Camera Physics Question

[Zach Matthews]

Can anyone explain why a full frame chip causes the background to be more out of focus at a given f/stop (say f/2.8) than a smaller chip (i.e. DX in Nikon-speak?)

[Ben Cochran]

Zack, it has to do with the “Circle of Confusion:CofC” aka “Circle of Incidence”. The larger the sensor the higher or larger the CofC and this is the reason why P&S sensors have such a shallow hyperfocal distance. This is also the reason why there are great applications for the DX over the FX and vice versa. Hope this helps.

[Mike McKeown]

Zack, it has to do with the “Circle of Confusion:CofC” aka “Circle of Incidence”. The larger the sensor the higher or larger the CofC and this is the reason why P&S sensors have such a shallow hyperfocal distance. This is also the reason why there are great applications for the DX over the FX and vice versa. Hope this helps.

Thanks Ben, took the words right out of my mouth.

[Zach Matthews]

Wow.

http://en.wikipedia.org/wiki/Circle_of_confusion

That is one hell of a Wikipedia entry.

Thanks guys.

[kurt budliger]

Woah, that link makes my brain hurt this early in the morning Zack.

Here’s a good one as it specifically relates to this discussion

http://www.bobatkins.com/photography/technical/digitaldof.html

[Tim Schulz]

As Bob Atkins explains, when you set the field-of-view equal for full-frame and cropped sensors, then the full frame sensor will need a larger focal length than the cropped sensor, and that will result in less depth of field, or more out-of-focus blur.  

Reading the links on this, though, one might come away thinking that larger sensors result in larger ‘circles-of-confusion’.  That would not be correct.  That is only the case for defocus blur with equal field-of-view.  ‘Circle-of-confusion’ blur can also result from fundamental diffraction limits, and these are smaller (relative to the scene) for full-frame cameras than they are for cropped sensor cameras.  

The ultimate resolution for a full-frame sensor camera will always be better than that for a cropped sensor camera (for equal field-of-view and f/#) because the ‘circle-of-confusion’ due to diffraction is larger (relative to the features in the scene) for a cropped sensor than it is for a full-frame sensor.   And with the large number of pixels in modern sensors, this matters.  

As a rule-of-thumb, the size of the diffraction circle-of-confusion on the sensor is the f/# times the wavelength of the light.  To make an easy calculation, use 1/2 micrometer for the wavelength of light, and the diffraction circle-of-confusion (measured in micrometers) is one-half the f/#.   When this is larger than the size of the pixels on the sensor, then you will start to see diffraction blur.  This will happen for a smaller sensor much more readily than it will for a larger sensor.

The diffraction circle-of-confusion at f/8 has a width of about 4 micrometers.
For a 36 millimeter sensor, this is about 1/9000 of the width of the sensor.  This means the sensor could resolve about 9000 pixels across its width.  
For a 24 millimeter sensor, this is about 1/6000 of the width of the sensor.  This means the sensor could resolve about 6000 pixels across its width.
For an 8 millimeter sensor (point-and-shoot), this is about 1/2000 of the width of the sensor.  This means the sensor could resolve about 2000 pixels across its width.  More pixels will start to reveal the blur caused by diffraction.

Sorry for getting a little off topic, but discussions about circles-of-confusion can quickly become causes-of-confusion.  I hope I haven’t been a creator-of-confusion with this post.  
😉
Cheers,
Tim

[Ben Cochran]

Tim, I am by no means an expert in physics and with my limited knowledge, I needed to try and find a way to make this, Prozac laced CofC knowledge, a controllable an applicable tool.

I may have completely missed the boat on this, taken Zanax as opposed to Prozac, but this is my understanding and the mapping guidelines that I use for mapping out “some” shots. Lets say that I want a shot with a DOF that is no greater than 4’ and I only have 10’ of space. It is vital that I use primes so, with the FX format I can use a 50mm prime and achieve a DOF at 3.75’; the CoC is .03mm. In order to get the same frame on a DX, I would have to use a 31mm prime (no such creature) so, I would have to use an off brand 30mm prime (good luck finding a Nikon one). My DOF would now be 7.63’ and the CofC is .02mm. Clearly the DX format will not work, for the mapped out shot.

Lets say that I have more room and use the same 50mm prime on both formats. I would have to stand at 16’ to subject, with the DX format and my DOF is now 6.47’ and, of course, the CofC is a constant .02mm. Again, does not meet the requirements of the shot.

Lets now say that I want to shoot and frame a shot with a hyperfocal length at aprox. 80’. Using the same 50mm prime, I can reach hyperfocal at 81.5’ with the DX format. For the same frame and distance, I would have to use an 80mm on the FX format and my hyperfocal is now 139.1’. Making the DX format a better choice.

Granted there are ways to work around this, like cropping in post but that is at sacrifice and for assignment work, might as well nail my foot to the ground. As I said, I am not a physics major, just a photographer. You clearly have a much better knowledge of the physics behind optics law. Am I missing something here, as this is a topic that can require medication?  😀 I say this all respectfully as I only focus on the applicable knowledge that applies to the business side of my tools and not so much into all of the technical details that would not serve my business side any. Meaning, I don’t manufacturer cameras, just use them. You clearly understand the physics better than I so, thanks for any and all information. 🙂

[Zach Matthews]

What it boils down to is, if I want a camera that throws the background more out of focus at, say, f/2.8, I need to go with a full frame camera, correct?

That was my experience playing with a Nikon D700.

[Ben Cochran]

Exactly!! That is how I incorporate the optics law into my photography and the best part. It keeps your other DX format as a very viable tool! 🙂

In addition, not only is the chip larger, there is a change in the size of the CofC and this is what really made the difference.

[John Bennett]

Pretty much Zack but its usually cheaper (and more versatile) imo to buy a good lens fast lens with a longer focal length. Its also why PnSs make decent macro camera’s. Really what it boils down to is more DoF for smaller sensors all else being equal. Also keep in mind that the separation between your subject and the BG plays a big role.

The tulips here are about 1 foot into the BG

BG here is about 3 feet away

and here about 100 feet

So really when going for shots that throw the bg way out.
focal length, f/stop and distance to subject determine DoF.
BG distance *from* subject also Quality of glass also plays a big role

All of the above were shot with the 85 f1.2 wide open.
Less FoV than a 50mm but better separation/isolation of the subject

Thats why I’ll likely never buy a 50mm and stick with my 24-70 at f2.8 when I want to throw the bg out, or now the 85 f1.2. On my 1D bodies (1.3 or apc sized sensor). 100mm (or greater) macro lenses are also fantastic for these kinds of shots.

[Ben Cochran]

Keep in mind John and I think that this is what Zack was talking about. If we use a 50mm 1.4 (which is an awesome lens in our Nikon world! 🙂 ) and want the same frame size, with both DX and FX sensors. The DOF will be shallower on the FX, compared to the DX. Granted there are work arounds but there is a point of “no” work around.

Think I saw your same photographs down in Peru, that is where that other web sites administrators are;)

[Tim Schulz]

Zach,

If you took a photo with the same lens (50mm, f/1.8) on FX and DX cameras, then either the distance to desired focus or the field-of-view would need to be different.  

If the distance to desired focus is the same, then the field-of-view will be different.  In this case, both sensors will show the same defocus blur, but the DX sensor will record an image that is cropped relative to the FX sensor.  

If you want the field-of-view to be the same, then the distance to desired focus will need to increase by 50%.  If you were 2 meters away, you’d have to move back another meter.  If you were 4 meters away, you’d have to move back another 2 meters.  In this case, the size of the ‘circle-of-confusion’ blur for objects that are not in focus will decrease by a factor of about 1/2 for objects close to the focus to about 2/3 for objects that are far from the focus.  In short, the blur for objects in the scene that are close to focus will be 1/2 as much because you will have had to move farther away.  

So, yes, you will get more out-of-focus blur with a full-frame sensor because  you will be able to stay closer to the focused object for a desired field-of-view.  If you use a cropped sensor and want the same field-of-view, then you’ll have to move back or shorten the focal length.  But both of these things will reduce the out-of-focus blur.  (As a rule-of-thumb, the out-of-focus blur is proportional to the square of the focal length, and inversely proportional to the square of the distance to the focused object.)  

Ben and John:  based on the photos you take, you clearly have a sound working understanding of these principles.  

Cheers,
Tim

[jacob g]

If you really want to have fun, go shoot some medium format for the day. Razor thin depth of field with beautiful bokeh.

[Chad Simcox]

I recently bought a Mamiya RB67 (6×7 cm frame size) for this reason

http://society6.com/grainfarmer Fly Fishing and Landscape open edition Photography prints.

http://grainfarmer.vsco.co/ iPhone photos
http://instagram.com/chad_simcox Instagram

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