756 PHOTOGRAMMETRIC ENGINEERING
We find the following expression:
(x — b)"* 2 , ( 2C0s?$ , 3A? sin? ba
Qardr = — + 7 {h cos $ + (x — b) sin da}? ( TTT )
le z-bute 3, 3 a cos? 2 2 sin? de)
— j -— —— + — i (x — b) cos à» — h sin 91?4 — — + —__
| ET dt a mant 3 §
_ A Ke. 67) m
b b bY baz
HS + (x — b) sin 4s] ((x — b) cos de — 1i sin 4] s" ET
— Tf x — Sin $» XN COS $» — /s —T——-)$ M
p 1 COS $» X sin | à (x 1n $» Sii 352 Sin 2$». (23)
The standard error of the elevations due
to the errors of the relative orientation
only is then found as
my = u^/ Qahah (24)
where y is the standard error of the y-
parallax measurements. Assuming u=1,
and the following data, which are typical
for the application of convergent photog-
raphy (see [6]):
$e = — 20°
b= 1.234
d = 0.64h
expression (24) has been plotted for vary-
ing x and y within the neat model area. The
result is shown in Figure 3. The corre-
sponding diagram for vertical, wide-angle
pictures is shown in Figure 4. Both these
figures are for dependent pairs. Under such
circumstances the model from convergent
photographs obviously has much smaller
vertical deformations than the model from
vertical pictures. This is of great impor-
tance for the elevation measurements after
the absolute orientation and consequently
also for aerial triangulation. The elevation
standard errors, obtained in this way, refer
to the vertical distance between the air
base and the model surface. Each model
elevation is a function of the adjusted ele-
ments of orientation. Consequently the
standard error of elevation differences in
the model are obtained as the standard er-
ror in a function of functions. This prob- cally determined elevations in the ground
lem introduces no particular difficulty and system after the absolute orientation has
the standard error may be found directly been completed, the number and position
rom the normal equations or by applying of the ground control points must be
the general law of propagation of errors known.
(see [5] $32, p. 101). In order to determine It is apparent that Figures 3 and 4 can-
the standard errors of the photogrammetri- not be compared directly unless the stand-
FrG. 4. Standard errors of the distance from
air base to model surface for near vertical wide
angle pictures. The standard error of the 5-
parallax measurements is assumed to be 1.
*)' Weight numbers
* A closer investigation of this equation shows that the trigonometric functions disappear—
Author.
