- Email: [email protected]
The new Santoni solar periscope for aerial triangulation and the organization of colonial survey
23 Trotzdem wird die Luftbildmessung nicht zur Entwieklung ge!angen, solange die gro~en Institute auf diese Weise wetter arbeiten. Man m u f den Mut zum E x p e r i m e n t i e r e n a u f b r i n g e n und deshalb die Untersuchungsarbeit nicht yore Zufall abh~ingig maehen, sondern diese so organisieren, wie die Industrie dies macht und wie es auch bet verschiedenen BehiSrden gehandhabf wird. Man m u f in einer gewissen Unzufriedenheit beziiglich des erreiehten t/esultates eben weiterstudieren. Yon dieser Unzufriedenheit habe ieh auf dem Kongre~ allerdings etwas zuwenig bemerkt. N u t mif dem G l a u b e n an die Vortreffliehkeit der erreichten Ergebnisse werden wir nichts erzielen. Allerdings wird m a n auf einem Kongrel~ eher dazu geneigt seth, einige Schattenseiten, die man aueh selber wohl kennt, zu iibersehen u n d die Arbeit etwas rosiger darzustellen, als sic in W i r k l i & k e i t ist. Auch yon diesem Eindruck habe idl mieh ant d em Kongrefi nicht immer fret machen k6nnen. In der Photogrammetrie arbeitet man oft am Rande des tatsiichlieh Erreichbaren, lieber sogar noeh etwas jenseits dieser Grenze. Dies bringt viele Schwierigkeiten u n d eine nicht u n b e d e u t e n d e Anzahl yon Fehlsdd~gen mit sieh. Der Verfasser weifl dies aus eigener Erfahrung, und, wie idl aucb schon einmal w/ihrend des Kongresses b e m e r k t babe, ieh m i f t r a u e allen den Mitteilungen, die diese Schwierigkeiten iiberhaupt nicht erwiJhnen. Es ist natiirlieh mbglich, daft diese Tendenz, die auf einem solchen Kongrel~ auch immer v o r h a n d e n ist, mich efwas b e e i n f l u f t hat u n d mehr Selbstbewul~tsein bet den Phofogrammetern v e r m u t e n 1/ifit., als sie tats/iehlieh besitzen. Ich hoffe yon ganzem Herzen, daft das letztere der Fall ist, denn n u r d a n n wird die in der Zwisehenzeit ansgefiihrte Arbeit giinstige Resultate ergeben, u n d man wird auf 'dem n~iebsten K o n g r e f yon ether Verbesserung sprechen k6nnen: Neben der Arbeit der gro~.en Institute ist gewif noeh Raum fiir individnelle Leistungen yon Einzelpersonen, die sieh vielleieht etwas mehr um die Probleme als solehe u n d etwas weniger um die Ergebnisse zu k i i m m e r n brauehen als die gegenw/irtig in der Photogrammetrie arbeitenden Institute.
The new Sanloni Solar Periscope ior Aerial Triangulalion and lhe Organizalion oi Colonial Survey -" By Ermen~gildo Santoni, Florence. hdroduction. The principle of the method which has been invented and developed by me for d e t e r m i n i n g tile outer orienfation of an aerial photograph is shown in the drawing reproduced on fig. I of the Italian licenee No. 175863 of May 16th 1919. As can be seen on the aforesaid drawing, an a u x i l i a r y camera D has been superimposed on the main camera A. The a u x i l i a r y camera can be turned, so that its axis is directed approximately towards the sun. The image S" of the sun is reproduced on the film of the camera D together with the image of a chronometer E, at the same instant at which the camera A takes the photograph of the ground. On the latter we have to determine the position of points B C, the images of which appear on the photograph. The a n g u l a r values, m a r k e d b y the graduations G and the S'-position allow us to determine the orientation of the camera A with regard to SS" b y which a point S" can be constructed, which is identical with the point at which a sun ray passing through the centre of the lens of camera A meets the photograph. The knowledge of the direction of the sun ray computed from the astronomical values based on the time at which the photograph was taken and on the geographical position of one of the ground points (B, C), simplifies the problem into one in which the position of a point must be determined in an explicit may as the apex of a pyramid rising into space, the direction Of one of its edges being knomn.
24 The elements of the outer orientation are thus completely and separately defined for each photograph at once. This readily enables us to use the method for an elaboration of a series of consecutive photographs. But, i n d e p e n d e n t l y from the mathematical equations of the problem, the function of the sun ray, being the axis formed by a knomn direction (5* S') around which the camera would be free to revolve, were it not that it is fixed b y its position relative to the ground, which is d e t e r m i n e d by the two directions to the k n o w n ground features, is specified in an attestation (added to the abovementioned licenee 1) dealing with an a r r a n g e m e n t which makes itpossible to re-establish in an optic-mechanical way tLD_~ the spatial position of the camera station and implicitly, to determine the tilt and swing of the photograph. Fig.
/ /
!A A
.
/y
t\
This method, as already explained'L lends itself particularly well to the development of spatial aerial triangulations. All my studies and the constructions in connexion therewith, are based on this f u n d a m e n t a l idea. Naturally, since the time of my very first praetieal developments, I have applied ph0togoniometrical measuring, in order to obtain the values relative to the sun's direction and to the ground features.
To this end, I have built a special s u r v e y i n g camera (schematic fig. 2a) with two ground eameras and a sun camera, as well as a special photogoniometer (schematic fig. 2b) which makes it possible to measure directions to points on the photographs, after having them exactly ~ " , ~ ¢ ~ recentered on the same s u r v e y i n g camera, through their corresponding lenses.
1 S u p p l e m e n t a r y Licence, May 2nd 1920. Reg. Gen. 185 254. 2 Cfr. Fotogrammetria aerea Santoni. L'Universo, ~mo.I, p. 17, 1926.
25 This idea has allowed me to obtain by way of calculation the really satisfactory results of some experiments on spatial t r i a n g u l a t i o n of series of photographs carried out by me in 1926 and 1930 at the Istituto Geografieo Militate, an account of which was given by me during the fifth session of the Third Commission of the I n t e r n a t i o n a l Congress of P h o t o g r a m m e t r y in Rome 1938. Although it reduces to a m i n i m u m the sources of error, this method, being exclusively based on calculation, would be too complicated when we have to t r i a n g u l a t e a large .number of photographs, and I ~ o u l d recommend its application only when all sorts , s of special improvements (very high quality of flying, special surveying" cameras, etc.) have r e n d e r e d a t r i a n g u l a t i o n system with large i ") j/' meshes possible. / m
On the other hand, wishing to facilitate the immediate application of my solar method for surveys of a colonial character, I have invented and constructed a new Solar Periscope and developed methods for its use, which form the principal object of the present paper.
I t( I~ ~ / ~cl.,n'
~i./: I T,
/
t ~",
"(~ i
\ lk
1
~&~
~
~
~---'
B
Fig. 2a, 2b Part I. Aerial T r i a n g u l a t i o n with the new Solar Periscope. a) The photographing (surveying) device. This i n s t r u m e n t (see fig. 3 and schem, fig. 4a, b,c) actually consists of the solar camera A proper, a film chassis B with all the necessary devices for its automatic working, a magneti6 compass C, a gyroscopic directional D, and a statoscope E. So as to be able to reproduce on the film (t) the image of the sun, whatever the latter's elevation above the horizon and the direction of the route (course of the airplane), the solar camera A is furnished with 9 lenses, one central and 8 peripheric and with a crown of single reflecting prisms. O n e of the characteristics of this camera - - made possible by the fact that it serves for photographing the sun - - consists of a strong superposition on the film of the various encompassing spaces, thus r e n d e r i n g it possible to make out afterwards whi& lens produced the solar image with which we are concerned. An electric shutter allows of rapid and simultaneous opening of the 9 lenses at ea& moment at which the main camera, to wllidl the periscope is fixed, takes a photograph of the ground. At the same moment, a second multiple circular shutter (2) and some suitable optical devices, enable us to fix on the film the images of the marks of a chronometer (5), and the variations of the atmospheric pressure measured with a statoscope (5, 6, 7, 8). Finally, the simultaneous lighting of some small electric lamps, enable us to record on the same film the magnetic azimuth, measured with the compass C and the variations of swing, measured by the gyroscopic directional (Variometer) D. While the size of the solar camera is 130 X 130ram in the m o d e l now used, the progress of the film for ea& photograph of the ground is only 30 mm and it consists of five partial forward movements of 6 mm each. While all the images produced b y the various devices mentioned above are reproduced simultaneously with the photographs of the ground, at the end of ca& of the partial progresses (of 6mm) only the index marks (rep~res), the magnetic compass, the graduation of the variometer, and
26 the index of the statoscope are reproduced. This allows a greater precision in reading the diagrams. The film thus obtained is shown in fig. 4 c . . T h e time at which each p i c t u r e was taken and the a n g u l a r values marked by the variometer can be read directly from the fihn. b) The Photogoniometer and its use. The apparatus is represented on the schematic fig. 5. Pointing with telescope 15 at the S' image of the sun, through the very optical system that prodneed it, the telescope axis will find itself exactly placed in the direction of the m o m e n t a r y sun rays. The vertical angle, which we shall call cop, formed between the direction of the sun and the solar camera's axis, can be read by means of microscope 17. The horizontal angle, which we shall call fi, referred to an axis of the photograph (measuring the marks) and Fig. 3 can be read by means of microscope 16. 0 u the circle 15, on which the telescope is mounted, a double microscope 21 is also provided, by means of which the sighting at all the images m u' ol the magnetic compass' graduation can be effeeted, reading the angular value with the microscope 16. The rotation of microscope 21 around its own axis, makes it possible to eliminate the eccentric effect of the graduation, which is always rather strong, owing to the p e n d u l a r suspension of the magnetic rose. c) Calculation of the outer (angular) Orientation of the Solar Photograph. The periscope being immovably fixed to the main camera and the photograph of the sun being t a k e n simultaneously with that of the ground, the outer (angular) orientation of the solar photograph is similar to that of the corresponding" ground photograph, with the restriction of the discrepancies and approximations of the instrumentM mounting. In the following e l e m e n t a r y analysis we shall assume, for tile sake of simplicity, that the solar camera has only one central lens, and that the ground camera consists of a single camera, the axis of which Coincides with that of the solar camera. Suppose: U--p (fig. 6) axis of the solar camera, U centre of the system, and K the corresponding photograph, in the a n g u l a r position corresponding to the survey u n d e r
27
B
B
3.
10
l
i |
Fig. 4
c
b
c o n s i d e r a t i o n ; . U - - S solar direction, and S' image of the sun on the photograph. Considering a sphere the centre of which is U, Z determines the local vertical, ]/INVE the horizon, S the sun's direction, and P the axis of the solar camera. The sighting on the photogoniometer, effected by means of the telescope (15) at the S'-image of the sun, gives ns the value of the angle ~p, formed between the axis of the camera (U--P), and the direction of the sun (S--U), as well as that of the angle ~, formed between the line connecting the m e a s a r i n g marks (rr) and the plane (SUP) determined by the axis of the camera and the direction of the sun. On the other hand, the measuring on the images of the rose of the magnetic compass, taking into account also the reading of graduation 19, gives us tile value of the angle x
28 formed between the magnetic North (M') and the aforesmd line (rr). To simplify our explanation let us suppose that the magnetic declination is k n o w n to tls, and that consequently the line pM' represents the direction of the geographic North. The sum of the angles a and ~ gives us the value of the angle represented by an angie 0p on the plane surface of photograph K. The angle formed between the plane of the photograph K and the horizontal surface MNVE being practically only a few degrees, the 0p value
Fig. 5
iCl
/(A) / r ~ measured on t h e photograph in a first approximation horizontal surface MNVE.
might
be
transferred
to the
In these conditions the angle Op expresses the value of the geographical azimuth of the horizontal line UE of the surface passing through the sun and through the camera axis. We shall call Op the periscopic solar azimuth. In the same way the angle Op immediate])- measured on the photogoniometer will be called periscopic zenithal solar distance. On the other ]land the time at which the photograph was taken and the knowledge of the geographical position of the camera eliable us to determine, with a sufficient degree of accuracy, the value of the angle Os which is that of the geodetic solar azimuth and that of the angle ~p3, that is of the geodetic zenithal solar distance. The difference between the two solar azimuths (Op--Os = e) gives us the value of the cathetus VE of the spheric rectangle triangle SVE, the second cathetus SV whidl is the supplement to the k n o w n q~s value. The solution of the triangle SVE gives us the values of the dihedron formed b y the two surfaces passing through the sun which contain the vertical UZ and the axis UP of the periscope respectively. The subsequent solution of the spheric triangle PZS gives us the value of the inclination (PZ) of the axis of the
29 periscope and that of the azimuthal difference (PZS) between the geodetic solar azimuth and the azimuth of the axis of t h e periscope. The value of the angle ZPS, taking into account the known angle ~, gives us the value of the sroing of the photograph, the a n g u l a r orientation of photograph K being thus completely determined. In order to be able to orientate a photograph with the above mentioned angular ,~alues of outer orientation in the plotting apparatus, it is necessary that the rotation axes of the s u r v e y i n g cameras inside the p l o t t i n g a p p a r a t u s should be disposed as follows: P r i m a r y axis - - of orientation - - (angle SZP); Secondary axis - - of inclination - - (side PZ); T e r t i a r y axis - - of swing - - (angle ZPS-4-~). But as the disposition of the rotation axes in the modern plotting apparatuses differs, for obvious reasons, from the ones mentioned above, the computation of the second triangle (SZP) is replaced by that of a second triangle c o n v e n i e n t l y chosen to match the plotting apparatus used. The method used so far in working with the Santoni-Galileo stereocartograph III is the following: for the elaboration of a series of photographs, we estimate the azimuth of the plotting axis, the value of which is attributed to the line x formed by the instrumental base, which is kept constant throughout the entire series. Thus: UN for this axis and On for the value of the pre-established plotting azimuth. From the calculation of the triangle S V E (the VE -= ~ and the S V = 90 ° _ cos being known) we obtain the values of the angle S E V (k) and of the side SE (~). From the calculation of the triangle N P E (the sides NE = 0 n - - 0p; PE = cop q- ~ and angle ~. being known) we obtain the value of the angle P N E (i) and N P E (o) and those of the side N P (x). Now, making use of the s u p p l e m e n t a r y rotation of both cameras of stereocartograph III a r o u n d the base line x (which serves for the absolute orientation of the model) as if it were that of a p r i m a r y axis, the photograph can be orientated in the plotting apparatus using directly the above mentioned values (i), (o), (x), that is: the angle i, or its complement (I) is a measure for the p r i m a r y rotation or that of the oblique (transversal) inclination which we shall simply call inclination (I) ; -
-
- - the angle x or its complement (C) is a measure for the secondary rotation or that of the longitudinal inclination, which we shall call convergence (C); - - the angle o, algebraically added to ~, is a measure for the tertiary rotation of the swing (O); the q u a r t e r l y rotation around the UA axis, which is still an approximatively transversal rotation, necessary to realize the rotation for the plotting of the contiguous photographs in the fan-like m u l t i - c a m e r a apparatus, can still be disposed of in stereocartograph III. -
-
It is at any rate possible to use this method with a n y type of plotting apparatus, the true and proper t r i a n g u l a t i o n developing itself only b y means of the central photograph. The degree of accuracy of the a n g u l a r values obtained in this way, depends above all on the degree of approximation obtained by the value s and on the reciprocal position of the axis US (solar direction) and on the axis UN (x plotting axis).
30 As angle ~ can be obtained with the aid of the photogoniometer with fairly good approximation, and angle Os can be determined with a still greater precision, the error of the angle s depends m a i n l y on the u n c e r t a i n azimuth a, obtained with a magnetic compass, even when the local magnetic declination is given with sufficient approximation. After all, as it is possible to determine with a fair degree of accuracy, the angle q~p with the aid of the photogoniometer, the a n g u l a r position of the axis of the periscope UP will be determined with fair I approximation in regard to the ' e~. ~ ',~? I I! angle SUP, while it will be affected I b y a perceptible error in regard to t~ ' t I' b/ its rotation around the solar ray US.
1
I
As in reality the angle PZ is only a few degrees, the error s by virtue il III IV of all the precautions mentioned below, will only be a few sexagesiFig. 7 real minutes and the differentials of the inclination, conoergence and sming angles could be easily calculated in regard to s. Practically, for the sake of simplicity, we only calculate the differentials of the transversal inclination (dI) and that of the convergence (dC) in regard to the swing variations (dO), using the following formulas, computed by me: __~
|
.
.
.
.
.
G /I:= =~_ l g_~_ . I_}:___J.1. . . . . . . .
dI= dO tang ~vp cos so sin x
(I)
dC= dO tang ~p sin o
(If)
In addition, the computer furnishes the plotter with a table containing a selection of values relative to the sming (0), inclination (I), and convergence (C) of each photograph of the series and of the differentials of the latter two in regard to the first. The calculation for this purpose effected either b y means of logarithms or the calculating machine, requires only a few minutes. d) Connection o~ successive photographs in the plotting apparatus b y means of the method of the transported azimuth. The plotter orientates in the apparatus, by means of the calculated values, a first pair of photographs containing the starting ground bases (b, fig. 7); he corrects the swing of the two photographs with the aid of this base, reads the small variations (dO) on the i n s t r u m e n t a l graduations and makes the consequent inclination and conoergence corrections, based on their respective differentials (dI, dC). In this operation, starting from an x Composing line of the approximated base, he will obtain the corresponding g composing line, while the composing line z will be obtained by comparison on two of the lateral points, ll, l',. The possibility of choosing the points 11, I'1, on the middle line of the o+-erlapping area, makes the determination of z free from possible errors caused by distortion. After the above simple a r r a n g e m e n t the model remains free from compass error, is deprioed of parallaxes and oriented angularly in an absolute direction. After having d e t e r m i n e d the scale by means of the starting base (b), we determine, by means of p l a n i m e t r y and of the elevation a point tl, chosen, in the overlapping zone of the third photograph. The second photograph is then m a t e r i a l l y put in the place Of photograph 1 in the s t e r e o c a r t o g r a p h (in the i n s t r u m e n t s furnished with an optical inversor, it could remain in its own place), and the third photograph is put into the plotting apparatus in the place of the second, orientated according to the calculated ~.'alues. After correcting the swing of the third photograph with regard to the second and having made the
31 differential corrections of inclination and convergence, by which the /j is determined, all that has to be done is to determine, the z on points 12, !'2 and to proportion the model by means of the variations of the air base, till we obtain t,, the value of the elevation given by the preceding pair. This p r o c e d u r e can be r e p e a t e d ad infinitum.
The great simplicity mith mhich each photograph is oriented on the preceding one, is oboious mhen roe consider that the elimination of the parallaxis on the nadiral points (needed to obtain the correction of the sming and the y composing base l i n e ) i s not, influenced by the successioe elimination of the parallaxes on the transoersal points (1, l') needed to obtain the z composing line. I h a v e called the aforesaid method a transported azimuthal method transported azimuth).
(method with
e) Connecting of successive photographs in the plotting apparatus applying the method
of independent azimuth° In order to be able to effect the correction of the swing of each photograph with r e g a r d to the preceding one, we can effect a relative (independent) correction for each pair, based on the data of the gyroscopic directional, c o n v e n i e n t l y compensated, as I e x p l a i n e d in the integral text of my Report to the Congress. This procedure, which enables us to avoid the systematic e r r o r of transport of the azimuth, is p a r t i c u l a r l y suitable for long distances. f) Use of the statoscope. The elements furnished by the statoscope h a v e so far n ev er been used in the application of the solar method. In fact, as I demonstrated in the integral t e x t of my Report, the data of the statoseope would in most cases contrast with the elements deduced from the solar direction. The statoscope may perhaps be used in p a r t i c u l a r l y unf a v o u r a b l e cases, and especially when the sun lies low above the horizon or in a direction transversal to the route. It will, however, be impossible to realize cases such as these during the surveys in regions lying near the Equator, such as Italian East Africa. P a r t I]. Analysis of causes of e r r o r and method of compensation. For the analysis of the influence of errors on the precision obtainable with my methods in regard of the direction of the sun in relation to the direction of the route, I must r efer the r e a d e r to the complete text of my Report. The result proves, at any rate, that as long as the zenithal distance of the sun is smaller than 45 °, the e r r o r of the inclination of the camera axis' (which is composed of an e rr o r of t ran s v er s a l inclination and an e r r o r of convergence) is inferior to the er r o r to be feared from the correction of the r e l a t i v e swing, so that the principal ad v an t ag e of my method, even in those cases when, for various reasons, a systematic transport of the error of the azimuth is still used, lies in its facilitating the planimetric a d j u s t m e n t of the total model enly by means of a control of the final (astronomical) azimuth, or of a difference of level, m e a s u r e d b e t w e e n the two features of the last p ar t i al model. On the other hand, when using the solar method, triangulation in space, errors in scale are always to know, are of a proportional kind when they depend on base of the initial model; they are of an incidei~taI
or any other method of aerial be feared. These errors, as we an error of scale in the starting" kind w h e n e v e r they depend en
32 accidental errors in the transfering of the scale from one side of the aerial polygon to the following one (each of which influences its successor as a proportional error); finally t h e y are of a systematic kind if, in passing from one photograph to the next, we commit an e rr o r in t r a n s p o r t i n g the a p p r o x i m a t i v e l y constant scale into an absolute value with an identical sign. The e r r o r which is most to be f e a r e d in spatial triangulations of successive photographs - - considering the m a n y sides of an airpolygon - - , is a systematic error, for it works by the law of squaring. So that an e r r o r of leiigth of the covered distance (/iS) can be totally attributed - - in the absence o f any other element of judgm e n t - - to a systematic e r r o r in the transport of scale (dr) and it has to be consequently compensated. The various causes of an error of that kind, which I intend to ex am i n e .lr~ .e, m i n u t e l y in a future study dedicated to this 'subject, are r! I! all to be attributed to slight deformations of the spatial bundles of plotting rays in v.~c relation to the bundles of rays 0 of the exposure. For these deformations, more f r e q u e n t l y caused by the p a r a l l e l o g r a m than by the true and proper fl~+3aH Ho projection system of the plotting apparatus, are not subject to the displacements of the principal point and cannot be a p p r o x i m a t e l y compensated by O' the relative c o n v e r g e n t adjustment, as occurs in other cases. This causes an er r o r comparable with the one depending Fig. 8 on a systematical longitudinal inclination (c', fig. S) of the exposure axes, unaccompanied by a corresponding inclination of the air base. The (theoretical) rectangle formed by t h e points of exposure (camera position) and the respective nadiral points, becomes, however, t r a n s f o r m e d into a trapezium, so that all the ground points become subject to an inclination 2 c'. Consequently, the whole net assumes a trapezoidal form. In the solar method, as the longitudinal inclination of the e x p o s u r e axes is connected with previously d e t e r m i n e d elements, the air base becomes subje c t to a corresponding inclination (d-c'), while the ground points become subject to an opposite direction ( - - c ' ) , that is a value half that to be feared when using other methods. This discrepancy could be traced along the entire net, unless, after having provided for the control of the coordinates of one of the ground features, P, we should r e t u r n to a general correction of the longitudinal inclination data, (C), attributing this e r r o r ( - - c ' ) to the relative fitting of the solar c a m e r a to the ground camera. Thi~ correction, even when the - - c ' e r r o r is not due to the above cause, has tile practical advantage of k eep i n g the coordinates of the model correct, i n d e p e n d e n t l y of the error of scale transfer which can be deducted later on with g r eat er precision and can then be compensated afterwards.
7;
At all events, and with e v e r y method - - presuming the existence of an original system with equal sides (pointed as in fig. 8) not considering the inclination of the chain,
33
the vertical t t size is enlarged with regard to its original real vah, e (that is in our case, at Ho) by a q u a n t i t y d H given b y the formula: ½ d H = l o tang c' from the similitude of the deformed net triangles, the increases in regard to the side lo by the value d t derived from the dt dH
-
I H
making d t = 2 y
12
tang e
The consequent error of length (dS) corresponding to the apex (n) is evidently derived from n ( n - - 1) A S = dt ~ (IX) Assuming that n is very large, producing n (n -- 1) = n ~, taking account of n = S and giving d t its original value, the above formula can also be written as follows: 1 A S = @ tang c' S 2
(X)
while the error in scale of the In side is given by the d S = n dt. W h e n e v e r it was possible to determine a new isolated ground base after a few pairs of photographs, which we shall call a p r e l i m i n a r y control base, discovering in it an error in scale, we were able to deduct from this the size error of transfer Ab[ from d bt d r - - bt
In n
(xf)
So as to automatically compensate this error in its further development the most practical method, adapted by me to the stereoeartograph llI, was to alter by a value 2 d l i the position of the scale index of the z eoInposing base line, at the exact place where it is joined to the camera whi& must receive every second photograph of the series. With this proeeeding, every side Hn is enlarged by 2dH" before being used for the d e t e r m i n a t i o n of the length of the new aerial side of the polygon. The a p p a r e n t disadvantage of this method of effective transfer of the photographs from one camera to the other, replacing the optical inversion, is compensated by a more easy p r e v e n t a t i v e eorrection on the dr, deduced from the length between the starting base and the p r e l i m i n a r y control base. On the other hand, even the very brief time needed for the transfer of the photograph from one camera to the other, is eompensated by the elinfination of all the operations eonneeted with the inversion of the base. When we reach the controlling base, or point, at the end of the flying strip the longitudinal error becomes greatly reduced., so that the r e m a i n i n g d t is generally reduced to one tenth. The solar method caff at all events be employed, even without a p r e l i m i n a r y control base, by effecting the total compensation on the arrival base. In using the formula XI for deducing" the;d/, the arrival base ean be i n d e p e n d e n t of the starting base. These bases, whidl are about i to 2 k m long, are measured by applying the well known indirect method with the aid of a horizontal stadia (substense bar). Their orientation is astronomically effeeted, and this can also take plaee during day time by making use of observations of the sun. Part III. Experiments with n e w periscope and the results obtained. Carlo Trombetti referred at length to these experiments in a Reportt which he presented to the Yth Congress of Photogrammetry. I shall confine myself to summing up the principal facts. C. Trombetti: Preparazione dei punti a terra per la triangolazione aerea col metodo Santoni e risultati conseguit con questo metodo.
34 The Tripoli E x p e r i m e n t (August 1955). C o n n ex i o n of 11 photographs which have been taken at a flying altitude of about 5500 m, with the i n d ep en d en t azimuth method, the values of the swing being p r o v i d e d by a magnetic compass. The total unadjusted model, about 9 km 10ng, r e v e a l e d no altimetrical deformation of a systematic character. In fact, in the It sections passing from one pair to the next, the following av er ag e errors in square meters w e r e r e v e a l e d : 5,11; 2,85; 5,19; 2,57; 5,26; 4,10; 5,19; 4,29; 2,96; 5,15; 4,29. G e n e r a l a v e r a g e (medium) 5,54. The model, on the contrary, proved to be considerably too large (4%o), which was p a r t l y due to the size a d j u s t m e n t of the first partial model, based on an existing map at the scale of 1/25.000, and p a r t l y to a systematic er r o r of transfer of scale. The C a r m a g n o l a - B a r o l o E x p e r i m e n t. This e x p e r i m e n t consists of a connexion of 27 successive photographs covering a distance of about 5t km, car r i ed out by applying" the method of transported azimuth. A ground base appearing on the first pair of photographs, and a point appearing on the seventh pair, at a distance of about 6,5 km from the starting ground base, w e r e used. This point re~ealed a length er r o r (As) of - - 1 6 , 18 meters from which, by means of the formula (IX) the systematical transport error (dr) was calculated. This proved to be about 1 m, the a v e r a g e length of the air polygon sides being 1200m. This e r r o r was taken into account during the subsequent elaboration of the strip, by means of an alteration of the scale index of the z composing base line a l r e a d y mentioned. A n o th e r elevation e r r o r of --5,09 m was discovered in the same point, corresponding to a systematic inclination of 0,75% 0 based on the ultimate distance, with a p r e v e n t a t i v e correction applied to the value of the longitudinal inclination (convergence), resulting from the calculations. Owi n g to this precaution, the ultimate model was found to be correct as regards elevation. In fact, errors of about l m only ,*-ere found at two known intermediate trigon o m et r i cal points and at the end base. A r e m a i n i n g error in length of + 52,95 m was found, from which the r e m a i n i n g e r r o r of transfer of scale w a s c a l c u l a t e d . This e r r o r p r o v e d to be 0,218 m. In addition, an e r r o r / J y of + 8 8 , 6 0 m and an er r o r in orientation of - - 2 5 ' were found at the end base, unanimously r e v e a l i n g a systematic error of transfer of azimuth of about 1' for each station. A definitive p la n i m e t r i c a d i u s t m e n t of the entire strip was effected, based on the above dt and on the e r r o r of transfer of azimuth. When v e r i f y i n g after the a d j u s t m e n t the position of the two i n t e r m e d i a t e trigonometrical points, an a v e r a g e p l a n i m e t r i c e r r o r of about 3 m was found in both. No altimetrical a d j u s t m e n t was t h e r e f o r e needed. The results obtained by this e x p e r i m e n t are so far significant, that they p r o v e that the general model obtained with the solar system, even if subject to the influence of systematic errors, just as is the case with other methods, presents v e r y r eg u l ar deformations, which can be adjusted in an easy way. The A r o n a T u r i n Experiment. This e x p e r i m e n t consists of the connexion of 92 successive photographs which were taken at a relative flying altitude of 5~00 m, covering a distance of about 10~- km. The elaboration was car r i ed out, applying the method of the transported azimuth b e t w e e n the starting base and the base for a p p r o x i m a t i v e control, situated in the area covered by the 9th pair of photographs and by the i n d e p e n d e n t azimuth method for the r e m a in in g part of the strip between the base for a p p r o x i m a t i v e control and the end base. The systematic size e r r o r of transport (dt) calculated from the data of the part be t w e en the starting base and the base for approxilnative control, p r o v e d to be about 1 m, just as in the p r e c e d in g e x p e r i m e n t and in the r em ai n i n g part a corresponding correction has been applied. The control at the end base, situated in the area covered
35 by the 92th pair, has revealed a r e m a i n i n g error of transfer of scale of about 0,08 m. Based on this amount, the a d j u s t m e n t of the strip was effected. A comparison after a d j u s t m e n t with a trigonometric point situated at about the centre of the strip revealed the following definitive r e m a i n i n g errors:
,4X=-- 15,05;
AY=--46,38 m:
z/Z= +14,50.
Conclusion. The Santoni solar method presents a safe and easy means of aerial t r i a n g u l a t i o n in space. With special precautions, the method is possible in every kind of country and is especially suitable for tropical and subtropical areas. The pllo~ogoniomeiric operations and the calculations needed for obtaining the outer orientation values of the photographs being very simple, they can be entrusted to persons of an average education. The connexion of the successive photographs in the plotting apparatus can be effected with great rapidity, being essentially based on the adjusting of the swing. The general model is affected by x ery slight regular deformations, indicated by the control at the end bases, which is easily adjusted. The intermediate base for first approximative control is not indispensable. 'The certain control of the inclination of the model in the flying direction, permits the use of multiple camera covering a very great transversal field, actually consisting of photographs taken with several cameras, whi& greatly reduce the amount of photographing and plotting" operations. The Santoni quadruple camera, provided with a solar periscope, rendered it possible last summer to survey an area of about 5500 km 2 on a scale of 1/100.000, the photographs of which are now being" elaborated. The same quadruple camera using plates and a new triple camera using films are soon to be used in the Empire for a 1/100.000 survey of very large areas. These surveys will require the building of a net of approximately square meshes formed by p r i m a r y triangulation strips, the sides of whirl1 will be of about 100 km long. A ground base will be measured at every junction, applying the normal terrestrial s u r v e y i n g methods, whilst an astronomical station will also be determined at each of these points. The method of a d j u s t m e n t used to attach the correct importance to the astronomical observations will be published later. For a relative flying altitude of abont 3500 m (the elevation of the area itself being 2000. m) both in the case of the oscillating quadruple camera using plates and the new camera using films, five secondary strips will be needed to fill the entire quadrangle of each mesh.
Le nouveau p~riscope solaire Sanloni pour la lriangulalion a~rienne R6sum6 par E. Santoui, Florence. Pr6face. Par l ' e x a m e n de mes brevets italiens obtenus en 1919 (fig. 1 du texte) je montre comment mes ~tudes f u r e n t dirig6es, d~s le d6but, vers la r~alisation d'une chambre d o n n a n t les 616ments d'orientation de la chambre de prise de vues ~t chaque station en p a r t a n t de point6s effectu~s sur le soleil et de deux points connus du t e r r a i n photographi6, Ce proc~d6 repose sur le rel~vement dans l'espace du sommet d'une pyramide dont la direction d ' u n e ar6te est connue. Uu brevet italien obtenu en 1920 montre quc la solution 6tadi6e repose sur le fait, que la direction qui joint l'appareil au soleil est connue et que c'est elle qui serf de base ~ l'orientation des cliches. ]e montre enfin les progr~s successifs accomplis par rues r6alisations qui ont pr6cdd6 le n o u v e a u p6riscope solaire.
The new Sanloni Solar Periscope ior Aerial Triangulalion and lhe Organizalion oi Colonial Survey -" By Ermen~gildo Santoni, Florence. hdroduction. The principle of the method which has been invented and developed by me for d e t e r m i n i n g tile outer orienfation of an aerial photograph is shown in the drawing reproduced on fig. I of the Italian licenee No. 175863 of May 16th 1919. As can be seen on the aforesaid drawing, an a u x i l i a r y camera D has been superimposed on the main camera A. The a u x i l i a r y camera can be turned, so that its axis is directed approximately towards the sun. The image S" of the sun is reproduced on the film of the camera D together with the image of a chronometer E, at the same instant at which the camera A takes the photograph of the ground. On the latter we have to determine the position of points B C, the images of which appear on the photograph. The a n g u l a r values, m a r k e d b y the graduations G and the S'-position allow us to determine the orientation of the camera A with regard to SS" b y which a point S" can be constructed, which is identical with the point at which a sun ray passing through the centre of the lens of camera A meets the photograph. The knowledge of the direction of the sun ray computed from the astronomical values based on the time at which the photograph was taken and on the geographical position of one of the ground points (B, C), simplifies the problem into one in which the position of a point must be determined in an explicit may as the apex of a pyramid rising into space, the direction Of one of its edges being knomn.
24 The elements of the outer orientation are thus completely and separately defined for each photograph at once. This readily enables us to use the method for an elaboration of a series of consecutive photographs. But, i n d e p e n d e n t l y from the mathematical equations of the problem, the function of the sun ray, being the axis formed by a knomn direction (5* S') around which the camera would be free to revolve, were it not that it is fixed b y its position relative to the ground, which is d e t e r m i n e d by the two directions to the k n o w n ground features, is specified in an attestation (added to the abovementioned licenee 1) dealing with an a r r a n g e m e n t which makes itpossible to re-establish in an optic-mechanical way tLD_~ the spatial position of the camera station and implicitly, to determine the tilt and swing of the photograph. Fig.
/ /
!A A
.
/y
t\
This method, as already explained'L lends itself particularly well to the development of spatial aerial triangulations. All my studies and the constructions in connexion therewith, are based on this f u n d a m e n t a l idea. Naturally, since the time of my very first praetieal developments, I have applied ph0togoniometrical measuring, in order to obtain the values relative to the sun's direction and to the ground features.
To this end, I have built a special s u r v e y i n g camera (schematic fig. 2a) with two ground eameras and a sun camera, as well as a special photogoniometer (schematic fig. 2b) which makes it possible to measure directions to points on the photographs, after having them exactly ~ " , ~ ¢ ~ recentered on the same s u r v e y i n g camera, through their corresponding lenses.
1 S u p p l e m e n t a r y Licence, May 2nd 1920. Reg. Gen. 185 254. 2 Cfr. Fotogrammetria aerea Santoni. L'Universo, ~mo.I, p. 17, 1926.
25 This idea has allowed me to obtain by way of calculation the really satisfactory results of some experiments on spatial t r i a n g u l a t i o n of series of photographs carried out by me in 1926 and 1930 at the Istituto Geografieo Militate, an account of which was given by me during the fifth session of the Third Commission of the I n t e r n a t i o n a l Congress of P h o t o g r a m m e t r y in Rome 1938. Although it reduces to a m i n i m u m the sources of error, this method, being exclusively based on calculation, would be too complicated when we have to t r i a n g u l a t e a large .number of photographs, and I ~ o u l d recommend its application only when all sorts , s of special improvements (very high quality of flying, special surveying" cameras, etc.) have r e n d e r e d a t r i a n g u l a t i o n system with large i ") j/' meshes possible. / m
On the other hand, wishing to facilitate the immediate application of my solar method for surveys of a colonial character, I have invented and constructed a new Solar Periscope and developed methods for its use, which form the principal object of the present paper.
I t( I~ ~ / ~cl.,n'
~i./: I T,
/
t ~",
"(~ i
\ lk
1
~&~
~
~
~---'
B
Fig. 2a, 2b Part I. Aerial T r i a n g u l a t i o n with the new Solar Periscope. a) The photographing (surveying) device. This i n s t r u m e n t (see fig. 3 and schem, fig. 4a, b,c) actually consists of the solar camera A proper, a film chassis B with all the necessary devices for its automatic working, a magneti6 compass C, a gyroscopic directional D, and a statoscope E. So as to be able to reproduce on the film (t) the image of the sun, whatever the latter's elevation above the horizon and the direction of the route (course of the airplane), the solar camera A is furnished with 9 lenses, one central and 8 peripheric and with a crown of single reflecting prisms. O n e of the characteristics of this camera - - made possible by the fact that it serves for photographing the sun - - consists of a strong superposition on the film of the various encompassing spaces, thus r e n d e r i n g it possible to make out afterwards whi& lens produced the solar image with which we are concerned. An electric shutter allows of rapid and simultaneous opening of the 9 lenses at ea& moment at which the main camera, to wllidl the periscope is fixed, takes a photograph of the ground. At the same moment, a second multiple circular shutter (2) and some suitable optical devices, enable us to fix on the film the images of the marks of a chronometer (5), and the variations of the atmospheric pressure measured with a statoscope (5, 6, 7, 8). Finally, the simultaneous lighting of some small electric lamps, enable us to record on the same film the magnetic azimuth, measured with the compass C and the variations of swing, measured by the gyroscopic directional (Variometer) D. While the size of the solar camera is 130 X 130ram in the m o d e l now used, the progress of the film for ea& photograph of the ground is only 30 mm and it consists of five partial forward movements of 6 mm each. While all the images produced b y the various devices mentioned above are reproduced simultaneously with the photographs of the ground, at the end of ca& of the partial progresses (of 6mm) only the index marks (rep~res), the magnetic compass, the graduation of the variometer, and
26 the index of the statoscope are reproduced. This allows a greater precision in reading the diagrams. The film thus obtained is shown in fig. 4 c . . T h e time at which each p i c t u r e was taken and the a n g u l a r values marked by the variometer can be read directly from the fihn. b) The Photogoniometer and its use. The apparatus is represented on the schematic fig. 5. Pointing with telescope 15 at the S' image of the sun, through the very optical system that prodneed it, the telescope axis will find itself exactly placed in the direction of the m o m e n t a r y sun rays. The vertical angle, which we shall call cop, formed between the direction of the sun and the solar camera's axis, can be read by means of microscope 17. The horizontal angle, which we shall call fi, referred to an axis of the photograph (measuring the marks) and Fig. 3 can be read by means of microscope 16. 0 u the circle 15, on which the telescope is mounted, a double microscope 21 is also provided, by means of which the sighting at all the images m u' ol the magnetic compass' graduation can be effeeted, reading the angular value with the microscope 16. The rotation of microscope 21 around its own axis, makes it possible to eliminate the eccentric effect of the graduation, which is always rather strong, owing to the p e n d u l a r suspension of the magnetic rose. c) Calculation of the outer (angular) Orientation of the Solar Photograph. The periscope being immovably fixed to the main camera and the photograph of the sun being t a k e n simultaneously with that of the ground, the outer (angular) orientation of the solar photograph is similar to that of the corresponding" ground photograph, with the restriction of the discrepancies and approximations of the instrumentM mounting. In the following e l e m e n t a r y analysis we shall assume, for tile sake of simplicity, that the solar camera has only one central lens, and that the ground camera consists of a single camera, the axis of which Coincides with that of the solar camera. Suppose: U--p (fig. 6) axis of the solar camera, U centre of the system, and K the corresponding photograph, in the a n g u l a r position corresponding to the survey u n d e r
27
B
B
3.
10
l
i |
Fig. 4
c
b
c o n s i d e r a t i o n ; . U - - S solar direction, and S' image of the sun on the photograph. Considering a sphere the centre of which is U, Z determines the local vertical, ]/INVE the horizon, S the sun's direction, and P the axis of the solar camera. The sighting on the photogoniometer, effected by means of the telescope (15) at the S'-image of the sun, gives ns the value of the angle ~p, formed between the axis of the camera (U--P), and the direction of the sun (S--U), as well as that of the angle ~, formed between the line connecting the m e a s a r i n g marks (rr) and the plane (SUP) determined by the axis of the camera and the direction of the sun. On the other hand, the measuring on the images of the rose of the magnetic compass, taking into account also the reading of graduation 19, gives us tile value of the angle x
28 formed between the magnetic North (M') and the aforesmd line (rr). To simplify our explanation let us suppose that the magnetic declination is k n o w n to tls, and that consequently the line pM' represents the direction of the geographic North. The sum of the angles a and ~ gives us the value of the angle represented by an angie 0p on the plane surface of photograph K. The angle formed between the plane of the photograph K and the horizontal surface MNVE being practically only a few degrees, the 0p value
Fig. 5
iCl
/(A) / r ~ measured on t h e photograph in a first approximation horizontal surface MNVE.
might
be
transferred
to the
In these conditions the angle Op expresses the value of the geographical azimuth of the horizontal line UE of the surface passing through the sun and through the camera axis. We shall call Op the periscopic solar azimuth. In the same way the angle Op immediate])- measured on the photogoniometer will be called periscopic zenithal solar distance. On the other ]land the time at which the photograph was taken and the knowledge of the geographical position of the camera eliable us to determine, with a sufficient degree of accuracy, the value of the angle Os which is that of the geodetic solar azimuth and that of the angle ~p3, that is of the geodetic zenithal solar distance. The difference between the two solar azimuths (Op--Os = e) gives us the value of the cathetus VE of the spheric rectangle triangle SVE, the second cathetus SV whidl is the supplement to the k n o w n q~s value. The solution of the triangle SVE gives us the values of the dihedron formed b y the two surfaces passing through the sun which contain the vertical UZ and the axis UP of the periscope respectively. The subsequent solution of the spheric triangle PZS gives us the value of the inclination (PZ) of the axis of the
29 periscope and that of the azimuthal difference (PZS) between the geodetic solar azimuth and the azimuth of the axis of t h e periscope. The value of the angle ZPS, taking into account the known angle ~, gives us the value of the sroing of the photograph, the a n g u l a r orientation of photograph K being thus completely determined. In order to be able to orientate a photograph with the above mentioned angular ,~alues of outer orientation in the plotting apparatus, it is necessary that the rotation axes of the s u r v e y i n g cameras inside the p l o t t i n g a p p a r a t u s should be disposed as follows: P r i m a r y axis - - of orientation - - (angle SZP); Secondary axis - - of inclination - - (side PZ); T e r t i a r y axis - - of swing - - (angle ZPS-4-~). But as the disposition of the rotation axes in the modern plotting apparatuses differs, for obvious reasons, from the ones mentioned above, the computation of the second triangle (SZP) is replaced by that of a second triangle c o n v e n i e n t l y chosen to match the plotting apparatus used. The method used so far in working with the Santoni-Galileo stereocartograph III is the following: for the elaboration of a series of photographs, we estimate the azimuth of the plotting axis, the value of which is attributed to the line x formed by the instrumental base, which is kept constant throughout the entire series. Thus: UN for this axis and On for the value of the pre-established plotting azimuth. From the calculation of the triangle S V E (the VE -= ~ and the S V = 90 ° _ cos being known) we obtain the values of the angle S E V (k) and of the side SE (~). From the calculation of the triangle N P E (the sides NE = 0 n - - 0p; PE = cop q- ~ and angle ~. being known) we obtain the value of the angle P N E (i) and N P E (o) and those of the side N P (x). Now, making use of the s u p p l e m e n t a r y rotation of both cameras of stereocartograph III a r o u n d the base line x (which serves for the absolute orientation of the model) as if it were that of a p r i m a r y axis, the photograph can be orientated in the plotting apparatus using directly the above mentioned values (i), (o), (x), that is: the angle i, or its complement (I) is a measure for the p r i m a r y rotation or that of the oblique (transversal) inclination which we shall simply call inclination (I) ; -
-
- - the angle x or its complement (C) is a measure for the secondary rotation or that of the longitudinal inclination, which we shall call convergence (C); - - the angle o, algebraically added to ~, is a measure for the tertiary rotation of the swing (O); the q u a r t e r l y rotation around the UA axis, which is still an approximatively transversal rotation, necessary to realize the rotation for the plotting of the contiguous photographs in the fan-like m u l t i - c a m e r a apparatus, can still be disposed of in stereocartograph III. -
-
It is at any rate possible to use this method with a n y type of plotting apparatus, the true and proper t r i a n g u l a t i o n developing itself only b y means of the central photograph. The degree of accuracy of the a n g u l a r values obtained in this way, depends above all on the degree of approximation obtained by the value s and on the reciprocal position of the axis US (solar direction) and on the axis UN (x plotting axis).
30 As angle ~ can be obtained with the aid of the photogoniometer with fairly good approximation, and angle Os can be determined with a still greater precision, the error of the angle s depends m a i n l y on the u n c e r t a i n azimuth a, obtained with a magnetic compass, even when the local magnetic declination is given with sufficient approximation. After all, as it is possible to determine with a fair degree of accuracy, the angle q~p with the aid of the photogoniometer, the a n g u l a r position of the axis of the periscope UP will be determined with fair I approximation in regard to the ' e~. ~ ',~? I I! angle SUP, while it will be affected I b y a perceptible error in regard to t~ ' t I' b/ its rotation around the solar ray US.
1
I
As in reality the angle PZ is only a few degrees, the error s by virtue il III IV of all the precautions mentioned below, will only be a few sexagesiFig. 7 real minutes and the differentials of the inclination, conoergence and sming angles could be easily calculated in regard to s. Practically, for the sake of simplicity, we only calculate the differentials of the transversal inclination (dI) and that of the convergence (dC) in regard to the swing variations (dO), using the following formulas, computed by me: __~
|
.
.
.
.
.
G /I:= =~_ l g_~_ . I_}:___J.1. . . . . . . .
dI= dO tang ~vp cos so sin x
(I)
dC= dO tang ~p sin o
(If)
In addition, the computer furnishes the plotter with a table containing a selection of values relative to the sming (0), inclination (I), and convergence (C) of each photograph of the series and of the differentials of the latter two in regard to the first. The calculation for this purpose effected either b y means of logarithms or the calculating machine, requires only a few minutes. d) Connection o~ successive photographs in the plotting apparatus b y means of the method of the transported azimuth. The plotter orientates in the apparatus, by means of the calculated values, a first pair of photographs containing the starting ground bases (b, fig. 7); he corrects the swing of the two photographs with the aid of this base, reads the small variations (dO) on the i n s t r u m e n t a l graduations and makes the consequent inclination and conoergence corrections, based on their respective differentials (dI, dC). In this operation, starting from an x Composing line of the approximated base, he will obtain the corresponding g composing line, while the composing line z will be obtained by comparison on two of the lateral points, ll, l',. The possibility of choosing the points 11, I'1, on the middle line of the o+-erlapping area, makes the determination of z free from possible errors caused by distortion. After the above simple a r r a n g e m e n t the model remains free from compass error, is deprioed of parallaxes and oriented angularly in an absolute direction. After having d e t e r m i n e d the scale by means of the starting base (b), we determine, by means of p l a n i m e t r y and of the elevation a point tl, chosen, in the overlapping zone of the third photograph. The second photograph is then m a t e r i a l l y put in the place Of photograph 1 in the s t e r e o c a r t o g r a p h (in the i n s t r u m e n t s furnished with an optical inversor, it could remain in its own place), and the third photograph is put into the plotting apparatus in the place of the second, orientated according to the calculated ~.'alues. After correcting the swing of the third photograph with regard to the second and having made the
31 differential corrections of inclination and convergence, by which the /j is determined, all that has to be done is to determine, the z on points 12, !'2 and to proportion the model by means of the variations of the air base, till we obtain t,, the value of the elevation given by the preceding pair. This p r o c e d u r e can be r e p e a t e d ad infinitum.
The great simplicity mith mhich each photograph is oriented on the preceding one, is oboious mhen roe consider that the elimination of the parallaxis on the nadiral points (needed to obtain the correction of the sming and the y composing base l i n e ) i s not, influenced by the successioe elimination of the parallaxes on the transoersal points (1, l') needed to obtain the z composing line. I h a v e called the aforesaid method a transported azimuthal method transported azimuth).
(method with
e) Connecting of successive photographs in the plotting apparatus applying the method
of independent azimuth° In order to be able to effect the correction of the swing of each photograph with r e g a r d to the preceding one, we can effect a relative (independent) correction for each pair, based on the data of the gyroscopic directional, c o n v e n i e n t l y compensated, as I e x p l a i n e d in the integral text of my Report to the Congress. This procedure, which enables us to avoid the systematic e r r o r of transport of the azimuth, is p a r t i c u l a r l y suitable for long distances. f) Use of the statoscope. The elements furnished by the statoscope h a v e so far n ev er been used in the application of the solar method. In fact, as I demonstrated in the integral t e x t of my Report, the data of the statoseope would in most cases contrast with the elements deduced from the solar direction. The statoscope may perhaps be used in p a r t i c u l a r l y unf a v o u r a b l e cases, and especially when the sun lies low above the horizon or in a direction transversal to the route. It will, however, be impossible to realize cases such as these during the surveys in regions lying near the Equator, such as Italian East Africa. P a r t I]. Analysis of causes of e r r o r and method of compensation. For the analysis of the influence of errors on the precision obtainable with my methods in regard of the direction of the sun in relation to the direction of the route, I must r efer the r e a d e r to the complete text of my Report. The result proves, at any rate, that as long as the zenithal distance of the sun is smaller than 45 °, the e r r o r of the inclination of the camera axis' (which is composed of an e rr o r of t ran s v er s a l inclination and an e r r o r of convergence) is inferior to the er r o r to be feared from the correction of the r e l a t i v e swing, so that the principal ad v an t ag e of my method, even in those cases when, for various reasons, a systematic transport of the error of the azimuth is still used, lies in its facilitating the planimetric a d j u s t m e n t of the total model enly by means of a control of the final (astronomical) azimuth, or of a difference of level, m e a s u r e d b e t w e e n the two features of the last p ar t i al model. On the other hand, when using the solar method, triangulation in space, errors in scale are always to know, are of a proportional kind when they depend on base of the initial model; they are of an incidei~taI
or any other method of aerial be feared. These errors, as we an error of scale in the starting" kind w h e n e v e r they depend en
32 accidental errors in the transfering of the scale from one side of the aerial polygon to the following one (each of which influences its successor as a proportional error); finally t h e y are of a systematic kind if, in passing from one photograph to the next, we commit an e rr o r in t r a n s p o r t i n g the a p p r o x i m a t i v e l y constant scale into an absolute value with an identical sign. The e r r o r which is most to be f e a r e d in spatial triangulations of successive photographs - - considering the m a n y sides of an airpolygon - - , is a systematic error, for it works by the law of squaring. So that an e r r o r of leiigth of the covered distance (/iS) can be totally attributed - - in the absence o f any other element of judgm e n t - - to a systematic e r r o r in the transport of scale (dr) and it has to be consequently compensated. The various causes of an error of that kind, which I intend to ex am i n e .lr~ .e, m i n u t e l y in a future study dedicated to this 'subject, are r! I! all to be attributed to slight deformations of the spatial bundles of plotting rays in v.~c relation to the bundles of rays 0 of the exposure. For these deformations, more f r e q u e n t l y caused by the p a r a l l e l o g r a m than by the true and proper fl~+3aH Ho projection system of the plotting apparatus, are not subject to the displacements of the principal point and cannot be a p p r o x i m a t e l y compensated by O' the relative c o n v e r g e n t adjustment, as occurs in other cases. This causes an er r o r comparable with the one depending Fig. 8 on a systematical longitudinal inclination (c', fig. S) of the exposure axes, unaccompanied by a corresponding inclination of the air base. The (theoretical) rectangle formed by t h e points of exposure (camera position) and the respective nadiral points, becomes, however, t r a n s f o r m e d into a trapezium, so that all the ground points become subject to an inclination 2 c'. Consequently, the whole net assumes a trapezoidal form. In the solar method, as the longitudinal inclination of the e x p o s u r e axes is connected with previously d e t e r m i n e d elements, the air base becomes subje c t to a corresponding inclination (d-c'), while the ground points become subject to an opposite direction ( - - c ' ) , that is a value half that to be feared when using other methods. This discrepancy could be traced along the entire net, unless, after having provided for the control of the coordinates of one of the ground features, P, we should r e t u r n to a general correction of the longitudinal inclination data, (C), attributing this e r r o r ( - - c ' ) to the relative fitting of the solar c a m e r a to the ground camera. Thi~ correction, even when the - - c ' e r r o r is not due to the above cause, has tile practical advantage of k eep i n g the coordinates of the model correct, i n d e p e n d e n t l y of the error of scale transfer which can be deducted later on with g r eat er precision and can then be compensated afterwards.
7;
At all events, and with e v e r y method - - presuming the existence of an original system with equal sides (pointed as in fig. 8) not considering the inclination of the chain,
33
the vertical t t size is enlarged with regard to its original real vah, e (that is in our case, at Ho) by a q u a n t i t y d H given b y the formula: ½ d H = l o tang c' from the similitude of the deformed net triangles, the increases in regard to the side lo by the value d t derived from the dt dH
-
I H
making d t = 2 y
12
tang e
The consequent error of length (dS) corresponding to the apex (n) is evidently derived from n ( n - - 1) A S = dt ~ (IX) Assuming that n is very large, producing n (n -- 1) = n ~, taking account of n = S and giving d t its original value, the above formula can also be written as follows: 1 A S = @ tang c' S 2
(X)
while the error in scale of the In side is given by the d S = n dt. W h e n e v e r it was possible to determine a new isolated ground base after a few pairs of photographs, which we shall call a p r e l i m i n a r y control base, discovering in it an error in scale, we were able to deduct from this the size error of transfer Ab[ from d bt d r - - bt
In n
(xf)
So as to automatically compensate this error in its further development the most practical method, adapted by me to the stereoeartograph llI, was to alter by a value 2 d l i the position of the scale index of the z eoInposing base line, at the exact place where it is joined to the camera whi& must receive every second photograph of the series. With this proeeeding, every side Hn is enlarged by 2dH" before being used for the d e t e r m i n a t i o n of the length of the new aerial side of the polygon. The a p p a r e n t disadvantage of this method of effective transfer of the photographs from one camera to the other, replacing the optical inversion, is compensated by a more easy p r e v e n t a t i v e eorrection on the dr, deduced from the length between the starting base and the p r e l i m i n a r y control base. On the other hand, even the very brief time needed for the transfer of the photograph from one camera to the other, is eompensated by the elinfination of all the operations eonneeted with the inversion of the base. When we reach the controlling base, or point, at the end of the flying strip the longitudinal error becomes greatly reduced., so that the r e m a i n i n g d t is generally reduced to one tenth. The solar method caff at all events be employed, even without a p r e l i m i n a r y control base, by effecting the total compensation on the arrival base. In using the formula XI for deducing" the;d/, the arrival base ean be i n d e p e n d e n t of the starting base. These bases, whidl are about i to 2 k m long, are measured by applying the well known indirect method with the aid of a horizontal stadia (substense bar). Their orientation is astronomically effeeted, and this can also take plaee during day time by making use of observations of the sun. Part III. Experiments with n e w periscope and the results obtained. Carlo Trombetti referred at length to these experiments in a Reportt which he presented to the Yth Congress of Photogrammetry. I shall confine myself to summing up the principal facts. C. Trombetti: Preparazione dei punti a terra per la triangolazione aerea col metodo Santoni e risultati conseguit con questo metodo.
34 The Tripoli E x p e r i m e n t (August 1955). C o n n ex i o n of 11 photographs which have been taken at a flying altitude of about 5500 m, with the i n d ep en d en t azimuth method, the values of the swing being p r o v i d e d by a magnetic compass. The total unadjusted model, about 9 km 10ng, r e v e a l e d no altimetrical deformation of a systematic character. In fact, in the It sections passing from one pair to the next, the following av er ag e errors in square meters w e r e r e v e a l e d : 5,11; 2,85; 5,19; 2,57; 5,26; 4,10; 5,19; 4,29; 2,96; 5,15; 4,29. G e n e r a l a v e r a g e (medium) 5,54. The model, on the contrary, proved to be considerably too large (4%o), which was p a r t l y due to the size a d j u s t m e n t of the first partial model, based on an existing map at the scale of 1/25.000, and p a r t l y to a systematic er r o r of transfer of scale. The C a r m a g n o l a - B a r o l o E x p e r i m e n t. This e x p e r i m e n t consists of a connexion of 27 successive photographs covering a distance of about 5t km, car r i ed out by applying" the method of transported azimuth. A ground base appearing on the first pair of photographs, and a point appearing on the seventh pair, at a distance of about 6,5 km from the starting ground base, w e r e used. This point re~ealed a length er r o r (As) of - - 1 6 , 18 meters from which, by means of the formula (IX) the systematical transport error (dr) was calculated. This proved to be about 1 m, the a v e r a g e length of the air polygon sides being 1200m. This e r r o r was taken into account during the subsequent elaboration of the strip, by means of an alteration of the scale index of the z composing base line a l r e a d y mentioned. A n o th e r elevation e r r o r of --5,09 m was discovered in the same point, corresponding to a systematic inclination of 0,75% 0 based on the ultimate distance, with a p r e v e n t a t i v e correction applied to the value of the longitudinal inclination (convergence), resulting from the calculations. Owi n g to this precaution, the ultimate model was found to be correct as regards elevation. In fact, errors of about l m only ,*-ere found at two known intermediate trigon o m et r i cal points and at the end base. A r e m a i n i n g error in length of + 52,95 m was found, from which the r e m a i n i n g e r r o r of transfer of scale w a s c a l c u l a t e d . This e r r o r p r o v e d to be 0,218 m. In addition, an e r r o r / J y of + 8 8 , 6 0 m and an er r o r in orientation of - - 2 5 ' were found at the end base, unanimously r e v e a l i n g a systematic error of transfer of azimuth of about 1' for each station. A definitive p la n i m e t r i c a d i u s t m e n t of the entire strip was effected, based on the above dt and on the e r r o r of transfer of azimuth. When v e r i f y i n g after the a d j u s t m e n t the position of the two i n t e r m e d i a t e trigonometrical points, an a v e r a g e p l a n i m e t r i c e r r o r of about 3 m was found in both. No altimetrical a d j u s t m e n t was t h e r e f o r e needed. The results obtained by this e x p e r i m e n t are so far significant, that they p r o v e that the general model obtained with the solar system, even if subject to the influence of systematic errors, just as is the case with other methods, presents v e r y r eg u l ar deformations, which can be adjusted in an easy way. The A r o n a T u r i n Experiment. This e x p e r i m e n t consists of the connexion of 92 successive photographs which were taken at a relative flying altitude of 5~00 m, covering a distance of about 10~- km. The elaboration was car r i ed out, applying the method of the transported azimuth b e t w e e n the starting base and the base for a p p r o x i m a t i v e control, situated in the area covered by the 9th pair of photographs and by the i n d e p e n d e n t azimuth method for the r e m a in in g part of the strip between the base for a p p r o x i m a t i v e control and the end base. The systematic size e r r o r of transport (dt) calculated from the data of the part be t w e en the starting base and the base for approxilnative control, p r o v e d to be about 1 m, just as in the p r e c e d in g e x p e r i m e n t and in the r em ai n i n g part a corresponding correction has been applied. The control at the end base, situated in the area covered
35 by the 92th pair, has revealed a r e m a i n i n g error of transfer of scale of about 0,08 m. Based on this amount, the a d j u s t m e n t of the strip was effected. A comparison after a d j u s t m e n t with a trigonometric point situated at about the centre of the strip revealed the following definitive r e m a i n i n g errors:
,4X=-- 15,05;
AY=--46,38 m:
z/Z= +14,50.
Conclusion. The Santoni solar method presents a safe and easy means of aerial t r i a n g u l a t i o n in space. With special precautions, the method is possible in every kind of country and is especially suitable for tropical and subtropical areas. The pllo~ogoniomeiric operations and the calculations needed for obtaining the outer orientation values of the photographs being very simple, they can be entrusted to persons of an average education. The connexion of the successive photographs in the plotting apparatus can be effected with great rapidity, being essentially based on the adjusting of the swing. The general model is affected by x ery slight regular deformations, indicated by the control at the end bases, which is easily adjusted. The intermediate base for first approximative control is not indispensable. 'The certain control of the inclination of the model in the flying direction, permits the use of multiple camera covering a very great transversal field, actually consisting of photographs taken with several cameras, whi& greatly reduce the amount of photographing and plotting" operations. The Santoni quadruple camera, provided with a solar periscope, rendered it possible last summer to survey an area of about 5500 km 2 on a scale of 1/100.000, the photographs of which are now being" elaborated. The same quadruple camera using plates and a new triple camera using films are soon to be used in the Empire for a 1/100.000 survey of very large areas. These surveys will require the building of a net of approximately square meshes formed by p r i m a r y triangulation strips, the sides of whirl1 will be of about 100 km long. A ground base will be measured at every junction, applying the normal terrestrial s u r v e y i n g methods, whilst an astronomical station will also be determined at each of these points. The method of a d j u s t m e n t used to attach the correct importance to the astronomical observations will be published later. For a relative flying altitude of abont 3500 m (the elevation of the area itself being 2000. m) both in the case of the oscillating quadruple camera using plates and the new camera using films, five secondary strips will be needed to fill the entire quadrangle of each mesh.
Le nouveau p~riscope solaire Sanloni pour la lriangulalion a~rienne R6sum6 par E. Santoui, Florence. Pr6face. Par l ' e x a m e n de mes brevets italiens obtenus en 1919 (fig. 1 du texte) je montre comment mes ~tudes f u r e n t dirig6es, d~s le d6but, vers la r~alisation d'une chambre d o n n a n t les 616ments d'orientation de la chambre de prise de vues ~t chaque station en p a r t a n t de point6s effectu~s sur le soleil et de deux points connus du t e r r a i n photographi6, Ce proc~d6 repose sur le rel~vement dans l'espace du sommet d'une pyramide dont la direction d ' u n e ar6te est connue. Uu brevet italien obtenu en 1920 montre quc la solution 6tadi6e repose sur le fait, que la direction qui joint l'appareil au soleil est connue et que c'est elle qui serf de base ~ l'orientation des cliches. ]e montre enfin les progr~s successifs accomplis par rues r6alisations qui ont pr6cdd6 le n o u v e a u p6riscope solaire.