163

At =

i

1

[arc sin C - y - W - 6Wt ]

6W o i

Next with the exact value of viewing time t^

for the point M^, it is possible to calculate

the osculatory parameters (p,R,I,W,e x ,e y ) and

the shuttle coordinates X and S'.

Referring again to Figure 1, we can then write

the following vector equation in a non-inertial

(terrestrial) reference system:

SMi = OMi - OS

which is equivalent to the vector slant range that

one can rewrite in terms of elements of Figure 3

as follows:

r= xi - fx(t ± ) - tiVe]

Normalizing the vector s’, one obtains

s = IIsit *u which gives the direction cosine of the

line SM^. One can obtain a more accurate value

of the scalar slant range directly from the image

data, so that only the orientation u of the vector

slant range need be kept from 3. By combining

these two parts, image scalar(s) and vector(H), a

refined value is obtained for Is:

Snew = s TT

Referring to Figure 1, note that the local

incidence angle 0^ is the angle between the two

lines M^S and OM-^. The coordinates for the

three points S, Mj[ and 0 (intersection of the

first normal and the Z axis) are known and allow

one to compute the direction cosine (l,m,n) of

each line. Thus, the local incidence angle 0 L

is given by:

cos©l = 1}I2 + m^n^ + n i n 2

The advantage to use the image slant range module

in the calculation of the new shuttle position at

time t^ has been shown when comparing both slant

range values as obtained from image and from orbit

calculations. In fact, such a comparison has

shown an average difference of 613 metres (based

on a twenty point dataset). A second calculation

on the same dataset but with a second initial

shuttle position (modified with only one

checkpoint for image slant range value), has shown

the average difference reduced to approximately 50

metres. This second approach has been finally

preferred due to the consistency of both measures

of slant range.

2.2 Image resampling and filtering

The rectification of raw SIR-B images into the

intermediate level was achieved by using a

polynomial fit between GCP locations obtained from

raw image (but with a modified pixel location

which excludes terrain parallax effect from the

model) and those extracted from topographic maps.

Using respectively 14 and 13 GCPs for the 29 and

53 degree SIR-B dataset, a quadratic polynomial

regression was found to best fit the

transformation with few independent check points

(see Table 1). The residuals obtained for each

image and for both sets of GCPs (test and model

points) were always less than 37.5 metres (1.5

pixel) in either line or pixel direction. These

results are in agreement with those published by

Welch and Ehlers in 1985.

Table 1. Quadratic polynomial fit residuals for

SIR-B image rectification at the intermediate

level.

Incidence Residuals On Test On All Points

Angle RMS (Pixel Points (Model & Test)

Unit): (Total) (Total)

29°

Pixel

1.49(5)

1.44(19)

Line

1.28

1.22

53°

Pixel

1.30(3)

1.28(16)

Line

1.44

1.43

The SIR-B images were then resampled into a

rotated UTM intermediate grid defined also at 25

metre pixel size. A 50 degree UTM rotation was

applied in order to minimize the differences in

geometry between the raw and the intermediate

level products. Figure 4 shows both resampled

images which cover an area 56.75 km long by

15.125 km. These images have also been

radiometrically corrected by applying a 3 by 3

pixel window filter (Lee, 1981) in order to reduce

the speckle effect (which was found to be

necessary at the digital stereo matching level).

Figure 4. SIR-B images (29° left, 53° right)

processed at intermediate level.