## Confusion About f Number Relation With Sensor Size

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lonepal
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### Confusion About f Number Relation With Sensor Size

Hi;

I have a confusion about f numbers of lenses and if it changes according to sensor size

For example;

We have a 45mm f/1.8 lens for m4/3 and we also have a 45mm f1.8 lens for FF.

They both have same FL and f number.

If we want to take the same photo at same light conditions, do the exposure times will be same or because of 2 crop factor m4/3 camera will have the half exposure time of FF camera? (Same ISO)

For example;

FF Camera : 1/160s
m4/3 Camera : 1/160s

or;

FF Camera : 1/160s
m4/3 Camera : 1/80s

Thanks!
Regards.
Omer

RobertOToole
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Hi Omer,

You would need a 22.5mm f/0.9 lens to get an image that looks the same as the FF camera.

If you want to read a quick post about it, this is a good one:

https://www.dpreview.com/learn/27991004 ... a-nutshell

dickb
Posts: 275
Joined: Mon Jul 05, 2010 1:54 am
Hi,

FF Camera : 1/160s
m4/3 Camera : 1/160s

When you look at the definitions of the terms you are using it may become more easy to understand. The f number is the focal length (in mm) of the lens divided by the linear aperture (in mm) of the lens. So the f number tells you how large the aperture opening is in relation to the focal length.

The problem with comparing lenses between different sensor sizes is that the focal length in mm is not a very useful measurement. Ideally you would compare lenses by their field of view (FoV). When you put the same 45mm lens on a FF camera and a m4/3 camera, the latter uses only the middle bit of the projected image. To get the same FoV on both cameras you would need a 90mm on FF and a 45mm on m43.

Camera and lens manufacturers would have you believe that a 45mm f/1.8 when used on a m43 camera turns into a 90mm f/1.8. This is not true. If you double the focal length to get an equivalent field of view you must also double the f number to get the equivalent depth of field (DoF). It would act as an 90mm f/3.6 lens on FF with regards to FoV and DoF.

For light measurement, this is not relevant though. F numbers and ISO are defined to be the same for all focal lengths and all sensor sizes. If you measure 1/160s at f/1.8 and ISO 100, than all cameras should give you properly exposed photos at 1/160s at f/1.8 and ISO 100.

The smaller the sensor, the poorer the image quality at a given ISO though. Assuming a similar sensor technology, ISO 100 on a m43 camera can be compared to ISO 400 on a FF camera.

In conclusion, at a given FL, f number and ISO you get less FoV, more relative DoF and poorer image quality the smaller your sensor is.

That being said, there are of course reasons why not everyone is hauling medium format digital cameras around. Smaller sensors are cheaper, the sensor technology keeps improving and not everyone needs/wants razorthin DoF.

RobertOToole
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dickb wrote:Hi,

FF Camera : 1/160s
m4/3 Camera : 1/160s
Problem with this is Omer mentions same f/stop, SS, and ISO.

Correct me if I am wrong but the same f-number, both cameras set to f1.8, the full frame camera will see four times as much light as a camera with a m4/3 sensor, since it is exposed to the same light-per-unit-area but has a sensor with four times the area.

The M4/3 f1.8 lens shot wide open will be the equivalent of f/3.6 reaching the full frame sensor.

So when you shoot these two different sensors with the same shutter speed, f-number and ISO setting, the camera with the smaller sensor has to produce the same final image brightness (which the ISO standard demands) from less total light so the signal to noise ratio will be higher, or nosier.

The only way to make the same image is with a 22.5mm f/0.9 lens on the M4/3 body.

BTW, The Forum software keeps making f/1.8, f/1,8,f1.8 into a smily face with sunglasses!

dickb
Posts: 275
Joined: Mon Jul 05, 2010 1:54 am
Robert, you are not wrong, you are saying part of the same thing I said.

Omer asked about the same f/stop, shutter speed and ISO. You get equally bright images on any sensor size, but not images of equal quality and DoF.

Your example results in getting almost the same image on FF and m43, for instance:
FF 45mm f/1.8 1/160s ISO 400
m43 22.5mm f/0.9 1/160 ISO 100

This is true. But Omer asked about equally bright photos at different fields of view, so for that my previous statement is correct. My first post wasn't a response to your post, I was just very slow typing mine..

rjlittlefield
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### Re: Confusion About f Number Relation With Sensor Size

Another take on the question...

Omer wrote
We have a 45mm f/1.8 lens for m4/3 and we also have a 45mm f1.8 lens for FF.

They both have same FL and f number.

If we want to take the same photo at same light conditions...
Given a 45 mm lens on both cameras, the only way to take the same photo is to crop to the center 1/2 x 1/2 of the FF sensor.

If you do that, then you are effectively using the same sensor area in both cameras, by throwing away 3/4 of the information captured by the FF sensor.
... do the exposure times will be same or because of 2 crop factor m4/3 camera will have the half exposure time of FF camera? (Same ISO)
The exposure times will be the same. Also the image noise will be the same (per same area on subject). And if you render the two images (m4/3 and cropped FF) at the same size, they will have the same DOF.

On the other hand, if you want to use the whole FF sensor, and also take the same photo, then you have to adjust the lens FL to capture the same FOV, and you have to adjust the lens aperture so that the entrance pupil diameter is the same. If you're shooting a scene at long distance, that could be accomplished either by sticking a 22.5mm f/0.9 lens on the M4/3 body (matching 45mm f/1.8 on FF) or more practically by sticking a 90mm f/3.6 lens on FF (matching 45mm f/1.8 on M4/3).

Assuming there is something moving in the scene, then to take the same picture you also must use the same shutter speed, so this will require setting ISO on the FF camera to be 4X higher than on the M4/3, for example ISO 400 on FF versus ISO 100 on M4/3.

All this is the essence of what is called equivalent images analysis. If you want the same image from two different sensor sizes, then you have to shoot through an entrance pupil that has the same size and position, for the same amount of time, using a lens FL that gives the same FOV. This implies that the effective f-number (as seen by the sensor) will scale in proportion to the linear size of the sensor, and the ISO setting will scale in proportion to the area of the sensor. The resulting DOF, diffraction, and shot noise per subject area will all be the same in both cases.

One corollary of this analysis is that if you want to get less noise from the FF sensor, then you cannot "take the same photo at same light conditions". You have to either use a longer exposure time (potentially sacrificing motion blur), or a wider entrance cone (definitely sacrificing DOF), or increase the illumination intensity by adding light. The advantage of a larger sensor is that it gives you more freedom to do these things.

--Rik