User:Benh/Camera Formats Equivalence

This article tries to explain the equivalence between the different camera formats, and to help realise why, in certain conditions, a full frame camera won't produce a better image than an APS-C camera or a 1" sensor camera.

Disclaimer

I'm not a physicist, I sucked at optics at school. This is based on this article (add link), own observations, and common sense.

Also, it's a work in progress. I need to fact check some of the points I wrote (I know they are mostly correct, but my memory is not like wine: doesn't age well).

Sensor Formats

We'll focus on these formats (but there are of course plenty of others)

• FF = Full Frame sensor camera (36x24mm)
• APS-C = Advanced Photo Sensor type C (24x16mm for most or 22.5x15mm for Canon).
• 1" = One inch format (13.2x8.8mm)

Why Bigger Sensors Won't Gather more light

If one photon reaches the sensor, the results will be the same whether the sensor is 1x1mm or 10x10km.

It's the same as how much water a sink collects. Smaller sinks collect as much water as bigger ones. It's how wide open the tap on top is which counts.

For a camera setup, it's how wide open a lens is which counts.

Crop Factor

The reference is FF.

Let's consider a sensor being c times smaller than an FF on each side. Capturing an image on it with a same lens used on FF will yield a picture cropped by the same factor, on the center area of the frame. c is the crop factor.

APS-C has a crop factor of 1.5(Nikon, Sony, Fuji) or 1.6 (Canon)

1" has a crop factor of 2.7 (2.72727272... exactly)

The following table summarises this:

Format	Sensor Dimensions	Crop Factor	FOV	Focal Length (and effective Focal Length)
FF	36x24mm	1		50mm
APS-C 1.5	24x16mm	1.5		50mm (75mm)
APS-C 1.6	22.5x15mm	1.6		50mm (80mm)
1"	13.2x8.8mm	2.7		50mm (135mm)

A Common Misconception Of Equivalence

Because of the above table, one common misconception is that the equivalent APS-C 1.5 setup of a FF + 50mm f/1.4 camera is

• APS-C + 35mm f/1.4 (actually would be 33mm but for simplicity sake)

This is wrong, because the depth of field property depends on the absolute aperture size, and not the relative one. f/1.4 on a 50mm lens means 35.7mm diameter aperture. To have the same absolute aperture on a 35mm, we would need a 35/35.7 = 0.98 relative aperture. So the equivalent APS-C lens is a 35mm f/0.95.

Real Equivalent Setups

The following table gives the equivalent setup of a FF + 50mm f/1.4 on different formats:

Format	Sensor Dimensions	Crop Factor	Focal Length	Aperture
FF	36x24mm	1	50mm	f/1.4
APS-C 1.5	24x16mm	1.5	35mm	f/0.95
1"	13.2x8.8mm	2.7	18mm	f/0.5

We can more or less guess from that table why we often associate big sensors with better low light capabilities. It's hard to make a f/0.95 and, even harder, to make a f/0.5 lens.

So it's true that bigger sensors are better in low light. Not because of their size, but because they allow "easier" design of brighter lenses for a given field of view.

Why setup on smaller sensors can produce same image quality as setup on bigger sensors...

...on certains conditions!

Let's look at a common case where we take a landscape photo. Again, the reference being a FF. It is often said that we can use f/8.0 because this will get of enough depth of field, and f/8.0 is often close to the sweet spot of a lens on a FF camera.

If we derive the previous table to have the reference setup being FF + 24mm f/8.0, we have:

Format	Sensor Dimensions	Crop Factor	Focal Length	Aperture
FF	36x24mm	1	24mm	f/8.0
APS-C 1.5	24x16mm	1.5	16mm	f/5.6
1"	13.2x8.8mm	2.7	8.8mm	f/3.0

The figures we have for APS-C and 1" are very standard setup. A camera like a Sony RX100 can do 8.8mm@f/1.8 so it can of course do 8.8mm@f/3.0.

In theory, a 1" camera like a Sony RX100 can shoot a picture with equal quality that of a FF's 24mm@f/8.0. But make sure to read the section about ISO speed to get the full story (spoiler: not quite, but close)!

Bottom line: for landscape photos, APS-C or 1" cameras are perfectly valid choices! Almost no concession.

How About Smartphones?

Can we extend that thinking to smartphones?

If we take a 1/2.5" inch sensor (iPhone X and others), we have a crop factor c of 6. So the equivalent FF 24mm@f/8.0 in smartphone format is:

Format	Sensor Dimensions	Crop Factor	Focal Length	Aperture
FF	36x24mm	1	24mm	f/8.0
1/2.5"	5.8x4.3mm	6	4mm	f/0.5

Again, we have that f/0.5 figure, which is like impossible (or at least very difficult) to produce. Typical apertures on smartphone camera is more around f/2.0. When translated back to FF equivalent, that gives 24mm@f/12.0. That's very narrow, and very little light getting in, which explains the poor quality of the photos coming from these devices (even though they sort of mitigate it by using machine learning, AI, and other tricks).

And the aperture is fixed here. There's no altering it to try to get "closer" to FF result like we can with APS-C and 1".

Bottom line: smartphones suck, however you look at it. But advanced software can mitigate (a little) that fact, and the result is more than enough to share on Instagram and alike.

There is a But, And It's Called ISO Speed

ISO speed is a scale which tells how bright a picture ends up for a given exposure.

Exposure

Exposure is more or less the product of the relative aperture A and the time the shutter is open T.

In other words, it's how long (shutter time) we let a certain throughput of light (relative aperture) traverse the lens to reach the sensor.

In other words, it's how much light is collected.

Sensor Sensitivity

Sensor sensitivity is not the ISO scale, but rather the electrical response to a light stimuli on the sensor. Better sensors have better sensitivity. They will produce higher signal for a given amount of light hitting them.

ISO Speed

ISO Speed is more a scale to help ensure that for a given combination of A and T, a sensor will produce a picture with a given exposure.

Whatever the sensor (and its sensitivity), an 100 ISO speed yields the same exposure. Amplification of the resulting signal occurs under the hoods to achieve this.

Better sensors (with better sensitivity) obviously need less amplification to achieve a given exposure, giving that the noise is also less.

Contrary to some belief, ISO 100 is not the native sensitivity of a sensor.

How ISO Speed Affects Setup Equivalence?

Looking back at our equivalence table and adding an ISO speed column:

Format	Sensor Dimensions	Crop Factor	Focal Length	Aperture	ISO Speed
FF	36x24mm	1	24mm	f/8.0	100
APS-C 1.5	24x16mm	1.5	16mm	f/5.6	?
1"	13.2x8.8mm	2.7	8.8mm	f/3.0	?

We want to know of to fill the "?" cells to get the full equivalence of 24mm@f/8.0@ISO100 for APS-C and 1".

And no, it's not 100. If you do so, the pictures on the smaller sensors camera will end up more exposed.

As we mentioned, ISO speed scale is a mean to normalise exposures between different type of camera. We also mentioned exposure is the product of A and T. Assuming T is constant, the exposure equivalence table for the 3 setup we look at is:

Format	Sensor Dimensions	Crop Factor	Focal Length	Aperture	ISO Speed
FF	36x24mm	1	24mm	f/8.0	100
APS-C 1.5	24x16mm	1.5	16mm	f/8.0	100
1"	13.2x8.8mm	2.7	8.8mm	f/8.0	100

Two things to note:

• The DOF equivalence is lost.
• A same ISO will yield noisier results on the smaller setup. That is because less light reaches the sensor so more amplification has to be applied.

We can basically assume that half the light reaching the sensor will need twice as much amplification to achieve given exposure or ISO speed value.

Still using FF as reference, we tweak the table and get:

Format	Sensor Dimensions	Crop Factor	Focal Length	Aperture	ISO Speed	Light Quantity	Amplification factor
FF	36x24mm	1	24mm	f/8.0	100	1	1
APS-C 1.5	24x16mm	1.5	16mm	f/8.0	100	0.44	2.25
1"	13.2x8.8mm	2.7	8.8mm	f/8.0	100	0.13	7.44

To achieve the same exposure for a given (A, T), APS-C needs twice as much amplification, and 1" needs 7 times (!!) as much amplification. But Since we don't get same DOF across the different setup, we need to look at the ISO speed in that case.

Full Equivalence

Since we said the amplification factor of APS-C is 2 and the one of 1" is 7, we can fill the previously incomplete full equivalence table like this:

Format	Sensor Dimensions	Crop Factor	Focal Length	Aperture	ISO Speed
FF	36x24mm	1	24mm	f/8.0	100
APS-C 1.5	24x16mm	1.5	16mm	f/5.6	50
1"	13.2x8.8mm	2.7	8.8mm	f/3.0	14

The full APS-C and 1" equivalents of FF 24mm@f/8.0@ISO100 are

• APS-C 16mm@f/5.6@ISO50
• 1" 8.8mm@f/3.0@ISO14

Some observations:

• ISO50 is not common on APS-C (don't ask me why, I don't know!)
• ISO14 is not common on 1" (same)
• Funnily, we do have very low ISO on smartphones. That's because of their high relative apertures. Not having those low ISO values would render them useless in bright conditions.

So let's move the ISO scale up a bit, and have ISO80 placed on the 1" sensor (it's a common value we can find):

Format	Sensor Dimensions	Crop Factor	Focal Length	Aperture	ISO Speed
FF	36x24mm	1	24mm	f/8.0	500
APS-C 1.5	24x16mm	1.5	16mm	f/5.6	250
1"	13.2x8.8mm	2.7	8.8mm	f/3.0	80

Assuming same sensor and lens quality:

• I own an APS-C Fuji (X-T2) and it's base ISO is 200. I also own a Sony RX100m4. Based on these figures (which are estimates), my little Sony should easily be a match for my bigger Fuji setup for landscape photos.
• Both my Fuji and Sony lag behind a proper FF setup for landscape in bright conditions.
• If conditions aren't so bright, and we still need DOF though, then the APS-C and 1" will perform as good as the FF.
• If conditions aren't so bright, and we can compromise on DOF, then the 1" lags behind and the APS-C is a match for FF.
• Generally speaking, 1" is a perfectly fine tool for landscape. FF ISO500 equivalence is nothing these days.

Comparing With a Smartphone Again

Adding iPhone X's wide camera (FF equiv. 18mm@f/1.8), just to see how it stacks up. We set the smartphone ISO to 22 (its lowest possible value) and derive all other values from that

Format	Sensor Dimensions	Crop Factor	Focal Length	Aperture	ISO Speed
FF	36x24mm	1	28mm	f/11.0	800
APS-C 1.5	24x16mm	1.5	18mm	f/7.1	400
1"	13.2x8.8mm	2.7	10mm	f/4.0	100
1/2.5"	5.8x4.3mm	6	4.6mm	f/1.8	22

This highlights two reasons why smartphones are no match to the other formats (whatever the use case)

1. The very narrow aperture means diffraction already kicks in, degrading the quality even before the light hits the sensor. f/1.8 being a very misleading number here.
2. The high amplification needed (as implied by the FF equiv. ISO800) even at lowest ISO.