Too many megapixels? Six is enough for an 8x10.

Started Apr 26, 2009 | Discussions thread
Daniel Browning Senior Member • Posts: 1,058
[1/2] Noise power is a function of spatial frequency

David Clarke29 wrote:

Even on SLR's pushing up the sensor count increases
high iso noise.

It does not, despite the fact that 99% of photographers, web sites, and magazines promote the idea.

Read the tests on comparison sites - mid range SLR's
will show an increase of noise filtering the higher the photodiode
count given the same physical size sensor.

Yes, camera manufacturers are adding more noise reduction on JPEGs, but the raw files and sensors themselves still have the same noise (or less), despite the smaller pixels.

The model used by "small pixels baaaad" proponents is this:

  • "A single pixel, in isolation, when reduced in size, has less sensitivity, more noise, and lower full well capacity."

So far so good. In the case of a single pixel, it's true. Part two is where I disagree:

  • "Therefore, a given sensor full of small pixels has more noise and less dynamic range than the same sensor full of large pixels."

The briefest summary of my position is Noise scales with spatial frequency. A slightly longer model describing what I think happens with pixel size follows:

  • "The amount of light falling on a sensor does not change, no matter the size of the pixel. Large and small pixels alike record that light falling in certain positions. Both reproduce the same total amount of light when displayed."

My research and experiments bear that out: when small pixels and large pixels are compared in the same final output, smaller pixels have the same performance as large.

Spatial frequency is the level of detail of an image. For example, a 100% crop of a 15 MP image is at a very high spatial frequency (fine details), whereas a 100% crop of a 6 MP image is at a lower spatial frequency (larger details). Higher spatial frequencies have higher noise power than low spatial frequencies. But at the same spatial frequency, noise too is the same.

A high megapixel image can always be resampled to the same detail level of a low megapixel image. This fact is sometimes disputed, such as by Phil Askey in a recent blog post; however, it was thoroughly debunked:

There is ample proof that resampling works in practice as well as in theory. Given that fact, it's always possible to attain the same noise power from a high pixel density image as a large-pixel one. And it follows that it's always possible to get the same noise from a high resolution image as a low resolution image.

The "small pixels have worse noise" idea has become widespread because of the following unequal comparisons:

  • Unequal spatial frequencies

  • Unequal sensor sizes.

  • Unequal processing.

  • Unequal expectations.

  • Unequal technology.

Unequal spatial frequencies.

This is the most common type of mistake. To compare 100% crops from cameras of different resolutions is the most frequently-made error. This is magnifying one to a greater degree than another. It would be like using a 2X loupe to examine one and an 8X loupe to examine another. Or examining a small part of a 30x20 print vs. a wallet-size print. It's necessary to scale for size in order to measure or judge any aspect of image quality.

The standard measurements for sensor characteristics such as noise are all measured at the level of one pixel. Sensitivity is measured in photoelectrons per lux second per pixel. Read noise is variously measured in RSM electrons/pixel, ADU/pixel, etc. Dynamic range is measured in stops or dB per pixel. The problem with per-pixel measurements is that different pixel sizes have different spatial frequencies.

Nothing wrong with per-pixel measurements, per se, but they cannot be used for comparison with sensors of unequal resolution because each "pixel" covers entirely different spatial frequencies.

Using 100% crops and per-pixel numbers is like comparing two lenses at different MTF frequencies. If they have the exact same MTF curve, but you measure one at 50 lp/PH and the other at 100 lp/PH, you will draw the incorrect conclusion that one is better than the other. Same if you measure one at MTF-75 and the other at MTF-25. (Most people do not make this mistake when comparing lenses, but 99% do it when comparing different pixel sizes.)

Pixel performance, like MTF, cannot be compared without accounting for differences in spatial frequency. For example, a common mistake is to take two cameras with the same sensor size but different resolutions and examine a 100% crop of raw data from each camera. A 100% crop of a small pixel camera covers a much smaller area and higher spatial frequency than a 100% crop from a large pixel camera. They are each being compared at their own Nyquist frequency, which is not the same frequency.

Continued in part 2...

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