# DOF and Cropping take 2

Started Feb 11, 2014 | Discussions thread
One of the worst explanations
1

Ian Stuart Forsyth wrote:

awaldram wrote:

awaldram wrote:

Great Bustard wrote:

Here we are:

http://www.josephjamesphotography.com/equivalence/#quick

I don't the provenance of this but it's going to throw people

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.

OK we've done this to death. The bending power of the lens and the size of the hole in the diaphragm don't change depending on what is behind it to receive the image. Everyone got that ? Good.  We all know that the circle of confusion for a point at infinity formed by a lens of focal length f focused a distance d is given by the equation c=  f^2/da
where a is the aperture as an f/ number

Next

• The effect of the focal length and f-ratio of a lens, however, do change as a function of format.

This we also know to be true. A circle-width which is insignificantly small on one format can take up a huge part of the image on a smaller format  Once you set a format dependent value for c you can rearrange the equation to give the hyperfocal distance which is the core number for d.o.f so
d = f^2/ca

• The DOF is the same for all systems for a given perspective, framing, aperture diameter, and display display size.

This one seems wrong. And then you realise he isn't talking about aperture in the same terms as everyone else. He talks about Aperture DIAMETER not an f/ number, but the width of the hole in mm. Stop and read what I just said again. when you or I might talk about a 50mm lens at f/2 he talks about a 50mm lens with a 25mm aperture.

Now to keep the DOF the same from the same perspective (camera position) and framing (field of view) when you double the sensor size you double the focal length so our 50mm is replaced by a 100mm and if the aperture DIAMETER is fixed at 25mm the f/ number goes from 2 to 4, so
f^2/ca  is the same.

Hands up who says "two lenses have the same aperture when their f/ numbers are the same"
and who says "two lenses have the same aperture when the diameters in mm are the same"

• 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).

For the same f/ number the illumination, in terms of luminous flux (or photons per square mm per second, or any other way you want to count it) is the same. But he is not talking about illumination. What he is saying is for the same diameter of hole, you get the same number of photons going through to the sensor. If the hole is a long way from the sensor and spreads the light out over a wide area the sensor is less illuminated, than if it is close.  This is true. But normally when we talk about amount of light we mean illumination. But he is right, if you double the sensor width, double the focal length, and stop down from f/2 to f/4 (which keeps the hole the same size) then you 1/4 of the illumination of the sensor (light per unit area) over 4 times the area.

• 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.

At best this is unproven. I think you can say if sensors have the same efficiency, and the same pixel count, and same well depth, and same read noise then then one with 4 times the pixel area will have a base ISO 4 times higher. But when you have different well depths and pixel counts I think this his assertion breaks.

• 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.

Again by talking about diameter (mm) not f/ number tends to cause confusion. I think what he is saying is that if you double the focal length, say from 50mm f/2 to 100mm the aperture is not a fixed at 25mm so you get something wider than f/4 though maybe not as wide as f/2  And when the cameras are in auto it will tend to select the same f/ number regardless of format, which means a wider diameter on the larger formats.

• Equivalence says nothing about shallow DOF being superior to deep DOF, as this is entirely subjective.

It doesn't Sometimes you want D.o.f. from you nose to infinity, and sometimes you want to isolate a subject from the background.

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.?

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.

There is a very basic argument that more light falling on sensor means less noise.

This is why Iso 100 on dx is the same as iso 225 on FF Full Frame needs less gain to start with

what happens if FF shoots at Iso 100 and DX shoots at iso 100 for the same exposure?

Define "the same".

Lets say for arguments sake two sensors have the same well depth and efficiency. Both need 100,000 photons to hit a pixel for that pixel to register "MAX" Both have the same number of pixels but sensor one is 50% longer on a side than the other, so it's area is 2.25 times the size. Both the pixels and the gaps have been scaled up, so the pixels are 2.25 the area. Lets say the smaller sensor gets 100,000 photons in 1/100th sec. The larger one will get them in 1/225 sec. The base ISO goes up.
BUT ONLY IF THE WELL DEPTH AND EFFICIENCY ARE FIXED. Usually they aren't

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.

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

Generally when the pixels get smaller the well depth also gets smaller. That means that few photons hit the pixel and fewer photons are needed to get it to register MAX, so MAX comes at the same illumination (photons per sq-mm per sec).

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