perspective and the illusion of depth

When you think about it, perspective is an interesting trick: a means of creating the illusion of depth on a flat surface. It is not inherent in the subject: it is partly convention, partly observation, and (above all, as with everything we see) a construct of our brains. The manipulation of perspective is a means of supplying our brains with enough cues to create the necessary illusions. Some cues are stronger than others, but even if there are no cues at all (as in Greek vase paintings or mediaeval icons, for example) we may still 'know' that there is some depth in a picture: for example, that someone's nose sticks out in front of their face, instead of being drawn on to it.

This is central to understanding perspective and the illusion of depth: we see with our brains, not our eyes. Everything we see is processed, analyzed, compared with what has gone before and with whatever other evidence is currently available. It is possible, too, that our ability to see perspective is culturally determined: linear perspective, in particular, is essentially a European phenomenon of the last few centuries. But we cannot guess how another living person sees anything, let alone how (say) a stone-age head-hunter from Papua New Guinea or an 18th century Japanese wood-block maker would see things.

Terraced fields, near Lake Erhai, China

What gives us the sense that there is any depth at all? Well, there is linear perspective: we assume (not necessarily accurately) that the longest field is roughly the same width all the way through. Arguably more important is scale constancy: we know more or less what size grass is, so these fields must be a long way behind the grass in the foreground (a cheap compositional trick, but no less effective for that). That is of course an example of receding planes: if A obscures B, we assume A is in front of B. Aerial perspective plays a small part, too: the distance is detectably slightly hazier than the foreground.

eight ways to create the illusion of depth

If perspective were inherent, linear perspective in particular would always have existed instead of appearing quite quickly in the 15th century: Paolo Ucello (1397-1475) is generally credited with being the first to use linear perspective, quickly followed by Filippo Brunelleschi and Leo Batista degli Alberti.

Aerial perspective appeared rather later in painting, mostly with the Dutch realist painters of the 17th century, though it is arguable that some Chinese ink paintings have some aerial perspective in them, with distant mountains portrayed with thinner or weaker brush-strokes than closer ones.

The perspectives of scale and of receding planes can be taken as special cases of linear or vanishing point perspective, but there is also a strong case for treating them separately, as they appear in Japanese and Chinese art (and indeed Tibetan) without any accompanying linear perspective; and, of course, they antedate linear perspective.

Lighting perspective is seldom regarded as perspective but as soon as you define perspective as a means of creating the illusion of depth, it is hard to exclude. What, after all, is 'roundness' but the illusion of depth? And certainly, the illusion of depth can be created by portraying the light sources in the picture, then having the things that are closer, better lit, and the ones that are further away, more dimly lit.

Similar arguments apply to perspective and texture, perhaps the most contentious question in creating the illusion of depth, but one that cannot be ignored.

Differential focus may be regarded as a uniquely photographic means of conveying depth. Again it may be decried from a classical point of view of what constitutes perspective, and we find it disputable which conveys depth better, differential focus or 'deep field', but it warrants discussion.

Backstreets, Pondicherry

Vanishing point perspective; aerial perspective; perspective of scale (we assume the bridges across the gutter are roughly constant in size); receding planes (one thing in front of another); lighting (and shadows); all are used to create the impression of depth in this shot, taken by Roger on Kodachrome 64 using his Leica M4P and 35/1.4 Summilux.

There is also a form of perspective, known to the Ancient Greeks, called sculptural perspective. If a statue is high on a building, or on a tall plinth, so that we always look up at it, it will appear foreshortened from our lowly viewpoint. The trick, therefore, is to 'stretch' the sculpture vertically: it may look odd when viewed square-on, but it will look more natural when viewed from below. For similar reasons, bas-reliefs that are placed high on a building must be carved deeper than those that are placed lower down. This may seem to be of limited interest to photographers but we shall return to its practical implications later.

bokeh

Bokeh or boke (pronounced 'bow-kay' or 'bo-ke') is a word of allegedly Japanese provenance that was first bandied about at the end of the 20th century and gained wide currency in the early 21st.

It means 'the quality of the out of focus image', which indeed was a concept that occasionally surfaced earlier: Roger's mentor, the late Colin Glanfield, praised the quality of the out of focus image of the original Braunschweig Apo-Lanthars in the early 1990s or maybe even 1980s.

Some people are very much more sensitive to it than others, and according to some of those who are sensitive, it can be a powerful tool for creating the illusion of depth.

We are not convinced, not least because we are very insensitive to it: bokeh must be very nasty indeed before we even notice it, and we have never looked at any picture and said, "What magnificent bokeh!"

 

Thambar flowers

The pre-war Leitz Thambar soft-focus lens is deservedly a legend, and we would buy one if we could possibly afford it. A few may have been made after World War Two but it is doubtful.

It has, however, some of the worst bokeh we have ever seen (except, of course, for the horrible doughnut-shaped highlights produced by mirror lenses). With the centre-stop in place, it is even nastier.

Admittedly, this picture labours under many disadvantages. It is somewhat underexposed, and the film (Kodak Elite Chrome EBX) does not seem to have been ideally suited to the colour of the flowers. But for an example of bad bokeh, we think it's pretty convincing.

It's worth adding that this shows up far worse with lines than with anything else, so the moral is simple. Don't compose a subject with lines in the background!

linear perspective

Linear or vanishing point or classical perspective is the first sort of perspective that most people consider; indeed, many people who have never thought about the subject may believe that it is the only kind. As this module demonstrates, it isn't.

It is most usually portrayed in the horizontal plane, e.g. railway tracks meeting at infinity, but not in the vertical: we expect the sides of a building to remain parallel, when a moment's thought will reveal that the same rules apply vertically as horizontally. Painters just ignore vertical perspective, while photographers resort to levelling their cameras carefully and then using rising fronts, perspective 'correction' or PC lenses (actually perspective distortion), or to manipulating the captured image either by enlarging onto a sloping easel or (more usually nowadays) via Adobe Photoshop or other image manipulation programs.

Interior, Mision de la Purisima Concepcion, Lompoc, California

As well as classical vanishing-point perspective, this picture (on Ferrania 1000D) creates a feeling of space via generous exposure: the most Frances could give without 'blowing' too much of the picture to a featureless white. Now, if you think about it, a feeling of space necessarily creates a feeling of depth, so maybe exposure is yet another way of creating the illusion of depth. The camera and lens are forgotten, but from the lack of distortion in the corners, it wasn't either the 14mm Sigma or 17mm Tamron. It might have been the 21/2.8 Elmarit-M on a Leica but the likeliest bet is 35mm, probably (from the viewpoint and true verticals) the 35/2.8 PC-Nikkor on a Nikon F. This would also explain why it 'feels' wider than 35mm: the perspective you get from a shift lens often resembles what you would expect from the next wider lens (28mm for 35mm, 24mm for 28mm).

perspective and viewpoint

It is often said that perspective depends solely on viewpoint. The argument for this is that if you shoot a scene with (say) a 35mm lens and then crop it down to the area you would get if you had used a 90mm lens from exactly the same spot, the perspective will be identical to that produced by a 90mm lens.

This is only true if the two images -- the cropped 35mm image and the all-in -- are enlarged to the same degree and viewed from the same distance. The easiest way to think about this is via the concept of the 'magic distance'.

New York from the Empire State Building

Perspective, as well as investments, can go up as well as down. Because Frances was looking down when she took this picture from the top of the Empire State Building, using a Nikkormat FTn and 35/2.8 PC-Nikkor with Ilford XP2, the verticals diverge instead of converging. We believe that this actually helps to create an impression of the yawning depth below the observation deck, which is why she chose not to correct it.

Anyone who has ever looked hard at photographs will have experienced a 'magic distance', often by accident. A certain picture -- most commonly a portrait, sometimes a cityscape, sometimes some other type of photograph -- will have a remarkable three-dimensionality, almost as if you could poke your finger into the paper. They will have noticed, moreover, that this effect is strongest across a limited range of viewing distances. Get too close, and the effect vanishes. Go too far away, and it vanishes again. The distance at which it exhibits this three-dimensionality is what we call the 'magic distance'.

The effect is almost impossible to re-create on a computer monitor, because you never know what size monitor someone else will be using, and it is far from the most important way of creating an impression of depth, but because it is so striking when it happens (and so relevant to viewpoint and focal length) we felt justified in dealing with it very early in the module.

magic distance: the explanation

'Magic distance' can be explained, we are convinced, with a (relatively) simple mathematical argument. It happens when the angle subtended at the eye by every single element in the picture is similar to the angle that was subtended at the camera by the object itself.

If 'angle subtended' has escaped your memory since your schooldays, do not worry. It is a simple concept. Imagine a person standing six or seven feet/two metres away. Draw an imaginary line from the top of their head to your eye. Now draw another imaginary line from the soles of their feet to your eye. This is the angle subtended. In this example, it will be about 50 degrees. For a person standing twice as far away, it will be about 25 degrees. (These are very rough figures).

From this example you can see that everything in your field of view subtends a particular angle. If it is something really big, really close, so that you have to crane your head back to see the top, this may be as much as 160 degrees (obviously it can't be more than 180, or it would be curving around you -- and if it were 180, you would need to be standing inside a giant hoop that stretched above your head and beneath your toes).

At the other extreme, the limit of human visual acuity is often taken as 1 second of arc. This corresponds to a human hair at 3 metres/10 feet or so, or a human figure at around 5 km or a bit over 3 miles. There are wide individual variations, and there is also the point that visual acuity can be measured in a number of ways, but 1 second will do.

Bridge and road, Mertola, Portugal

Roger shot this on Ilford HP5 using a Nikon F and 200/3 Vivitar Series 1 (with 2.8x orange filter). At a screen image height of 10cm/4 inches (effectively just under a 3x magnification), you may find that it is uniquely three-dimensional at a viewing distance of about 50-75cm/20-30 inches -- or you may not. It should, however, look more '3-D' at roughly this distance than it does from closer or further away, which is what 'magic distances' are about. It would be extremely difficult to reproduce a shot taken with a 35mm lens in a way that would give the 'magic distance', as the screen image would need to be too big and you would need to be too close to the screen.

In fact, if you don't like subtended angles, there's an easier way of thinking about magic distances which gives exactly the same results. Use similar triangles. Again, fear may clutch your heart at the mention of these, the memory of interminable geometry classes, but again you will see in a moment that they are not difficult. Similar triangles are triangles of the same shape (the same angles at all three corners) but different sizes. They have the happy property that if you scale up one side, the others scale up in proportion.

Now, let's suppose you have taken a half-length portrait at 3 metres, 10 feet. Allowing for a bit of space above the top of the subject's head, the vertical height of the field of view is 1 metre. This subtends an angle of 36 degrees at the camera.

If you made a print 1 metre high and viewed it from 10 feet away, the angle subtended by everything in the picture would be exactly the same as the angle subtended at the camera and the perspective would be extremely convincing. But such large prints and viewing distances are scarcely convenient, so both can be shrunk in proportion. This is where the similar triangles come in. Let's say you want to view the print from 60cm, a couple of feet. This is one-fifth of the shooting distance, so the print needs to be one-fifth as high: just 20cm, 8 inches. And now let's say you want to put it into a book, which you assume will be read at a distance of 30cm, one foot. The print must now be a mere 10cm high, 4 inches: rather small.  Fortunately there is a way around this: you can use lenses of different focal lengths, as described below.

Javits Center, New York City

Something we have not mentioned elsewhere is fisheye perspective. Frances shot this with her 15/2.8 Sigma fish-eye on a Nikkormat, using Fortepan 400 film. There is certainly an impression of depth, but it shows the extent to which all renditions of perspective are conventions and constructs rather than anything inherent. It is probably much easier for someone living in the early 21st century to accept this as more or less 'natural' (though it does tilt slightly to the left) than it would have been for someone in the 16th century, simply because we are more familiar with fish-eye images than they would have been -- though they did use convex mirrors...

focal length

Traditionally, the focal length that gave the most 'natural' perspective was reckoned to be identical to the diagonal of the negative on which it was used. This is often referred to as the 'standard' focal length. Thus the 'standard' lens on an 8x10 inch camera, negative diagonal approximately 12 inches or 300mm, was 300mm, while for quarter-plate (3¼ x 4¼ inches), diagonal near enough five inches or 127mm, it was 127mm.

This reflects the simple truth that in general, we will look at big pictures from further away than smaller ones: we hold the smaller ones closer (and reach for our glasses, as we get older) in order to see the same level of detail. In fact, we are likely to examine the picture from a distance roughly equal to its diagonal, though the smaller the picture, the less true this is: we may well look at a quarter-plate from six or seven inches, 150-175mm, rather than five inches, 127mm, simply because for most people, five inches is too close.

Daroca, Spain

The picture on the left was taken with a 15/2.8 Zeiss Distagon; the one on the right with a 50/2 Zeiss Planar. Both are enlarged to the same size. This well reflects the simple truth that as soon as we see different perspectives side by side, we tend to lose all sense of what is 'right'.

We would suggest that the picture on the left has considerably more impression of depth than the one on the right; but we would also suggest that this is very much a question of subject matter.

Roger shot both on Kodak Elite Chrome 100, EBX, using his Leica MP.

Traditional 'standard' lenses and viewing distances are all well and good until you start to consider enlargements. Obviously, very few people are going to look at 24x36mm images from a distance of 43mm (the negative diagonal), except perhaps when they are going through contact sheets with a magnifying glass. So let's imagine we use a 43mm lens (the nearest we know of is the 42.5mm Biogon for the pre-war Contax) and blow it up 6x to 144 x 216mm, a bit under 6x9 inches. The optimum viewing distance for the 'magic distance' is now 6 x 43 = 258mm or a bit over 10 inches -- an ideal viewing distance for a print that size.

Now make a 40x50cm/16x20 inch print from the same negative: people do. You'll have to crop the negative a bit to make it fit, but for a borderless print this size you are looking at almost a 17x enlargement. Your optimum viewing distance is now 17 x 43 = 731mm or about 29 inches: probably a bit closer than most people would normally look at such a big picture unless they were examining it fairly closely, for example in a gallery.

Now change the focal length. Shoot the same scene, from the same spot, with both a 21mm lens and an 85mm lens. For the same size prints, we can establish the optimum viewing distances using our dear friends the similar triangles. For the 21mm, the viewing distance is 21/43 the distance for a 'standard' 43mm lens, and for the 85mm it is 85/43.

For the small print, the viewing distances go from 258mm/10 inches with the 'standard' lens to 126mm (near enough 5 inches) with the 21mm and 510mm, a bit over 20 inches, for the 85mm. With the big print (optimum viewing distance 731mm/29 inches for the 43mm lens) they are 357mm, 14 inches, for the 21mm shot and 1445mm, near enough 57 inches, for the 85mm. You will have noted that because we chose focal lengths that were roughly half the 'standard' and roughly double, the viewing distances in both cases are roughly halved and doubled. Similar arguments would apply to 14mm (about 1/3) and 135mm (about triple).

Now, imagine that our 85mm shot is a portrait, and we make a 40x50cm/20x16 inch print from it. We often look at portraits of ths size from a distance of around 1.5 metres or 5 feet, so the perspective will be much more pleasing than it would have been with a 43mm portrait covering the same subject, but (necessarily) closer to the subject. Conversely, if we shot a landscape with our 21mm lens, and made a 40x50cm/20x16 inch print from that, we might well find a magical sense of being 'inside' the landscape if we stood close enough to it.

Lights, Las Vegas

With a very long lens -- Roger shot this with either a 600/8 or 800/11 Vivitar Series 1 on a Nikon F -- there will never be 'natural' perspective at any believable enlargement size or viewing distance because we never see anything like this with our eyes except perhaps when we are looking through binoculars.

perspective and portraiture

The example given above of a portrait is particularly interesting if we work backwards. Let's say we want an 8x10 inch (20x25cm) portrait to be examined from 60 to 90 cm (two to three feet). This print size is approximately an 8.5x enlargement from 35mm, so we can get the ideal focal length for 35mm by dividing 600mm and 900mm by 8.5. This gives us a fraction over 70mm for a viewing distance of 60cm/two feet, and about 105mm for the viewing distance of 900mm/three feet: clear illustration of why longer-than-standard lenses are usually recommended for portraiture.

This may be taken as evidence that perspective does, indeed, depend solely on viewpoint; our counter-argument is that if in order to get the right viewpoint, you have to use a different focal length, then choice of focal length is indeed central to perspective.

Mandi and rose

Roger took this a very long time ago, in about 1974. The camera would have been either a Leica IIIa with 50/3.5 Elmar or a Pentax SV with a 55/1.8 Super-Takumar. The film was called Barfen (honestly!) and was ISO 50. This image has been desaturated to make it look even older than it is, but the relevance to perspective is that with a young girl (Mandi was 14) without prominent features, 50mm can provide a pleasingly intimate portrait. Of course the very flat lighting (deliberately echoing Japanese 'notan') makes for very little impression of depth, though there is some differential focus.

borders

All perspective clues usually work better when the image is isolated from its surroundings with a good, wide border. This can be a border to the image itself; some form of frame; or simply hanging the picture on a reasonably featureless wall. This is, we believe, because the eye and brain are denied visual perspective clues that are external to the picture, and are forced to rely on the clues that the photographer has incorporated into the image.

This would also help to explain why small, 'crowded' layouts, with numerous pictures on the same page, are so often so unsatisfactory, especially from the point of view of perspective. Unless the perspective in all the pictures is identical, or at least very similar, the eye and brain are forced to try to accommodate numerous 'magic distances' all at once, with the result that at best, one or two pictures may succeed, but most often, none of them does. The two pictures of Daroca, above, well illustrate this.

Thirsty, miserable, always wanting more

On most monitors, this will fill the screen, with a broad white border. The extreme perspective and drunken verticals create a somewhat vertiginous impression of depth, as if one were staggering and reeling. Other graffiti in the same hand included 'Bukowsky died for your sins'. Frances shot this some years ago in New Orleans with a 17/3.5 Tamron SP on either a Nikon F or a Nikkormat. The film stock was Ilford XP1; a 'grittier' film such as Ilford HP5 or Kodak Tri-X might have been even more successful.

paper surface

This is not something we have seen addressed elsewhere, but increasingly, we are convinced that the 'magic distance' works better with some kinds of paper than others, namely, unobtrusive matt surfaces. A hard shiny gloss is too much of a barrier between the viewer and the image; a clear texture draws attention both to itself and to the fact that the image has been laid upon it. This is one reason, we suspect, why 'alternative processes' are often so effective when seen as original prints: their image seems to sink into the paper. A computer monitor places a really solid barrier between the viewer and the picture: similar to what Sylvia Plath, in another context entirely, called 'the bell jar'.

the origins of perspective and the camera obscura

The camera obscura or 'dark room' (camera = room, obscura = dark) was first described by the Arab scientist Alhazen in the 11th century, in terms that made it clear he expected most of his peers to be familiar with it. Latin translations followed in the next 100 years or so; Leonardo da Vinci was familiar with it before 1519, and he was far from alone. Indeed, it is likely that the very first cameras obscuras were noted by accident: a white-walled room, shuttered against the noon-day sun, with a well-made shutter where the only light was admitted through the finger-hole that was used for closing it.

Until the mid-16th century, all cameras obscuras used 'pinholes' -- which may well have been big enough to stick your finger in, if the camera obscura was literally a white-walled room, as it was for the first few centuries of its existence -- but Daniello Barbaro described the use of a lens (and diaphragm!) in 1568. Small portable cameras obscuras were used by artists, cartographers, solar astronomers and more.

Alembic, Portugal

It may be hard to believe nowadays, but for centuries the Arab world was in the forefront of science and technology. The word 'alembic' and indeed 'alcohol' come from the Arabic, though apparently 'al-kohl' refers to anything produced through any process of refinement including distillation, pulverization or sublimation. Portugal, where Roger photographed this distilling apparatus, was of course under Arab occupation for several centuries.

Those who have been paying close attention will have noted that the late 15th and early 16th century was also the time that linear perspective was -- what? Invented? Discovered? It is therefore entirely possible that linear perspective owes its very origins to the camera, long before photography was invented: or more accurately, realized, because the idea of fixing the image from a camera obscura must be very nearly as old as the camera obscura itself.

camera movements and perspective

Both the decentering movements of rise/fall and cross, and the out-of-parallel movements of swing and tilt, can be used to affect perspective, but to include them here would make the module inconveniently long, so as noted in the free introduction the reader is referred to the (future, paid) module on camera movements; sorry.

aerial perspective

Things that are further away are hazier and fuzzier to the naked eye, and so they record on film. In colour, they also tend towards the blue or even the purple. Aerial perspective can be accentuated or reduced in at least four ways, as described below.

Morning mist, Chengde

Aerial perspective is at its most obvious on a misty day, but not when the mist is too thick, or you cannot see the more distant parts of the scene: too much disappears. Also, contrast may be more important than is immediately obvious. Without the silhouetted and quite contrasty tree and reeds on the left, this picture is flat and dull. Cover up the left hand side of the picture with your hand and you will see what we mean. Roger shot this on Kodak EBX with a Leica MP and 75/2 Summicron.

weather and time of day

Some days are clearer than others; this is a commonplace. If you have the luxury of being able to wait until weather conditions are right, you can find days that are all but devoid of aerial perspective, apart from a slight blue shift. At the other extreme, there is mist and fog. Often, winter is clearer than summer, but you cannot rely upon it.

Equally, the air is normally a lot clearer in the morning than in the evening, so if you want to keep aerial perspective to a minimum, shoot in the mornings, or for more aerial perspective, shoot in the evenings.

The popular photographic belief that rain 'washes' the atmosphere, making it clearer so that there is less aerial perspective after rain, is widely decried by meteorologists and physicists. Even so, the mere fact that so many people believe it and (more importantly) believe they have seen it and photographed it is enough to cast doubt upon this scepticism. From personal experience we would say that the atmosphere is quite often less hazy after rain, and whether this is the result of the atmosphere being 'washed' or some other meteorological phenomenon that often manifests itself after rain, we do not really care. It works often enough.

filtration

This is much more important with black and white than with colour. Atmospheric haze is bluish, and can therefore be reduced with 'minus blue' filtration. A yellow filter will have some effect; orange, more; red, more still; and infra-red film with an infra-red filter can cut through haze as if it is not there. In the unlikely event that you want to accentuate haze, blue filtration will do it: even quite a weak blue can have a surprising effect. In colour, anything more than the weakest filtration (CC05) is likely to have such undesirable effects upon colour as to be inadvisable.

Lake Mono, California

Frances loaded her Nikkormat FTn (with 35/2.8 PC-Nikkor) with Ilford SFX and used a deep red filter to cut through the haze and accentuate the strange, straight clouds -- which add a sort of curious false perspective of their own, echoed by the ripples in the water.

focal length

Some telephoto lenses -- especially those of very long focal lengths -- are denigrated as 'lacking contrast' when a moment's thought will reveal that a long lens is normally called upon to cut through more atmospheric haze than a short one: instead of the subject being between one and ten metres away, it may well be between ten and a hundred metres, and quite possibly further. Obviously, if you go closer with a lens of shorter focal length, you will have less of a problem with haze between you and your subject.

lens design

The fewer glasses and (especially) glass-air surfaces a lens has, the less its flare and the greater its contrast. As a loss of contrast is already an effect of aerial perspective, it follows that the less flare the lens has, the better it is likely to differentiate subtle tones at a distance. This is less of a problem than it might seem, in that flare is more important in the shadows than in the highlights (because it forms a greater percentage of the illumination in the shadows) but it is still important enough to make a difference.

This is why long-focus lenses, rather than tele designs, are contrastier than telephotos: the telephoto (diverging) lens or group behind the main image-forming group never has any beneficial effect on optical quality or contrast, and is there purely to make the lens shorter and handier. Taken to its extreme, the quest for simplicity in lens design led to such lenses as the 400/5.6 and 560/5.6 from Leica in 1966: a single cemented doublet, two-glass, one-group. They were necessarily slow -- more speed would have required more glass for more correction -- but they were astonishingly good. At the other extreme, long-range zooms have for the most part been notoriously lacking in contrast, especially at the long end of the range.

Daroca, Spain

You would expect more aerial perspective here, but several things militated against it. It was fairly early in the morning; on a winter's day; and Roger used a contrasty 35/2 Zeiss Biogon on his Leica MP to shoot this on Kodak Elite Chrome EBX. In fact, there is arguably too little perspective: in the absence of any real clues about the size of the castle in the background, this almost has the 'stacked' look of a picture taken with a much longer lens.

perspective of texture

This can be viewed as merely another aspect of aerial perspective, but several leading authorities on perception apparently regard it as separate. The argument is simple: we can see more detail and texture in things that are closer to us. The better the textural rendition of close objects, therefore, the greater the impression of depth.

If on the other hand texture is obscured or 'smoothed out', this particular visual clue is lost. This is a major drawback, in our view, of the low-pass filters adopted by so many small-format digital cameras: in order to 'lose' unwanted Moire patterns created by everyday textured objects (such as woven fabrics) they simply throw away fine detail in skin textures, rock and many other natural subjects.

control of rendition of texture

Obviously there are two main ways of improving rendition of texture -- apart, of course, from eschewing digital imaging or removing low-pass filters. The easiest in some ways is the adoption of larger formats, but this necessarily entails a loss of depth of field. The other option is the use of sharper lenses or films (or higher-resolution sensors) or both.

Arguably, the ideal solution is a combination of the two: a top-flight roll-film camera such as an Alpa or 'baby' Linhof offers the dual advantages of a big image capture area and lenses that are not far behind 35mm when it comes to resolution.

Boonesboro museum

The sheer level of detail invites us 'into' the picture, and maximum possible rendition of texture will do so still more. This picture (shot by Frances on Ilford XP1 with a 17/3.5 Tamron SP and Nikon F) well illustrates both the advantages and drawbacks of electronic media: you cannot see the level of detail, and we could easily have lied to you and said it was shot on medium format -- which would have been a better idea, except that it would have needed a 35mm lens to cover 6x9cm, which we did not own at the time. It's also a good example of the 'false texture' noted below: the brain supplies information that isn't there.

false texture

An intriguing aside, especially applicable to black and white photography, is that photographic grain can surprisingly convincingly mimic the texture of a wide variety of things including skin, feathers, stone, sand and more. As soon as you start to look hard at the grain (or if it is over-enlarged) it ceases to look convincing, but what is happening is yet another illustration of the fact that we see with our brains, not our eyes. Our brains already have an excellent idea of what sort of texture to expect from a wide range of subjects, and as long as there is a texture present in the representation that is more or less right, they will read it in a way that fits the preconceptions.

perspective of scale

Another name for perspective of scale is 'size constancy', and this is another example of seeing with our brains, not our eyes. An example makes it clear. We know how big adults are, and what the natural variations are: more or less 160-190cm, five foot three to six foot three. We know that some people are shorter, and some taller, but not many, and rarely by all that much, and we know that the likelihood that one person is twice as tall as another is vanishingly small.

We also know that people rarely shrink or grow dramatically, Alice in Wonderland notwithstanding, and that their actual height is likely to remain constant whether we are standing next to them or if they are so far away we can barely see them. If, therefore, we see two people in a picture, and one is twice as tall as the other, we assume that the smaller one is twice as far away.

Similar considerations apply to many familiar objects, such as aeroplanes and motor-cars, and we can be surprised when our expectations are overturned: because a jumbo jet looks very much like a smaller aeroplane seen from further away, the first time you get close to one, its sheer size is remarkable. And we used to know a photographer who was six foot seven (two metres) tall and rode an unfaired 1200cc flat-four Honda Goldwing. Of course there were two clues at work here, the size of an average man and the size of an average motorcycle. At any great distance, he looked like an average-sized man on an average-sized motorcycle. Close up, you realized just how big they both were.

Perspective of scale can be taken as a special case of vanishing point perspective, but the lie is given to this by the way that it is sometimes used in trick pictures. A grid is drawn that mimics vanishing-point perspective, but it is deliberately drawn much 'steeper'. Two objects of the same size are then placed on the grid. The one that is further away is usually perceived as bigger, even when it is actually smaller, because vanishing point perspective is a stronger cue than perspective of scale.

 

Sighisoara, Transylvania

As well as vanishing point perspective, there are several clues of scale here. Apart from the size of the people, we automatically assume that the the paving stones are more or less constant in size and that the arches are more or less the same height.

Repetition of this kind can be a powerful tool in establishing the illusion of depth via size constancy. Running the picture fairly big also helps to create a 'magic window'. Get as close to the screen as you can and you may see the effect, even though Roger used a 35mm f/1.4 Summilux on his Leica MP, shooting on Ilford HP5 Plus. The print is on Ilford Multigrade Warmtone.

 

control of perspective of scale

Perspective of scale is controlled by viewpoint: the closer something is to the camera, the bigger it looks. But it is also controlled, for a given viewpoint, by choice of focal length. With a wide-angle lens, things that are closer to the camera appear disproportionately larger than more distant subjects, as compared with the rendition of a 'standard' lens (see above) while with a long-focus or tele lens they appear much closer to their normal size relationships.

Paradoxically, though, the 'stacked' or 'compressed' perspective that is associated with longer lenses may give more of an impression of depth than the 'stretched' or 'extreme' perspective that is associated with wide angles. The thing about the wide-angle is that unless you have a very strong foreground, the viewer's attention may be focused on irrelevant and possibly unwelcome foreground detail.

perspective of receding planes

Again, this may be taken as similar to perspective of scale or linear perspective; and again, it isn't. If we can't see one thing because it is partially obscured by another, we assume that the thing that is doing the obscuring is in front, and the thing that is obscured is behind. Millions of years of evolution convince us of this, though we may also suspect that (for example) someone has been playing around in Adobe Photoshop again. It doesn't matter, of course, if the mountain is half-obscured by a mouse, or a mouse half-obscured by a matchbox, though this does give us some idea of scale and of the relative distances apart of the different picture elements.

Outside photography, the most familiar example of the perspective of receding planes is in Oriental ink-paintings. Yes, we know that the bamboo is smaller than a mountain (unless Lu Tze has been making bonsai mountains again) but we neither know nor really care whether the more distant mountain is about the same size but just behind the one in front, or really big and a very long way behind.

Tree and mountains, Southern California

Perspective of receding planes, in a mountain shot like this, is simplified almost to line (rather than form) by aerial perspective. Roger shot this on Kodachrome 64 with a Leica and 90/2 Summicron.

control of perspective of receding planes

The perspective of receding planes is normally only an important clue when it exists on its own: otherwise, we don't really notice it. This in turn means that it is normally most important in landscapes, especially mountainscapes, where the three-dimensional landscape is reduced almost to line: the important thing is the edges of the planes themselves. This almost invariably entails the use of longer-than-standard lenses to 'compress' perspective, as described above for perspective of scale.

lighting perspective

Three separate factors are at work here. The first is shadows and their direction. These are very easy to understand, because we know that a shadow requires a light source at some distance from the subject; the subject, to cast the shadow; and something for the shadow to be projected upon. This can all be seen very clearly in the Pondicherry shot near the beginning of the module, and clearly enough in the 15mm Daroca shot a bit later.

The other two factors are equally easy to understand, but have somewhat forbidding scientific labels. One is the inverse square law, which states that the intensity of a light falling on a subject is proportional to the inverse square of the distance from the light, and the other is Snell's law, which states that the intensity of a light falling on a subject is proportional to the fourth power of the cosine of the angle of incidence.

Sedan chairs, Chengde

You can see all forms of lighting perspective at work here. The shadows are not very important, but they are clearly there, from the awning of the chair on the left and the wall itself at the entrance. The inverse square law is well illustrated by the fall-off in the brightness of the wall, the further it is from the entrance; and the 'limb effect' (see below) which is a consequence of Snell's Law can be seen on the poles. Of course, there's a healthy dose of vanishing point perspective too. Roger shot this on Kodak Elite Chrome 100 EBX using his Leica MP and 35/1.4 Summilux. The location is rather unpleasant: it was built by the Chinese emperors as an imitation of the Potala, and is now used to 'justify' the Chinese occupation of Tibet and (via the sedan chairs, which are seen nowhere else in Chengde) to hint at how the 'serfs' were 'exploited' by the Dalai Lama's regime in a free Tibet.

inverse square law

If one thing is twice as far as another from a given single light source, it will be one-quarter as brightly illuminated (two squared = 4, and it's an inverse law so it's 1/4). If it were three times as far away it would be 1/9 as brightly illuminated, and so forth.

From this it might seem that on-camera flash was an ideal way of conveying depth in a picture, and indeed it is. It's just that the results are, for the most part, visually very nasty indeed. Anything too near the camera is 'blown' or burnt out to a featureless white: anything too far away is dark and murky. Also, there's no modelling: it's a flat, ugly light.

It is generally much more effective to use a light source well separated from the camera: arguably, in shot, and quite possibly behind some of the foreground subjects (in which case they may be more or less backlit or rim-lit, creating a perspective of receding planes.

Also, you don't normally want just a single light source, except for very dramatic, tight shots where the subject matter in the background is unimportant. More often, you want some sort of broad fill -- the agglomerate of street lighting in a square, perhaps -- plus a single dominant light.

snell's law

Anyone who has already read the paid module 'White on White' will have encountered the 'limb effect', illustrated by the picture shown on the right, a frankly dull (but, we hope, very informative) illustration of a roll of paper towels on a paper towel holder.

Stripped of the fourth-power-of-the-cosine business, Snell's law and the 'limb effect' (so called because it is normally seen in arms and legs) are formalizations of something we all know: if something is square-on to a light source, it reflects more light than it does if it is at an angle. Anything cylindrical (such as the roll of paper towels) or roughly cylindrical (such as an arm) or even more or less spherical (such as a head) presents a range of angles of incidence to any light source, ranging from 90 degrees (square on) to 180 degrees (glancing past).

The variations in the amount of light reflected at these different angles are what create the illusion of roundness, or the 'limb effect'. The light source can be as big as you like, but it must be directional, and it must not be so hard and so close to the subject that the brightest part of the limb (or paper towels, or whatever) are 'blown' to a featureless white.

This kind of lighting is at its most effective when it is close to the camera, and it will even work with on-camera flash, though you need to be careful not to have anything important going on behind the main subject or you will have the same problems of ugly pictures as mentioned above. In the studio, of course, you can light the background separately, preferably with broad, soft light though you may also choose more dramatic lighting as long as you do not draw more attention to the background than the foreground.

'Paramount' or 'butterfly' lighting, perhaps one of the most successful lighting plots for portraiture and widely used in the golden days of Hollywood (yes, that Paramount), owes much of its modelling and roundness to the limb effect. The key light is placed above the camera, and slightly to one side: this casts the 'butterfly' nose shadow that gives the plot its other name. The weaker fill is placed on the other side of the camera, and below it.

 

Stacked muskets

The limb effect is clearly visible on the stock of the nearest musket; indeed it is accentuated by the polish on the wood. Frances shot this with a 90/2.5 Vivitar Series 1 using an old Nikkormat. Film stock was Ilford XP2, printed on Ilford Multigrade.

differential focus

As noted near the beginning of this module, we were hesitant about including this, for a number of reasons. One is that very few other writers treat it under the heading of perspective, which isn't a very good reason, and still worse (and downright ignoble) is that we thought we might be able to wring another paid module out of it. We decided, though, that it was close enough to a part of perspective that it needed to go in here.

Now, the magazines (and some books) often advocate differential focus -- that is, putting the subject (or part of it) in sharp focus, and throwing the rest out of focus -- as a means of conveying depth, as well as being a useful way of suppressing messy backgrounds: the classic example of the latter is a hedge behind a portrait, or a picture of a songbird, where obtrusive leaves and twigs dissolve into an unobtrusive greeny-brown mush. For suppressing messy backgrounds, differential focus can indeed be invaluable.

Its usefulness as a means of creating an impression of depth is another matter. In fact, we suspect it is substantially irrelevant, and either succeeds or (more usually) fails for other reasons.

Let us take one of the applications for which it is most successful, and most popular: close-up portraits. Think about being close to someone: arm's length, or less. Normally, you will look at their eyes: other features, especially ears, may well barely impinge upon your consciousness. True, you will not be able to see their ears without moving your eyes and refocusing, but the important thing is not so much the focus of your eyes, but the focus of your attention. The camera, by focusing on the eyes, echoes this concentration; but it is almost a metaphor, rather than being strictly analogous. Much the same is true, we would say, of the songbird.

 

Windmill

Slightly to our own surprise, we found another example of a subject in which selective focus echoes how we concentrate on one part of what we are looking at. Frances could not hold both the tree and the mill in focus, but the out-of-focus foreground does indeed echo the way we see; we are aware of the foreground, but neither out attention nor our eyes are focused on it.

The more we thought about it, the more we reckoned that this sort of selective focus -- an unsharp frame -- is more effective than the out of focus background as a means of conveying depth. Voigtlander Bessa-T, 75/2 Summicron, Ilford XP2 Super printed on Ilford Multigrade Warmtone.

We believe that selective focus usually fails if there is any important context surrounding the main subject, and it is out of focus: an environmental portrait of someone surrounded by their possessions, for example. Yes, you can get away with a load of out-of-focus books to suggest a measure of scholarliness, but if they are sitting in the middle of their doll collection, or their stuffed pigs, or their shrunken heads, you generally want a fair amount of detail in these. Even in an ordinary room, there may be quite a lot that you can get from the background: the number and kind of pictures on the walls, the state of the decor, what's on the mantelpiece. All of this, we believe, invites you 'into' the room via the picture.

Of course, every picture must be considered on its own merits, and there are bound to be times when for one reason or another you have to compromise: usually, lack of light. But as a means of creating an illusion of depth, we have generally found 'deep field' photography to be more convincing than differential focus. This is equally true of the pictures we take ourselves, and of others' pictures that we see.

sculptural perspective

This is the joker in the pack. As we have already said, sculptural perspective was known to the ancient Greeks as a means of making statues look more lifelike by deliberately distorting them and even, on occasion, coarsening them so that subtle details were not lost.

The relevance to photography is that if you shoot upwards, with the intention of restoring converging verticals later in Adobe Photoshop or something similar, you need to bear in mind the same lessons the Greeks learned thousands of years ago. This is most easily illustrated with an example, as shown on the right.

 

Apartments, New York City

Above: The original shot shows dramatically converging verticals.

Above right: 'Trueing up' the shot in Adobe Photoshop (bringing the verticals into parallel) makes for a squat, ugly and unconvincing image

 

 

Right: Stretching it by some 60 per cent vertically restores roughly the same proportions as the original. Actually we think the original looks better anyway...

Roger used Fuji RFP ISO 50 in a Leica M4P with a 35/1.4 Summilux.

the bottom line

In one sense, we have probably told you nothing that you did not already know; apart, perhaps, from a couple of definitions and historical footnotes. On the other hand, we may have helped you organize your thoughts, and put them into a framework where you can more quickly and easily apply the techniques you need. And we'll finish with:

the magic window

Time and again we have seen pictures that really do seem to be the gateway to a miniature, magic universe; where you could, you feel, somehow be reduced to a tiny size and walk through the frame of the picture to the world on the other side, as Alice walked through the looking-glass.

Often, perspective -- or at least, the illusion of depth -- is fundamental to the existence of such a magic window. But one strange thing we have noticed is that usually, magic windows are surprisingly small. A few are as small as 6x9cm or 2x3 inches, though quarter-plate (image size 3x4 inches, 75x100mm) is normally as small as they go, and postcard-size magic windows are quite common. They are very rarely bigger than 5x7 inches/13x18cm, though a few are as large as whole-plate, 6½ x 8½ inches, 16.5 x 21.6cm. By 8x10 inches they are very rare indeed. A lot are contact prints. More are black and white than colour, though when they work in colour, they are doubly magical.

What is it about these pictures? We don't know. We suspect it is something to do with perspective of texture: the images are more perfect than we can see. There is always more there, even if we get out our magnifying glasses. But we don't know.

10th Century Church of St. Martin, Noize

Another thing about magic windows is that they very seldom have people in them; somehow, people make them seem too real, too immediate. The only exception is old pictures, so old that anyone in them is unlikely to be alive today. Roger shot this on Maco Cube 400 using our old KowaSIX with its 85/2.8 standard lens. The 6x6 format helped to capture texture. In addition we see vanishing point perspective; the repetition of shapes; receding planes...

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© 2006 Roger W. Hicks