# Zoom vs. crop

#### Doug Kerr

##### Active member
In a recent thread here there was a discussion about two ways to, from a certain vantage point, more closely frame a "distant" object:

• Use a lens with a "greater" focal length.

• Crop the taken image to produce the delivered image.

I mentioned the matter of, among other considerations, the effects of the two approaches on depth of field (and its cousin, out-of-focus blur performance, this being a factor in the properties of the "bokeh" created from out-of-focus objects).

As always, we need to remember that "depth of field" is an artificial, and rather arbitrary, construct, not a basic optical property. And a parameter of our calculation of this situation is our adoption of a value of the criterion that defines "negligible", or "acceptable" blurring: the circle of confusion diameter limit (COCDL).

Consider now two cases. In each, the camera position is the same, the camera is focused on a subject at the same distance, and the aperture (as an f-number) is the same. Suppose that we start with a 50 mm lens, and conclude that the framing of the desired scene is "not tight enough". Consider these two cases:

Case A: We replace the 50 mm lens with a 100 mm lens, and use the full frame for our delivered image.

Case B: We leave the 50 mm lens in place, but crop the taken image to a portion having half the linear dimensions of the full taken frame.

We note that:

• The resolution of the system for the subject, in terms of "lines per subject height", is half as much in case B as in case A. (This is not an announced topic of this note, but is significant nevertheless.)

• As always, the depth of field depends on which philosophy of choosing a COCDL is used.

If we choose a COCDL based on the amount of blurring that would be noticeable by a typical human observer, and assume that both images would be viewed at the same delivered size and from the same distance, then:

•• The depth of field for case B would be about twice that for case A.

If we choose a COCDL based on the amount of blurring that would "noticeably degrade" the resolution potential of the system, then:

•• The depth of field for case B would be about four times that for case A.

Now, as to out of focus blur performance: The two cases are as described earlier. We will assume the camera, in each case, to be focused at the same distance, and a consistent aperture, as an f-number. We will consider the size of the blur circle created in the image from a "background" point source at the same distance in each case.

We will compare the diameter of the blur figures in the two cases compared to the delivered image size (we can also say, compared to the size of the principal subject as seen on the delivered image).

Then:

• The (relative) diameter of the blur figure in case B would be about 1/2 the diameter of the blur figure in case A.

Interesting.

Best regards,

Doug

#### Nicolas Claris

Thanks Doug for these explanations…
I'm not sure that my English and my tech things understanding is good enough to understand the last point ('blur figure').
I'm more a 'real life' guy (which doesn't mean I'm "against"' the tech, I just don't understand although I admire the knowledge) I can tell :
2 shots (focused at the same distance, and a consistent aperture, as an f-number) with, say a FF camera (everyone does not use a MF camera
When one crop the 50 mm shot to be the same framing that the 100 mm shot, then:
- Both won't look the same
Print both at a large but common scale i.e.20 x 30″ (51cm x 76cm)
- Both won't look the same either!

#### Doug Kerr

##### Active member
Hi, Nicolas,

Thanks Doug for these explanations…
I'm not sure that my English and my tech things understanding is good enough to understand the last point ('blur figure').
Sorry. "Blur figure" is what we get in the image (usually more-or-less a circular "disk") from each point of an object that is not in focus.

If for example an out-of-focus "background" object is essentially a point (for example, a small decorative light), then what we get from it in the image is the "blur figure", whose diameter is dictated by the various optical values.

If an out-of-focus background object is of "significant" size (perhaps a leaf on a tree), then what we get from it in the image is made up of "blur figures" for each point on the object.

The diameter of the blur figure dictates the degree to which we see the out-of-focus object as "blurred". This is one of the attributes of the blurring that contributes to the overall nature of the "bokeh" we see from out-of-focus objects.

I'm more a 'real life' guy (which doesn't mean I'm "against"' the tech, I just don't understand although I admire the knowledge) I can tell :
2 shots (focused at the same distance, and a consistent aperture, as an f-number) with, say a FF camera (everyone does not use a MF camera
When one crop the 50 mm shot to be the same framing that the 100 mm shot, then:
- Both won't look the same
Print both at a large but common scale i.e.20 x 30″ (51cm x 76cm)
- Both won't look the same either!
Indeed!

Best regards,

Doug

#### Asher Kelman

##### OPF Owner/Editor-in-Chief
Doug,

Can you calculate the apertures needed to obtain the same DOF and yes, even Bokeh approximate look, with a 50 mm 1.4 or 1.2 Canon lens on a "full frame" 35 mm camera with 50 MP and then a MF camera, the Pentax 645Z with its nearly "645", (44 X 33mm), sensor and "50 MP" using a 90 mm 2.8 lens at the same distance?

Asher

#### Doug Kerr

##### Active member
Hi, Asher,

Doug,

Can you calculate the apertures needed to obtain the same DOF and yes, even Bokeh approximate look, with a 50 mm 1.4 or 1.2 Canon lens on a "full frame" 35 mm camera with 50 MP and then a MF camera, the Pentax 645Z with its nearly "645", (44 X 33mm), sensor and "50 MP" using a 90 mm 2.8 lens at the same distance?
I will work on that as soon as I get back from breakfast (we were eating all meals "out" while the kitchen is out of service for remodeling).

With regard to Bokeh, I I will be able to work on is the size of the "blur figure": (I assume that is what you meant).

And there will of course be a lot of caveats regarding the premises for comparing these two "situations".

Best regards,

Doug

#### Asher Kelman

##### OPF Owner/Editor-in-Chief
Caveats: no Petzvals or other special rendering, just assuming modern color corrected lens design with no curvature of the focal plane.

Viewing distance 6", 10" and 10 ft

Asher

#### Doug Kerr

##### Active member
Hi, Asher,

Doug,

Can you calculate the apertures needed to obtain the same DOF and yes, even Bokeh approximate look, with a 50 mm 1.4 or 1.2 Canon lens on a "full frame" 35 mm camera with 50 MP and then a MF camera, the Pentax 645Z with its nearly "645", (44 X 33mm), sensor and "50 MP" using a 90 mm 2.8 lens at the same distance?
Here we go.

Predicates

I will refer to the first setup (ff 35mm sensor size camera) as "Case A" and the second setup (44 mm × 33 mm sensor camera) as "Case B".

To get the same "scene" in the delivered image in both cases, I will assume that:

• We will take the entire frame of the Case B shot.

• We will crop out of the Case A taken frame a crop of dimensions 24.4 mm × 18.3 mm.

This is required in light of the different image magnifications in the two cases as a consequence of the different lens focal lengths. The decision to crop the case A image was dictated by the available frame sizes of the two cameras.​

Now, to the results.

Depth of Field

I will assume that we will choose our circle of confusion diameter limit (COCDL) to be the same, relative to the size of the (used) frame, in both cases. I will use 1/1400 of the diagonal of the (used) frame.

That means that if both final frames were printed to the same size, and viewed from the same distance, the limiting circle of confusion would appear the same size to the viewer in both cases.​

I will assume a focus distance of 10 m. For the case A camera, I will assume an aperture of f/4. The resulting depth of field is 7.98 m.

To get that same DoF with the Case B setup (based on the various predicates stated above) would require an aperture of f/7.3.

Blur figure diameter

Here the issue is the diameter of the blur figure for an out-of-focus object. We will "judge" blur figure diameters relative to the dimensions of the (used) frame in each case.

That means the relative diameters of the blur figures as seen by the viewer if both final frames were printed to the same size, and viewed from the same distance.​

We will again assume that both cameras are focused at a distance of 10 m, and further assume that the object whose blurred image we consider is at a distance of 100 m.

We will assume an aperture on the case A camera of f/4.0. Then, on the Case B camera, to get the same diameter of the blur figure (as seen, for example, on equal size prints viewed from the same distance,. or relative to the size of an actual subject in the scene) would require an aperture of f/7.3.

That is the same aperture required for equal depth of field with the two cameras under the predicates above.

************

Breakfast, by the way, was superb: a cinnamon raisin waffle with hashed brown potatoes, one egg (over easy), and sausage patties. This was at the lovely "Waffle and Pancake House" operated by one of our friends, a former mayor of Alamogordo.

Best regards,

Doug