depth of field in different cameras

[Wampatom]

Does anyone know how depth of field relates to the size of the image plane, focal length, and the f stop? With my Nikon 990 I seem to get good depth of field at about f8.8 (the minimum f stop in macro mode). With my D100 and 105mm micro lens I seem to have to stop the lens way down, f45 for example, to get similar depth of field. (I haven’t actually measured it, this is just my impression.) There are two differences—the size sensor is much smaller in the 990 and the lens has a shorter focal length. For simplicity, lets break the problem up into two parts.

1) Assume I am using the same camera with two lenses, one with a focal length of 105 mm and the other 52 mm. I am taking a picture of the same subject and I want it to completely fill the image. Obviously I will have to get closer with the 52mm lens. At the same f stop will I have better depth of field with the 52 mm lens?

2) Assume I am using different cameras. The small camera has a sensor half the size of the large camera. I am taking a picture of the same subject and I want it to completely fill the image. I also want to be the same distance from the subject. To do this the lens on the small camera has to be half the focal length to the large camera. Assume a 52.5mm lens on the small camera, a 105mm lens on the large camera. At the same f stop will I have better depth of field with the small camera?

I have asked these questions to several people and gotten contradictory answers. Fire away.

 

[Anonymous]

1) Depth of field is inversly proportional to focal length. Bigger depth of field at smaller focal lenghts.

2) Dunno. All my photo books were printed way before digital cameras came out.

(I'll check on the image-capturing-size question in relation to 35mm to say 8x10 film.)

B

 

[Anonymous]

now that I re-read the second question, the same answer aplies to both.

The shorter lens will give you greater DOF.

B

 

[Anonymous]

now that I re-read the second question, the same answer aplies to both.

The shorter lens will give you greater DOF.

Your exposure will be different too. Twice the light will be getting to the sensor in the closer camera. Light follows and Inverse-square rule. Twice the distance away from a subject, 1/4 the amount of light will hit the film. So, you're gonna have to open up the shutter two full stops.

if the far camera is shooting f4 @ 125, the closer one will have to be f4 @ 500 for the same exposure, but you'll still have greater DOF in the closer camera.

B

 

[mkirda]

Does anyone know how depth of field relates to the size of the image plane, focal length, and the f stop?

All consumer-level digicams have a small sensor, much smaller than 35mm.
Because of this, the DOF is greater.

And, yes, stopping down to 8.8 on a digicam is like stopping an SLR with 105mm macro lens down to f16 at least, maybe f22.

This is actually the biggest advantage to a digicam, IMO, besides film costs.

Regards.
Mike Kirda

 

[Wampatom]

If a smaller sensor provides a greater depth of field this is a huge advantage for macro work.

 

[jamesw]

I love answering this one!

The depth of field is a function of the focal length and the aperture ONLY. It has nothind DIRECTLY to do with the size of the recording medium (sensor or film size).

However, since digital cameras sensors are smaller than film, the lenses have to have MUCH shorter focal lengths to compensate.

What this means is that the depth of field goes up because the focal length goes down because the sensor is very small.

In fact, that's why your consumer camera's have a maximum f-stop of like f11. At that f-stop and focal length, the aperture is TINY. If the aperture gets any smaller than that, you get diffraction and a blurry image.

HTH
James

HTH
James

 

[Wampatom]

OK. Thank you for the responses. Between these and some searching on the internet I think I understand. I am about to repeat what I think I know. I am not writing as an authority, rather, to make sure my understanding is consistent.

I think part of the confusion with depth of field is that it is not well defined. Here is the definition I found on the internet:
“The distance between the nearest and farthest points that appear in acceptably sharp focus in a photograph. Depth of field varies with lens aperture, focal length, and camera-to-subject distance.”
To answer my questions above you have to define what you mean by acceptably sharp when you are using different cameras. The following web site is quite complete. It has a history of the measurement.
http://www.luminous-landscape.com/tutor ... /dof.shtml
If you would like all the equations:
http://dfleming.ameranet.com/equations2.html

Traditionally, depth of field measurements are based on the Circle of Confusion (COF). See the link for details, but COF is essentially how large an out of focus spot you can have on a negative, such that, when it is blown up your eye can’t detect it is out of focus. The problem with this definition is that it depends on how far you enlarge a negative. The standard enlargement for 35mm film is 5x7 inches. Now when you talk about depth of field in medium format cameras sometimes the same size picture is assumed, sometimes it is assumed you will enlarge to get a bigger picture. This gives different answers.

In my summary below I am assuming we are taking the whole negative or digital image and looking at it on the same monitor. I am not going to discuss absolute values just relative changes. My summary is approximate, see the equations or online calculator for an exact solution.

1) Change In Sensor Size With a Corresponding Change in Lens Focal Length = Inverse Change In DOF

This is covered in the response by Mike Kirda and James Wiseman. Here, assume you are comparing different cameras with different sensor sizes. You are changing the sensor size by s. You must also assume you are changing the lens on the new camera so your picture covers the same subject at the same distance. To match the lens, the focal length will have to change by s as well. (Assume distance to subject and f-stop remain constant). The resulting depth of field will change by approximately 1/s.

For example compare a 35mm camera with a 50mm lens to a medium format camera with a film size of 60mm. To get the approximately the same images the camera you will need a lens with a focal length of 85mm. The depth of field in the medium format camera will be about half that of the 35mm camera.

Thus, since a prosumer digital camera has a sensor about a quarter the size of a 35mm camera, it has 4 times the DOF (with a corresponding lens and the same f-stop). As Mike and James pointed out this is why I get better DOF with my Nikon 990.

2 ) Change In Sensor Size Alone=Proportional Change In DOF
If the sensor size is changed by s, the DOF is also changed by s. (Same lens, distance to subject and f-stop).

3) Change In Distance To Subject=Squared Change In DOF
Assume the distance to a subject is increased by d. The camera, lens, and f-stop remain constant. Then the DOF changes by approximately d squared.

4) Change In Lens Focal Length = 1/Square Change In DOF
You change lenses so the focal length changes by L. Assume the same sensor, distance from the subject, and f-stop. The DOF will change by approximately the inverse of L squared.

5) Change In Lens Focal Length And Move So The Subject Remains The Same Size On The Sensor = No Change In DOF
This is the answer to my original question 1. This means I can use my 105mm macro, and as long as the subject fills the frame, it has the same DOF as a 20mm lens (no change in sensor or f-stop). Here is a link that gives a beautiful example of this:
http://www.luminous-landscape.com/tutorials/dof2.shtml