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A parallax converter for the Santoni Stereomicrometer
Photogrammetria - Elsevier Publishing Company, Amsterdam - Printed in The Netherlands
A PARALLAX CONVERTER FOR THE SANTONI STEREOMICROMETER M. TIENSTRA International Training Centre for Aerial Survey, Delft (The Netherlands)
(Received February 15, 1966) INTRODUCTION The economy of any photogrammetric instrument, but especially of a relatively cheap, approximate instrument depends to a large extent on the time required for the orientation of a model. Using any stereometer type of instrument, much time is lost in computing height differences from parallax differences and vice-versa.
~p
Fig.1. Schematic sketch of the parallax converter. Photogrammetria, 21 (1966) 27-30
28
M. TIENSTRA
Therefore, instruments, slide rules and nomographs have been constructed to speed up these computations. All these devices have in common, however, the fact that they are not attached to the instrument. They have to be used together with it. That is to say, at best, a parallax has to be measured, and the reading introduced on the parallax converter to give the corresponding height. In other cases, parallax differences have to be calculated, then height difJerences are found on the parallax computer and finally heights have to be calculated. These operations are not only time consuming, but offer also too many possibilities to make mistakes. In his publication on the Santoni Stereomicrometer, ZORN (1960) suggested a solution for a direct height reading device for this instrument. Although the realisation of this suggestion, which included the use of hyperbolical shaped cams, was proved to be less suitable, the idea behind it, in short, the above considerations, finally led to the present device.
Fig.2. Parallax converter mounted on the Santoni Stereomicrometer.
Photogrammetria, 21 (1966) 27-30
PARALLAX CONVERTER FOR SANTONI STEREOMICROMETER
.~:_
~\'~,~o
ZR
-:1., /
29
tr~tote °z
ZR b a r ( .... position]
j45"
%. N Fig.3. Principle of the parallax converter.
THE CONSTRUCTION OF THE PARALLAX CONVERTER The formula on which the converter is based, is the well-known parallax formula:
d h -~
A p Z~ P~ + ,~lp
where Zz~ is the flying height over the reference point R, PI~ the stereoscopic parallax of the reference point R, J p the difference between the parallaxes of an arbitrary point and of the reference point R, A h the difference between the heights of an arbitrary point and of the reference point R. The units of Z~ and A h are metres, those of P~ and Ap millimetres. To obtain not too large a construction, it is advisable to introduce a scale factor 1/10 ~ for Zz~ and A h, which means that 1 m equals 0.01 mm. To measure Ah, a measuring dial with a smallest reading unit of 0.01 mm was therefore applied. For ZR a normal millimetre scale was sufficiently accurate. ~lp is directly obtained from, or introduced to the left-hand mirror of the stereoscope, so no measuring device was necessary. PI~ is introduced, in principle, on a millimetre scale. J p is a horizontal movement of the left-hand mirror of the stereoscope. It was found advisable to keep the measuring dial for A h in a vertical position. This led to the realisation which is shown schematically in Fig.1 and actually in Fig.2. Fig.3 explains the construction. The angle between the ZI~ bar and PR bar
Photogrammetria, 21 (1966) 27-30
30
M. TIENSTRA
was chosen as 45 °. As d p is introduced to the computer by shifting the left-hand mirror of the stereoscope, it was necessary to multiply PR by a scale factor of
½1/2. The computer solves the parallax formula as follows: Z ~ , / l p ½ 1/2 3 h = Zl~tan(l = p ) ~ . ½ p'2 4- a l p . ½ 1/2 Although in the above explanations use is made of height and parallax differences, it is of course possible to read heights directly. The converter is adjusted in such a way, that the ZI~ bar is horizontal when the left-hand mirror is in its zero position. In the Santoni Stereomicrometer it is possible, by changing the distance between the two diapositives, to set the floating mark on the reference point. Then the height of the reference point is introduced on the measuring dial, and for all points of the model heights can now be read directly and in metres. Setting the Cavalcanti surface to correct for model deformations, using the parallax converter, now closely resembles the normal levelling procedure. It should be noted, that this parallax converter can only be used with the newer type of stereomicrometers. That is to say, with those instruments in which the correction to the parallaxes for model deformations is introduced as a rotation of the left-hand mirror of the stereoscope.
REFERENCES OFFICINE leo, ZORN, H. AG,
GALILEO. Instruction Manual for the Stereornicrometer SMG 4. Officine GaliFlorence, 29 pp. C., 1960. The Theoretical Precision of the Santoni Stereomicrometer. I.T.C. Publ. Delft, 16 pp.
Photogrammetria, 21 (1966) 27-30
A PARALLAX CONVERTER FOR THE SANTONI STEREOMICROMETER M. TIENSTRA International Training Centre for Aerial Survey, Delft (The Netherlands)
(Received February 15, 1966) INTRODUCTION The economy of any photogrammetric instrument, but especially of a relatively cheap, approximate instrument depends to a large extent on the time required for the orientation of a model. Using any stereometer type of instrument, much time is lost in computing height differences from parallax differences and vice-versa.
~p
Fig.1. Schematic sketch of the parallax converter. Photogrammetria, 21 (1966) 27-30
28
M. TIENSTRA
Therefore, instruments, slide rules and nomographs have been constructed to speed up these computations. All these devices have in common, however, the fact that they are not attached to the instrument. They have to be used together with it. That is to say, at best, a parallax has to be measured, and the reading introduced on the parallax converter to give the corresponding height. In other cases, parallax differences have to be calculated, then height difJerences are found on the parallax computer and finally heights have to be calculated. These operations are not only time consuming, but offer also too many possibilities to make mistakes. In his publication on the Santoni Stereomicrometer, ZORN (1960) suggested a solution for a direct height reading device for this instrument. Although the realisation of this suggestion, which included the use of hyperbolical shaped cams, was proved to be less suitable, the idea behind it, in short, the above considerations, finally led to the present device.
Fig.2. Parallax converter mounted on the Santoni Stereomicrometer.
Photogrammetria, 21 (1966) 27-30
PARALLAX CONVERTER FOR SANTONI STEREOMICROMETER
.~:_
~\'~,~o
ZR
-:1., /
29
tr~tote °z
ZR b a r ( .... position]
j45"
%. N Fig.3. Principle of the parallax converter.
THE CONSTRUCTION OF THE PARALLAX CONVERTER The formula on which the converter is based, is the well-known parallax formula:
d h -~
A p Z~ P~ + ,~lp
where Zz~ is the flying height over the reference point R, PI~ the stereoscopic parallax of the reference point R, J p the difference between the parallaxes of an arbitrary point and of the reference point R, A h the difference between the heights of an arbitrary point and of the reference point R. The units of Z~ and A h are metres, those of P~ and Ap millimetres. To obtain not too large a construction, it is advisable to introduce a scale factor 1/10 ~ for Zz~ and A h, which means that 1 m equals 0.01 mm. To measure Ah, a measuring dial with a smallest reading unit of 0.01 mm was therefore applied. For ZR a normal millimetre scale was sufficiently accurate. ~lp is directly obtained from, or introduced to the left-hand mirror of the stereoscope, so no measuring device was necessary. PI~ is introduced, in principle, on a millimetre scale. J p is a horizontal movement of the left-hand mirror of the stereoscope. It was found advisable to keep the measuring dial for A h in a vertical position. This led to the realisation which is shown schematically in Fig.1 and actually in Fig.2. Fig.3 explains the construction. The angle between the ZI~ bar and PR bar
Photogrammetria, 21 (1966) 27-30
30
M. TIENSTRA
was chosen as 45 °. As d p is introduced to the computer by shifting the left-hand mirror of the stereoscope, it was necessary to multiply PR by a scale factor of
½1/2. The computer solves the parallax formula as follows: Z ~ , / l p ½ 1/2 3 h = Zl~tan(l = p ) ~ . ½ p'2 4- a l p . ½ 1/2 Although in the above explanations use is made of height and parallax differences, it is of course possible to read heights directly. The converter is adjusted in such a way, that the ZI~ bar is horizontal when the left-hand mirror is in its zero position. In the Santoni Stereomicrometer it is possible, by changing the distance between the two diapositives, to set the floating mark on the reference point. Then the height of the reference point is introduced on the measuring dial, and for all points of the model heights can now be read directly and in metres. Setting the Cavalcanti surface to correct for model deformations, using the parallax converter, now closely resembles the normal levelling procedure. It should be noted, that this parallax converter can only be used with the newer type of stereomicrometers. That is to say, with those instruments in which the correction to the parallaxes for model deformations is introduced as a rotation of the left-hand mirror of the stereoscope.
REFERENCES OFFICINE leo, ZORN, H. AG,
GALILEO. Instruction Manual for the Stereornicrometer SMG 4. Officine GaliFlorence, 29 pp. C., 1960. The Theoretical Precision of the Santoni Stereomicrometer. I.T.C. Publ. Delft, 16 pp.
Photogrammetria, 21 (1966) 27-30