Why "crop factor" is so pervasive

Roger Clark said:

I mentioned this myth in my post above: "but up and coming is the very misunderstood big pixels are less noisy idea."

A larger pixel enables the collection of more light, not that they collect more light. Consider this analogy: You have two buckets, one that holds 2 gallons of water and one that holds 1 gallon of water. You put the 2-gallon bucket under the faucet and turn on the water for 1 second. Now you put the 1 gallon bucket under the faucet and turn on the water at the same intensity for one second. Assume the amount of water was not enough to overfill either bucket. Which bucket has more water? (If you answer I hate story problems you fail the class.:w3) If your answer is both buckets have the same amount of water, you are correct. Now what controls how much water is in the bucket? It is not the size of the bucket; it is the force and duration of the water controlled by the fawcet.

In digital photography, the bucket is the pixel, the faucet is the lens and the time the faucet is on is the exposure time. There is one thing missing in the analogy, and that is focal length which spreads out the light so if the faucet has a spray nozzle on the end the spray would expand a further distance from the faucet. Now for the larger bucket, if it has a larger diameter, it would collect more water because it sees a larger area. But if the smaller bucket were moved closer to the sprayer, so it collected the same angular area, it would also collect the same amount of water. People talk about the same sensor field of view, but there is also the same pixel field of view. When the pixel field of view is the same, regardless of pixel size, the two pixels collect the same amount of light in the same amount of time and produce the same signal-to-noise ratio.

So in the case of digital cameras, the amount of light collected is controlled by the lens, its focal length and the exposure time. The larger pixels only ENABLE the collection of more light when the exposure time is long enough. With digital cameras, that only happens at the lowest ISO. At higher ISO, the buckets (pixels) never get filled.

So to manage noise in digital camera images, one must manage the lens aperture, the focal length, and the exposure time. The focal length manages the pixel field of view. So it is not the pixel that controls the observed noise in an image.

Roger

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Thanks. That "visual" helps me understand so much more.

Good Roger, thanks. What I see as noise is then varying "intensities" (number of photons) from pixel to pixel? "Intensity" (correct word?) being from, if expressed as 8 bit, 0 to 255? Trying so show this visually, here are three "red" pixels each after collecting different numbers of photons. The one on the left and the one on the right being noise?



"Average" more mathematically being the "mean", yes? And if the mean value is 100 as you use above, the variation is 10. While if the mean should be 36, the variation is 6. So, comparing 10 to 100 and 6 to 36, it is obvious that 10 is smaller proportion to 100 than 6 is to 36. Thus the 36 mean photon event will appear noisier (than the 100)?
Tom

Tom Graham said:

Good Roger, thanks. What I see as noise is then varying "intensities" (number of photons) from pixel to pixel? "Intensity" (correct word?) being from, if expressed as 8 bit, 0 to 255? Trying so show this visually, here are three "red" pixels each after collecting different numbers of photons. The one on the left and the one on the right being noise?



"Average" more mathematically being the "mean", yes? And if the mean value is 100 as you use above, the variation is 10. While if the mean should be 36, the variation is 6. So, comparing 10 to 100 and 6 to 36, it is obvious that 10 is smaller proportion to 100 than 6 is to 36. Thus the 36 mean photon event will appear noisier (than the 100)?
Tom

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Yes, you got it. While the 36 mean has a lower signal-to-noise ratio than the 100, perception is another factor. In an image. we tend to not see noise in the brightest pixels, and the darkest pixels don't show a lot of noise because they are so dark. It tends to be the middle gray where we perceive the most noise in our images. Also, we perceive less noise in strong colors, especially towards red or blue. We will perceive the most noise in gray-green mid tones. So there is the technical signal-to-noise ratio folded in with human perception. The apparent noise will also depend on the brightness. For example, examining a print in bright office light will usually show more noise than viewing the same print in dim room light.

Roger

Thanks again Roger, your explanations as always very lucid. Our eye brain system is stranger than fiction!!! Been some excellent TV shows about it. Should be required viewing for all serious photographers.
Tom

Roger Clark said:

I mentioned this myth in my post above: "but up and coming is the very misunderstood big pixels are less noisy idea."

A larger pixel enables the collection of more light, not that they collect more light. Consider this analogy: You have two buckets, one that holds 2 gallons of water and one that holds 1 gallon of water. You put the 2-gallon bucket under the faucet and turn on the water for 1 second. Now you put the 1 gallon bucket under the faucet and turn on the water at the same intensity for one second. Assume the amount of water was not enough to overfill either bucket. Which bucket has more water? (If you answer I hate story problems you fail the class.:w3) If your answer is both buckets have the same amount of water, you are correct. Now what controls how much water is in the bucket? It is not the size of the bucket; it is the force and duration of the water controlled by the fawcet.

In digital photography, the bucket is the pixel, the faucet is the lens and the time the faucet is on is the exposure time. There is one thing missing in the analogy, and that is focal length which spreads out the light so if the faucet has a spray nozzle on the end the spray would expand a further distance from the faucet. Now for the larger bucket, if it has a larger diameter, it would collect more water because it sees a larger area. But if the smaller bucket were moved closer to the sprayer, so it collected the same angular area, it would also collect the same amount of water. People talk about the same sensor field of view, but there is also the same pixel field of view. When the pixel field of view is the same, regardless of pixel size, the two pixels collect the same amount of light in the same amount of time and produce the same signal-to-noise ratio.

So in the case of digital cameras, the amount of light collected is controlled by the lens, its focal length and the exposure time. The larger pixels only ENABLE the collection of more light when the exposure time is long enough. With digital cameras, that only happens at the lowest ISO. At higher ISO, the buckets (pixels) never get filled.

So to manage noise in digital camera images, one must manage the lens aperture, the focal length, and the exposure time. The focal length manages the pixel field of view. So it is not the pixel that controls the observed noise in an image.

Roger

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I've been ruminating a bit on this one Roger! What caught my eye on initial reading was the analogy of a faucet and a bucket, but particularly the faucet. The water coming out of your faucet is light = photons, and indeed if light poured onto a pixel bucket like a faucet, and the stream coming out of the faucet were a lot narrower than the mouth of the bucket, then I agree that buckets of different size would collect the same amount of light. Even buckets that had different sized openings at the top would collect the same amount of light. However, intuitively (remember, I'm biologist!) I don't view light this way- to me it's more like a heavy, drenching, minutely fine mist (of photons) falling on the pixels at the speed of light. If light is more like this than tiny streams from faucets, then the width of the pixel opening would hugely affect how much light the pixel would collect with the amount of light collected being proportional to the pixel area (pixel pitch squared). An 64 square micron pixel should collect twice as much light as a 32 square micron pixel, in the same amount of time. Therefore I would conclude that big pixels collect more light than small pixels per unit time, therefore have a higher signal to noise ratio, and therefore appear less noisy.

What is wrong with this logic? Can my intuitive view of light be so wrong???

John Chardine said:

I've been ruminating a bit on this one Roger! What caught my eye on initial reading was the analogy of a faucet and a bucket, but particularly the faucet. The water coming out of your faucet is light = photons, and indeed if light poured onto a pixel bucket like a faucet, and the stream coming out of the faucet were a lot narrower than the mouth of the bucket, then I agree that buckets of different size would collect the same amount of light. Even buckets that had different sized openings at the top would collect the same amount of light. However, intuitively (remember, I'm biologist!) I don't view light this way- to me it's more like a heavy, drenching, minutely fine mist (of photons) falling on the pixels at the speed of light. If light is more like this than tiny streams from faucets, then the width of the pixel opening would hugely affect how much light the pixel would collect with the amount of light collected being proportional to the pixel area (pixel pitch squared). An 64 square micron pixel should collect twice as much light as a 32 square micron pixel, in the same amount of time. Therefore I would conclude that big pixels collect more light than small pixels per unit time, therefore have a higher signal to noise ratio, and therefore appear less noisy.

What is wrong with this logic? Can my intuitive view of light be so wrong???

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Hi John,

While part of the explanation is correct, you changed a critical parameter in the middle. When you changed the area of the pixel, you reduced the resolution (e.g. pixels on subject). While the mist idea is a first approximation, light in a camera system is not like mist falling uniformly all over. It is more a focused beam, so more like a spray nozzle spraying water and that is why I used the spray nozzle idea in my explanation.

So what you say is correct, that the larger area pixel collects more light, and one can certainly look at the problem that way (and most photographers do just that). But it is a situation like crop sensors giving the impression of greater telephoto reach. The crop is not the reason for more telephoto reach, it is pixel pitch. Similarly, it is not pixel size that determines the amount of light gathered, it is the lens diameter and the angular area of the pixel that enables the pixel to collect the light. So if you equalize the angular area of the pixel, the amount of light collect is the same for a given exposure, regardless of pixel size. In your example of the 32 and 64 square micron pixels, put a 2x TC on the camera with the 64 sq micron pixels using the same lens (lets say a 300 f/2.8 lens) then the 64 sq micron pixel system puts the same pixels on subject as the 32 sq micron pixel system and then both cameras get the same amount of light in a given exposure time. The larger pixels didn't magically get more light.

In summary, the control of how much light we get in the camera is: 1) lens diameter, 2) angular area seen by the pixel, and 3) exposure time. (I'm assuming all similar focal length lenses would be pretty close in transmission--which they are.) So like crop factor, pixel area is actually not part of the equation for the resolution on subject and the amount of light a pixel receives. The angular area of a pixel is proportional to the ratio of the pixel size and lens focal length, not pixel size alone. I've written this up in more detail at:
http://www.clarkvision.com/articles/telephoto.system.performance/
but I plan to add a lot more to the page with examples of how this works.

But once one realizes this paradigm, we see that adding a TC is no different than decreasing pixel size by a corresponding factor (when working at higher ISO so the pixels don't overflow). This then leads to no high ISO/low light advantage to large pixels.

Did you every decide on the 300 f/2.8 versus 500 f/4? Given the choice today, I would choose a 300 f/2.8 and body with 5 micron pixels. Gee, that's a D800.

Roger

John, I think you hit the nail on the head. Roger, thanks for the explanation. I think I finally got it (of course, I've thought that before).

Roger Clark said:

So what you say is correct, that the larger area pixel collects more light, [...]

Click to expand...

So one might reasonably conclude for individual pixels:

More light less noise.
Larger pixel more light.
Larger pixel less noise.

The catch is in comparing noise at the image level. Right?

Which brings in:

Roger Clark said:

So if you equalize the angular area of the pixel, the amount of light collect is the same for a given exposure, regardless of pixel size.[...]

Click to expand...

Isn't this the same as saying, normalizing for pixel size? which is also the same as normalizing resolution?

Cheers,

-Michael-

Thanks Roger. I'll take a look at your write-up.

Still not decided on the 300 or 500. I have a (used but new to me) 400DO right now and I plan to give it a good going-over in the next few weeks.

Michael Gerald-Yamasaki said:

John, I think you hit the nail on the head. Roger, thanks for the explanation. I think I finally got it (of course, I've thought that before).



So one might reasonably conclude for individual pixels:

More light less noise.
Larger pixel more light.
Larger pixel less noise.

The catch is in comparing noise at the image level. Right?

Which brings in:



Isn't this the same as saying, normalizing for pixel size? which is also the same as normalizing resolution?

Cheers,

-Michael-

Click to expand...

This has helped clarify things Michael, except for one slight modification to your thesis:

More light same amount of noise
Larger pixel more light.
Larger pixel same amount of noise.
Larger pixel higher signal to noise ratio

all of this at the individual pixel level, like you said.

"Photons arrive at random times and we are counting photons for a relatively short interval (the exposure time in a camera). The noise is the square root of the number of photons collected."
"More light same amount of noise"
No, more light more noise? That is, if 64 photons the noise is 8 (standard deviation) but if more light 225 photons noise is 15.
How about - "More light less apparent noise"?
Tom

John Chardine said:

This has helped clarify things Michael, except for one slight modification to your thesis:

More light same amount of noise
Larger pixel more light.
Larger pixel same amount of noise.
Larger pixel higher signal to noise ratio

all of this at the individual pixel level, like you said.

Click to expand...

This again just repeats variations on the larger pixels produce less apparent noise, like that along the same false idea that crop factor multiplies focal length.

More light = more noise, but higher signal-to-noise ratio, so we perceive less noise.

"larger pixel more light" again is incorrect (crop factor analogy). Correct statement is larger angular pixel field of view = more light (for a given lens diameter and exposure time)

"larger pixel same amount of noise" is only true if the angular field of view of the pixel is the same. Pixel size is irrelevant. (again for a given lens diameter and exposure time)

"Larger pixel higher signal to noise ratio" again pixel size is irrelevant. Angular area of the pixel for a given lens diameter is the key.

We need a clean slate (or clean etch a sketch): forget linear pixel size and think only in terms of the angular pixel size.

Example: you photograph a bird in flight with a 500 mm lens + 2x TC wide open. You want more light without changing exposure. What to do? Take off the TC. For the same exposure, you get 4 times the light per pixel without changing the linear pixel size. Why? The angular area of the pixel has changed 4x. But now you have 4x less pixels (area) on the bird. If you want the same pixels on subject, move 2x closer without the TC. Now you have the 4x more light and the same number of pixels on the subject. And we didn't change the linear size of a pixel. If you moved 2x closer without taking off the TC, you would get the same light per pixel, because we didn't change the angular area of a pixel. Linear pixel size is irrelevant and just causes erroneous ideas.

Roger

Roger Clark said:

"larger pixel more light" again is incorrect (crop factor analogy). Correct statement is larger angular pixel field of view = more light (for a given lens diameter and exposure time)

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Roger, For two pixels sitting next to each other on the same sensor, isn't larger angular pixel field of view equivalent to a larger pixel?

So if larger angular pixel field of view = more light
then larger pixel = more light

Right?

Cheers,

-Michael-

Tom Graham said:

"Photons arrive at random times and we are counting photons for a relatively short interval (the exposure time in a camera). The noise is the square root of the number of photons collected."
"More light same amount of noise"
No, more light more noise? That is, if 64 photons the noise is 8 (standard deviation) but if more light 225 photons noise is 15.
How about - "More light less apparent noise"?
Tom

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I was incorrect Tom for this (thanks) and other reasons mentioned by Roger. More light means a little bit more noise (noise = square root of signal?)

Thanks Roger. You can probably tell this is a tough one for me to grasp (the pixel size/noise myth) but I promise to work on it. I see you call it an advanced topic on the link you provided. Advanced it is.

Roger is (as you may know) a world recognized/renowned scientist in signal processing. It is great he can explain this at a level most of us can understand - if we try long enough :S3: . Come back to it and eventually it will come together for you. I have had college course in statistics and it is not "intuitive" (unless you have Roger's brains). Yet is fundamental, and largely hidden, in our everyday lives.
Tom

Tom Graham said:

Roger is (as you may know) a world recognized/renowned scientist in signal processing. It is great he can explain this at a level most of us can understand - if we try long enough :S3: . Come back to it and eventually it will come together for you. I have had college course in statistics and it is not "intuitive" (unless you have Roger's brains). Yet is fundamental, and largely hidden, in our everyday lives.
Tom

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Yeah, and I can be wrong too! I can also be confused. :w3

Actually, while I do this stuff for a living, it still took a while to sink in for digital photography, as the old film paradigm was pretty entrenched in me. But once I started thinking about the total system (lens, its focal length, and the sensor with pixels), it became no different than a spacecraft sensor, and it still took a while to purge the old film and f/ratios ideas. I probably still am purging and changing the paradigm. And I probably still need to fix some web pages that are in the old paradigm. These discussions help me refine my explanation.

Roger

Michael Gerald-Yamasaki said:

Roger, For two pixels sitting next to each other on the same sensor, isn't larger angular pixel field of view equivalent to a larger pixel?

So if larger angular pixel field of view = more light
then larger pixel = more light

Right?

Cheers,

-Michael-

Click to expand...

Yes, but the linear pixel size argument is similar to the crop sensor = more telephoto reach argument; it seems to work to explain some situations. So the larger pixel has a capability to collect more light, but it is the lens that delivers the light. So the lens is the key, not the pixel. In a specific situation, one can use the linear size as a substitute for angular size, but that keeps one in the wrong paradigm. For example, the scenario I gave in changing TCs and/or distance to the subject changed the light received and the pixel size was not changed.

Roger

John Chardine said:

Thanks Roger. You can probably tell this is a tough one for me to grasp (the pixel size/noise myth) but I promise to work on it. I see you call it an advanced topic on the link you provided. Advanced it is.

Click to expand...

I understand. Whenever there is a paradigm shift, it takes a while to sink in. I've been working on this for months, and it is still sinking in.

Roger

Tom Graham said:

Roger is (as you may know) a world recognized/renowned scientist in signal processing. It is great he can explain this at a level most of us can understand - if we try long enough :S3: . Come back to it and eventually it will come together for you. I have had college course in statistics and it is not "intuitive" (unless you have Roger's brains). Yet is fundamental, and largely hidden, in our everyday lives.
Tom

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Yes Tom, we are certainly privileged to have someone of the calibre of Roger to interact with.

I'm OK with the stats part myself but my weakness is on the light and lens technology side. I think if I can crack angular pixel size I'll be getting there.

I think what makes BPN such a great site is there are so many knowledgeable people in so many areas.

Roger