512 MP.

One day, I met someone in the field who was using a P1000 to photograph small birds and I had my Canon R5 with Canon's RF100-400/5.6-8 lens, and he would say, "I am going to get a lot worse IQ than you", and he was rather surprised when I said to him that I needed a much larger lens than what I was using, to get better subject quality in any way, when he could actually use the "3000mm" (539 real mm).
 
camera-user said:
Hi,

I am wondering about changing my actual camera and I would like to understand the concept of focal equivalent.
Indeed, my current camera is the hx60 which has a 1/2.3 sensor and a 24-720mm zoom lens.
So, if my computation are rights, when I am zoomed at maximum, i.e. 720mm, this would translate to 2595mm for an APS-C, up to my knowledge there is no such lens on the market (and I guess I understand why).

Computation is one thing but on the field is another.
So, in practice, let's say I am at 30 meters of a paper which has a 1 cm letter printed on it.
If I zoom at 720mm, i.e. * 30, I would be able to read the text like if it was at 1 meter from me.
Then, how does equivalent focal works in this situation?
Or am I am totally mixing up different things?

My question may seem really dumb, but any enlightments would be really welcome to help me learn on this photography journey!

Best,
Click to expand...
If you don't understand aperture (which your other post suggests) then you will get more benefit reading a book or watching a video on the basics of photography than buying a new camera. At this point, you are not gear limited.
 
It may be worth buying this book: https://a.co/d/84UfQSV

Forget all about equivalence and f stops for a moment. What do you want from photos? Do you want shallow depth of field or deep depth of field? Do you want to be able to take photos wide to really far away made close by zooming in? What weight do you feel like carrying?

I own a small sensor camera or two. I own a large full frame. I own an apsc camera. The choice of what I carry varies depending on the goals. If I want something simple to carry and I don't want to rely on the smartphone an RX100VI goes with me. It's got a 24-200 equivalent focal length and reasonable controls and a 1" sensor which is smaller than apsc but larger than the camera sensor you have.

Don't assume a larger camera will make better images either. The other factor is HOW you plan to use the images. If these will be shared on facebook and instagram and only ever displayed on a monitor the detail needed is much lower than if you plan to print very large images (measured in feet).
 
Thank you! Replying inline to this post, but I for sure read the full thread and took note about it!
Michael Fryd said:
camera-user said:
Michael Fryd said:
camera-user said:
OldNikonFan2025 said:
camera-user said:
...
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Click to expand...
Click to expand...
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OK! Thank you!
Using this animation:
https://fr.wikipedia.org/wiki/Profo...ier:Profondeur_de_champ_selon_l'ouverture.gif
I think I am now clearer!

So, the f/N denotes the aperture, with f constant, the bigger N the lower the aperture is.
Click to expand...
f/N is a fraction, so when N is larger the result is smaller. For instance 1/8 is smaller than 1/2.

To bring this to cameras, 50/8 is a smaller number than 50/4. Those are the aperture diameters for a 50mm lens at f/8 and at f/4.
Michael Fryd said:
And, as DOF = (2u²Nc)/f², with f constant the bigger N the deeper the DOF!
It then makes sense to have a small N for portrait, since we want to have small DOF to get Bokeh!
Click to expand...
Sort of. First of all, I think you mean you want a small DoF in order to have the background out of focus. "Bokeh" is a term coined to refer to the quality of that out of focus area. Different lenses can render the out of focus areas differently.

Secondly, small DoF is not the only way to get the background out of focus. You can also move the subject further from the background.

One should be careful in thinking that DoF is directly dependent on f/stop. While that works if you are only dealing with a single sensor size, the reality is that it is the aperture diameter that's more important. F/2.8 may yield shallow DoF on a full frame, and deep DoF on a smart phone.
Michael Fryd said:
Michael Fryd said:
Michael Fryd said:
...
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I understand for the bigger DOF with the crop sensor because (I fix u and c as constant to simplify):
1. 6.3/106² = .0005607
2. 6.3/600² = .0000175

So, I would indeed get a biffer DOF with the small sensor, but more details with the FF one, as I get more light in due having a bigger sensor.
Am I correct?
Click to expand...
Sort of. but that's like saying you get a wider field of view with a full frame. Sure that's true if you shoot a full frame and a crop at the same focal length, but why would you choose to do that? If you want a normal angle of view (about 46°), you would choose a 50mm lens on a full frame and a 25mm lens on a 2X crop body. When you choose the appropriate focal length for the sensor size, you get the same angle of view.

Similarly, why would you shoot a crop body and a full frame at the same f/stop? You're going to get different results. If you are shooting your full frame at f/8, then shoot your 2X crop body at f/4. Then you get the same DoF, same diffraction, same overall image noise, and same sharpness (assuming similar quality lenses, processing and pixel counts).
Click to expand...
All these computations were there only to be sure I understand the underlying concept.
Michael Fryd said:
Suppose you are shoot a 2X crop body with a 25mm lens and need to use f/5.6 in order to get enough DoF. You need to use 1/60 to stop motion, and you are getting good lightness at ISO 400. perhaps you want to reduce image noise, so you splurge and buy a full frame camera with an expensive 50mm f/1.2 lens.

The problem is that in order to get your needed depth of field, you need to at f/11. You still need 1/60 in order to stop motion, so you change the ISO to 1600.

Now you are getting the same results from your full frame as you got from your 2X crop body. In this situation there is no advantage to using the larger sensor.

Where the larger sensor helps, is in situations where you can tolerate a DoF shallower than what you can get on your crop body.

With a APS-C crop body, the difference is a little over one stop. At the same angle of view, you can generally find full frame lenses that open up about one stop wider in diameter than with an APS-C crop body. So if you can tolerate that shallower DoF, you can get an image with less noise.

,

But let's step back for a moment. Why the fixation on sharpness? You should be able to get reasonably sharp images with just about any modern 2X crop (or less) camera. If you are not getting sharp images, the issue may be technique, or a camera malfunction. It's probably not a limitation of the sensor size.
Click to expand...
I focused too much on sharpness because I thought I would rather need it as I do not take a lot of portrait but rather landscape.
But, I could also add a bit of out-of-focus part to some landscape photographies, playing with the aperture, to make them better!
Michael Fryd said:
Keep in mind that content is almost always more important than sharpness. Increasing sharpness won't turn poor composition into a great image. There are lots of great images that are not sharp.
Click to expand...
Sure! I do totally share this thinking about "composition first"!
Michael Fryd said:
While there are certainly situation where one needs to absolutely maximize sharpness, they are not as common as some people think.
Click to expand...
 
Belle04 said:
camera-user said:
Hi,

I am wondering about changing my actual camera and I would like to understand the concept of focal equivalent.
Indeed, my current camera is the hx60 which has a 1/2.3 sensor and a 24-720mm zoom lens.
So, if my computation are rights, when I am zoomed at maximum, i.e. 720mm, this would translate to 2595mm for an APS-C, up to my knowledge there is no such lens on the market (and I guess I understand why).

Computation is one thing but on the field is another.
So, in practice, let's say I am at 30 meters of a paper which has a 1 cm letter printed on it.
If I zoom at 720mm, i.e. * 30, I would be able to read the text like if it was at 1 meter from me.
Then, how does equivalent focal works in this situation?
Or am I am totally mixing up different things?

My question may seem really dumb, but any enlightments would be really welcome to help me learn on this photography journey!

Best,
Click to expand...
If you don't understand aperture (which your other post suggests) then you will get more benefit reading a book or watching a video on the basics of photography than buying a new camera. At this point, you are not gear limited.
Click to expand...
I share your opinion here!
I though I could maybe learn about aperture later, because it is not tied to what photography style I do, but I did a mistake here...

Do you have some resources you can recommend on it?
I know I can google about it, but there are so many links that I feel a bit like I am drowning :(.
On other hand, my current gear (HX60) is not forcefully state of the art, but I could indeed learn aperture on it!
 
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UncleVanya said:
It may be worth buying this book: https://a.co/d/84UfQSV
Click to expand...
I will take a clooser look at it! Thank you!
UncleVanya said:
Forget all about equivalence and f stops for a moment. What do you want from photos? Do you want shallow depth of field or deep depth of field? Do you want to be able to take photos wide to really far away made close by zooming in? What weight do you feel like carrying?

I own a small sensor camera or two. I own a large full frame. I own an apsc camera. The choice of what I carry varies depending on the goals. If I want something simple to carry and I don't want to rely on the smartphone an RX100VI goes with me. It's got a 24-200 equivalent focal length and reasonable controls and a 1" sensor which is smaller than apsc but larger than the camera sensor you have.

Don't assume a larger camera will make better images either. The other factor is HOW you plan to use the images. If these will be shared on facebook and instagram and only ever displayed on a monitor the detail needed is much lower than if you plan to print very large images (measured in feet).
Click to expand...
I wrote a topic about this here:

Loading…

www.dpreview.com
Your advice would be welcomed :)!
I definitely do not think to print them on large support, the biggest would be 15*10 cm and only the photos I like the most.
 
camera-user said:
Hi,

I would like to thank all of you for your replies! This really helps me understanding this concept better!
dazzerfong said:
The HX-60 actually has a lens with a real focal length of 4.3-129mm. Owing to the 'crop factor', its focal length equivalent to FF is 24-720mm. If you want it to have a similar field of view to an APS-C, it's 16mm-480mm.

I've never seen cameras besides those using FF, MFT, APS-C or MF sensors (or basically any interchangeable lens camera) will state their true focal length, and instead choose to state the focal length equivalent to FF.

With regards to optical zoom factor, your eyes don't work like a sensor. 30x just means that the longest focal length (720mm) is 30x your widest focal length (24mm). It does not necessarily mean you put a pair of 30x binoculars to your eyes.
Click to expand...
So, it means that if I capture a scene with the following configurations:

1. 1/2.3 sensor with a 129mm focal lenght,
2. APS-C sensor with a 480mm focal lenght
3. and FF sensor with a 720mm focal lenght

I would get the exact same picture?
Click to expand...
Yes
camera-user said:
For zoom, I understand this is just a way to navigate the focal length of a lens, so it is just relative to this lens.
For example, a lens with a focal lenght ranging from 12mm to 36mm would offer a 3x zoom.
But this would really make sense to compare its zoom to another lens for another sensor.
Click to expand...
Thinking of it as "3x" makes more sense. "1x" would roughly be a 50mm lens on a FF sensor.
 
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