A 24-70mm F/4 on a full frame camera is essentially equivalent to a 16-47mm F/2.8 on APS-C in terms of everything. Including DoF, light captured, and shot noise.
Let's compare 24 mm f4 on FF vs. 16 f2.8 on Dx, assuming same shutter speed and same sensor technology (like shooting with an FF camera either in FF mode or using its Dx crop mode). Here is how I understand what you are trying to say:
- Angle of view are the same (obviously)
- DOF is the same
- The lens at F2.8 will transmit twice as much photons as the lens at F4, regardless of the format used
- That light is projected over a surface which is a little more than twice as large on the FF camera (we'll call it 2 fold larger to simplify)
- Therefore the overall number of photons captured by the sensors will be the same, because the collection of photons over a surface which is about twice as large cancels out the difference in apertures.
Is this what your reasoning is?
To avoid confusion, I think it's important to separate inputs & outputs and to introduce focal lengths.
In terms of equivalent outputs, here is what I am saying:
- Angle of view are the same
- DoF is the same
- Noise is the same
- Dynamic range will be the same (until reaching the lowest base ISO (100) of the larger sensor, which is outside of the possible range of the smaller sensor. But for all others, it will be the same.
- The end result pictures will look the same
There are tiny, immaterial nuances such as diffraction limits, but that's the general rule.
But each will take a different path to get there. Below is that path, and diagrams to illustrate. Let's start with the light path:
There are many steps, with multiple enlargements, digital processings, etc.
- First, the subject, lighting, distance, etc. is the same. The subject is just sitting there reflecting scattered photons in all directions.
- In step 3, some of these photons must be caught by a "glass net"--this is the entrance pupil of the lens. The larger the entrance pupil ("aperture") is, the more photons one can catch. A 24mm F/4 lens and a 16mm F/2.8 lens have the same aperture, regardless of format. Each has a 6mm diameter, and a 28.3mm² surface area (round).
Let's visualize this again for emphasis. Here are what a lens' specs mean:
And here they are compared for a 24mm F/2.8, a 24mm F/4, and a 16mm F/2.8:
Step 3 (the aperture) is where you are catching all of your light. Also where almost all of the shot noise comes from. Because if photons only sparingly get captured in the first place, you'll have noise. The electronic noise from the sensor is so tiny today it's almost non-existent, and it happens further down the stream.
All of the other steps are just how you record & store what you caught. Note that 24mm F/4 & 16mm F/2.8 capture the same light, but just refract it differently. 24mm F/2.8 actually captures more light. Let's say 24mm F/4 and 16mm F/2.8 at a given shutter speed allow you to capture 100 photons. 24mm F/2.8 would capture 200--and it does so from even more oblique angles of incidence (which is why aperture & distance also determine DoF, but that's another story).
And step 4--the movie projector step--is very important too.
The movie projectors by this point are projecting the same light: both have 6mm apertures (24mm F/4 or 16mm F/2.8). They basically have the same light bulbs inside them, and the same image.
You can change the intensity of light by moving a projector further from the screen (making it dimmer), but you never actually change the quality or amount of light. This is changing the focal length. The screen on the tail end is like the sensor size, and the combination provides the angle of view.
So if you were projecting 100 photons, they're either going to be spread across a smaller 1mm² area (meaning 100 photons per mm²) or a larger 2mm² area (meaning 50 photons per mm²) or anything else.
But your camera still counts 100 photons regardless of format.
And then finally, the ISO--and digital processing in general--is also a source of confusion. The ISO just digitally brightens the light you already captured. If you capture the same amount of light (input), and you have the same final projection (output), you will apply the same brightening. The ISO is different because of where this happens--it's only the first half. But on the tail end, you also have to enlarge the image.
Digitally enlarging an ISO 3200 from an APS-C means enlarging it twice as much as ISO 6400 from a full-frame. So these effects offset each other, and you end up with the same image.
This, btw, is also why you'll see dynamic ranges and ISOs scale 1 stop between these formats. Because the measurements assume the same sized output & viewing conditions. For example, on bclaff's photonstophotos.net site, you'll see
this blurb :
- The Photographic Dynamic Range Axis
Recall that this value is normalized for the Circle Of Confusion (COC) that is appropriate for the sensor size. PDR is the dynamic range you would expect in an 8x10" print viewed at a distance of about arms length.
And when you compare an APS-C sensor to a similar generation full-frame at the same ISO, its PDR is roughly 1 stop behind. Eg. A Z50 at ISO 3200 has a PDR of 6.1, while a Z6 at ISO 3200 has a PDR of 7.19 (and at 6400, it is 6.18). 6.1 and 6.19 are essentially the same--they are a tiny fraction of a stop.
So now, the two equivalent paths are:
Note: equivalent, not equal. Same input scene. Same output photograph. Different paths to get there.
So at the end of the day:
- Both a 24mm F/4 and a 16mm F/2.8 lens have the same apertures, and different f-numbers.
- A 24mm F/4 on full frame and a 16mm F/2.8 on APS-C will capture the same amount of light (noise), from the same surface area (DoF), and same angles of view
- The FF in the above scenario will have a recorded ISO of twice higher, but the light captured will be the same
- When viewed at the same size, the APS-C will need to be scaled twice as much, resulting the same output
And again, I will include an even more extreme example. This is a micro four thirds vs full frame, from the same distance, with the same shutter speed (1/40). Micro four thirds is a 2x crop factor, which is twice the difference between full-frame & APS-C.
Micro four thirds:
- 20mm focal length
- F/2 (=10mm aperture)
- ISO 1600
Full-frame:
- 40mm focal length
- F/4 (=10mm aperture)
- ISO 6400
Equivalence means you ended up with the same picture, regardless of the path you took.
Equivalent settings are easy to determine for given shooting conditions:
- Same shutter speed
- ISO is twice as much on FF than APS-C
- F-number is 1 stop slower on FF than APS-C
- Focal length is 1.5x longer on FF than APS-C
. The bottom line from a photographic perspective is. If you take an image on APS with a 16mm lens at F/2.8 and one on FF with a 24mm.
