Correction: Rough, Qualified Approximations Surrounding Settings

Detail Man wrote:

There are certain quantitative characteristics arising out of camera-lens system settings that are measurable (with varying degrees of complexity, for the most part not without aid of instrumentation).

Field of View - Easy to determine (but not as simple as Focal Length when focused at infinity).

Depth of Field - Possible to determine (but varies with any given individual viewers' visual acuity).

Signal/Noise Ratio - Possible to determine (but varies in perceived impact dependent upon the image itself, viewing conditions, and individual viewers, especially where it comes to periodic noise).

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When we use simplified models that replace complex multi-element lens-systems with single, symmetrical thin lenses, a number of rough approximations are made when scaling settings.

(1) Effective Focal Length should be used instead of the Focal Length when focused at infinity.

(2) Scaling Focal Length as well as the F-Ratio by the ratio of the sensor Crop Factors ignores the fact that the Depth of Field (also) changes as a function of the ratio of the Camera (lens-system front nodal plane) to Subject (plane of focus) Distance to the Hyperfocal Distances involved - by an amount directly proportional to the ratio of the Focal Lengths of compared systems.

My bad, Magister. The Circle or Cornfusion scaling with Sensor Size, all is well. I now recall my once upon a time previously doubting you in surrounding this very issue, and the derivation in your Golden Tablets which showed this illustrious truth was so graciously revealed by you at that time.

Therefore, the inter-format transformations made are only valid when the Camera to Subject Distance is substantially longer than the Focal Length, and are also only valid when the Camera to Subject Distance is substantially shorter than any of the Hyperfocal Distances involved.

It (also) appears that variations due to Effective Focal Length [ EFL = (L) * (1+M/P) ] at close range are also minimal. One thousand apologies for doubting the veracity of your Unified Theory of Everything. I know that I have wandered from The Way, and I humbly ask your forgiveness ...

(3) The relationships of image-noise to sensor size are valid only for Photon Shot Noise when the relative Quantum Efficiencies are known and also factored-in. The additional element, that is ...

... Read Noise (even the entirely random, and not periodic components of), is design-specific in nature, and does appear to reliably follow simplistic assumptions regarding scaling with photosite geometries. Further, the magnitude of (input-referred) Read Noise as well as its (output-referred) proportion (relative to the maximum recorded or recordable peak level) is camera system specific, and is thus a complicated and individualized function of ISO settings.

Therefore, quite a bit of specific actual test-data and knowledge is required in order to meaningfully make such comparisons and assumptions surrounding Signal/Noise Ratio - and such numerical comparisons may not necessarily accurately reflect viewers' subjective perceptions.