Abstract

An optical method for the correction of slant range distortion in high-altitude radar recordings is presented. The line image of the scan is converted into a circular disk by rotation about the zero slant range point and an appropriate line from this disk is selected. This method is strictly geometrical (not an approximation) and readily accomodates altitude changes.

The method employs a reflecting cone as an optical element. The laws of reflection and image formation for this element are formulated, including the light efficiency.

A simple method for testing the quality of the conical surface is also given.

© 1958 Optical Society of America

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Figures (7)

Fig. 1
Fig. 1

A geometrical method of slant range correction.

Fig. 2
Fig. 2

Conversion of a line image into a circular disk image by means of a reflecting cone.

Fig. 3
Fig. 3

Imaging in a radial plane of a reflecting cone.

Fig. 4
Fig. 4

The reflection of skew rays.

Fig. 5
Fig. 5

Imaging of a distant object by a reflecting cone.

Fig. 6
Fig. 6

Method of testing a reflecting cone.

Fig. 7
Fig. 7

Oblique aperture at cone axis.

Equations (27)

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Δ r a 2 / 2 r .
a a cos α ,
Δ r a c sin α ,
g = r cos φ d g = - r sin φ d φ , h = r sin φ d h = r cos φ d φ ,
d g = - tan φ d h .
Δ g - tan φ Δ h ,
Δ g = Δ r sec φ .
x = broadening due to finite slit width ground range corresponding to one pulse length
x = Δ h tan φ Δ r sec φ = sin φ Δ h Δ r .
E 4 B ( a / 2 r ) sin θ z η ,
tan θ / 2 = p / 2 P C ,
I × n = n × R ,             I = R ,
I = r i - a j - b k , n = i - k , R = x i + y j + z k ,
I × n = a i - ( b - r ) j + a k n × R = y i - ( x + z ) j + y k .
y = a
b - r = x + z or b 2 + r 2 - 2 b r = x 2 + z 2 + 2 x z .
a 2 + b 2 + r 2 = x 2 + y 2 + z 2
b 2 + r 2 = x 2 + z 2 .
- 2 b r = 2 x z .
x b - x r - x 2 = - b r
x 2 + ( r - b ) x - b r = 0.
x = b , - r .
x = b ,
z = - r .
Δ r b = C G B G = a sin α r - a sin α .
Δ r ( a b / r ) sin α = a c sin α ,
a = B C B G · F C = r r - a sin α · a cos α a cos α .