Abstract

Ghost images of distant objects are sometimes visible in twin-glazed window units. This is often caused by a pressure differential between the enclosed airspace and the surrounding atmosphere, which distorts the window. The ghost images result from internal reflections where the panes are not parallel. Even if the window is distortion-free for a particular atmospheric pressure and temperature, variations in either of these parameters will introduce distortion. Expressions are derived that relate the magnitude of the ghost separation to the structural parameters of the window and variations in atmospheric pressure and temperature of the enclosed airspace. Ghost separations of half a degree may often be expected as a result of environmental changes.

© 1972 Optical Society of America

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References

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  1. W. Swindell, H. Morrow, Glass Digest, in press (1972).
  2. M. M. Filonenko-Borodich, Theory of Elasticity (1885), trans. from Russian by M. Konayeva (P. Noordhoff, Groningen, The Netherlands, 1964), p. 322.

Filonenko-Borodich, M. M.

M. M. Filonenko-Borodich, Theory of Elasticity (1885), trans. from Russian by M. Konayeva (P. Noordhoff, Groningen, The Netherlands, 1964), p. 322.

Morrow, H.

W. Swindell, H. Morrow, Glass Digest, in press (1972).

Swindell, W.

W. Swindell, H. Morrow, Glass Digest, in press (1972).

Other (2)

W. Swindell, H. Morrow, Glass Digest, in press (1972).

M. M. Filonenko-Borodich, Theory of Elasticity (1885), trans. from Russian by M. Konayeva (P. Noordhoff, Groningen, The Netherlands, 1964), p. 322.

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Figures (6)

Fig. 1
Fig. 1

Tilted glass plates in a double-glazed window give rise to a ghost at an angular subtense S from the true object direction.

Fig. 2
Fig. 2

Dimensions of glass plate and the reference system used in Eq. (2).

Fig. 3
Fig. 3

Deformation of a sagging rectangular plate freely supported around its perimeter. k is the aspect ratio of the rectangle. Sag values are normalized to unity at the center. Contour intervals are 0.1.

Fig. 4
Fig. 4

Tilt of a sagging rectangular plate freely supported around its perimeter. k is the aspect ratio of the rectangle. Tilt values are normalized to unity at the midpoint of the longer side and are zero at the corners and the center. Contour intervals are 0.1.

Fig. 5
Fig. 5

Cross section of window showing (a) equilibrium configuration of a solid window; (b) increase in external pressure dP and internal temperature dT results in volume change of 2v and pressure differential of P0.

Fig. 6
Fig. 6

f(a,k) multiplied by dP/P or (−dT/T) gives the maximum ghost angle that will occur in a window of size a in. × ak in. Graph is drawn for ¼-in. (6.35-mm) thick glass with nominal ½-in. (12.7-mm) separation.

Tables (1)

Tables Icon

Table I Table of Parameters θ(k) and λ(k) Referred to in Text

Equations (20)

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S = 4 t .
W ( x , y ) = 192 P 0 ( 1 - σ 2 ) π 6 E h 3 m odd > 0 n odd > 0 sin ( m π x / a ) sin ( n π y / b ) m n ( m 2 / a 2 + n 2 / b 2 ) 2 ,
W ( x , y ) = α P 0 ( A 2 / h 3 ) ϕ ( x , y , k ) ,
α = [ 192 ( 1 - σ 2 ) ] / π 6 E
ϕ = m odd > 0 n odd > 0 sin ( m π x / a ) sin ( n π y / b ) m n ( m 2 k + n 2 / k ) 2 ,
k = b / a , the aspect ratio of the window ,
t ( x , y ) = [ ( W / x ) 2 + ( W / y ) 2 ] 1 2 .
t max = α P 0 ( A 2 / h 3 ) ( π / b ) λ ( k ) ,
λ ( k ) = m odd > 0 n odd > 0 sin ( m π / 2 ) m ( m 2 k + n 2 / k ) 2 .
v = 0 a 0 b W ( x , y ) d x d y = α P 0 A 2 h 3 × m odd > 0 n odd > 0 4 a b m 2 n 2 π 2 ( m 2 k + n 2 / k ) 2 .
v = β P 0 ,
β = ( α A 3 / h 3 ) θ ( k )
θ ( k ) = m odd > 0 n odd > 0 4 m 2 n 2 π 2 ( m 2 k + n 2 / k ) 2 .
v / t max = ( A b / π ) [ θ ( k ) / λ ( k ) ] .
P V = r T .
( P + d P - P 0 ) ( V - 2 v ) = r ( T + d T ) .
v = P V 2 P + V / β ( d P P - d T T ) .
S max = 4 π A b λ ( k ) θ ( k ) P V ( 2 P + V / β ) ( d P P - d T T ) .
S max = f ( a , k ) ( d P P - d T T ) degrees ,
f ( a , k ) = λ ( k ) θ ( k ) 2160 a k { 120 + 10 6 / [ 1.2 a 4 k 2 θ ( k ) ] } .

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