Discussion of 'Equivalence'

[bclaff]

... One also immediately realises there is no change in dynamic range, again as expected from photographic theory because the same sensor is involved and the same aperture/exposure time is used.

You may not see a difference in this scene and at this resolution but it is there and would show in the right circumstances.
Analysis of NEF files would be ideal but even a quick and dirty check on these small jpegs shows a difference in favor of the FX.
I selected a 120x80 pixel area in the "uniform" gray in the back.
For the DX I got a Signal to Noise Ratio (SNR) of 6.7. For the FX it is 7.5
Additional enlargement to the same viewing size comes with an unavoidable cost.

[Bjørn Rørslett]

I've done similar experiments myself and arrive at the exact same result as Bent. Different magnification impacts noise as well. I'll stop there.

[Bent Hjarbo]

My surprise was mostly based on the fact that there is a lot of websites that explain that we nede to use other f-stops on the smaller formats
But the DOF is consistent with other observations, and facts.

[Bjørn Rørslett]

Changing the aperture would directly alter exposure as exposure is about intensity of light. Not the photographed area. Another of those cornerstones of basic photographic theory apparently forgotten in the digital age.

One should at this stage take a break and try to understand that two different things can *never* be the same over all possible dimensions, unless they are identical in the first place. No manner of normalisation and/or clever massaging of metrics chan change this fundamental fact. Again obviously forgotten in the digital era.

[Bent Hjarbo]

The change in aperture to get the same DOF, the shutter speed needs to be changed to get the same exposure.
But I was surprised that the DOF did not look exactly the same

[Bjørn Rørslett]

Remember magnification. There is no escape for differences introduced though this primary variable.

[Bent Hjarbo]

Ok, I see, and get educated 

[JohnMM]

The change in aperture to get the same DOF, the shutter speed needs to be changed to get the same exposure.
But I was surprised that the DOF did not look exactly the same

Why do you need the same exposure?

Which apertures did you use when you tried to get the same DOF?

[bclaff]

Changing the aperture would directly alter exposure as exposure is about intensity of light. Not the photographed area. Another of those cornerstones of basic photographic theory apparently forgotten in the digital age.

One should at this stage take a break and try to understand that two different things can *never* be the same over all possible dimensions, unless they are identical in the first place. No manner of normalisation and/or clever massaging of metrics can change this fundamental fact. Again obviously forgotten in the digital era.

Agreed. This is why equivalence doesn't interest me.
Obviously I feel normalization can be appropriate. It's the attempt to "massage" normalized results to form "equivalence" that I take issue with.

[Bjørn Rørslett]

At least some aspects of which we can agree.

[Bent Hjarbo]

Why do you need the same exposure?

Which apertures did you use when you tried to get the same DOF?

I used the same aperture to get the same DOF, and the small difference is explained by Bjøn above.
I need the same exposure as the sensor is the same, and has a constant ISO regardless of how much of it I use.

[Bjørn Rørslett]

Why do you need the same exposure?
--

Ref. answer #34 and what follows in the thread therefrom.

[simsurace]

I used the same aperture to get the same DOF, and the small difference is explained by Bjøn above.
I need the same exposure as the sensor is the same, and has a constant ISO regardless of how much of it I use.

You did not get the same size of blur circles, so you should have used different apertures if the goal was to get the same degree of background blur.
The same with DOF as it is also expressed in terms of blur circles.

I will post a detailed answer later.

[bclaff]

I used the same aperture to get the same DOF,...

Not that I care (because it's an equivalence argument), but you did not get the same DOF.

[Bjørn Rørslett]

You did not get the same size of blur circles, so you should have used different apertures if the goal was to get the same degree of background blur.
The same with DOF as it is also expressed in terms of blur circles.

I will post a detailed answer later.

This is not the approach a photographer would follow in practice. Entirely different considerations determine the aperture and exposure settings. By heavily massaging factors one might shoehorn something into a semblance of what genuine theory had provided easily without the extra steps. Feel free to follow down that lane if you deem it fruitful and productive.

Not that I care (because it's an equivalence argument), but you did not get the same DOF.

Of course not - anything else would be a surprise given the setup. It is, however, the exact result expected by basic photographic theory. Nice to see yet another validation of principle known for a very long time.