ON first looking at a vertical air photograph there is a feeling of bewilderment. The strangeness is the result of the airman’s unusual viewpoint. As air travel becomes more general the strangeness will vanish. The photograph is an exact picture of what the aeroplane passenger sees when he looks below him.
A GEOLOGICAL SURVEY of Qishm Island, in the Persian Gulf, necessitated the taking of sixty photographs to form a mosaic of the area. The remarkable circular formation shown in this picture is a salt plug of Cambrian age intruding as a cylinder through the normal strata of Miocene-Pliocene beds. The plug itself has a diameter of about fourteen miles. The black area is the sea.
Photographs reproduce the tones, or shades of the scene in front of the camera lens, but conventional maps are concerned with line and not with tone. Before converting air photographs into maps it is necessary to understand what is represented by the various tones. They may range from the pure white of brilliant sunlight reflected from a cement road to the dense black of the shadow cast by a high mountain, and most air photographs exhibit a multitude of intermediate shades. Before a conventional map can be drawn these tones must be interpreted. No prolonged study is necessary; and once the basic principles are understood the matter is simply one of common sense.
The first step is to deduce the direction in which the sun was shining from the direction of shadows cast by such unmistakable objects as trees. After that, everything becomes sufficiently clear, and any remaining uncertainty is immediately dispelled by stereoscopic examination of the photographs.
Examination of a pair of photographs in a stereoscope takes advantage of the fact that an object presents a slightly different picture as the viewpoint is changed. Air photographs taken in sequence from viewpoints some hundreds of feet apart are not identical even in the region of ground common to both. The stereoscope permits two photographs to be examined at the same time, but allows one photograph of a pair to be viewed by one eye only. The brain fuses the two images into one whole, so that the fused picture is seen in relief in its three dimensions, length, breadth and depth, whereas each photograph viewed singly exhibits only the two dimensions of length and breadth. Railway embankments are immediately distinguished from cuttings, and hills and valleys are seen in their natural shapes.
The most important thing about any map or air photograph is its scale. Maps and plans are drawn on an extremely wide range of scales. When it is necessary to study a large area on a single piece of paper a scale of 1 : 1,000,000 may be suitable, but a railway engineer may need his track plans to be on a scale of say one inch to 40 feet or 1 : 480.
A map on a scale of 1 : 1,000,000 is really a diagram, and does not give a true picture of the Earth. In small-scale maps the size of important features is deliberately and artificially exaggerated. Consider a road, drawn boldly by two parallel lines on such a map. The width of the road may be perhaps 60 feet - generally less. Divide this width by a million and the result is something less than a thousandth part of an inch - a width so small that it could not be seen, and obviously too small to be drawn true to scale. Air photographs on such a scale would fail to record essential features and would thus be almost useless.
Obviously it is no use obtaining photographs on such scales that the images of important features are so small as to be invisible. If a 50-feet road is considered as a unit that must be shown on the map, and if it is admitted that the photographic image of the road may be as narrow as 1/100-in and still be visible, there is established as a lower limit of usefulness a scale of 1 : 60,000. For an upper limit of usefulness it is necessary to bear in mind various technical considerations of speed, size and weight, but successful air survey photographs on scales as large as 1 : 300 have been secured.
The scale of an air photograph is settled by two simple factors - the height of the aircraft above the ground and the focal length of the camera lens. The focal length - that is, the distance of the lens from the sensitive emulsion - may be anything between about two inches and forty inches, and the height of the aircraft anything between 1,000 feet and, say, 20,000 feet. By a judicious choice of flying height and focal length, it should be easy to obtain photographs on any desired scale between 1 : 120,000 and 1 : 300. But the Earth is not flat; it is not even spherical, and its surface is a mass of irregularities. An aircraft in flight cannot follow all the changes in contour of the ground. Moreover, there has not yet been developed any reliable instrument to measure aircraft height. Present-day instruments merely measure differences in air pressure, and air pressure is not an altogether sound guide. It is, however, reasonably easy to obtain photographs of flat country true to scale within fairly narrow limits. When it is a matter of precise mapping it is necessary to know the exact length of some distance on the ground that can be identified and measured on the photograph - or on a strip of photographs. The negative can then be printed to the desired scale in an ordinary enlarging lantern.
The chapter beginning on page 131 describes how air survey photographs are taken. Fig. 1 (shown below) shows the flying map taken into the air by the photographer. The area to be surveyed is surrounded by a heavy broken line. According to the scale required, the parallel flying lines are ruled on the map an appropriate distance apart. It is the pilot’s task to keep his aircraft exactly over these lines. After the photographs have been developed, an index chart (Fig. 2) is made on tracing paper pinned down over the map; the centre of each photograph is indicated on this index chart by a small circle with its serial number alongside.
Having arranged that each photograph shall include part of the ground that is included in the previous photograph in the strip, it is easy to cut each of them along common lines of detail and to butt them together and mount them with paste on a support of plywood or similar material. In the same way each strip of photographs can be joined to its neighbouring strip and a mosaic can, in this simple manner, be quickly produced to show the whole territory in one composite picture. The accuracy of the result will depend upon the constancy of the flying height of the aircraft and upon the flatness of the ground.
Variations of flying height and variations of ground contour will affect the scale of the photographs, and it is impossible to make two unequal images of the same ground coincide. Other things being equal, the higher the aeroplane flies the more accurate will the result be, for variations of ground contour will then have less influence. In spite of the small inaccuracies that must remain inherent in the mosaic system, reconnaissance maps made in this way are for many purposes extraordinarily valuable. Not the least valuable characteristics of the system are the high speed at which every topographical detail can be extracted, and the continuity of large ground features exhibited by the mosaic.
Once the air photograph has been brought to the desired scale, there are various methods of converting its information into the lines that form the conventional map. One simple method is to draw the detail over the photographic image with a fine pen and using waterproof ink. The photographic image can then be bleached away with chemicals, leaving only the ink lines on the white paper. This method has the drawback that the size of the map is limited by the size of the individual photograph.
Other methods involve the use of tracing paper and carbon paper. A non-greasy carbon paper is available which does not leave the smears that would result from the use of ordinary typewriting carbon paper. Metal scribers are used for tracing the detail from the photograph and the carbon impression is then inked up with a fine pen.
Another method, which is in use at the Ordnance Survey Office and elsewhere, is to ink in the detail lines on the air photograph itself, in a distinctive colour, generally red, and then to place the photograph in an epidiascope. This instrument throws a bright image of the photograph with its red lines on to the map paper, and any small local, residual inequalities of scale are corrected optically. The lines are then drawn on the map paper, in coincidence with their red light images, with pen and ink as before.
FIG. 1 FLYING MAP (left) taken into the air by a photographer. The heavy broken line indicates the area to be photographed and the vertical parallel lines indicate the courses to be flown by the pilot; their distance apart depends on the scale of the required photographs.
FIG 2. INDEX CHART (right), made after the photographs have been developed. The chart is made on tracing paper placed over the flying map and the centre of each photograph is marked by a small circle with a serial number alongside. Some of the numbers have been omitted above, for clarity.
All these methods except the bleaching out method involve the drawing of lines more than once, and although this may perhaps add to the ultimate precision, or have some other advantages, it is evident that any method needing only one manual drawing operation offers scope for greater speed and economy.
The process of mapping described above is based on the assumption that the lens of the air camera was pointing downwards in a truly vertical direction at the moment of exposure. Unfortunately this ideal is seldom entirely realized, for an aeroplane behaves in much the same way as a bird or a fish, and is rarely in a truly level position. There is nearly always some slight tilt, either fore and aft or laterally or both. The camera shares the movements of the aircraft, and the resisting tilt of the air photograph is objectionable in precise mapping work, particularly when the drawing of contour lines is involved.
These unwanted tilts are generally very small - mere fractions of a degree, and they are not important for many classes of work, but strenuous efforts are being made to eliminate them altogether. All pendulum and spirit-level devices are without avail because of the phenomenon known as acceleration. Acceleration, like centrifugal force, in a moving body makes the pendulum or spirit level entirely unreliable. The gyroscope has been used to solve the problem in somewhat the same manner as it is used to stabilize big ships and to maintain a compass course at sea. But gyroscopes working about the three axes that are involved in the air present certain technical problems that have not yet been completely solved.
The Effects of Tilt
Every year shows some slight progress towards the ideal, and no doubt this tilt nuisance will be entirely overcome before long. Tilt is a nuisance because the map is to be drawn on a horizontal plane - the datum plane parallel with sea level. If the photographs are taken in a plane not parallel to the datum plane - that is, if the negatives are tilted, the equal and parallel sides of a square on the ground will not be quite equal and parallel on the photographs.
The photographic image will, however, be very nearly square, and, so long as tilts are small, the falsity will not be of much moment in drawing plans; but, as will be shown later, the falsity will be detrimental to the measurement of contour.
The mathematics of tilted air photographs has been thoroughly investigated and a most valuable feature has been discovered. This is that, although lengths measured on a tilted photograph may not be always entirely reliable, radial angles measured at the centre of the photograph are much less sensitive to departures from the ideal.
The centre of each air photograph can thus be regarded as a theodolite station from which horizontal angles are read to a number of other stations, and a chain of horizontal triangles can be established along a strip of air photographs closely equalling (except of course in scale) a similar chain of triangles on the ground below. So long as tilts are small, this system of radial triangulation, which is known in Great Britain as the “Arundel” system, can be carried out rapidly by graphical methods without computation, and will yield planimetry of moderately flat country so accurate as to be entirely acceptable, on such scales as three inches to the mile.
RADIAL TRIANGULATION can be used to yield reasonably accurate planimetry of moderately flat country from a series of air photographs. This is possible because radial angles measured at the centre of each photograph are not seriously affected by camera tilt. By using the centres of the photographs (A, B, C, D and E) as theodolite stations (see central diagram above), a chain of horizontal triangles can be established along a strip of photographs, closely corresponding (except in scale) to a similar chain on the ground itself. Except on the first and last photographs every point is well fixed by three intersecting lines.
Hilly country, however, presents a more difficult problem, because the scale of the air photograph depends on the height of the aircraft above the ground. If, then, the ground is mountainous, the air camera will be nearer to the tops of the mountains than to the valleys, and the mountain-tops will be photographed on one scale while the valleys are photographed on another scale - all in one photograph. How is it possible to deduce from the photographs the true scale of all the features? The answer is that it is not possible on a single photograph. But it can be done from a pair of photographs, and that is one reason why the ground is always photographed twice by arranging that each photograph includes sixty per cent of the ground covered by the preceding photograph in the strip; The arrangement is known as “overlap”.
FIG 3. ELEVATED DETAIL is displaced radially outwards in an air photograph. If the top of a chimney stack is at A, its image in the camera will be at a. If the height of the chimney were increased to B, the image formed by the lens L would appear on the negative at b. Similarly with C and c.
From the diagram of Fig. 3, it is clear that the images elevated detail must be displaced radially outwards on an air photograph. The outward displacement is the way in which the inequality of scale is manifested. There are no means of detecting or measuring this outwards displacement on a single photograph, but the same system of graphical radial triangulation already mentioned for combating camera tilt can be used for determining plan positions. Untilted air photographs of the most mountainous country can be used in this way for mapping with ease and certainty, but the presence of camera tilt over mountainous country compels the surveyor to depart somewhat from simple graphical methods and to resort to mathematical solutions.
Differences of ground elevation are calculated in air survey from measurements of exceedingly small differences between a pair of photographic images. Somewhat similar differences can be caused by unwanted tilts of the air camera. In the absence of sufficient knowledge of the true positions of a number of controlling ground points, it is impossible to determine whether these measured differences are due to changes of ground slope or to tilt of the air camera. The differences may be so small as to be negligible in determining the plan positions of the ground points; but, small as they are, they can lead to considerable errors in contouring, unless the amount of tilt is first determined.
The manner in which contour can be measured from a pair of air photographs is explained by Fig. 4. The air camera during flight makes its first exposure at C1, and its second exposure at C2. If the ground were at an infinite distance below the aircraft all photographic images of ground points would be formed by parallel pairs of light rays such as P1 and P2.
As the ground increases in elevation a point such as A would have its photographic images formed at a1 and a2 and any higher ground point such as B would have its images formed at b1 and b2. As the elevation of the ground increases, so does the distance between twin photographic images increase, e.g. a1 a2 is greater than P1 P2, and b1 b2 is greater than a1 a2. The
difference between a1 a2 and P1 P2 is known as the parallax of the point A and the difference between b1 b2 and P1 P2 is known as the parallax of the point B. It can be shown that all points in any horizontal ground plane such as the plane through A have an equal amount of parallax.
By measuring the parallax of any ground point, we can, if we know the focal length of the camera and the length L1 L2 of the air base, calculate the vertical distance between the ground point and the air camera. By comparing the parallax of any ground point with that of any other ground point, we have a measure of the difference in elevation of the two ground points. Remembering the rule that equal parallax accompanies equal elevation we are able to. draw contour lines.
The human eye is extremely sensitive to differences of parallax, and differences as small as one-thousandth part of an inch can be readily appreciated in the stereoscopic viewing of photographs. This characteristic is of such vital importance that the stereoscope is unquestionably the most essential instrument in the air-survey mapping office. The ability to depict the three dimensions of the Earth’s surface is essential in any system of survey and, although the advantages of air survey in the drawing of plans are overwhelming, its power to produce a precise record of levels can never be so great. Precise levelling on the ground can deal with fractions of inches, but from air photographs the differences that can be extracted are best expressed in feet. A proper understanding of this circumstance does not belittle the value of air survey, but rather emphasizes those fields of usefulness in which its value is supreme.
FIG 4. MEASURING CONTOURS from air photographs. In this diagram C1 and C2 represent two consecutive positions of the camera in flight. In the first position the point A on the ground is photographed at a1 on the negative, in the second position at a2. If the camera were at an infinite height above the ground all photographic images would be formed by parallel rays such as P1 and P2. The difference in length between the distances a1 a2 and P1 P2 is known as the parallax of the point A. Differences between the parallax of A and that of B determine the difference of elevation between these points.
Every normal survey starts with the measurement of a base line. Great pains are taken to secure the maximum accuracy in this measurement and, from the two ends of the base, angles are read to new stations. The whole territory is divided in this manner into a network of triangles, and the topography is drawn on the map, within each triangle in turn. All modern, precise air survey starts similarly with a base line.
The base line which is used is the line in the air joining two successive camera stations; that is, the line joining the two positions in space occupied by the air camera when the two photographs were exposed. Now the measurement and location of a line in space must always be a matter of some difficulty, and precise measurements must always be made if accuracy is to be secured. The importance of this line in space lies in the fact that it can be used as a base from which angles in space can be measured to various ground stations of which it is desired to fix the situations. The air base thus becomes similar to a base line on the ground and the position of each ground point can be determined in relation to the air base. It is then simple to fix the positions of all the ground stations in relation to one another - which is the essence of mapping.
Steel Rods Simulate Rays
The positions of two photographs are first determined in relation to each other before any attempt is made to relate the photographs to the ground. The ideal relation is that the photographic negatives should all be exposed in one common horizontal plane. This ideal is seldom, if ever, entirely realized. Each photograph may be inadvertently tilted a small amount about two axes, and the line joining the two camera stations may not be exactly horizontal, i.e. the aeroplane may have gained or lost height in the short time between successive exposures. But if precise measurements are taken on a pair of photographs, of the images of the ground common to both, that is, in the “overlap” portion, it is possible, without any knowledge of ground dimensions, to determine by mathematical computation the angular relations that existed between the two photographs when they were exposed. Then, if the actual situation of at least three of the photographed points on the ground is known it becomes possible to determine the exact position in space that each negative occupied at the moment of exposure. Thereafter, it becomes possible to determine the exact situation of every ground point common to the pair of photographs.
Light travels in straight lines - so far as most everyday problems are concerned - and it is the intersection of straight rays of light that is the basis of mapping from air photographs. Fig. 5, below, will make this clear. A point A on the ground is first photographed by the air camera C1 at A1. The aircraft moves on to C2 and the same ground point A is photographed again and its image falls at A2.
If now, after development the first photographic negative A1 is replaced in its original position in relation to the lens L, and the light rays are made to retrace their path backwards, we know that the ground point A must lie somewhere on the ray A1 L1 A. We cannot know more than that its true situation is somewhere on this light ray. But if the second negative is similarly treated, the ground point A must lie somewhere on the ray A2 L2 A. If we know or can compute the angular relation between the two photographs Ax and A2 and a horizontal plane, as well as the distance apart (L1 L2) of the two camera stations, we can fix the actual ground position of point A at the intersection of the reversed light rays. In the same way the position of every other ground point common to the two photographs can be fixed both in plan and in elevation. The distance separating the two air stations generally amounts to some hundreds of feet and, instead of reconstructing the actual circumstances, a small scale model of them is made. The points P1and P2 are the centres of the photographs.
FIG 5. THE ANGLES MADE BY LIGHT RAYS inside the air camera are later used to determine the situation of points on the ground. Thus, the point A is photographed at A1 and A2 and the distances A1 P1 and A2 P2 are measured on the photographs. The focal lengths (P1 L1 and P2 L2) are known, and the point A can thus be fixed by geometry in relation to the air base L1 L2.
This principle of reversing the light rays of a pair of photographs was developed as a surveying technique long before air photography came into existence. The credit belongs in large part to Deville, Surveyor General of Canada, to Fourcade of South Africa, and to von Pulfrich of Germany. Photo survey on the ground is relatively easy because it is generally possible to arrange that each photograph of a pair is exposed in a common vertical plane. In air survey it is necessary to admit photographs that do not comply with ideal conditions and to modify the technique accordingly.
The assertion has been made that light travels in straight lines. In the development of photo survey it has been realized that straight steel rods could replace straight light rays, and machines using this principle have been developed to facilitate mapping from photographs. These mapping machines are nearly all based on the principle of making steel rods simulate light rays. All the machines are based on the use of photographs in pairs.
Fig. 6, below, is a schematic diagram showing in its simplest form the manner in which such machines copy the light rays that formed the photographic images in the air survey camera. Modem machines of this type are extremely complicated, but their complications are due almost entirely to the necessity of dealing with various departures from ideal exposure conditions.
FIG 6. DIAGRAM OF MAPPING MACHINE in its simplest form. The two telescopic rods represent a reversal of the light rays which formed images on the negatives. The universal joints are fixed at the position of the lenses and the distance piece represents the air base. The hinge which joins the two rods thus represents - if the upper ends follow identical details on both negatives - the common origin of light rays which formed the images of those details.
The machines consist essentially of two carriers for the photographs and two rods pivoted near their middles on universal joints. These universal joints take the place of the lens of the air camera and they are separated by a distance piece. The length of this distance piece can be varied and it represents in miniature the air base, that is, the distance between two successive camera stations. The rods are hinged together at their lower ends and the hinge carries a drawing pencil. At the upper ends of the rods indexes are provided which can be brought into coincidence with the twin images of any point of ground detail on the two photographs. The rods are telescopic.
The two photographs are set above the universal joints at exactly the same distance as the negatives were above the camera lenses. Each light ray forming the original photographic pictures can be reproduced in turn by making the two indexes at the tops of the rods simultaneously coincide with the twin images on the two photographs. The rods then make the same angles with the photographs as the original light rays travelling through the lens from the point on the ground, made with the two negatives in the air camera.
As any pair of light rays started from a common origin on the ground, this origin is reproduced by the hinge at the intersection of the rods. A pencil fixed at the hinge will draw the plan position of each point on the ground in turn as the indexes are moved from point to point on the photographs. The pencil is carried in a telescopic mounting from which can be read the elevation of each point.
How Contour Lines are Drawn
The hinge thus describes in space a small scale three-dimensional model of the ground surface. If the hinge is constrained, by locking mechanism, to move only at one particular height above the drawing surface the pencil will draw a contour line so long as the indexes are kept continuously in simultaneous coincidence with the twin photographic images.
Provision is made in the machines for plotting the detail on any desired scale and for setting each photograph in its appropriate tilted position and for inclining the “air base” to the horizontal as desired.
Some form of binocular stereoscopic device is used for viewing the simultaneous coincidence of the indexes with the photographic images. The complexity that seems to be inherent in the system has necessitated the provision of some exceedingly intricate optical systems.
The best known machines of this type have been developed in Switzerland by Wild, and in Germany by Zeiss. Other interesting machines - notably the Italian Nistri - are based on the old Camera Plastica principle, depending on the observed coincidence of two separate light images on the drawing surface. The photograph below shows one of these automatic mapping instruments. The turning of three controlling wheels automatically draws the map on any desired scale for a plan and draws contour lines at any desired vertical interval. The instrument illustrated is the new Wild Autograph.
THE WILD AUTOGRAPH, a modern type of automatic mapping apparatus made in Switzerland. The operator places a pair of air photographs in their carriers, adjusts them for orientation and tilt and sets the instrument for scale. By turning the controlling wheels he keeps two indexes in simultaneous coincidence with the pairs of photographic images of a series of ground points. The lines on the map are drawn by a mechanical pencil, the movements of which are controlled by the turning of the wheels.
The illustration at the end of this chapter shows the kind of map produced on an automatic mapping instrument from a pair of overlapping vertical photographs. The photographs were taken from a flying height of approximately 15,000 feet and the aeroplane travelled nearly a mile between the two exposures. Each photograph reproduced approximately five square miles of mountainous country, and covered roughly 60 per cent of the ground covered by the other.
It is only in comparatively rich and highly developed countries that the production of maps and plans on large scales such as 1: 500, 1:1,000 or 1: 2,500 can be justified. Elsewhere maps on smaller scales must serve, for the cost of producing a small-scale map is only a fraction of the cost of producing a map on a large scale.
This question of scale is of outstanding importance in air survey. For the production of a 1 : 2,500 plan from air photographs it is usual to fly at a height of 8,000 or 9,000 feet and use a lens of 20-in focal length. In this way a scale of approximately 1 : 5,000 is obtained. The photographs can be enlarged two diameters without difficulty to yield the desired map scale of 1 : 2,500.
In such circumstances the width of the strip of ground photographed as the aeroplane progresses amounts to about two-thirds of a mile. The cost of an air survey is governed largely by the amount of flying involved and, if the width of each strip can be increased, the number of strips will be reduced and the cost of the flying and other operations will be correspondingly lowered. Various obvious solutions present themselves. First, the aircraft can fly higher; secondly, a lens with a particularly wide angle of view can be used; and thirdly, the size of the negative can be increased. Any one or a combination of all of these expedients will help, but each has its practical limits.
Aircraft cannot often carry out survey work at a greater height than 20,000 feet, and until recently manufacturers had not produced lenses covering a greater angle than 60° at a sufficiently large working aperture. Again, the increase in the size of the negative adds undesirable weight and bulk to the equipment and adds to the difficulty of manipulation.
Use of Ultra-Wide-Angle Lenses
A negative 9-in by 7-in is the largest in common use to-day. This compares with 5-in by 4-in commonly used twenty years ago, and although it is not unlikely that some further increase in negative size will occur, the problem is at present being tackled from the optical standpoint.
Air survey has contributed various improvements to the technique of photography, but perhaps the most important of these is the development of lenses of exceptionally wide covering power, capable of giving accurate images at large working apertures.
There is now available for air survey a British lens of 4-in focal length covering a negative 7-in square. Working at a flying height of 20,000 feet, an air camera fitted with this lens covers a band of country nearly seven miles wide. That is to say, by flying at 20,000 feet instead of at 8,000 or 9,000 feet, and by using a 4-in lens instead of a 20-in lens, it is possible to effect a tenfold increase in the width of the ground photographed. At the same time the amount of flying needed to cover a given area is divided by ten.
While the ultra-wide-angle lens was being developed, other solutions of the problem were being evolved. The most interesting of these is the multi-lens camera.
The basic advantage of the system is that a camera pointed obliquely at the ground embraces a wider strip of country than when it is pointed vertically. By the combination of a number of such oblique systems into one camera the area covered at one exposure could be made to stretch from horizon to horizon. As, however, the most distant parts of the view would clearly be on too small a scale to be of much value, this type of equipment is generally designed to include a view angle of about 130°.
MAP WITH CONTOURS produced by an automatic mapping apparatus from a pair of air photographs (not shown). The indexes on the machine are kept coinciding with the images of identical details on both photographs. Details of different heights have different positions on each negative and the instrument correlates them so that the contours are drawn by the mapping pencil.