Doug Kerr
Well-known member
People often want to speak of the "reach" of a lens, perhaps to recognize the impact of a certain focal length lens as used on a camera with a certain sensor size. Intuitively, the number should increase with focal length, and for a given focal length, should decrease with sensor size. In fact, if that was all we needed to do, the "full-frame 35-mm focal length" would be a credible metric for "reach".
But why do we want a lens of "longer" focal length on a camera for certain work?
Well, the simplistic reason (recognized in the above concept of "reach") is to make the field of view smaller. But is that really an advantage that warrants a longer focal length lens? After all, we can do that by cropping the image.
The usual actual reason (although we rarely articulate it) is to have a given subject covered by as many lines of resolution as we can, so long as the entire desired scene is included in the field of view. Increase in focal length increases that, proportionately to focal length if the longer focal lens does not significant degrade the overall camera resolution (as expressed, say, in lines per picture height).
So perhaps our metric for "reach" should reflect our success in achieving that objective (not just in making the field of view smaller).
To quantify this, we must think in terms of the number of lines of resolution embraced by a certain distance across a subject at a certain distance from the camera.
But, to generalize it, that turns out to be equivalent to a certain number of lines of resolution per unit of angle - the angular resolution of the camera with the lens of interest in place (and that is with resolution defined in a way that the number is larger for "finer" resolution - often angular resolution is defined the other way up).
Even though "line pairs" would be better, from a theoretical standpoint, than "lines" (it can be related more directly, for example, to the matter of MTF) I have suggested a metric based on "lines" of resolution. The reason is that there is a (very) approximate equivalence between lines of resolution (per picture height, for example) and pixels.
Now what unit should we use for our metric? We could use lines per radian. But the number would turn out to be very large for most cases we will work with. For example, if we assume a sensor 24 mm high, a resolution of 2000 lines per picture height, and a focal length of 200 mm, the "reach" would be about 16,700 lines per radian.
We could also do it in terms of lines per degree. For the example above, the "reach" would be about 290 lines per degree. That's easier to write. So why not use lines per degree.
Now, if we instead mounted a 400 mm lens, and the resolution at the sensor did not decline because of it, our reach would be about 580 lines per degree.
But if the optical performance of our 400 mm lens was so poor that the camera resolution with it in place was only 1500 lines per picture height, now our reach would be only about 435 lines per degree (only an increase of 1.5 times over the 200 mm lens).
Best regards,
Doug
But why do we want a lens of "longer" focal length on a camera for certain work?
Well, the simplistic reason (recognized in the above concept of "reach") is to make the field of view smaller. But is that really an advantage that warrants a longer focal length lens? After all, we can do that by cropping the image.
The usual actual reason (although we rarely articulate it) is to have a given subject covered by as many lines of resolution as we can, so long as the entire desired scene is included in the field of view. Increase in focal length increases that, proportionately to focal length if the longer focal lens does not significant degrade the overall camera resolution (as expressed, say, in lines per picture height).
So perhaps our metric for "reach" should reflect our success in achieving that objective (not just in making the field of view smaller).
To quantify this, we must think in terms of the number of lines of resolution embraced by a certain distance across a subject at a certain distance from the camera.
But, to generalize it, that turns out to be equivalent to a certain number of lines of resolution per unit of angle - the angular resolution of the camera with the lens of interest in place (and that is with resolution defined in a way that the number is larger for "finer" resolution - often angular resolution is defined the other way up).
Even though "line pairs" would be better, from a theoretical standpoint, than "lines" (it can be related more directly, for example, to the matter of MTF) I have suggested a metric based on "lines" of resolution. The reason is that there is a (very) approximate equivalence between lines of resolution (per picture height, for example) and pixels.
Now what unit should we use for our metric? We could use lines per radian. But the number would turn out to be very large for most cases we will work with. For example, if we assume a sensor 24 mm high, a resolution of 2000 lines per picture height, and a focal length of 200 mm, the "reach" would be about 16,700 lines per radian.
We could also do it in terms of lines per degree. For the example above, the "reach" would be about 290 lines per degree. That's easier to write. So why not use lines per degree.
Now, if we instead mounted a 400 mm lens, and the resolution at the sensor did not decline because of it, our reach would be about 580 lines per degree.
But if the optical performance of our 400 mm lens was so poor that the camera resolution with it in place was only 1500 lines per picture height, now our reach would be only about 435 lines per degree (only an increase of 1.5 times over the 200 mm lens).
Best regards,
Doug