Determining the size of the viewfinder image

An important attribute of a camera viewfinder (regardless of its type) is the size of its image (which we must state in angular terms).

This is almost never mentioned in camera specifications or reported in camera test reports.

Directly measuring the viewfinder image angular size is tricky to do without instruments we rarely have at our disposal.

But we can easily determine the viewfinder image angular size if we know the image magnification of the viewfinder (often stated in specifications and test reports), the lens focal length upon which that is predicated (rarely stated), and the size of the camera's frame (sensor).

In full-frame 35-mm film cameras and digital SLRs with that same frame size, the convention is to predicate the viewfinder image magnification on a 50 mm lens focal length. Curiously, the same is often true for cameras in with frame sizes such as those often called "APS-H" and "APS-C".

With other frame sizes there is no convention. And often with electronic viewfinders, the magnification is rarely even stated.

But a simple test can give us all the information we need to determine the (angular) size of the viewfinder image without measuring it directly.

Note that the image magnification of a viewfinder usually varies with eye position along the axis, and the angular size of the also varies with eye position. So we must decide for which eye position we want to know the angular size of the viewfinder image, and do our testing (as described below) with that same eye position.

The procedure requires the use of a zoom lens.

We will need to know the diagonal size of the camera's frame (but see below for an alternative).

The procedure is as follows:

1. With a fairly distant object as the "test subject" (and focus on it), adjust the focal length (zoom setting) until the apparent size of the test subject as seen through the viewfinder is the same as the test subject as seen directly ("around the camera").

2. If the zoom lens has a reliable and fairly precise focal length scale, not the indicated focal length. If not, fire the camera without allowing a change in zoom setting (no need to have the camera aimed at any particular subject then) and determine the focal length from the Exif metadata.

3. Now, the diagonal (angular) size of the viewfinder image is calculated as:

Av = 2 arctan(d/f1)

where Ay is the diagonal (angular) size of the viewfinder image, d is the diagonal size of the frame, F1 is the focal length we determined above, and arctan is the trigonometric arc tangent (inverse tangent) function. The values d and f1 must be in the same units (perhaps millimeters).

Of course is we want the result in degrees, we must use the form of the arctan function that gives the result in degrees.

If we do not know the diagonal size of our frame

We can use the same procedure, but for d use 43.3 mm (the full-frame 35-mm frame diagonal size) and for f1 use the full-frame 35-mm equivalent focal length of the focal length determined in step 1 above.. Perhaps your viewing software will report that as an adjunct to the Exif metadata, or perhaps you know the equivalent focal length factor for your camera's frame size and can apply that to the reported actual focal length.

Best regards,

Doug

Now why didn't I know that?
Thanks, Doug. You have just added another level to my ignorance.

Hi, Tom,

Tom dinning said:

Now why didn't I know that?
Thanks, Doug. You have just added another level to my ignorance.

Click to expand...

Well, we do the best we can with what we have to work with!

Best regards,

Doug

Tom dinning said:

Now why didn't I know that?
Thanks, Doug. You have just added another level to my ignorance.

Click to expand...

I've got a simpler way to assist your ignorance Tom… You take the camera you're interested on, try the lens you mostly use or two of them on it …and see if you like the view! …If you find my assistance helpful, you may buy me a drink!

Theodoros Fotometria said:

I've got a simpler way to assist your ignorance Tom… You take the camera you're interested on, try the lens you mostly use or two of them on it …and see if you like the view! …If you find my assistance helpful, you may buy me a drink!

Click to expand...

Gladly, Theo. now you're talking my language.
What's your poison?

Tom dinning said:

Gladly, Theo. now you're talking my language.
What's your poison?

Click to expand...

Whatever is yours… no, wait! …whatever makes the viewfinder wider!

I just discovered three errors in my original note. They are corrected here in red.

My apologies for any confusion this might have caused.

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

An important attribute of a camera viewfinder (regardless of its type) is the size of its image (which we must state in angular terms).

This is almost never mentioned in camera specifications or reported in camera test reports.

Directly measuring the viewfinder image angular size is tricky to do without instruments we rarely have at our disposal.

But we can easily determine the viewfinder image angular size if we know the image magnification of the viewfinder (often stated in specifications and test reports), the lens focal length upon which that is predicated (rarely stated), and the size of the camera's frame (sensor).

In full-frame 35-mm film cameras and digital SLRs with that same frame size, the convention is to predicate the viewfinder image magnification on a 50 mm lens focal length. Curiously, the same is often true for cameras in with frame sizes such as those often called "APS-H" and "APS-C".

With other frame sizes there is no convention. And often with electronic viewfinders, the magnification is rarely even stated.

But a simple test can give us all the information we need to determine the (angular) size of the viewfinder image without measuring it directly.

Note that the image magnification of a viewfinder usually varies with eye position along the axis, and the angular size of the also varies with eye position. So we must decide for which eye position we want to know the angular size of the viewfinder image, and do our testing (as described below) with that same eye position.

The procedure requires the use of a zoom lens.

We will need to know the diagonal size of the camera's frame (but see below for an alternative).

The procedure is as follows:

1. With a fairly distant object as the "test subject" (and focus on it), adjust the focal length (zoom setting) until the apparent size of the test subject as seen through the viewfinder is the same as the test subject as seen directly ("around the camera").

2. If the zoom lens has a reliable and fairly precise focal length scale, not the indicated focal length. If not, fire the camera without allowing a change in zoom setting (no need to have the camera aimed at any particular subject then) and determine the focal length from the Exif metadata.

3. Now, the diagonal (angular) size of the viewfinder image is calculated as:

Av = 2 arctan(d/2f1)

where Av is the diagonal (angular) size of the viewfinder image, d is the diagonal size of the frame, f1 is the focal length we determined above, and arctan is the trigonometric arc tangent (inverse tangent) function. The values d and f1 must be in the same units (perhaps millimeters).

Of course is we want the result in degrees, we must use the form of the arctan function that gives the result in degrees.

If we do not know the diagonal size of our frame

We can use the same procedure, but for d use 43.3 mm (the full-frame 35-mm frame diagonal size) and for f1 use the full-frame 35-mm equivalent focal length of the focal length determined in step 1 above.. Perhaps your viewing software will report that as an adjunct to the Exif metadata, or perhaps you know the equivalent focal length factor for your camera's frame size and can apply that to the reported actual focal length.

Best regards,

Doug

The premise of my original note is that the "size" of a viewfinder image should be reckoned as the angular subtense of its diagonal dimension to the viewer's eye.

But a complication would seem to be that the viewer may place his eye over a range of axial positions (the range being greater the larger the "eye relief" parameter of the particular viewfinder system).

Thus we might imagine that the angular subtense of the viewfinder image would vary with the user's choice of eye position - smaller as the user moves away.

That would then suggest that it would only be meaningful to state the size of the viewfinder image in angular terms if we prescribed a reference eye position.

But an interesting matter intervenes to eliminate this complication.

Although the actual image (such as on an EVF screen) is only a fraction of inch away in space, as viewed through the eyepiece optical system (a small telescope), in most viewfinders, with the default setting of the vision correction adjustment, the image that the user sees appears to be at a distance of about 1 meter (1000 mm).

We usually only think of this in terms of its implications on focal accommodation by the user: he must focus on the image as if it were at a distance of 1 meter (which is usually the most "comfortable" to attain, thus that choice for the design). But usually, this equally applies to the apparent position of the entire viewfinder image "frame".

Thus, if we begin by regarding the viewfinder image with our eye held as "close" as it practical, and then move back 10 mm (let's assume we can do that and still see the whole viewfinder image through the "port"), won't any feature of the viewfinder image, or the image frame itself, now subtend a smaller angle?

Yes, one whose half-angle tangent is just about 0.99 times * that of the original subtended angle:

That is an almost imperceptible change.

Thus the notion that the "size" of the viewfinder image can be characterized in terms of the subtended angle of its diagonal remains valid without practical need to concern ourselves with eye position.

The calculation I gave above (once I fixed my typographical errors!) takes that outlook.

Best regards,

Doug

This is to give more general equations for determining the size of the viewfinder image, and to give greater insight into what "size" is meant by the result.


Background

Note that we characterize the "size" of the viewfinder image (more later on just what that is) in terms of the angular size of its diagonal to the viewer's eye.

It is tempting to think that this angular size depends on the axial position of the viewer's eye. It does indeed, but only very slightly, since the axial location of the finder image (a virtual image) is typically one meter or so forward of the eyepiece port. Thus we can ignore eye position.

The rectangle whose size angular is given by the equation below is the portion of the viewfinder image that corresponds to the portion of the scene that will be captured by the sensor.

For many viewfinders (with "coverage" less than 100%) this is actually a rectangle larger than the whole image generated by the viewfinder (part of the captured portion of the scene is not visible).

For other viewfinders (such as the "bright frame" type and their equivalents), that is a rectangle smaller than the whole image generated by the viewfinder (more of the scene is visible - albeit outside a frame line - than is captured).

I will call that rectangle the viewfinder frame rectangle.


The equations

The equation is as follows:


where A is the angular size of the diagonal of the viewfinder frame rectangle, m is the magnification of the viewfinder with a lens of (actual) focal length f in place, D is the diagonal dimension of the sensor, and arctan is the arc tangent (inverse tangent) function.

If we want to get A in degrees, then we must use the form of the arc tangent function that gives a result in degrees.

An alternative form, working in terms of "ff35 equaivelent focal length", is:


where A is the angular size of the diagonal of the viewfinder frame rectangle, m is the magnification of the viewfinder with a lens of ff35 equivalent focal length F in place, and arctan is the arc tangent (inverse tangent) function.


Typical results

To give some idea of the results for various cameras:

For the Canon EOS 6D, A is 34.2°.
For the Canon EOS 40D, A is 28.8°.
For the Canon PowerShot G16, A is 22.3 °.
For the Fujifilm X100 and X100S in OVF mode, A is 34.3° (likely EVF mode as well).


Best regards,

Doug