Discussion of 'Equivalence'

[Andrea B.]

Bjørn, noise and dynamic range are NOT part of the definition of equivalence.

[Jakov Minić]

Hi Jakov, thanks for voicing your concerns!

The PDR is a measure of the noisiness of images that result from a certain sensor. Cameras with the same PDR should produce images that are similarly noisy.
When you use only a DX-sized portion of the FX sensor, it is similar as if you are using a native DX sensor of the same technology.
Of course, if the images are otherwise not similar at all, you will not be able to observe this.
But if you use your FX cam in crop mode and set everything in order to get a similar image, you will probably see this in effect.

As an example:

Shoot the same scene from the same position (entrance pupil location) using:
1) a 150mm lens on FX, exposed at 1/100s f/8 at ISO3200
2) a 100mm lens in DX crop, exposed at 1/100s f/5.6 at ISO1600

The two resulting images will look very similar and have similar noise when viewed at the same output size. The fact that the DX crop has a lower PDR results in getting the same noise as the FX image at half the ISO setting.

Simone thank you for the explanation. As for the test, why on earth would I do that? I will probably make the images blurry anyway

I don't see the point in shooting an image in DX mode and then blowing it up to FX size just to see the drop in dynamic range
At least I now know why you are a scientist and I am an engineer

Bjørn, thank you too, I won't go into the DX/FX magnification business for sure!

[simsurace]

As for the test, why on earth would I do that?

1) To verify that the statements written by Joseph James and others are not BS. I get it, you are not a scientist. But sometimes it's better to test things, if only for your own sanity.
2) Because you need to take an image using DX that you would have rather used FX, but don't have the possibility to do so, and you want to make sure to get exactly the same result (perhaps for a client that demands results that are consistent with images of a previous shoot).

Otherwise, it's just a thought experiment to clarify the concept. It is possible to get similar images from different formats, and if one does not need the similarity, one can leverage the advantages of one format vs. the other to get a better result.

Cheers!

[Andrea B.]

And equivalent photos do NOT have the same density of light. So if you make "Equivalent" FX and DX fotos with the same camera, the DX FX foto will have been created using less dense light. Same framing, same TOTAL amount of light over the used sensor area but less dense light. I think this part is what gets missed by a lot of folks?

Added:  Apologies for the typo above.

[Bjørn Rørslett]

OK, let's walk that list sequentially;

• Same Perspective => means same distance camera-subject. This is the definition of the term 'perspective'
• Same Framing => magnification of detail is identical (from 1). With (1) in mind, focal lengths must be identical, plus (2) adds the further constraint the angle of coverage view is the same; both combine to imply the same lens. If the lenses are different, magnification would have to be different to get the same framing, however, we might violate further points on the list below, in particular those of (3)
• Same DOF, Diffraction, Total Amount of Light on the Sensor => same aperture and same focal length and same camera settings and same camera, same secondary magnification (also implied by (2)). If different lenses were to be used, the aperture have to be different and either DOF, diffraction, or amount of light reaching the sensor would not be the same, or ISO have to be different (possibly in conflict with the total amount of light criterion); or finally, the number of photosites differ which possibly conflict with (2) or (3) 
• Same Exposure Time => constant input of illumination, for example a flash with identical placement and setting, or any suitable lamp with constant output; alternatively, different ISO settings which might conflict with part(s) of 3)
• Same Brightness => (scene brightness? unclear) Same photometric response of the sensor => same camera or same sensor kind or both; or different ISO, but again (3)
• Same Display Dimensions => This is unclear, but probably implies a fixed print size (?). From (1)-(5), it follows this point is redundant if all the earlier points hold. If some of the earlier points are violated, (6) has no degrees of freedom

If this be the definition of "equivalence", the term is superfluous as it only means one takes another shot immediately following the first one.
 

[Andrea B.]

How do you derive that you need the "same lens" from the Same Framing requirement? If using the same lens for the FX/DX photos, then for one of the photos you will have to change your distance from the subject. Thus changing the Same Perspective.

Focal Length must be changed to preserve "Equivalence".

Same Framing means same Angle-of-View.


Same Brightness => (scene brightness? unclear)
Well, then, go read the darned Definitions.

If different lenses were to be used, the aperture have to be different
Yes, the aperture setting is different. The physical aperture diameter on the two lenses at the appropriate setttings are the same.

and either DOF, diffraction, or amount of light reaching the sensor would not be the same
No. Display size comes into this.

[Bjørn Rørslett]

Read the text. Alternatives are presented including the use of a different lens. I should perhaps have used angle of view instead of angle of coverage, though thus going back and rephrasing that point.

However, as one soon enough finds out, there a pretty few degrees of freedom available. One simply cannot avoid violating one or more of these criteria if different optical systems are compared. Simple fact of life. One cannot have two different systems to be the "same", if they really are different ...

[Andrea B.]

Physical aperture. Not f-stop.
Display size. (CoC, etc.)

Equivalence is a specialized definition. But no physics is violated. The CoC thing and display size could be a bit of a fuzzy area. (pun probably intended).

[Andrea B.]

One cannot have two different systems to be the "same", if they really are different.

Equivalence of perspective, framing, DOF, diffraction (physical aperture) total light, exposure time, brightness and display dimensions between two different systems DOES NOT IMPLY equality or sameness of other factors.

Image quality and noise, for example, are not part of the definition of Equivalence.

[Bjørn Rørslett]

I'm very well aware of the difference between f-number (not "f-stop" which is undefined and should not be used) f/N and physical aperture N. I learned my calculations the hard way from German textbooks some of which from the '50s - they were thorough. To say the least.

My point however is that is well nigh impossible to avoid violating any of all these constraints so as to shoehorn the photographic data into the "Same display size" (and incidentally, probably throwing away a lot of the data already captured to make that final output unless it is huge). Drop the fixed display/print criterion and we gain a lot of degrees of freedom including the opportunity to violate a little here and there.

[Bjørn Rørslett]

One cannot have two different systems to be the "same", if they really are different.

Equivalence of perspective, framing, DOF, diffraction (physical aperture) total light, exposure time, brightness and display dimensions between two different systems DOES NOT IMPLY equality or sameness of other factors.

Image quality and noise, for example, are not part of the definition of Equivalence.

I welcome you do spend some time setting up reliable test beds for this. Let us discuss further when results are obtained.

[Andrea B.]

Drop the fixed display criterion and you no longer have Equivalence. Simple as that.

We may not like the definition of Equivalence, but it is what it is. It violates no princples of physics. Or of engineering either. (Or mathematics.  )

We all know that in the practice of photography, none of this really matters. Nobody is arguing differently on that score.

And yes, I've made the experiments. But who really cares to see them? We go make photographs with none of this in mind.

[simsurace]

OK, let's walk that list sequentially;

• Same Perspective => means same distance camera-subject. This is the definition of the term 'perspective'
• Same Framing => magnification of detail is identical (from 1). With (1) in mind, focal lengths must be identical, plus (2) adds the further constraint the angle of coverage view is the same; both combine to imply the same lens. If the lenses are different, magnification would have to be different to get the same framing, however, we might violate further points on the list below, in particular those of (3)

I agree on the first point.
On the second, I think that our usage of the word 'framing' is different.
For me and for Joseph James (I presume), same framing means that the same content is seen on the frame. I.e. if I frame a person to fill the frame on one format, I have to fill the frame on the other format as well. Since I am not allowed to change perspective (1), I cannot move my camera. Therefore I need to choose a focal length that gives me the correct angle of view.

What does 'framing' mean for you?

With framing (as I intend it) fixed, the magnification at the sensor will not be the same between formats, but it will be proportional to the linear size of the format! This is an important point, since a lot of things depend on the magnification.

Maybe the further points will be cleared up when we agree on what 'framing' means.

[Andrea B.]

Bjørn, and I know what you are aware of and not (including thorough familiarity with Poisson processes). But I'm not sure what other readers might be knowing. Thus it is important to stress Physical Aperture to make the point about Same Diffraction, for example, for those readers who might not understand immediately the need for different focal length lenses with "equivalent"  f-stops to produce the same physical aperture, etc., even when performing this experiment on the same FX/DX camera.

Actually, I think you have got it now. I hope others have. If not, keep trying. It's only a few definitions and some physics/engineering/mathematics.

Framing - AoV. That's all.

[simsurace]

Image quality and noise, for example, are not part of the definition of Equivalence.

They are, to some extent, subsumed by 'Total Amount of Light on the Sensor', which is part of the definition.
That is a separate topic to do with photon noise and its statistical properties. The validity of theories about how photons behave is independent of 'Equivalence'. But most that is known about it, has been known for several decades, so there is little that cannot be found in textbooks.
Other sources of noise are specific to the way the sensor and A/D works, and much too complex to be included in such a coarse model. They have to be discussed on a case-by-case basis.
Regarding the discussion of PDR and Bill Claff's graphs, this is actually the bit we should focus on.
But let's first clarify the definitions.