DOF and Cropping take 2

Started Feb 11, 2014 | Discussions thread
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awaldram Forum Pro • Posts: 12,317
Re: ISO, noise, exposure, and total light

Great Bustard wrote:

awaldram wrote:

awaldram wrote:

Great Bustard wrote:

Here we are:

This nicely cover off everything in this thread

  • Equivalence is only relevant when comparing different formats. For example, if we are comparing the performance of a 50mm lens designed for FF to a 50mm lens designed for APS-C or mFT (4/3), both lenses being used on the same camera, Equivalence does not come into play.
  • Neither the focal length nor the f-ratio of a lens change as a function of format: 50mm = 50mm and f/2 = f/2 regardless of the format the lens is used on.
  • The effect of the focal length and f-ratio of a lens, however, do change as a function of format.
  • The DOF is the same for all systems for a given perspective, framing, aperture diameter, and display display size. For the same aperture diameter and shutter speed, the same total amount of light will fall on the sensor for all systems, resulting in a lower exposure for larger sensors systems (same total amount of light distributed over a larger area results in a lower exposure, since exposure is the density of the light falling on the sensors).
  • The same total amount of light falling on the sensor will result in the same noise for equally efficient sensors, regardless of pixel size or the ISO setting. Typically, sensors of the same generation are rather close in efficiency, but there are most certainly exceptions.
  • Larger formats do not necessarily have a more shallow DOF than smaller formats. Larger formats have the option of a more shallow DOF than smaller formats for a given perspective and framing when using a lens that has a larger aperture diameter, as the lenses for larger formats usually, but not always, have larger aperture diameters for a given AOV. However, people using Auto, P, or Tv modes on the camera will likely find that the larger format camera will choose a wider aperture in many situations, resulting in a more shallow DOF. In addition, many choose to use a wider aperture (resulting in a more shallow DOF) to get more light on the sensor and thus less noise.
  • Equivalence says nothing about shallow DOF being superior to deep DOF, as this is entirely subjective.
  • The resolved detail is a function of the lens, the AA filter, the sensor, and the processing (RAW vs default jpg, for example). A sharper lens (greater lp/mm) on a smaller sensor will not necessarily resolve more than a less sharp lens on a larger sensor. Instead, we need to compare the resolutions in lw/ph, as DPR does with their MTF-50 tests (discussed in more detail here). Furthermore, the resolved detail is also a function of the number of pixels on the sensor (discussed in more detail here), and all systems suffer the same amount of diffraction softening equally at the same DOF, although the system that began with more detail will retain more detail (although the advantage asymptotically vanishes as the DOF deepens -- discussed in more detail here).
  • Equivalence makes no claims whatsoever about which system is superior to another system, especially given that there are so many aspects about systems that Equivalence does not address. For example, in terms of IQ, Equivalence says nothing about bokeh, moiré, distortion, color, etc., and in terms of operation, Equivalence says nothing about AF, build, features, etc. In fact, Equivalence can even work against larger sensor systems by denying them their "noise advantage" when they need to match both the DOF and shutter speed of smaller sensor systems.
  • However, Equivalence does make the argument that it makes no sense to artificially handicap one system or the other by requiring identical settings for a comparison, when identical settings result in different effects on different systems.

This point

The reason that smaller sensors are more noisy than larger sensors is not because they are less efficient, but because less light falls on them for a given exposure. If the larger sensor is more efficient than the smaller sensor, then the noise gap will widen, if the smaller sensor is more efficient, the noise gap will shrink.

I don't think tells the whole story , because we use ISO to define the sensitivity of the sensor then surely for a give ISO every sensor will be identical.?

It is as written:

The reason so many feel that smaller pixels result in more noise is that smaller sensor systems usually have smaller pixels than larger sensor systems. While smaller pixels, individually, will be more noisy (for a given exposure and sensor efficiency) because they record less light, there are more pixels. That is, the noise in a photo is not determined by a single pixel, but the combined effect of all the pixels where a greater number of smaller pixels will capture the same total amount of light as a fewer number of larger pixels, and thus have the same photon noise, so long as the QE (Quantum Efficiency -- the proportion of light falling on the sensor that is recorded) is not adversely affected by pixel size, which is the case for sensors of a given generation.

However, the other primary source of noise in a photo is the read noise, which is the additional noise added by the sensor and supporting hardware. If the read noise of the pixels scales linearly with the size of the pixel, the overall read noise will be the same. For example, if a 1x1 pixel had half the read noise of a 2x2 pixel, then the combined read noise for four 1x1 pixels would be the same as a single 2x2 pixel (noise adds in quadrature, not linearly, which is discussed in the link on read noise). While the QE of a pixel tends to be the same across the board for pixel sizes for any given generation of sensors, the read noise per pixel varies dramatically. If any generalization can be made, it would be that the read noise per pixel also tends to be about the same, regardless of the pixel size (although, as stated, there is tremendous variation, even for sensors of the same generation).

While the photon noise is usually the dominant source of noise in a photo, as the exposure gets lower and lower, the read noise becomes more and more important compared to the photon noise. Thus, for very low light scenes where a photographer might be using, say, a setting of ISO 3200 or more, a sensor with more pixels will tend to be more noisy than a sensor with fewer pixels, all else equal, and will become worse as the exposure gets even lower. How much worse depends very much on the specifics of the differences in read noise per area between the sensors.

Another additional wildcard is NR (Noise Reduction, or, more properly, Noise Filtering), which is a much more efficient method of dealing with noise than downsampling. More pixels will record more detail, but how much more detail depends on the specifics of the scene (e.g. motion blur) and the sharpness of the lens. If the photo with more pixels has "enough" more detail than the photo with fewer pixels, then the application of NR to normalize the detail between the two photos may tip the noise advantage in favor of the photo with more pixels, even if the initial image file were more noisy.

Thus, for fully equivalent images, where both the DOF and shutter speeds are the same, all systems will collect the same amount of light, regardless of the pixel size. The system that will have the lesser amount of noise will be the system that has the more efficient sensor and/or the system that resolves "enough" more detail since that additional detail can be traded, via NR, for less noise.

Furthermore, the belief that higher ISOs result in more noise is a common misinterpretation as to what is actually taking place. Yes, higher ISO images usually result in greater noise, but this is because using a higher ISO results in either a faster shutter speed and/or a smaller aperture for a given scene, the effect of which will be less light on the sensor. It is the lesser amount of light falling on the sensor that results in the greater noise, not the higher ISO per se. In fact, the higher ISO setting results in slightly less noise for a given exposure (that is, for a given f-ratio and shutter speed, the higher ISO setting will result in less noise) for some sensors. For example, if we took a photo of a scene at ISO 100 and ISO 1600, both with the same f-ratio and shutter speed, and pushed the ISO 100 photo four stops in the RAW conversion to achieve the same brightness as the ISO 1600 photo, it would be more noisy than the ISO 1600 photo on some sensors (discussed in more detail here, with some examples linked). The same would be true if we took a photo at ISO 1600 and pulled it down four stops to match the brightness of the ISO 100 photo, but at the expense of four stops of highlight detail. In other words, the cause of noise is the amount of light falling on the sensor, and the efficiency of the sensor, not ISO setting, per se.

Thus, while it is not news to anyone that lower exposures result in greater noise, it is news to many that it is not the higher ISO setting that causes more noise, but instead the lesser amount of light falling on the sensor. To minimize the noise in a photo, we want to maximize the exposure within the constraints of how much light the sensor can absorb before oversaturating, the DOF / sharpness we wish to achieve, and the shutter speed necessary to offset motion blur and/or camera shake.

So my view would be

The reason smaller sensors are more noisy than larger sensors is because less light fall on them (light density) they therefore have higher internal gain per ISO to compensate.

It's simply because less light falls on the sensor. If anything, larger sensor systems apply a greater amplification to the signal than smaller sensor systems, but this is neither here nor there.

See my points on exposure constants.

This gain increases the noise for any given exposure solution.

It really doesn't.

Acording to ISO 12232:2006 it does

and though not often used in consumer cameras two of the calibration methods do exactly that

These  specify the highest exposure index that can be used while still providing either an “excellent” picture or a “usable” picture depending on the technique chosen.

(see niose based speed below)

As per Nikon USA

How much light is needed is determined by the sensitivity of the medium used. That was as true for glass plates as it is for film and now digital sensors. Over the years that sensitivity has been expressed in various ways, most recently as ASA and now ISO.

The sensitivity of the sensor is fixed, that is, it is not a function of the ISO setting, except inasmuch as the read noise is lower at higher ISO settings for cameras with non-ISOless sensors.

Not sure what your saying here ?

ISO (loosely) is the gain applied to a fixed output to achieve a standard between imaging devices.

So though this gain may be applied externally (CCD always) or internally (on-chip cmos) or a hybrid (extended ISO's)

do you mean sensitivity of the sensor or sensitivity of the pixel.?

So for any sensor size ISO 100 will deliver the same exposure (and why external light-meters work across formats)

The exposure is determined by three, and only three, factors:

  • The scene luminance
  • The t-stop of the lens (the f-ratio is usually close)
  • The shutter speed

The only effect the ISO setting has on the exposure is in how it indirectly affects the f-ratio, shutter speed, and/or flash power the camera uses as a function of the shooting mode you are using.

Unfortunately, many think that "exposure" means "brightness", which is discussed, in detail, here:

This section will answer the following four questions:

  • For a given scene, what is the difference in exposure, if any, between f/2.8 1/200 ISO 400 and f/5.6 1/200 ISO 1600?
  • What role does the ISO setting play?
  • What role does the sensor size play?
  • What does any of this have to do with the visual properties of the photo?

Whilst I understand what your saying I can’t agree 100%

ISO in a digital camera is calibrated acording to ISO 12232:2006

Main article: Signal to noise ratio (imaging) Digital noise at 3200 ISO vs. 100 ISO The noise-based speed is defined as the exposure that will lead to a given signal-to-noise ratio on individual pixels. Two ratios are used, the 40:1 ("excellent image quality") and the 10:1 ("acceptable image quality") ratio. These ratios have been subjectively determined based on a resolution of 70 pixels per cm (180 DPI) when viewed at 25 cm (10 inch) distance. The signal-to-noise ratio is defined as the standard deviation of a weighted average of the luminance and color of individual pixels. The noise-based speed is mostly determined by the properties of the sensor and somewhat affected by the noise in the electronic gain and AD converter

Also bear in mind on a cmos sensor a lot of processing is done on chip, Because of the higher noise of CMOS technology.

So separating pixel noise from system noise at that level may not be possible.

Then you have manafacturers using different Exposure Constants (termed calibration constants)

Canon and Nikon assume that the medium tone is approximately 3.15 EV lower than the highlights

Sony and Pentax assume .4 ev higher

While printing, the midtone is usually represented as 18% grey (if you count in stops, then that is 2.47 EV lower than 100% white), thus the first group of photo equipment manufacturers imply the compression of approximately 0.7 EV of the range from the midtones to highlights, while the second imply the compression of about 0.3 EV.

As such it is virtually impossible to separate QE from Exposure Index so making statement on noise related QE cna only at best be a generalization.

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