why do we call wide angles rectilinear?

How much distortion (pincushion, or barrel, I can never remember which!) does a wide angle lens have to suffer before we decide it's no longer rectilinear.

It's pretty clear to me that a wide angle lens with bags of distortion certainly isn't rectilinear, even if its manufacturers may want us to think so.

So at what point do we stop calling it rectilinear? And at what point does it become a fisheye?

Thanks if you know the answer

Because the designers have at least attempted to keep horizontal and vertical lines straight. This results in distortions towards the corners of the frame.

If it looks like a fisheye then its a fisheye, not a rectilinear.

There is a tendency to barrel curvature, but good rectilinear lenses will resist this. Even so, the desperate measures needed to keep the lines appearing straight - even though we are getting closer and closer to a 180 degree view whereby it is impossible for the lines to be straight - can make us consider even the most perfectly rectilinear ultrawide angle lens, as distorting of shape and proportion. It's inescapable.

In more normal fields of view, rectilinear is the usual ideal, and any departure from that (fisheye or pincushion) is an aberration. But with very wide fields of view, rectilinear can be very problematic pictorially.

These problems do go away (in theory) if the correct specific viewing distance is used for the print or the screen - but that is, usually, uncomfortably close.

RP

Interesting. But in a pinhole camera you wouldn't see any such distortion would you? Sure, you can't achieve 180 degrees with linear perspective, and even as you approach that figure you'd need an infinitely large projection plane, incredibly close to the pinhole, and the material from which the pinhole is constructed would have to be incredibly thing....but practical issues aside, the pinhole model would strike me as in theory rectilinear up to but not including 180 degrees.

That's assuming I've got that right. I think there's a lot to be learned from pinholes in terms of perspective and whatnot

info333 said:

Interesting. But in a pinhole camera you wouldn't see any such distortion would you?

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What we perceive as distortion, here, comes from the attempt to represent on a 2D surface, a very wide angle of view. Some kind of representational trick is needed in order to do this, a single classic rectilinear projection just doesn't meet the bill. This problem has been addressed in many ways by figurative artitsts, and generally, a multiple-perspective "fudge" is used - and the photographic equivalent of that is a pano stitch. Using certain slightly artificial visual conventions, even scenes wider than 180 degrees can be portrayed. It is a constructed portrayal though, basically - no longer a simple capture.

info333 said:

That's assuming I've got that right. I think there's a lot to be learned from pinholes in terms of perspective and whatnot

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Scene 3D, paper 2D - to explore that, you need simply draw a picture of the scene onto paper with a pencil. It will quickly be clear what the inherent problems are - without any lenses, or pinholes, or whatever, to confuse things. Artists have devoted entire lifetimes to these issues, from many cultures and traditions and through many centuries. No lens is ever going to just resolve all representational problems in 1/100 sec.

RP

What distortion? People claim that linear perspective distorts. It doesn't. If you put your eye at the centre of perspective you don't see any distortion of columns or spheres at the edge of the picture. These so called flaws of linear perspective are to do with viewing the image, not projecting it.

Things only look wrong when you don't view a perspective projection from the centre of perspective. So yes, in theory there's only one correct place to view an image constructed in rigorous linear perspective. The artists' challenge was to design their pictures in such a way that they would look OK from a wider region, not just one point. But as photographers we don't have that option.

Sure, if you decide to project an entire sphere (eg a map, or a pano stitch) onto a flat piece of paper then you inevitably distort. But if you're just projecting what the eye would see anyway, and if you view it from the centre of projection, there is no geometric distortion.

And better close one eye, to make sure we don't get stereopsis effects.

What we see is never 'real',
an image built from years of learning,
no matter how we feel,
no matter how discerning.

It is a construct by our mind,
merely a compromise to help me and you,
and though it works most of the time,
it is far removed from being 'true'!

Optical illusions show this lie
and how unknowing we are deceived.
So, no matter how much we try,
nothing is exactly as perceived.

--
2010 : My new year's resolution - to be a year of poetry!

Nice poem! But projection will record perfectly the angles and directions of objects that you observe with your own eye.

It might not trick your brain into ignoring the fact that you're looking at a flat plane, but it will still present the geometry of the scene perfectly, as long as you view the image from the correct centre of perspective.

This point is surely irrefutable

info333 said:

What distortion? People claim that linear perspective distorts. It doesn't. If you put your eye at the centre of perspective you don't see any distortion

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I fully realise that. But we consume images as a standardised commodity - on the pages of a publication, in a gallery, on a screen, on a poster across the street. Where one has complete control over the viewing conditions one can set up a fully credible presentation, but this is the exception. Normally one does not have this specific control image-by-image: the magazine reader in the train, say, is simply not going to put his eye two inches away from one photo, two feet away from the next just because they happen to have been taken with different lenses.

He has learnt to do this sufficiently well "in his imagination", one may say, and to decipher and navigate the image's pictorial space accordingly. Where this mental transformation is mild it tends simply not to be noticed. Where it needs to be severe the "learnt suspension of disbelief" thread can snap, so he becomes conscious that, no, "that picture really does look all wrong".

This is the practical reality: images routinely ARE viewed in a way that ignores the circumstances of their making, so such mismatches DO inevitably happen and those have characteristic consequences. As I have pointed out elsewhere, that is not inherently a bad thing; it can be deliberately exploited for expressive purposes.

RP

Superb explanation. That makes a lot of sense.

I think if more photographers actually understood the simple concept behind the perspective centre, this forum would be a better place. It really does explain why telephotos or wide angles may be thought to "distort perspective", even though perspective is very clearly defined by the camera-to-subject distance.

I often see texts which talk of linear perspective's 'flaws', normally citing columns or spheres (which Leonardo explored in his notebooks), but those books rarely point out that this flaw is a function of the viewing environment, and that it can be circumvented by viewing from the correct place. That's what I find annoying because it leaves readers with an incomplete understanding.

If a lens is advertised as being "rectilinear" (few are actually designated as such) we judge them on just how close to rectilinear they are. In other words, we judge it by how much or how little distrortion it has. It seems of little value to assign what is necessarily an arbitrary figure for distortion and then decide the lens is no longer rectilinear but a "fisheye" lens.

I mean, what do you say about a zoom which has variable distortion or a telephoto lens with lots of pincushion distortion?

If you had a wide angle lens that was advertised as a "fisheye" but had no distortion at all, would you consider it a failure?

It is better I think to just test each lens, give the figure in terms of percentage of distortion, mention any irregularities such as "moustache" distortion, make a statement about how severe or significant the distortion is and post some examples so we can see for ourselves.

info333 said:

What distortion? People claim that linear perspective distorts. It doesn't. If you put your eye at the centre of perspective you don't see any distortion of columns or spheres at the edge of the picture. These so called flaws of linear perspective are to do with viewing the image, not projecting it.

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Though the above is technically accurate, it's an unrealistic expectation. In photography, a whole range of different lenses are used, from extreme telephoto through 'normal' to extreme wideangle. The whole point of using such lenses is to not change the viewing position for each and every shot. Otherwise, when watching tv or a movie, the viewers seat would have to be on rails, in order to move closer or further from the screen with each shot.

The intention of course is to view the image from a range of 'typical' distances, and indeed angles, such as the range of distances encountered when viewing a computer monitor or a the screen of a TV set.

info333 said:

Things only look wrong when you don't view a perspective projection from the centre of perspective.

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Which of course is most of the time.

info333 said:

So yes, in theory there's only one correct place to view an image constructed in rigorous linear perspective. The artists' challenge was to design their pictures in such a way that they would look OK from a wider region, not just one point. But as photographers we don't have that option.

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I thought the aim of the photographer was broadly similar, to produce a satisfying image, while having no control over viewing conditions.

Certainly the "compression" effect of the long telephoto, and exaggerated perspective of the wideangle are effects chosen on the basis that the viewer will see each image under much the same conditions, bearing in mind that this includes not just one 'ideal' distance and position, but a whole range of distances and viewing angles.

info333 said:

Sure, if you decide to project an entire sphere (eg a map, or a pano stitch) onto a flat piece of paper then you inevitably distort. But if you're just projecting what the eye would see anyway, and if you view it from the centre of projection, there is no geometric distortion.

And better close one eye, to make sure we don't get stereopsis effects.

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The viewing of such panoramas is a rather different situation to that of mainstream photography, and does indeed present its own challenges. By mainstream, I'm referring to the practice of generating an ordinary rectangular print, or image for viewing on an ordinary flat screen.

Regards,
Peter

Those are most excellent points Peter. There would be no point having lenses of different focal lengths if we were going to view them all from the proper centre of perspective. While the telephoto doesn't bring the action closer to us, it magnifies the image giving the impression that we are closer, which of course we aren't.

I'm now intrigued to figure out what relevance the centre of perspective has for the human eye, and what relevance this has for scaling prints