Discussion of 'Equivalence'

[simsurace]

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.

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.

Yes, we established a few pages ago that there is no contradiction between what you call standard theory and equivalence theory. It is just a matter of different definitions. I'm willing to demonstrate that using the example provided.

There is no 'approach of the photographer' here, since the photographic goal is not stated (even though Bent himself stated that he wanted the same DOF, and he did not obtain that result).

It's just two test shots on different formats that will help illustrate the different concepts that have been discussed so far.

[Bjørn Rørslett]

Whatever floats your boat. It is very difficult to keep an interest in the Emperors' Cloths over time. Sorry.

I'm more worried about these futile discussions flooding our NG site and make members not equally eager on these theories to shun the site. Participants of this thread should perhaps follow my advice about taking a break, or time-out, and contribute on other topics here on NG? I think I'll do that myself. Starting as of now.

This is not a signal about any immediate clamping down on the thread, merely that I have posted [more than] enough here. Real and significant disagreement exists and is still unchanged. No amount of further posting can alter that.

We need fresh material (images etc.) elsewhere on NG. Let that be the new challenge.

[Andrea B.]

Bjørn:  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.

Equivalence does not yield the "Same" or "Identical" and does not claim to do so.

[simsurace]

I don't understand the emotional reaction to a perfectly rational, civilised discussion. My impression was that there is a very good spirit in this.
Did site traffic go down because of this? Maybe people are just out enjoying the sun? 
The reactions to this thread are mixed, some very positive. So I think it is reasonable to go on and see where we end up.

[simsurace]

An important thing to know when we decide on which equipment to use is how it impact the picture, DOF, AOV etc.
I think that all agree that there are difference in noise performance on different sensor sizes, and that this changes with time due to development in the IC technology.
I will not go into the discussion on the PDR, but I would like to throw a couple of pictures into this thread
I took my D800, which has a DX mode, and found a 24mm and a 35mm as they have nearly the AOV in the two modes.
I placed three objects to see the DOF in the two modes.
The result was that the background blur was less in DX mode, but it also seems that the exposure was different even though the D800 was in manual mode?
Maybe there is an explanation in some of this discussion.

First of all, thanks for running the test shots and providing an example.

Let me analyse what we see. I encourage anyone to point out any flaws in my reasoning or other kinds of mistakes!

- First of all, you resized both shots to the same final resolution of ~1200x800px. I think this is good, as it gives us an apples-to-apples comparison.
- You framed the shots the same or very close, by having almost the same perspective and choosing appropriate focal lengths of roughly f2/f1=1.5, which is the ratio
of the linear dimensions of FX/DX.
- You chose the same relative aperture f/5.6
- You shot both at base ISO 100 and 1/200s
- There is, as you point out, a very minor brightness difference. Let's ignore that here, because it is very small and probably within the tolerance of the stop-down lever of the camera

So, according to Joseph James' definitions, the two shots are equivalent in terms of perspective, framing, exposure time, brightness, and display dimensions.
They are not equivalent in terms of DOF, diffraction, and total light on the sensor.

You stated that you want the same DOF for the two shots. You did not achieve that in my opinion. Also, the distant background is not blurred to the same extent. Do you agree with my observations?

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Regardless of what you wanted, let us do a little calculation, using standard photographic theory, AKA geometrical optics, to see what kind of blur circles we would expect from the distant background. Using elementary geometry, we find that the diameter of the blur circles from a light source at infinity in the image plane is equal to

d=M*f/N,

where M is the magnification, f is the focal length and N is the aperture number. The size on the final image is given by

dfinal= m*M*f/N, where m is the secondary magnification.

Now, since the two images are displayed at the same size, the product of primary and secondary magnification are the same:

m1*M1=m2*M2.

Therefore, we obtain that

dfinal2/dfinal1 = f2/f1 * N1/N2.

Now, since you chose the same aperture number, but different focal lengths, we obtain

dfinal2/dfinal1 = 35/24 * 5.6/5.6 = 1.46.

Thus, from optics, we expect the blur circles of the distant background to be roughly 50% bigger in diameter on the FX image compared to the DX image.
Can you verify this?

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If you had wanted to get the same background blur (double emphasis on the if, since I'm not saying that this is in any way desirable in general, but a hypothetical situation), you would have needed to choose either f/8 on the FX shot and f/5.6 on the DX, or f/5.6 on the FX shot and f/4 on the DX. Indeed,

dfinal2/dfinal1 = 35/24 * 5.6/8 = 1.02, and
dfinal2/dfinal1 = 35/24 * 4/5.6 = 1.04,

which are both close enough to 1.

The same would be predicted by equivalence, where it is stated that the aperture that is equivalent to f/5.6 on FX is f/4 on DX, and the aperture that is equivalent to f/8 on FX is f/5.6 on DX.

Note that the exposure will be different by doing this, so we have to change something else to compensate and get back the equal brightness.
There is no normative aspect to any of this discussion. I merely explained how to get the same background blur on both formats, and explained that equivalence and geometrical optics are fully consistent in that regard.

Next up will be exposure and noise. But let's first see whether this is understandable.

[simsurace]

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.

This is an aspect (perhaps the only one) where I think our disagreement is genuine and not merely a question of definitions.
I think this is an instance where the theory from the analog era falls short and leads to methods that are no longer optimal.
I would really welcome an exchange on this aspect.

With digital sensors, the only sweet spot for exposure is exposing to the right. There is no other sweet spot in my view. For any given scene, we determine what the brightest part is that needs to be recorded. We ensure that this part of the scene does not clip. Any other exposure setting would be suboptimal.

Often, our exposure is suboptimal. But there is no other 'more correct' exposure than ETTR. I think this is a fundamental difference to film, where the sweet spot is somewhere in the middle.

The desired brightness of the final image can be achieved by post processing. The ETTR ensures that if we have to brighten the shadows, we have the best possible signal-to-noise ratio given the circumstances. If we have to darken it, there is no penalty to have exposed more than necessary since ETTR ensured that we did not clip anything that was pictorially relevant. The only reason to not ETTR is because of motion blur.

Our cameras are still designed according to the old way of doing things, but my opinion is that it would be better to change them to make it easy to expose optimally for the way digital sensors work.

[bclaff]

Changing the aperture would directly alter exposure...

This is an aspect (perhaps the only one) where I think our disagreement is genuine and not merely a question of definitions.
I think this is an instance where the theory from the analog era falls short and leads to methods that are no longer optimal.
I would really welcome an exchange on this aspect.
...

My reply might not be what you have in mind :-)

Remembering that I'm not a proponent of "equivalence"...

As I understand it "equivalence" would be from the reference point of the final image.
So DX at f/5.6 1/200s and FX at f/8 1/100s
These are the same Exposure Value and the same Depth Of Field (DOF).
(However noise will be more apparent in the DX image, lower Signal to Noise Ratio (SNR) due to nigher noise.)

[bclaff]

...Often, our exposure is suboptimal. But there is no other 'more correct' exposure than ETTR. ...

Implicit in what you said is that ETTR at a higher setting ISO is also suboptimal compared to ETTR at a lower ISO setting.

Another way to phrase the philosophy of ETTR is to simple say "gather as much light as is possible without clipping relevant highlights (specular is OK for example)"
Generally this means operating at the lowest (non-extended) ISO setting since this is where Full Well Capacity (FWC) is available.

[JohnMM]

This is an aspect (perhaps the only one) where I think our disagreement is genuine and not merely a question of definitions.
I think this is an instance where the theory from the analog era falls short and leads to methods that are no longer optimal.
I would really welcome an exchange on this aspect.
...

My reply might not be what you have in mind :-)

Remembering that I'm not a proponent of "equivalence"...

As I understand it "equivalence" would be from the reference point of the final image.
So DX at f/5.6 1/200s and FX at f/8 1/100s
These are the same Exposure Value and the same Depth Of Field (DOF).
(However noise will be more apparent in the DX image, lower Signal to Noise Ratio (SNR) due to nigher noise.)

One is allowed to take photos with different exposure values. This can result in photos with the same amount of Total Light and thus the same amount of Photon Shot Noise.

[simsurace]

This is an aspect (perhaps the only one) where I think our disagreement is genuine and not merely a question of definitions.
I think this is an instance where the theory from the analog era falls short and leads to methods that are no longer optimal.
I would really welcome an exchange on this aspect.
...

My reply might not be what you have in mind :-)

Remembering that I'm not a proponent of "equivalence"...

As I understand it "equivalence" would be from the reference point of the final image.
So DX at f/5.6 1/200s and FX at f/8 1/100s
These are the same Exposure Value and the same Depth Of Field (DOF).
(However noise will be more apparent in the DX image, lower Signal to Noise Ratio (SNR) due to nigher noise.)

Different shutter speeds have implications on motion blur. That has to be kept in mind. Practically speaking you trade noise with motion blur. However, to stay with Joseph James' definition, the equivalent shot would be obtained with the same shutter speed and a higher ISO or gain in post (to preserve brightness).

You don't have to be a proponent, neither am I, in my understanding. My question for this thread was merely whether there is something wrong with equivalence in terms of the science behind it. I'm fairly convinced that there isn't, but I'm open to be proven wrong.

[JohnMM]

The only reason to not ETTR is because of motion blur.

Or because the choice of a large DOF, or the need to use a lens at it's "sweet spot", requires us to use a smaller aperture. Or is that implicit in our story so far?

[simsurace]

Or because the choice of a large DOF, or the need to use a lens at it's "sweet spot", requires us to use a smaller aperture. Or is that implicit in our story so far?

If you have to stop down, you can also expose longer to compoensate unless you have moving stuff. So I understood that scenario to be accounted for.

[simsurace]

Implicit in what you said is that ETTR at a higher setting ISO is also suboptimal compared to ETTR at a lower ISO setting.

Another way to phrase the philosophy of ETTR is to simple say "gather as much light as is possible without clipping relevant highlights (specular is OK for example)"
Generally this means operating at the lowest (non-extended) ISO setting since this is where Full Well Capacity (FWC) is available.

I've generally found ETTR to yield more usable exposures than any other method.
But what I've been puzzled with is that some people propose 'exposing to the left' for digital.
Regardless of whether you want the final shot to have a dark mood, what good is it to push the histogram to the left? Can it even be defined as anything else than having no light recorded at all?

Also a mystery is the fact that people keep referring to how different sensors have different degrees of 'recoverable highlights'. In my mind, this is an illusion created by the fact that we don't see whether we clip RAW data, short of running the file through RAWdigger. But I'm not so certain, maybe there still is something to it. My understanding is that sensor clipping occurs at a certain precise light intensity, up to uncertainties due to photon noise. But you might know more about this..

[David H. Hartman]

One simply does not take the "equivalent" picture with the different gear, it's that simple.

Sort of equivalent? Close but no cigar?

I have a problem with Equivalence also: I'll sign on. Equivalence' six parameters don't work for me.

Dave

Different Gear, Different Format = Different Photograph

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I've started reading Equivalence by Joseph James. I suspect I'll have a problem with the six parameters as important ones are left out. I'm probably will skim it more but it's unlikely that I'll read the article.

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Equivalence does not yield the "Same" or "Identical" and does not claim to do so.

Perhaps a less confusing name would help: perhaps "Sort of Equivalence." I believe the name *implies* that it can give an identical or nearly identical photography but that is not possible.

Dave Hartman

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Oh My **God! He is going to post another site with graphs...

Background blur versus background distance with four real world cameras and real world lenses.

This is a quick and hopefully not dirty illustration of what can be done with cameras I now own and in one case a lens I could buy but haven't. There are sites on the Net that clearly show that DoF and Background blurring are not one and the same. If one is interested in a more scholarly site or paper they are available by searching.

When the background is well outside the DoF zone longer lenses with larger physical apertures will blur the background more. One may also wish to consider pupillary magnification. The additional background blurring is not proportional to the increase in focal length so if one wishes to keep the perspective identical the larger format with the longer lenses will produce the greatest background blurring.

If greater background blurring is desired use a larger format. If less background blurring is desired use a smaller format.

Dave Hartman who now should probably don fire protective clothing and hug a fire extinguisher.

**Please substitute your favorite deity or Charles Darwin as you prefer.

[bclaff]

...
But what I've been puzzled with is that some people propose 'exposing to the left' for digital.
...

These people are generally misapplying the concept of "ISO Invariance" (not close to the topic of this thread)