Re: What is Equivalence

Since a lot of it is about the angle, in linear measure the smaller is the pixel the more positioning precision may be needed. The idea that lighter cameras need less sturdy tripods doesn't always play well in practice.

This is the exact reason the Zone System was developed by Fred Archer, Ansel Adams and refined by Minor White and Fred Picker who also documented it to the photographic world. First of all - one could not trust the ASA rating of film. The rating method was highly dependent on the testing method so the ASA was not adequate for insuring "proper exposure." The true ASA would even vary between different batches of the same film. The first task when Adams got a new batch of film was to determine his unique ASA to shoot the film. That was done by the use of a precision instrument called a densitometer. The "personal ASA" was a function of exposure, development method and developer used (Adams used mostly dilution B of HC110).

To be able to calculate N-1 (for high contrast scenes) and N+1 for low contrast scenes one first needs to know normal. While the Zone System works best for sheet film where each sheet is developed independently, it is applicable to medium format where multiple film backs can hold film for N, N-1 and N+1 use.The film calibration also took into account various offsets in the camera - e.g., the shutter was 5% too slow which could happen in mechanically timed shutters.

But the key is in film the actually negative density based on the readings of a densitometer were used. That is as close as one can get to the raw capture. In digital it is whatever spin the camera company wants to put on the JPEGS. Then there is the issue of a CFA. With my Leica monochrome I can hang a white sheet, sit the camera on a tripod and spot meter the center of the sheet and use raw digger to tell me at what ISO middle gray corresponds to middle gray. With a CFA - that is difficult to do since we were not directly measuring the sensitivity of the monochrome sensor below the CFA.

As some have pointed out there are really two issues here which sometimes get conflated. One is the geometric rendering of a scene or geometric equivalence. A lens projects light from the front on to light behind. The geometry is determined by the focal length that is the refraction that changes the cone angle in front to the cone angle behind. When a sensor is put behind the lens, the size of the sensor defines the field of view. Geometric equivalences can then be determined as a function of focal length and and focal length to get the same image projected on different sensors. Then factors such as DOF can be factored in once a circle of confusion is selected. Since one has defined CoC, diffraction can be factored into the model. While this model may be geometrically complete - it isn't really. The sensor images are not the same size. One needs to scale the smaller sensor image to the size of the larger or to better yet scale both to a standard size to take into account the enlargement ratio required to make the images the same size. That will modulate the impact of diffraction. Such things a noise, ISO, etc. have little to do with the geometric properties of "equivalent cameras."

I took at week long workshop with Fred Picker back in the late 1970's. Most of us there had just started using a view camera, however, were proficient otherwise. The first thing Picker said was there was only so much one can learn in the indoor "classroom" sitting on our butts. Sure we could talk about the Scheimpflug line and all sorts of other concepts from projective geometry.

sites.math.northwestern.edu/~len/photos/pages/vc.pdf

My field of expertise in real life is algebraic geometry so projective transforms are elements of my dreams or more like nightmares during my graduate school years 🙀. The important thing is not how the camera as a transforms from three space to two space as a projective transform works in theory but what the image looks like on the print. The best way to understand that is to "do the experiment" - take the image and make the print go back inside and discuss it. An internal part of photography - just as any discipline is to develop the intuition (we mathematicians call it "mathematical maturity" ) in order we can look at an image, visualize what we want to do with it and have the experience to make the correct choices or at least define a set of choices we can try that will maximize our success rate.

en.wikipedia.org/wiki/Mathematical_maturity

Ansel Adams was able to capture one of his more iconic images, "Moonrise" because he had the intuition to see it and the knowledge base to be able to set up his camera rapidly and let his intuition drive the exposure settings because he didn't have time to dig out his meter and get a workable negative. The rest is as we say, history.

Excellent post, Truman!

On the Z 6, I use the highlight-weighted metering mode. It leaves some headroom, but I'd rather have informative highlights and pulled-up shadows than blown highlights. Thom Hogan says the Z cameras in this mode put highlights at middle gray, so dialing in a +2EV is prudent. I recently tested that, in my images it let more highlights go to saturation than I desired, so I'm now trying +1EV. For the D7000 I just use regular matrix mode, tried all the ETTR pet tricks with no satisfaction, so I just try to pay attention to the range of light in the scene, sometimes dialing in some -EV. All of this is cognizant of the respective cameras' ability to resolve light measurements through a given range; whatever the measured DR, my practical experience is that I have not had to use denoise in post with the Z 6 except for one image, a grab shot in very dim light where I didn't get the time to properly consider metering. I probably had to deal with shadow noise in about 30% of my D7000 images.

I rather like Bill Claff's PDR definition for comparing cameras.

I do too, but the SNR threshold is getting to be too low as the resolution of cameras increases and we have the ability to make higher quality big prints. When we get to 340MP 4:3 cameras, the PDR SNR threshold will be the same as that of one of the the engineering dynamic range definitions (SNR = 1).

The idea is that the smaller mass of a smaller sensor is quicker to adjust. I do not know of any comparisons, but I feel that my m43 system has better working IBIS than my FF and MF systems.

There should be a Godwin’s law for car analogy.

Well, for smaller steering adjustments it is :)

Hmm, I thought I was describing my exposure decisions by telling you I let the matrix modes make the specific decisions, knowing pretty much how they behave. I think for any sort of shooting where there's subject movement and constantly changing light giving control to a well-reasoned decision-making tool is prudent. Frankly, I don't want to be fiddle-faddling with ETTR stupid pet tricks or even doing spot metering when I've got a steam locomotive heading toward me traveling through changing light. I want to concentrate on placement and timing of the objects in the scene for the best composition I can get.

Regarding Bill's PDR, that stop and a half at ISO 800 and above has proven significant in my low-light shooting. With the Z 6 I can get hand-holding shutter speeds and little-to-any appreciable shadow noise dialing up to around 1600 ISO, something I cringe at thinking of doing with the D7000. Staring at that stop-and-a-half in the PDR chart is what led me to the decision to procure the Z 6. And then, IBIS, which doesn't figure in any of the equivalence consideration, will let me hand-hold well-past my previous 1/30sec threshold, down to 1/10sec. These are the sort of mental discussions going on in my bear-of-little-brain head, comparing the D7000 and Z 6, not some arbitrary consideration of format equivalence...

Now, I realize my thinking may be a bit coarse, and my consideration set (Nikon) may over-simplify things, but I feel it has well-supported my procurement and use decisions. So, for the wider audience, it might be helpful if you could describe where that thinking might trip one up in the more general case. And be pragmatic about it, e.g., 1/2 stop differences are differences, but why would it be important?

Don´t try to be cute. You know what I mean.
There is a reason the Veiron will never be a competitive rally car. And it has everithing to do with weight and size.

For the same reason you never see a 300+ kg HD on a motocross event.

Mass vs inertia.

I don't know how universal it is, but my anecdote is that out of the three ILCs I own with IBIS, the largest sensor seems to have the most slop/error, and the smallest sensor is the tightest (Canon R5, Canon R7, Pentax Q).

Well, that's exactly it, I couldn't come up with an exposure strategy for the D7000 that allowed me to preserve highlights AND get acceptable shadows without post shenanigans AND keep from distracting me during the moment of capture. The Z 6 gave me that 1.5 stop AND an exposure mechanism that preserved highlights with no real-time consideration required. In practice I can even live with the 1-2 stops of headroom of the highlight-weighted matrix metering because the shadows are so much cleaner, and I can't account for that stop in the graph. And then, IBIS, which lets me collect more light with a lower shutter speed, hadn't even considered that in the purchase decision, but I'll always take lagniappe... 😆

There is a lot more to shooting than just exposure...