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P. A. Stonemann, CSS Dixieland

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CSS Dixieland

Probing the depths of knowledge

These essays by P. A. Stonemann, CSS Dixieland, cover a wide range of historical, philosophical, scientifical and technical subjects. Each page deals with a particular topic, divided into sections and explained by itself. Every page shows at its top hyper links to every other page. The Start page also has short descriptions of the other pages. CSS Dixieland expresses gratitude to the readers that make this work meaningful.

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Stereoscopy page

How to make three dimensional images
with any camera for still Photography
The realistic capture of the visual world,
technique adaptable to Cinematography

Walkyrie who takes our dead heroes to Walhalla in Asgard.
Wagner Frost Illustration

Sections in this page

  How to make Stereoscopy
  Hyper links

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How to make Stereoscopy

"La vue stereoscopique est la chose elle-meme, elle rend tangible la Nature, avec la profondeur de ses different plans, le relief naturel des objects, et la comparaison est tout a la avantage de ce genre de reproduction" (Monsieur F. Panajou, 1899).

A brief note on the History of Stereoscopy

On 21st June 1833 Mister Charles Wheatstone presented in the British Royal Society an essay about a phenomenon until then scarcely known: the importance of binocular vision in the perception of distance, depth and relief of objects in Nature. Continuing his research, Mr. Wheatstone published five years later, in 1838, an essay illustrated with stereoscopic hand-drawings. It was the start of one of the most strange (and little known nowadays) photographic techniques.

Traditionally, Stereoscopy is divided in Stereoscopic Drawing (Stereodrawing) and Stereoscopic Photography (Stereophotography or Stereography). The present essay deals with the later technique. The words are of Greek Etymology:
Stereos = Volume or Space, Skopos = Image, Photos = Light, Graphos = Record
"Image in volume recorded by light".

Shortly after the first public presentation of the Daguerreotype of Monsieur Louis Jacques Mande Daguerre, in August 1839, a number of photographers began experimenting the possibility of using cameras for making stereoscopic views. The first extant stereograph was made by Mister Wheatstone himself in 1841. He wrote that some stereographs had been made by Mister William Henry Fox Talbot in the late 1830's, but sadly they are now lost. Mister Talbot did not use the Daguerreotype, but his own Calotype, the first negative-positive process in the History of Photography.

In 1849 Sir David Brewster perfected the optical stereoscopic device for viewing stereographs, giving a great encouragement to those who cultivated this photographic technique, which in few years became enormously popular and began producing thousands of stereographs of landscapes, monuments, or famous people. About 1860 it was very common in the high class homes of Europe and North America to possess a stereoscope in the hall or studio, for enjoyment of visitors.

Herr Hermann Helmholtz performed in 1857 the first scientific research on Stereoscopic Optics, doing the mathematical calculations on focal length, convergence of axes and stereo base for the correct perception of the phenomenon. It became clear that Stereoscopy is based on an optical illusion that only happens in the brain of the observer, with the observer seeing simultaneously with the two eyes, each eye (or each image seen by each eye) from a slightly different angle. An image seen with a single eye, or an image drawn or photographed without using stereoscopic techniques, receives the name of Monoscopy: Monoscopic Drawing (Monodrawing) and Monoscopic Photography (Monophotography). Stereoscopy is also called tri-dimensional image, and Monoscopy bi-dimensional image.

In 1907 the Autochromatic Lumiere Plates were released to the photographic market. They were of panchromatic spectral sensitivity, developable by the reverse process to direct positive made public by Signore Rodolfo Namias in 1898. The process of Messieurs Louis Lumiere and August Lumiere gave colour images by additive trichromy. The first colour stereographs were thus made. Stereoscopy also was applied to Cinematography since the start of the XX Century, having a great importance in the decennium of the 1950's. There were also some efforts for making Stereoscopic Television and for Auto-Stereoscopy (this one used mainly for decorating walls or memorial books, and for tourist post cards), but since 1970 Stereoscopy began to fall into oblivion, in spite of the efforts made by camera and stereoscope factories for its revival. Nowadays Stereoscopy is mainly used for civil or military Aerial Photographic Survey, and for other scientifical or technical purposes.

There are in the World some associations devoted to Stereoscopy. Those photographers interested in the subject may consult the list of names and active hyper links after the main body of this essay. Some of them sell books and stereoscopic materials.

Methods for making Stereoscopic Photography

There are in existence four main methods for making Stereoscopic Photography, each one of them with possible variations. The main ones are:

Stereoscopic camera

Using a stereoscopic camera, with two optical objectives of parallel axes and a single camera body. It has the advantage of making possible to photograph moving scenes, but the two disadvantages that for any scenes (moving or not) the stereo base is fixed and the axes are parallel. It is possible to modify the stereo base and to converge the axes when photographing unmoving scenes, simply by using the stereoscopic camera as if it were a monoscopic camera shooting twice (see point four, below).

Beam splitter

Using a beam splitter, which can be adapted to a monoscopic camera. It splits the image from the scene into two stereogrammes, located side by side inside the space of a single monoscopic photogramme. It has the advantage of photographing moving scenes, like in the prior case, with also the same disadvantages of fixed stereo base and of parallel axes, plus the added disadvantage of producing stereogrammes of half size. It is also possible to use the beam splitter for unmoving scenes as if it were a monoscopic camera shooting twice, although it is more difficult to do it with a beam splitter than with a real stereoscopic camera.

Two monoscopic cameras shooting simultaneously

Using two monoscopic cameras of identical format and optical system, with the same pointing attitude and regulation of adjustments (focus, relative opening, exposure time, et cetera) and shooting simultaneously. It is the best solution, because it makes possible to modify stereo base as well as convergence, but it has the serious difficulty of needing an exact synchronisation between the two cameras when photographing moving scenes. For unmoving scenes, the synchronisation between the two cameras is not necessary.

One monoscopic camera shooting twice

Using a single monoscopic camera, shooting twice. The stereo base can in this case be modified or by moving the camera sideward or by rotating the subject to be photographed, between the two shots that will form the stereocopic image. This is the process that will be explained in the present essay. It makes possible to modify stereo base as well as convergence of axes at will, although it also has the very serious drawback of only making possible to photograph unmoving scenes. In most cases the stereoscopist photographer who choose this method must avoid a casual portrait, because his characters will appear somewhat moved in the ten or twenty seconds that are necessary for moving the camera sideward, pointing again, and shooting the second time. Only with models well trained for complete immobility, like statues, is possible the use of this method. You may try with hardened French legionnaires or with poker face British policemen, because it is a matter of fact that with most mortals this method does not work at all.

Method when using a single monoscopic camera shooting twice

Viewers

Viewers: get two small hand-held viewers for observing diapositives by transmitted light, in the format 135 of 24 X 36 millimetres. Viewers that are placed on a table or that are held at a distance from the eyes and have their own inner light are absolutely useless. You must get very simple viewers, of those which are approached to the eyes (either with their own inner light or -more commonly-, which are pointed to any external source of strong light). They must be identical. A pair of them costs less than five pounds. The focal length of these viewers is invariably 50 millimetres, which makes convenient to use in the camera objective lenses of the same or similar focal length in order to record correctly the stereoscopic image.

Camera

Camera: use preferently a camera with manual controls, format 135 of 24 X 36 millimetres. Any other format could be used, but there would be the problem of viewing the stereographs, because viewers in other formats are difficult or impossible to obtain in the market, and perhaps would have to be made under special order or by the photographer himself, while viewers for the 135 format of 24 X 36 millimetres can be easily bought. Photographers using an automatic camera must give priority to the relative opening of the diaphragm.

Objective lens

Objective lens (optical system): use an objective of normal focal length, which for the mentioned format is more or less between 45 and 60 millimetres, and ideally between 50 and 52 millimetres. It is possible to use other focal lengths, although for a correct reproduction of the stereoscopic effect it requires a compensation of the stereoscopic base according to mathematical formulae of some complexity. An approximation to solve the calculation will be given later in this essay. More precise results may be obtained by other, more complex equations. Using either too long or too short focal lengths without compensation, especially the short ones, will provoke distortion and change in the apparent size, distance and stereoscopic depth of the elements in the scene. Those aberrations, when well studied and partly compensated, will produce a strange vision of the World that is exclusive of Stereoscopy. The biggest relative opening of the diaphragm (f/2, f/1.4 or bigger) has no particular importance, except when wishing a short depth of field in order to discriminate the nearest plane by leaving the other planes out of focus, which is something that in Stereoscopy must be done rationally, so as not to lose the points of visual reference in the texture of the farthest plane, this is to say, of the background.

Film and developing

Film and developing: use a film for getting a direct positive image in a single developing process, this is, a film intended for diapositive slides (transparencies). It would also be possible to convert a negative into a positive by contact, but it would be a complexity and there would always exist a loss of quality. If having only films intended for negatives, then it is better to develop them by reversal process to direct positive. The above mentioned Namias process is the best one for this purpose.

Monochromy: most films accept reversal development to direct positive. Kodak Kodalith Ortho, Technical Pan, Infrared High Speed, Tri-X, Plus-X, T-Max, Ilford F-50 Plus, SFX, Delta, FP-4, HP-5, Agfa Pan, Scala, Fuji Neo Pan, Forte Pan, Foma Pan... all of them yield good results, but the exact process for reversal development varies from one emulsion to another. Films of low sensitivity are better, and also high contrast developers based on Hydroquinone and Caustic Hydroxide: Kodak D-8, D-11, D-19, D-72, D-85, Dektol, Kodalith A+B, Tetenal Dokulith, Dokumol... are some examples. Photographers who compose their own developers enjoy greater control on contrast, density of blacks and grain size, than what is possible with any commercial ready made developers. That is because small grain is a necessity in Stereoscopic Photography, but development in depth is a necessity in reversal development, and the only way to comply with these two apparently opposed conditions is by using an emulsion of low sensitivity, combined with a developer of high energy and adding a restraining agent: Potassium Bromide, Benzotriazol or Nitrobenzimidazol are the most common ones.

If possible avoid films of high sensitivity or developers of low contrast. Agfa Scala is the only film in the world especially made for yielding in the reversion a monochromatic positive image of the highest quality. There is also some self reversal duplication film for Cinematography: it yields a positive image when developed in a process for negatives. Another alternative is using chromogenic film Ilford XP-2 or Kodak T-400 CN and developing it in Kodak E-6 process for trichromy and polichromy, but the resulting positive image will not be true black and white, it will be cyan and white. All the mentioned films suffer a considerable loss of sensitivity when developed to direct positive (except Agfa Scala and the films for duplication, in which the nominal sensitivity has already been compensated). For instance, the chromogenic films XP-2 or T-400 CN whose sensitivity in the C-41 process for negatives is of 400 ASA 27 DIN, must be exposed at an approximate index of 70 ASA 19-20 DIN when wishing to develop in normal E-6 process for positives. That means a loss of about two and a half steps, and it is approximately like that with all emulsions.

Trichromy and polichromy: There are in the World about a dozen films for the already referred E-6 process for positives. Most of these films are made of three sensitive layers (trichromy), one or two are made of four layers (polichromy, or more precisely, tetrachromy). None of two layers (bichromy) is being made any longer. They are balanced either for day light or for tungsten light (wolfram). All colour films nowadays marketed in Photography are based in the substractive colour process, while about the additive colour process it can be said that it became almost exclusively restricted to photomechanical processes for graphic printing, where tetrachromy (polichromy), using four inks, is still a common process. In all cases of development to direct positive, be it monochromy or tri-polichromy, exposure is preferably calculated for the high lights, and in case of doubt it is better to sub-expose or to sub-develop.

That is exactly the opposite to what is done for developing into negative, in which exposure is calculated preferently for the shadows and in case of doubt super-exposure or super-development is the rule. The reason for the difference is that it is much easier to decrease by chemical means the high density of a dark image (even at the cost of losing detail in the high lights), than to increase the low density of a light image. Exposure latitude for diapositives is much narrower than for negatives, because in the negative-positive process it is possible to correct exposure errors during the positivation, inside certain limits, but exposure errors cannot easily be corrected in the direct reversal positive. In spite of that, strongly traditional photographers like Mister P. A. Stonemann, CSS Dixieland, do not use photometres (light metres), but only a posographic table of personal construction (a list of typical light conditions and their values in Lux), and apply mathematical formulae for determining all values that are determinable in Photography.

Scene

Scene: using a single monoscopic camera and therefore needing to make two records of the same scene from different angles, choose a scene having all elements still, or with slow or distant movements, or movements axial to the line of vision of the camera, so that in for instance thirty seconds it be not possible to detect important movement. Near leaves moved by slight wind, distant leaves moved by strong wind, slow or distant animals coming towards the camera or receding from it, following the axial line of vision, near rivers of slow waters, distant clouds or smoke moved by strong wind, all those are examples of scenes that can be photographed, in spite of not being completely still. It all depends on the speed, distance and direction of movement -relative whither the camera be pointing-, and of the time needed by the photographer for exposing the first stereogramme, moving the camera sidewards, pointing again, and exposing the second stereogramme, according to what will be explained later.

Near plane

Near plane: choose a main motive of pictorical interest, and be careful in avoiding the visualisation by the camera of any other element at shorter distance than the main motive of interest. If no angle of pointing could make possible the avoidance of those too near elements, then try to leave them at one side of the image composition, or then out of focus by opening diaphragm or by using an objective lens of longer focal length (in this last case a compensation of the stereoscopic base must be done). If any of those solutions prove to be impossible, then the nearest element in sharp view will be named as "near plane", and it will command the calculations coming later. The ideal goal is to have the main motive of interest also as the near plane. In Stereoscopy it yields good results a detailed and planned work, which includes looking for the best angle whence to make both photographs of the stereographic pair, without undesirable elements appearing in one or the other of the stereogrammes, or in both.

Far plane

Far (distant) plane: the visible background being apparently behind the main motive of interest (and in reality perhaps much farther), is named "far plane" or "distant plane". When seen by the camera, that distant background seems to surround all or the most part of the main motive. The farther the distance of the background will be the better, provided that it be clearly visible. It is also better to choose an angle of pointing that place the main motive against a far plane of well defined texture, for making easier the visualisation of the stereoscopic effect. A heterogeneus background of trees, clouds or mountains is better than a homogeneus background of grey sky or of sea flat like a looking glass. It does not matter if there exist in the scene other planes even farther. With regard to our calculations, the "far plane" is that one seeming to be behind the most part of the main motive.

Focus

Focus: focus the near plane when wishing a short depth of field , even if provoking a slight out of focus in the main motive. Notwithstanding, the desirable procedure would be to have the main motive also as the near plane. It is possible to focus the main motive when wishing a longer depth of field, but only if the near plane be still inside a good focus, because the important thing to remember is that the near plane must always be in excellent focus, except when being a small or lateral element just incidental to the scene. A calculation of circle of confusion diameters at a minimum and a maximum distance may be necessary for precision work.

Long depths of field are commonly used in Stereoscopy, but there are some situations in which for one reason or another it may be preferable to photograph with a short depth of field: for clearly distinguishing certain elements from their background, or for having a great resolution of details in a plane of special interest, even at the cost of leaving the other planes out of focus. Optical resolution of tiny details will diminish a little when enlarging depth of field, by closing diaphragm aperture or by using an objective lens of longer focal length and of similar quality. Regarding the far plane it does not matter if it be slightly out of focus, or even if it be considerably out of focus, always provided that some of its texture be visible enough for having a visual reference of the stereoscopic effect. A completely flat background will diminish the perception of stereoscopic depth.

Relative opening and exposure time

Relative opening and exposure time: as it has now been said, a big opening and a short time will give a little more of resolution of tiny details in the focused plane, at the cost of shorter depth of field for the other planes, which would therefore be out of focus, but in Stereo Photography it is generally preferred a long depth of field for having with good focus at least the nearest plane and the main motive, and perhaps also some focus in the farthest plane behind the main motive. This is the place for saying some words about chromatic sensitivity and general sensitivity of photographic emulsions.

By the Grottus-Draper Law, only actinic radiation will provoke a chemical reaction of development in the emulsion, this is, only the part of the electromagnetic spectrum to which the film or plate be sensitive will have an impact in the form of latent image, therefore only that part of the spectrum will be developed into a visible image. Using films of the ultra magenta (ultra violet), achromatic (blue sensitive) or orthochromatic (isochromatic) types, remember the low actinity possessed by colours of long wave length and low vibration frequency, when these colours be predominant in the scene (like for instance with tungsten light -incandescence lamps-), and increase proportionally the necessary exposure, respect to that which would be calculated for panchromatic films.

With infra red films it should in theory be the opposite: to decrease exposure before tungsten lit scenes, due to the high amount of infra red radiation possessed by incandescent lamps. But infra red Photography (approximately beyond 700 nanometres) is generally made with filtres that absorb a part of the visible radiation (Kodak Wratten 87 A, visually red), or the whole of the visible radiation (Kodak Wratten 89 C, visually black), and in these cases the exposure must be increased according to the factor of filtre. The "visual focus" does not exactly coincide with the "chemical focus" when working with non panchromatic emulsions. The image is formed in a different plane from the plane that a human photographer perceives as the correct focus. Therefore the focused distance must always be corrected, no matter which colour may be predominant in the environment.

Another problem is the Schwarzschild Effect of Reciprocity Failure, which substantially affects films of high sensitivity. With those of low sensitivity, however, this effect is not so pronounced, and the necessary increase when using very long or very short exposure times (or when using very small or very big relative openings) is comparatively minor. It comes to be almost zero for the Lippmann Emulsion used in scientific Photography -particularly in Astronomy-. However, with most films an increase of exposure will be necessary, calculated in multiplicative factors based on an exponential progression that varies according to the film and to its development. This is particularly important when the low intensity of environmentally available light force to exposures that may last for some minutes, some hours, or even some days for each photograph -or for each single stereograph-, or else when working with Fresnel zone plates or with stenopeic cameras ("pin hole" cameras), which usually possess extremely small openings.

Convergence of axes

Convergence of axes: When a stereograph be made with cameras in parallel axes, the vertical margins located at both sides of the combined image show no stereoscopic effect, because each margin has been recorded on only one of the stereogrammes, and not on the two stereogrammes that form the stereographic pair.

For preventing that, the axes of the cameras must converge on an easily distinguishable point located in the near plane, or located in the main motive if this motive be not too separated from the near plane. However, the convergence of axes must not be complete when photographing motives located too near to the cameras, because in that case it would produce the "convergence error", in which a scene element of square form would appear in the photograph with some form of parallelogramme, or rather, of trunk of a rectangle triangle lying horizontally. The left stereogramme would show the left side as bigger and the right stereogramme would show the right side as bigger, which would provoke a difficulty of visualisation. The cause of this phenomenon resides in the laws of perspective, and it cannot be completely corrected. As a safe working rule, the distance between the point of convergence in the scene and the cameras must not be smaller than the focal length of each camera multiplied by one hundred:

Convergence distance => focal length x 100.

For cameras of the 135 format with a focal length of 50 millimetres, it would be safe to converge the axes to a minimum of five metres between cameras and point of convergence.

The distance of convergence could be shorter than that, when the scene lack elements with well defined straight lines, in which case it would still be acceptable a minimum distance of convergence equal to the focal length multiplied by fifty:

Convergence distance => focal length x 50.

In the example given, of the 135 format and 50 millimetres of focal length, convergence could reach a minimum of two and a half metres. For precise photographic works, distances should always be measured from the immmergence nodal point of the cameras' optical objectives, and not from the plane onto which the real image be projected. The exact location of the immergence and emergence nodal points in complex optical systems can only be determined by mathematical calculations, which we shall not explain here. For more general works, measuring from the image projection plane as opposed to measuring from the nodal point would represent so small a difference, that no pains need to be taken in determining the location of the nodal point. Measurement can acceptably be done, as an approximation, from the centre of the image plane. This consideration will be valid throughout this essay for most of the formulae given, when measurement of distances be a necessary factor.

When it be imperative to photograph a motive located too close to the cameras, then it will also be necessary to converge the axes onto it, and therefore a compensation for a smaller stereoscopic base should be done, or else the mentioned convergence error would be unacceptable. We shall not enter now in the complexity of trigonometrical calculations for the correct convergence angle. At the moment it will be enough to say that in such cases the two cameras' axes could be pointing, as a safe working procedure, to some intermediate angle between the complete convergence (onto the nearest plane or onto the main motive) and the parallelism of axes pointing to the infinite. Using the camera's range finder or the polished glass, rotate the camera vertical or horizontally until having the chosen point of convergence in the centre, or in one of the four corners of the image (or in any other part of the image, but determine as precisely as possible which part it is, because the same framing operation will have to be done for recording the other stereogramme, in the second shot).

Near plane and far plane distances

Near plane and far plane distances: Measure as best as possible the distances in straight line from the cameras to the near plane and from the cameras to the far plane. Remember what has been said about measuring from the immergence nodal point for precision works, or from the centre of the image plane for more general works. The measurements must take as reference, at the other end, the centre of the most characteristic element located in the near plane, and the element in the far plane apparently located behind the most characteristic feature of the main motive. The distance of the main motive itself does not matter much, only an estimation must be done that the main motive be not much farther than the near plane, and even better, that the main motive be also the near plane. If photographing, for instance, the tower of a mediaeval castle from a levelled ground, know Ye that the distance from the cameras to the tower's base is one of the two cathets of the rectangle triangle, the tower's height (to the top or to another chosen point) is the other cathet, and the distance from the cameras to the tower's top (or to its chosen point) is the hypotenuse. Knowing the values of the cathets, apply the Pythagoras theorem to calculate the hypotenuse:

(horizontal cathet^2 + vertical cathet^2) v2 = hypotenuse

Example: horizontal cathet (distance from cameras to tower's base) twenty metres, vertical cathet (tower's height) ten metres. Therefore:

(20^2 + 10^2) v2 = (400 + 100) v2 = 500 v2 = 22.360 679 774 9

little more than twenty two point thirty six metres is the hypotenuse (distance from cameras to tower's top or to its chosen point).

The expression "^2" means "raised to the power of two", and the expression "v2" means "extracted to the root of two". For example, four raised to the power of two equals sixteen: 4^2 = 16, and its inverse operation is sixteen extracted to the root of two, which equals four: 16 v2 = 4
The expression "x" means "multiply" and the expression "/" means "divide".

If using a theodolite, a sextant, or another goniometric device, it is also possible to calculate it from the sinus of the angle formed by the camera's vertical inclination relative to a levelled ground. It has no need of being a precise measurement, Stereoscopy allows for an ample margin of tolerance when not used for technical ends. The distance to the near plane, however, must be measured more rigourously than the distance to the far plane. When the far plane be at a great distance relative to the near plane, then the far plane could be considered at the infinite.

Stereoscopic base: when using a single camera shooting twice, stereoscopic base is the lateral distance separating the location of the camera at the first shot, from its location at the second shot, giving slightly different views of the scene. Stereoscopic base could also be defined as the angle of rotation of the main motive between the first shot and the second shot (in some cases it is preferable to keep the camera immobile and rotate the motive instead). Using other procedures, stereoscopic base is the lateral distance separating the locations of the two cameras shooting simultaneously, or else the two optical objectives of a stereoscopic camera, or else the two mirrors of a stereoscopic beam splitter.

When the objectives of the two cameras (or of the single camera shooting twice, from different locations) rather than being parallel, happen to be converging onto any point of the scene, then the stereoscopic base will not be exactly a straight line, it will be an arc of circumference with centre in the point of convergence, and could be measured in radian or in any other angular unit. However, it could also be measured in metres or in any other length unit the internal string of the secant that connects the two extremes of the arc of circumference. We shall use this last measuring method in the present essay.

For simplicity, let us suppose that the focal lengths of the camera (or cameras), and of the viewers that will act as stereoscope, are all of them identical, let us say 50 millimetres.

Let us further suppose that we photograph with a near plane at a distance of more than five metres, and therefore we can quite well keep the camera (or cameras) axes in parallel without loosing much stereo effect in the main image. We have no need to converge axes.

We shall be confronted with one of two cases: either the far plane being so distant that it could be considered as being at the infinite (in which case we shall only need to measure the distance to the near plane and use a very simple formula), or else the far plane being comparatively close to the cameras in relation to the near plane (and therefore we have the need of measuring the distances to both planes and of applying a little more complex formula, derived from the previous one).

First case, far plane at infinite:

Distance from cameras to near plane / 50 = stereoscopic base

Formula where the number 50 was statistically obtained, after examining the stereoscopic perception in many human individuals and calculating average values. The stereoscopic effect that results by applying this formula multiplies by a factor of about two hundred the minimum stereoscopic perception, in binocular vision, considered normal for that species. The value of stereoscopic perception varies from an individual to another, existing some individuals who are capable of detecting a slight difference between the distances of two different planes, in fact in planes that for most observers would seem to be located at the same distance. On the other hand, there are also individuals who almost totally lack stereoscopic perception: they can see with their two eyes, but their brain does not interpret the combined image in terms of depth. They possess a binocular but a monoscopic vision, same as there are other individuals who are daltonic and do not perceive colours.

The average values of stereoscopic perception also vary from a race to another and from a species to another. The values given here are calculated for the White Race (Leucodermata) of Homo sapiens sapiens. Other specialists in Stereoscopic Photography suggest the number 30 in the same formulae where here we are suggesting the number 50, not only because they may be at least partly based on other statistical studies, but also because of their personal preference of provoking a rather exaggerated stereoscopic effect. An intelligent stereoscopist photographer must research by himself, and not accept with dogmatic faith what is being said in the present essay or what may be said by any other author. This advice is valid for every field of knowledge. The reader must think with critical intelligence, and then decide what he should do.

But, just as an initial experimentation, it may be reasonable to begin with the value of 50 given here, with the value of 30 given by other authors, or with another value in between, let us say about 40. Let us suppose that our divisor value of 50 be provisionally accepted. Let us remark that such a divisor must be used with parallel axes, because if photographing a very near motive or foreground it may be necessary to work with converging axes, and in such a case a divisor of 100 should be applied, making a smaller stereo base as it has already been explained in the appropiate epigraph.

Let us show some examples.

First example, near plane at 50 metres from the camera and far plane at the infinite:

50 / 50 = 1

The stereoscopic base must then be equal to one metre.

Second example, near plane at 4 metres and far plane at the infinite:

4 / 50 = 0.08

Here the stereo base must be 0.08 metres, or 80 millimetres.

We may have the case that the far plane be not "at the infinite" (meaning, so distant that it be unnecessary to measure its distance), but at a finite distance (meaning, that it be near enough to justify the measuring of its distance). Then we must apply a derived formula, which if using parallel axes will be:

((Far plane X Near plane) / (Far plane - Near plane)) / 50

Resulting in the correct stereoscopic base.

Third example, near plane at 50 metres and far plane at 150 metres from the camera:

((150 X 50) / (150 - 50)) / 50 = (7500 / 100) / 50 = 75 / 50 = 1.5

The stereoscopic base must be equal to 1.5 metres, one metre and a half. Observe that it was one metre when the far plane was at the infinite.

Fourth example, near plane at 4 metres and far plane at 6 metres:

((6 X 4) / (6 - 4)) / 50 = (24 / 2) / 50 = 12 / 50 = 0.24

Ergo the stereo base must here be 0.24 metres, or 240 millimetres. Observe that it was 80 millimetres when the far plane was at the infinite, but now the base has become threefold.

As it has been said, the divisor 50 must be applied when photographing with axes in parallel. If photographing at close range and using converging axes, then the divisor must be 100.

The result calculated as appropiate stereoscopic base for a scene with an "infinite" far plane could be multiplied by as much as five with a finite far plane, when this far plane be very close to the near plane. When photographing individuals against a wall, for instance, or when photographing coins or other nearly flat objects against a dark surface, or in Aerial Photography of the ground from a flying machine. The stereo base must not be exceeded much more than that, because in that case there would not be a frontal binocular vision, but two images representing each of the opposing sides of the main motive or scene, and for most observers it would be impossible to fuse the two images into one single combined image. They would see a double image, not a stereo image.

Another necessary condition is to have the two images absolutely identical, except in the angle from which they have breen recorded. Focal length, relative opening, exposure time, intensity, colour and direction of light, focusing, film and its development, framing, synchromism of the two shots (or immobility of the scene), everything must be as equal as possible in the two stereogrammes. To be sure, in the stereo base as well as in the other factors there is always some tolerance, in some of them more than in others, but for making perfect Stereoscopy it is necessary to control all the relevant factors with the maximum of precision reasonably possible.

Viewing

Viewing: Once the stereographs have been exposed and developed, simply mount separately each stereogramme in a slide mount, and so You will have two stereogrammes (in the form of two slides) for each stereograph. Then introduce each slide in the right position into a monocular viewer, having so a pair of monocular viewers, each one of them loaded with a stereogramme of the scene. In this combination, the two monocular viewers are now forming a single binocular viewer, called stereoscope, and the two stereogrammes are forming a stereograph.

It is important to take the care of having the left side image in the left hand and the right side image in the right hand, because accidental change of viewers to the wrong hand (which happens very often with beginners in Stereo Photography) will provoke an "inverted Stereoscopy", also called "anti-Stereoscopy" or "pseudo-Stereoscopy", in which the far elements of the scene seem to be near and the near elements seem to be far. This is a most strange vision of the World, particularly because sometimes the element that appears as nearer to the observer happens to be partly occulted by another element that appears as farther, a phenomenon that is an incomprehensible absurd, and which invariably astonishes and even fascinates those who observe it for the first time.

Approach the two viewers to Your eyes, not too near, and quietly rotate them in various directions until the two images that You are observing be fused in a single combined image, then keep the two viewers static in that position. At that instant You will enter into the magic world of Stereoscopy !

Resume of operations, step by step

1. Use a camera of the 135 format, with an objective lens of 50 millimetres or a little more.

2. Load the camera with film or plate for diapositives, obtainable through reversal development to direct positive, either in black and white or in colour.

3. Choose an immobile scene, or a scene with little observable movement.

4. Pay attention to not having any visible element of the scene located at a shorter distance than that at which the main motive of interest be located, and the main motive itself at not less than five metres distance.

5. Measure, calculate or guess the distance between the camera and the main motive (near plane), and also the distance between the camera and the background (far plane).

6. Apply the formulae that have been given for calculation of the stereoscopic base.

7. For this it will be better to use a tripod or another firm support: be sure that the camera be correctly pointing to a certain point of reference in the scene (in the background when using parallel axes, in the main motive when using converging axes), and that the main motive be well framed.

8. Photograph the scene from one of the angles, for example from the left side angle.

9. Advance film to the next photogramme. Keep all the other camera controls without alteration, including the control of focus.

10. Using a measuring tape, move the camera (or the tripod, if using it) the same distance right sidewards as it had been calculated as the appropiate size of the stereoscopic base. This movement must be perpendicular (transversal) to the axis in which the camera has been pointing for the first shot.

11. Frame again the main motive and point again to the point of reference in the background or in the main motive (depending on whether You be using parallel axes or converging axes). Then photograph again.

12. Repeat all prior steps with other scenes, or with the same scene by adjusting differently the camera controls.

13. Process the film by reversal development into direct positive, introduce each stereogramme into a different slide mount, and observe them simultaneously with a viewer in each hand.