Dynamic range difference of sensor operated in FF vs Crop

[Pentaborane]

Hello everyone,
Recently i have been looking through tests and various graphs of sensor tests and these usually come to the conclusion that a FF sensor has higher dynamic range than its APSC counterpart or itself if operated in crop mode.
I understand that aperture crop factor impacts the DOF but not the amount of light hitting a mm^2 of sensor this leads me to a confusion why would 2 sensors made in the same technology like ones found in Sony A7R5 and Sony a6700 that have basically the same pixel pitch and backend electronic processing would create a different DR value.
Especially if according to PhotonsToPixels dynamic range of A7R5 drops when going to APSC but we have the same pixels illuminated with the same amount of light.
This part makes no logical sense, what part of how sensors work am I missing that causes that difference?

 

[JimKasson]

My barometer says that the dew point and temperature are both 29.7. Coincidence?

29.7 inches

So a barometer is not the tool for measuring temperature or measuring dewpoint. Just like a histogram is not the tool for measuring noise or DR.

is that what he ment a barometer can be used to measure dew point

Also height of a building. But Niels Bohr came up with some creative ways to do that:

• Tie a string to the barometer, lower it from the top, and measure the length of the string.
• Drop the barometer from the roof and time its fall, then calculate the height from gravitational acceleration.
• Trade the barometer to the building superintendent in exchange for the building’s height.

 

[A74Me]

My barometer says that the dew point and temperature are both 29.7. Coincidence?

29.7 inches

So a barometer is not the tool for measuring temperature or measuring dewpoint. Just like a histogram is not the tool for measuring noise or DR.

is that what he ment a barometer can be used to measure dew point

Also height of a building. But Niels Bohr came up with some creative ways to do that:

• Tie a string to the barometer, lower it from the top, and measure the length of the string.
• Drop the barometer from the roof and time its fall, then calculate the height from gravitational acceleration.
• Trade the barometer to the building superintendent in exchange for the building’s height.

its termed "lapse rates"

 

[JimKasson]

The problem i see with your analogy and some others, is we are not measuring/comparing total capacitance are we

Coulombs per volt? No, the significant measurement is total photons captured.

the photo diodes are not connected in series or parallel, they are collecting/storing photons individually are they not ?

Pixels? They collect a large number of photons.

The photons don’t survive their encounters with the sensor. I’m sure you know that, but another person seems to be unclear on the subject.

the photons are not the actual source of electrical energy recorded that energy comes from the battery.

A photon with sufficient energy hits the semiconductor material (e.g., silicon).

The energy of a photon is:

𝐸photon = ℎ𝑐/𝜆

For silicon, the bandgap energy is about 1.1 eV. Therefore, only photons with energy > 1.1 eV (wavelengths shorter than about 1100 nm) can be absorbed effectively.

If the photon's energy exceeds the silicon bandgap, it can be absorbed by promoting an electron from the valence band to the conduction band.

• Valence band: where electrons are normally bound in atomic bonds.
• Conduction band: where electrons are free to move within the material.

This process creates two charge carriers:

• A free electron (in the conduction band),
• A hole (the absence of an electron) in the valence band.

Electron-hole pair creation is the fundamental microscopic event.

A typical photodiode is built around a p-n junction —
an interface between p-type (positive, hole-rich) and n-type (negative, electron-rich) silicon.

Around the p-n junction, there’s a depletion region:

• Built-in electric field due to immobile ionized donors and acceptors.
• Field points from the n-side to the p-side (electrons want to go to n, holes to p).

When an electron-hole pair is created inside or near the depletion region:

• The built-in electric field sweeps the free electron toward the n-side,
• And sweeps the hole toward the p-side.

This separates the charges before they can recombine.

The movement of these carriers generates a photocurrent —
a flow of electric charge that can be measured.

• Short-circuit mode (zero applied voltage): current is proportional to light intensity.
• Reverse-bias mode (small negative voltage across junction): improves collection efficiency and speeds up response.

Thus, the arrival of photons results in a measurable external current or voltage.

The battery provides the reverse bias. It is not the fundamental source of the energy of the electron, although it increases the QE at some wavelengths. All photon energy above the bandgap is lost to the lattice as heat.

 

[hjulenissen]

It’s best not to consider pixels at this level of analysis, and it’s unnecessary anyway. A purely geometric approach is both easier to understand and tells you most everything you need to know anyway.

Light falling on a small surface vs the same intensity of light falling on a surface that’s 2-½ times greater area, means that 2-½ times as much total light is being measured.
--
http://therefractedlight.blogspot.com

But if you pick a lens with the same focal length and same equivalent aperture, the larger sensor will get exactly as much total light as the smalle sensor for the same exposure time.

 

[Bill Ferris]

It’s best not to consider pixels at this level of analysis, and it’s unnecessary anyway. A purely geometric approach is both easier to understand and tells you most everything you need to know anyway.

Light falling on a small surface vs the same intensity of light falling on a surface that’s 2-½ times greater area, means that 2-½ times as much total light is being measured.
--
http://therefractedlight.blogspot.com

But if you pick a lens with the same focal length and same equivalent aperture, the larger sensor will get exactly as much total light as the smalle sensor for the same exposure time.

If you're trying to reference a situation in which different format systems make equivalent photos, both cameras would, by definition, be working at different f-stops; different exposures.

In other words, equivalence confirms what Mark has written. If different format systems work with the same exposure, the larger format camera will collect more photons. The only way for the smaller format system to collect as many or more photons as the larger is for the smaller format camera to work with a greater exposure.

 

[spider-mario]

The greater the dynamic range, the more discreet, subtle tonalities one can discern in a photo.

As far as I know, there is no necessary relationship between those two things (although I can definitely believe that there will be a correlation in general).

 

[hjulenissen]

It’s best not to consider pixels at this level of analysis, and it’s unnecessary anyway. A purely geometric approach is both easier to understand and tells you most everything you need to know anyway.

Light falling on a small surface vs the same intensity of light falling on a surface that’s 2-½ times greater area, means that 2-½ times as much total light is being measured.
--
http://therefractedlight.blogspot.com

But if you pick a lens with the same focal length and same equivalent aperture, the larger sensor will get exactly as much total light as the smalle sensor for the same exposure time.

If you're trying to reference a situation in which different format systems make equivalent photos, both cameras would, by definition, be working at different f-stops; different exposures.

In other words, equivalence confirms what Mark has written. If different format systems work with the same exposure, the larger format camera will collect more photons. The only way for the smaller format system to collect as many or more photons as the larger is for the smaller format camera to work with a greater exposure.

I am not trying to argue the physics here but how to describe a scenario with the most easy to comprehend intuition. As that is inherently subjective, I think it is hard to arrive at hard answers.

Equivalence was a great tool for my understanding in being able to reject certain theoretical claims made by people with (often) great practical photographic skill.

(BTW, my post contains an error. I should have written _equivalent_ focal length)