"Normal" focal length - how to mimic the human eye

[sebasj]

I have read that approximately a normal lens for a given sensor format is one whose focal length corresponds to the diagonal of the format, since this has a strong relation with the field of view of the human eye.

So, even if pretty much every format has a different normal lens (80mm for medium format, 50mm for 35 mm format, 28mm for 110 format for example), all of them do two things: they reproduce the field of view of the human eye and they also reproduce the relation of sizes between objects in the frame as they are seen by the human eye. Am I correct here?

When I think of a DSLR, I can't find a lens that both reproduces the field of view of the human eye AND reproduces also the relations of sizes between objects as I see them. The two options I think about are a 30mm and a 50mm lens. The 30mm reproduces the field of view correctly: I see the same field of view as if I'd have a 50mm on a 24x36mm camera. However, the relation of sizes between objects is not the same, and I can clearly see that I'm using a wide angle lens. Now, with the 50mm, the field of view is much smaller, approximately what would be the field of view of a 75-80mm lens on a 24x36mm format, but the relation of sizes between objects in the picture is just as I saw it, and just as if I had been using a 50mm on a 24x36mm camera.

When I look at different format systems, I can see that other things have been modified on them in order to reproduce the field of view and perception of the human eye -lens design, camera design, etc.-. The APS-C DSLRs are only a 24x36mm camera with a smaller sensor. When I try a 30mm lens on my camera, I can clearly see that I'm using a wide angle and not a "normal" lens. When I try a 50mm, at first glance you can say that it gives a " short telephoto lens" feeling, but none of my pictures taken with the 50mm appear as if they would have been taken with a short tele, they all indeed look like taken with a normal.

It seems that, when we're discussing which is the normal lens on an APS-C sized sensor DSLR, it comes down to what the photographers perceives as "normal", if the reproduction of the field of view, or the reproduction of the relation of sizes between objects in the frame.

How is the normal lens for an APS-C sized sensor camera determined?

Thanks in advance, this question is itching my mind and I can't seem to arrive to a good answer.

Best regards,
Sebastián

[McQ]

I have read that approximately a normal lens for a given sensor format is one whose focal length corresponds to the diagonal of the format, since this has a strong relation with the field of view of the human eye.

A lens whose focal length is equal to the camera sensor's diagonal will have a 53 degree angle of view across the diagonal, regardless of sensor size. This universality is partly why the "diagonal of format vs. focal length" metric is so useful. For a 3:2 sensor, this corresponds to a 45x31 degree (horizontal x vertical) angle of view in landscape orientation.

By comparison, the field of view of the human eye requires many qualifiers. Is this for each eye individually? Is it the angle over which any object can be detected, or just where both eyes can see stereoscopically? What is the cut-off point in resolution/acuity where we consider objects as no longer being "seen"? The only reason I say all of this is to emphasize that there's a lot of gray area here, and that's the main reason you will see so many different answers relating to the human eye and cameras out there on the net.

The image focal length of the human eye is approx. 22 mm, but drawing direct conclusions from this about the angle of view is more problematic because (i) the back of our eyes are curved, (ii) the sensing area (retina) is quite different than a digital camera and (iii) the resolution is not constant throughout (with greatest acuity at the center and gradually less towards the edges), amongst others. Each eye individually has anywhere from ~120-210 degrees angle of view. However, the dual eye overlap region is somewhere around 130 degrees-- corresponding to a a near fisheye lens focal length on a digital camera.

However, for evolutionary reasons the extreme perimeter of our vision is really only for sensing motion and large-scale objects (ie, the lion suddenly approaching you from the side). The central angle of view of say around 40-60 degrees or so is what most impacts our perception of a scene. Subjectively, this would roughly correspond with the angle over which you could recall objects from a scene if you had kept your eyes in the same position. Incidentally, this is pretty close to a 50 mm "normal" focal length lens on a 35 mm camera sensor (43 mm to be precise), or a 27 mm focal length on a camera with a 1.6X crop factor.

So, even if pretty much every format has a different normal lens (80mm for medium format, 50mm for 35 mm format, 28mm for 110 format for example), all of them do two things: they reproduce the field of view of the human eye and they also reproduce the relation of sizes between objects in the frame as they are seen by the human eye. Am I correct here?

The "normal" focal length does not reproduce the angle of view of the human eye, since this angle is much larger than 53 degrees by any measure. On the other hand, the "normal" focal length DOES correspond well with what we "perceive" as having the best trade-off between different types of distortion (when using a rectilinear mapping onto a flat surface, where straight lines remain more or less straight on paper).

left: narrower angle of view (less distorted grid), right: wider angle of view (more distorted grid)

Too wide an angle of view and the relative sizes of objects are exaggerated and objects near the edges of the frame become overly stretched, whereas too narrow an angle of view (telephoto) means that objects are all nearly the same relative size and you lose the sense of depth.

Finding the right angle of view is a bit like the Goldilocks story and porridge-- it's clear when things are too hot (wide) or too cold (telephoto)...but knowing when things are just right ("normal") is not as strictly defined.

When I think of a DSLR, I can't find a lens that both reproduces the field of view of the human eye AND reproduces also the relations of sizes between objects as I see them.

This is because these two goals are conflicting, as I think you've also observed
The eye's angle of view and our subjective perception of a scene do not correspond-- in part because of how our mind processes images.

UPDATE -- this and similar eye related topics are now the subject of a new tutorial here:
Cameras vs. The Human Eye

[sebasj]

That's a clear answer.

I had the same thought when I read that the reproduction of the field of view determined what was a "normal" focal length. Of course my knowledge didn't allow me to realize that, in part, the composition of the image in my mind was playing an important role in the process of space.

My reasoning was pointing in the direction of the difficulty to define what's the normal field of view of the human eye, and what's the role of perception when we pay attention to something.

My thought was more basic of course. Just like when you don't know a concept so you explain something through an example, I thought "Well, but when I'm having a coffee with someone my angle of view -because of my attention focus- is much smaller, and when I'm with my friends having a beer, my attention and perception of space is much more ample. I guess we'll have problems defining the normal field of view and hence the normal lens for a given format". I didn't know that the focal length of the human eye was approximately 22mm of course. As you see, much more limited reasoning, but on the same line of the problem of defining the normal field of view and mind attention.

At the same time, my definition of the normal lens was more empirical also. I thought that despite the size of the frame and the given format, I could define a normal lens by raising the camera with both eyes opened to one of my eyes. If I could see no distortion, then I consider the lens normal. The frame can be bigger or smaller, but if the reproduction of the perception of space is the same as my naked eye, I'm holding a normal, for whichever format and whichever frame size.

I have never used a view camera. The only formats I've tried are medium format cameras (6x9, 6x6, 6x4,5), 35mm and digital cameras. For all formats, their respective normal lenses correspond well to what we can define as "normal" perception of space, not too wide and not too shallow? And, do this normal lenses always have a similar (54° as you described) angle of view as long as they maintain 3:2 ratio between sides?

Thanks again for such a clear answer McQ.

Best regards,
Sebastián.

[Lindolfi]

Excellent discussion! Perhaps three points are noteworthy concerning the difference between our eyes and camera's.

1] A camera projects its image on a planar surface, that in our eye (the retina) is curved.

2] The projected image in a camera has similar quality over its area, but our eyes have widely varying quality over the retina in terms of resolution, light sensitivity and sensitivity of colour.

3] While sampling an image, a camera (preferably) does not move, our eyes our moving all the time

The first point is important, because a planar projection introduces perspective linear distortions, especially apparent in wide angles lenses. Our eyes do not have any problems with perspective distortions, although together they capture an image over an angle of more than 180 degrees, due to the fact that we do not use a planar surface for projection. Moreover, since we have a high visual acuity only over a limited visual angle (point 2] ), we move our eyes all the time (point 3]), while the brain stitches (by the use of visual memory) all these snapshots together into an illusion of an undistorted world. During the fast and short lasting eye-movements we make (saccades), the brain simply ignores the blurred image on our retina, but a camera does not.

If we look at these differences, the claim that a particular focal length is best suited to mimic our eyes, is a simplification that may hold, because it suits our impression roughly, but it does no justice to the beautiful way our eyes-brains combination works.

[Class A]

Thanks McQ, great answer!

... my definition of the normal lens was more empirical also. I thought that despite the size of the frame and the given format, I could define a normal lens by raising the camera with both eyes opened to one of my eyes. If I could see no distortion, then I consider the lens normal.

I tried a similar technique in which I chose a focal length such that two images formed by one naked eye and the viewfinder would match up seamlessly. Panning a little back and forth quickly tells you whether the images are really matching up. However, using this method, one must bear in mind that viewfinders often have a magnification factor, such as x0.85 which should be used to correct the focal length.

Next to the angle of view, you also want to achieve the same perspective, i.e., the same apparent distances between objects in the scene. Telephoto shots appear to shrink the distances between objects in the scene, whereas wide angle shots appear to increase them. However, and luckily, this perceived alteration of the distances between objects in the scene is not a function of focal length, but one of distance between camera and subject. Here's a corresponding explanation with illustrations: http://jamesmskipper.tripod.com/jame...rspective.html

The equivalent of a "normal" focus length for a digital camera with a 1.5 crop factor thus is ~29mm (giving a ~45 degree field of view, as 43mm would yield on a sensor with 35mm width). The equivalent for a 50mm lens is 50/1.5 ~ 33mm.

[Henry Peach]

My experience is that no matter how I set up my cameras and lenses they don't operate very similarly to how my eye operates.

If you really want to learn about transforming the 3D world into 2D take a basic drawing class. It doesn't matter if you can't or don't want to draw; beginning drawing classes are about retraining the eye and mind to see in 2D. It's amazing how bad most of us are at it without some conscious effort and practice. The brain is often less concerned with actuality, and happily distorts and manipulates our perception of reality.