Abstract

A novel periodic aperture size measurement optical system, which makes use of a coherent light beam/lens 2-D Fourier-transform property, is proposed. Measuring gain and errors is discussed. This optical system is able to produce aperture widths on a 3-D formed surface with the same accuracy as those on a flat surface and is well suited for measuring small aperture size variations in shadow masks for color TV tubes. These variations in shadow masks are considered to cause luminous and color nonuniformities and have been detected heretofore only by visual inspection. The minimum detectable size variation for this new measuring method is ∼0.1 μm.

© 1981 Optical Society of America

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References

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  1. A. L. Flamholz, H. A. Frost, IBM J. Res. Dev. 17, 509 (1973).
    [CrossRef]
  2. J. J. Moscony, RCA Eng. 25, 30 (1979).
  3. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  4. A. Iwamoto (to be published).

1979 (1)

J. J. Moscony, RCA Eng. 25, 30 (1979).

1973 (1)

A. L. Flamholz, H. A. Frost, IBM J. Res. Dev. 17, 509 (1973).
[CrossRef]

Flamholz, A. L.

A. L. Flamholz, H. A. Frost, IBM J. Res. Dev. 17, 509 (1973).
[CrossRef]

Frost, H. A.

A. L. Flamholz, H. A. Frost, IBM J. Res. Dev. 17, 509 (1973).
[CrossRef]

Iwamoto, A.

A. Iwamoto (to be published).

Moscony, J. J.

J. J. Moscony, RCA Eng. 25, 30 (1979).

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

IBM J. Res. Dev. (1)

A. L. Flamholz, H. A. Frost, IBM J. Res. Dev. 17, 509 (1973).
[CrossRef]

RCA Eng. (1)

J. J. Moscony, RCA Eng. 25, 30 (1979).

Other (2)

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

A. Iwamoto (to be published).

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Figures (8)

Fig. 1
Fig. 1

Shadow mask color picture tube system. Three electron guns emit electron beams, which pass through apertures in a metal mesh (shadow mask) and impinge on a phosphor screen.

Fig. 2
Fig. 2

A shadow mask is a steel plate having numerous regularly arrayed rectangular or circular apertures. Typical rectangular aperture dimensions are 170 μm (aH), 485 μm (aV), and 600 μm (PH and PV).

Fig. 3
Fig. 3

Experimental optical system. A shadow mask, placed on the front focal plane of a Fourier transform lens and illuminated by coherent laser light, makes its Fourier pattern at the back focal plane of that Fourier transform lens. To measure aperture size variations, the specific n th light spot on the ξ-axis bright spots array in the Fourier pattern is selected by a spatial filter or a pinhole and converted to an electric signal.

Fig. 4
Fig. 4

Measurement sensitivities given by Eqs. (17) and (28) behave as cotangent functions multiplied by ξ. Periodic patterns, like shadow masks, have discrete or spatially sampled Fourier spectral patterns. Accordingly, sensitivity curves are also sampled at the discrete spatial frequencies ξn, which are plotted on the abscissa.

Fig. 5
Fig. 5

The shadow mask spectral intensity envelope is given by that of a single aperture and is actually sampled by the repetitive property of the pattern. This photograph corresponds to the pattern of N = 15 in Eq. (18). The treelike pattern in the spectrum is due to a moiré (beat) effect between the aperture and the sampling patterns. In this photograph, fourth to ninth diffracted light components on ξ axis are specified. High measuring gain orders correspond to those of weak intensities.

Fig. 6
Fig. 6

Apertures in a specific area on a flat shadow mask [100 mm long and 10 mm wide (a)] are sized by use of a microscope (b).

Fig. 7
Fig. 7

Shadow-mask apertures in the same area as in Fig. 6 are sized by the measuring optics (Fig. 3), where (a) corresponds to the sixth diffracted position on the ξ axis, and (b), (c), and (d) are to seventh, eight, and ninth, respectively. These data vary in a similar manner as predicted by the sensitivity curves shown in Fig. 4. The eighth order turns out to be the optimum measuring point.

Fig. 8
Fig. 8

Sensitivity and error functions for an oblong aperture. Frequency characteristics of functions ϕ1,ϕ2, which give measuring sensitivity, and ϕ3, which is a numerator for the measuring error function, are calculated by Eqs. (21), (22), and (26). Spectral behavior around null response frequencies for ϕ1 function turns out to have a great influence on both sensitivity and error properties.

Equations (30)

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m ( x , y ) = ( P H P V ) 1 a ( x , y ) comb ( x , y ) ,
x = x 2 P H + y P V , y = x 2 P H + y P V ,
comb ( x , y ) = i , k = δ ( x i , y k ) ,
M ( ξ , η ) = m ( x , y ) exp [ j 2 π ( x ξ + y η ) ] d x d y
= | a H a V | A ( ξ , η ) comb ( ξ , η ) ,
ξ = P H ξ + P V 2 η η = P H ξ + P V 2 η ,
a rect ( x , y ) = { 1 , | x | a H 2 , | y | a V 2 , 0 , | x | > a H 2 , | y | > a V 2 ,
A rect ( ξ , η ) = | a H a V | sinc ( a H ξ , a V η ) ,
sinc ( x , y ) = sin π x sin π y π 2 x y .
a CCL ( x , y ) = { 1 , ( x 2 + y 2 ) 1 / 2 a d / 2 , 0 , ( x 2 + y 2 ) 1 / 2 > a d / 2 ,
A CCL ( ξ , η ) = ( a d 2 ) J 1 [ π a d ( ξ 2 + η 2 ) 1 / 2 ] ( ξ 2 + η 2 ) 1 / 2 ,
M ( ξ , 0 ) = ( a H a V ) n = sinc ( a H ξ ) δ ( ξ n P H ) ,
ξ n = n P H ( n = integer ) .
I ( ξ n , ) = ( a V ξ n π ) 2 sin 2 [ π ( a H + ) ξ n ] ,
S ( ξ , a H ) = I ( ξ , ) I ( ξ , 0 ) 1 ,
S ( ξ , a H ) = 2 π ξ cos ( π a H ξ ) sin ( π a H ξ ) = 2 π ξ cot ( π a H ξ ) .
R ( ξ , a H ) = π a H ξ cot ( π a H ξ ) .
F ( ξ , N ) = sin π ( 2 N + 1 ) ξ sin π ξ N comb( ξ ) ,
A oblong ( ξ , 0 ) = a H ( a V a H ) sinc ( a H ξ ) + ( a H 2 ) J 1 ( a H π ξ ) ξ .
S ( ξ , a H ) = 2 π ξ ϕ 2 ϕ 1 ,
ϕ 1 = ( a V a H ) sin ( a H π ξ ) + π a H 2 J 1 ( a H π ξ ) ,
ϕ 2 = ( a V a H ) cos ( a H π ξ ) + π a H 2 J 0 ( a H π ξ ) a H sinc ( a H ξ ) .
ϕ 1 = π ξ A oblong ( ξ , 0 ) ,
S ( ξ , a H , a V ) 2 π ξ ϕ 2 ϕ 1 + S a V Δ a V ,
S a V = a H ϕ 3 ϕ 1 2 ,
ϕ 3 = π 2 J 1 ( π a H ξ ) cos ( π a H ξ ) π 2 J 0 ( π a H ξ ) sin ( π a H ξ ) + sin ( π a H ξ ) sinc ( a H ξ ) .
I ( ξ n , ) = [ P H ( a d + ) 2 n ] 2 J 1 2 [ n π P H ( a d + ) ] ,
R ( ξ , a d ) = π a d ξ 2 J 0 ( π a d ξ ) J 1 ( π a d ξ ) ξ π a d ξ 2 cot ( π a d ξ π 4 ) .
R θ ( n P H cos θ , a H ) = π ξ ( a H cos θ ) cot ( π ξ a H cos θ ) = ( n π a H P H ) cot ( n π a H P H ) .
1 P H ( 1 1 cos θ ) .

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