What Is Equivalence?

A standard one doesn't, but nobody forbids to write an app for a phone, or to make a DIY one, costs very little - and it can even serve as a spectrometer ;)

Beginners question, what is equivalence in practice as I see it with few words:
(but are equivalence for beginners? ;-)) are beginners reading this

Smaller sensor can equivalence bigger sensor quality "in real world" only if you need huge depth of field and high shutter speed.

Example: seascape with frozen waves in storm 1/2000 sek aperture 16 FF (very high ISO). You can equivalence do that with APC also or 1" or mobile phone.
To get favour of bigger format, ie collecting more light, you have to use slower shutter speed, but then the waves will be blurry.

You'd use f/10 on a 1.6x-crop sensor (Canon APS-C) and 0.625x the focal length for the same image. You can change shutter speed freely on either. Change to 1/1000 on either camera, and you get twice as much total light, but total light is the same with the same shutter speed. No difference between the two systems, in total available light, with the same shutter speed.

good explaining:-) yes, f/10 on 1.6crop, about f/5.6 on 1" and about f/2.0 on mobile phone?, same shutter speed, same total light as FF f/16

If beginners reading (I know you are not beginner:-) : the other direction are more difficult, if we want narrow dept of field, like f/1.4 on FF. Equivalent lens doesn't exist on tex 1"sensor. FF can do everything smaller format can, but not in the other direction. A yet disadvantage for smaller cameras with smaller sensor are they have to use mostly "wasted high shutter speeds" in good light for ordinary photography. Stupid example: using 1" camera and picture of something that doesn't moving in sunlight you still have to use shutter speed of 1/1000 on lowest iso! wasted shutter speed and IBIS/VR doesn't give us anything. In the end the only advantage for smaller cameras are weight. Sorry for my English, its not my first language

At the same angle of view, same aperture diameter, and same shutter speed, you will get essentially the same image, independent of sensor size.

Aperture diameter is the physical focal length divided by the f/stop. A 2X crop body with a 25mm at f/2 offers a 46° angle of view and a 12.5mm aperture diameter.
A full frame with a 50mm lens at f/4, also offers a 46° angle of view and a 12.5mm aperture diameter.

If both are at the same shutter speed, the resulting images will be essentially the same. Same depth of field, same framing, same diffraction, same overall image noise, and same motion blur.

Equivalence helps one determine how to take the same photo across a wide range of sensor sizes.

Old thread but interesting, nonetheless.

Some sites also mention ISO as a parameter of equivalence via the crop factor c-squared. So, for c=2, 100 ISO is equivalent to 400 ISO. But which way round is it and why?

Apologies to Bill; the question is answered in the OP:

"As just mentioned, the first photo was made with a lower exposure. That photo was also made at ISO 1600, which allows it to match the second photo in lightness. The second photo was made with a greater exposure but at ISO 400. Since both photos have the same lightness, the fifth property of equivalent photos is met. Check."

The sensor with the larger area gets the higher ISO value.

Advanced phones use processes aided by advanced algorithms that reconstruct images using automatic settings that are completely different from what a user of a classic camera would do. There are difficult situations in which phones obtain sensational images (from a technical point of view, for someone who understands these details), which would require at least tens of minutes of work for an expert using classic photographic equipment.

A reference camera and a (true) equivalent camera produce respective images (assuming using ideal lenses on both cameras) which share the following properties:

Perspective

Field of View

Defocus blur, incl.:

    Depth of Field (subject depth appearing focussed in a printed photo)

    Background blur (blur of (infinity) subjects when out of focus)

Diffraction effects (blur due to diffraction)

Detail, resolution, number of pixels

Image noise (pixel noise due to photon shot noise)

Dynamic range

For this reason, it is impossible to tell the images apart. Which in turn means that sensor size is not an image property.

www.falklumo.com/lumolabs/articles/equivalence/index.html

Well, dynamic range is still heavily restrained by post-gain read noise, and post-gain read noise is sometimes more visible than other forms of noise due to higher spatial correlation. It is also undefined how much of the DR is highly-variable headroom, and headroom is irrelevant to equivalence. I don't know exactly why everyone rushes to DR as a relevant metric. Too much is made of DR and too much reference is made to it, IMO.

I tend to agree.

Lumo says: I think we all can understand easily why perspective and field of view don't change. Now, consider the following question: How many photons are captured and make up the image, in total? Well, it is all photons flying (while the shutter is open) towards the camera from within the field of view, and hitting the lens' aperture. All of them eventually reach the sensor as it is how we define field of view here. And because we keep the lens' aperture diameter da constant, this number of photons is indeed a constant too. Which immediately yields that dynamic range and image noise is a constant too.

I don't really get that unless he is talking only about shot noise, as opposed to the ISO Standard.

oops

But in any case, I don't think noise of any kind is a parameter of equivalence, nor DR for that matter.

If it were, how would one set a virtually noise-free full-frame camera versus an early Sigma Foveon camera equivalently, or vice-versa?

Assuming that ISO is the relevant setting; at a crop factor of 1.7 the ISO factor is 1.7 squared i.e. 2.89, meaning that the equivalent Sigma ISO to 100 ISO full-frame is 100/2.89 = 35 which is not possible for early Sigmas. Going the other way to 100 ISO on the Sigma, we get 289 ISO on the FF - hardly significant for a modern FF camera.In other words, I claim that noise and DR are irrelevant to conventional equivalence.

Just so that you know, Falk Lumo is a knowledgeable German, known on DPR as 'Falconeyes'

Would bokeh equivalence (size, but not shape or quality) result from the aperture diameter being the same on each camera?

If all sensors had the same quantum efficiency, then equivalence would mean the same total light and converted electron charges for the same field. Since QE can vary, then only the number of photons projected onto the sensor, and not the actual number of electron charges, is the same in equivalence.

An interesting view of camera equivalence ...