FRAME
s.
of Geodesy
(TsNII GAiK ~
13
I
s
of
respect
s
.-
e in camera
shown to bring forth an
ciency
surveing and. photographic processing or in caee of equal efficiency an increase in accuraof t
ights determination and resolution. However
increase in camera frame size causes additional coneumpt
of film, greater specific consumption of materials and
energy, greater camera dimens
and necessity to use carriers with high
e
1. INTRODUCTION
basic s
prod
cm size.
are bas
re-
on reso
ion of cae
mera; 3)
of air surveying that depends on proj
ion
a
ts plane onto t
The above features can be used to formulate two criteria
comparison of
different s
frame. The
two cameras
surcamethe better
ensures better productivity provided
t
ion
resolut
)
)
of
1-1
0
system, i.e. focal length, diameters of pupils and lenses,
thickness of lenses and air gaps in proportion to changes of
frame size but does not change angular parameters, such as angle of view and relative aperture. This transformation with
respect to basic parameters of a camera can be expressed as
- 11
c 1- = K
...._ -
2~
t
= canst,
f
= cons t ,
(1 )
10
Co
where K is coefficient of increase in frame size (coefficient of proportionalitY)t
c is camera focal length, 1 is a
side of a frame (photograph),
f is relative aperture denominator, 2~ is angle of view. Index "on in this (1) and other
formulas means basic (18x18 cm) camera frame size, index "1 n
referres to a camera with larger frame.
Let us compare the cameras under study from the standpoint
of the second criterion. Here we shall formulate two conditions. The first one lies in the fact that elements of resolution t:,. ensured by both cameras remain the same, i. e. relation between volumes of field and. office interpretation do not
change. This condition is characteristic of planimetry updating; the following expression holds true for the condition:
~1 =~o
(2)
The second condition is characteristic of map production. It
lies in the fact that equality in errors of terrain heights
determination ~ holds true for both cameras:
(3 )
2. COMPARISON OF CAMERAS WITH RESPECT TO THE IMAGE QUALITY
Let us compare two cameras from the standpoint of the first
cond.ition. Here we shall use a well-known formula
M
.6= 2Rq
where R is practical image resolution obtained und.er flight
condition, M is numerical photographic scale denominator, q
is constant coefficient when two cameras are compared; this
coefficient dependson contrast of terrain elements. Let us ooe
the expression (4) to write down the following:
where a,1 is coefficient of relative change of quality of large ....size photograph. After taking into consideration (2), we
shall obtain ratio of numerical photographic scale denominators which ensure equal resolution of cameras, i.e.
Mo
M1 :;; a 1
as well a.s ratio of surveying altitud.es
1... 18
H~
i.e.
(6 )
As is known, projection of stereopair's plane onto terrain is
expressed by
2 2
(7 )
S = (1-P )·(1-P )·l·M
x
Y
where P
and P
are constant coefficients of photographs'
lateralxand lon~tudinal overlaps. An increase in productivity can be written as a relation which, after allowing for (1),
(5) takes the following form:
:~
=
r
!1)2
(8)
The expressions (6) and (8) show that if a ==K, i.e. resolution of a large-size aerial photograph decrJased by a factor
of K and., consequently, angular resolution did not change,
then under the conditions given in (2) the altitude of air
surveying carried out with a large frame size camera cannot
be increased, hence there will be no increase in productiv1t~
On the oontrary, if a =1, i.e. resolution of a large-size
photograph did not ch;Jge and angular resolution increased by
a factor of2 K, then altitude of aerial surveying would. increase as K • The latter case corresponds, according to (5),
to aerial surveying at the same scales made with two cameras
und.er comparison i. e. !VI == M1 .. It appears from the above that
numerical value for an i~.provement in productivity can be fa .....
und. by d.etermining the factors that raise angular resolution
as eamera frame size is increased..
The resolution of an aerial photograph as is known, is mainly
due to the following components:
1. Resolution of lens R , which depends on quality of aberration correction only. °It is known from the theory of optics
that proportional changes of all parameters of a lens do not
bring Ch. anges in angular resolution.fBY expressing coefficient
a10 in ~erms of angular resolution
i. namely
a10;
r~ K, we can find out that in this case
2. Resolution that depends on image motion RIIf. Let us use a
well-known expression for a resolution elemen~ in an image Ow
which is caused by image motion
8=~ ,
w
M
and accept that values of W (speed of a carrier) and t (time of exposure) are constant. So we can write down the following relation:
01w
H
81 . = ~ = K· -!!Q ;
W
00w
H1
1. . 19
are
ame,
(10
same
3.
us
(11 )
)
s
are const
f
cameras
(12 )
= 1
we can
a
1
S
R
:::
1
=
,
+
1
+
+
1
we
g :::
,
one may
elements
e down
ing
+
::::
:::
(go
+
6f
+
+
(13 )
+
+
(14)
cons
:::
(5 )
::: W t
const
we shall obt
(15)
addit
to the above expressions, let us present formu(omitting their derivation) that determine relation bet~
ween general number of aerial photographs nand
ight
s
ne which are
to
an assigned terra.in
area
(16 )
no
(17 )
[1 ] )
(18)
where
area of film re
a
E
area of t
we
take parameters of AFAas
• The camera
rom focal
1000 field. of
tographic
were employ-
view
image
ad to
~re .members
~lements which
Of ::: 0,00217;
cid == 0,005
23x23 cm and
cameras. The resul ing coefficients of
were correspondingly the following:
•
we obt
from (15) that
1,063
•
JOx30 em frame
proportional
K 21 == 1,
;
1, 1
aBel
to survey an assi-
parameters
camera. are given
formulas (8,1
respect to
e 1. The
ers in
chan-
e 1:
ged
Frame
cm
M1
Mo
S1
-
s;-
0,
0,
°
3 Ox: 3
from
1,20
1,.44
1,45
2,10
1,
n
-no
-
~
0,69
0,48
0,83
0,69
1,13
1,33
from 18x18 em
1
E1
ne 1
neo
1
23x23 em frame size has the following effects on the process
of planimetry revision : when surveying the same area of terrain (resolution of the two cameras is the same) the scale of
aerial photograph will be larger by 6% and altitud.e of survelng can be increased by 20%. The latter raises produotivity
by approximately 40% hence the number of aerial photographs
decreases by 30% and number of flight strips as well as fuel
and lubricants consumption decreases by 17%. However consumption of aerial film increases by 13%. In case of transition
to 30x)O em frame size the above mentioned showings increase,
correspondingIy,by 13, 45, 110, 52 and 31%. Consumption of aerial film increases by 33%.
3. COMPARISON OF CAMERAS WITH RESPECT TO THEIR
MEASURING QUALITY
Let us compare two cameras from the standpoint of the second
condition. Here we shall use the following formula:
,
(19 )
where m6 is error of horizontal parallaxes difference determination. P Just like in the previous section let us 'Write the
relation;
mh1
mAp1
M1
M1
::
:: - - s
M
2
m
M
llbo
ApO
--
0
0
After taking into account (3 ) we obtain that
-M1
Mo
~
So
:: 8
::
(20)
2
(~t
and by analogy with the previous s
K
= -,
(21 )
ion
E1·
T
= a
2
2
(22 )
The expression (21) is similar to the formula (8), but in the
first case coefficient 81 depends on resolution and. in the
second, case it depends on both resolution and metric accuracy
of photographic image. That is why just like in the previous
case, if a2 = K, i.e. if all linear errors increase proportionally with increase in frame size or if their angular errors
remained unchanged, then increase in frame size does not bring
forth raise in productivity. However if a2 = 1, i.e. all linear errors of a photographic image remain unchanged,or their
angular error 2 d.ecreases by a factor of K , then productivity
raises as
K •
It is known that the main components that influence accuracy
of mL\
on (mP
value determination are: error due to lens distQ.rti), error due to non-flatness of filter surface
( rnA ft~r error due to atmospheric refraction ( m~pa ), error
due P to non-flatness of film surface ( m,6 n ),
error due
to casual deformation of aerial film (m~PdP ), error of measuring images with a photogrammetric
"instrument ( mA i)'
error of pointing and image points identification ( mt1pv)~
The first three factors are function of angular deviation of
light beam. One may assume to a
ien.t degree of accuracy
that in the case of proportional transformation the total angular value of their errors is constant, hence
m~pA1
=
(23)
K.m~pAo
axes difference de-
where m~
error of horizont
terminati8A due to angular parameters
m6pA
='\Im~pr
+
m~Pf
+ m!pa
(24)
Linear parameters of the three folloving factors do not change when camera frame size is increased thus their angular values decrease proportionally with K. Thus, for example,ca . . .
eual deformation of aerial film does not depend on the size
of the latter and systematic deformation is allowed for within sufficient degree of accuracy. Experience gained in the
course of developing cameras with large frame size shows that
to achieve flatness of aerial film surface it is necessary to
make additional efforts to ensure that residual errors do not
exceed those of cameras with 18x18 em frame size. As for the
accuracy of measurements made with photogramrnetric instruments, it depends on the accuracy rating of the instruments,
not on the size of a frame. Hence we may put down that
m6pC :;
where
m.(.\
\jm' 6pn
2
2
2
+ m.1pd
+ m.1pi
(25 )
is error of horizontal parallaxes difference de-
terminat~gR due to the factors linear values' of which remain
constant when frame s
is changed.
As for the error of pointing and identification, it remains
proportional to image resolution and contrast of the image paints under observatlon
1
(26 )
ml\pv ::: --qlr
If we B,ssume the value of q constant, just like in the previous case, we may write dow~
m~pvo
Thus the
=
=
(27 )
e camera with
can
a camera
smaller frame s
ed as
)
e,
paramet
remetera
to
taken
e 2
10
:3
5
12
5
Using the data one can
from
and
1,1
Changes in init
18x18 em frame s
las ( 16 , 17 ,20 . . . 22 ) t are
4
6
)
e
3.
ented
e 3:
era
s
Frame s
em
3
0,
3Ox30
O~
,14
1,
1,31
0,
0,
1,25
1,6.3
0,61
0,78
1,71
16Ii