Abstract

A technique observing contour lines of an object by the use of moiré is developed. Shadow of an equispaced plane grating is projected onto an object by a point source and observed through the grating. The resulting moiré is a contour line system showing equal depth from the plane of grating if the light source and the observing point lie on a plane parallel to the grating. A technique to wash away the unwanted aliasing moiré optimization of contour line spacing and visibility and the results of the application are described.

© 1970 Optical Society of America

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References

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  1. T. Tsuruta, Opt. Comm. 1, 34 (1969).
    [CrossRef]
  2. W. H. Carter, Proc. IEEE 56, 96 (1968).
    [CrossRef]
  3. G. Oster, Y. Nishijima, Sci. Amer. 208, 54 (1963).
    [CrossRef]
  4. R. E. Brooks, L. O. Heflinger, Appl. Opt. 8, 935 (1969).
    [CrossRef] [PubMed]

1969 (2)

1968 (1)

W. H. Carter, Proc. IEEE 56, 96 (1968).
[CrossRef]

1963 (1)

G. Oster, Y. Nishijima, Sci. Amer. 208, 54 (1963).
[CrossRef]

Brooks, R. E.

Carter, W. H.

W. H. Carter, Proc. IEEE 56, 96 (1968).
[CrossRef]

Heflinger, L. O.

Nishijima, Y.

G. Oster, Y. Nishijima, Sci. Amer. 208, 54 (1963).
[CrossRef]

Oster, G.

G. Oster, Y. Nishijima, Sci. Amer. 208, 54 (1963).
[CrossRef]

Tsuruta, T.

T. Tsuruta, Opt. Comm. 1, 34 (1969).
[CrossRef]

Appl. Opt. (1)

Opt. Comm. (1)

T. Tsuruta, Opt. Comm. 1, 34 (1969).
[CrossRef]

Proc. IEEE (1)

W. H. Carter, Proc. IEEE 56, 96 (1968).
[CrossRef]

Sci. Amer. (1)

G. Oster, Y. Nishijima, Sci. Amer. 208, 54 (1963).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic representation of moiré topography. G is a equispaced plane grating. The X axis is taken along with lines of grating and the Z axis is taken vertical to the grating surface. E is the view point and lies on the Z axis. S is a point source which lies on the YZ plane. The y coordinate of S is dS. Heights of E and S from the grating surface are lE and lS. Line spacing of the grating is s0, and is the initial phase of the grating. P is a point on a surface under test. Depth of P from the grating surface is h, which is taken positive to downward. The slightly curved dotted lines represent the shadow of a small area of grating around Q and the slightly curved thick lines represent a perspective from E of the shadow on the grating plane. The perspective is approximately a grating with line spacing s and line direction θ. The coordinates of Q and R are xQ, yQ, and xR, yR.

Fig. 2
Fig. 2

Contour line system of a 25 cent coin. Collimated light and a field lens were used for illumination and observation. s 0 = 1 8 mm. φ = 45°. Depth interval between successive fringe Δ h = 1 8 mm.

Fig. 3
Fig. 3

Contour line system of a cotton cloth disk of 36-cm diam revolving with flatter. One turn of a helical Xe flash is used for illumination. s0 = 1.0 mm, lE = lS = l = 100 cm, d = 20 cm, Δh ≈ 5.0 mm. The parts of the disk with fringe of greater visibility are close to the grating.

Fig. 4
Fig. 4

Contour line system of a mannequin of living size. s0 = 1.0 mm, lE = lS = l = 200 cm, d = 100 cm, Δh ≈ 2.0 mm, and vertical distance of white lines = 10.0 cm. The grating is stationary during exposure. Note shadow of lines of grating on left cheek, and aliasing moiré on left and right cheeks.

Fig. 5
Fig. 5

Contour line system of a mannequin of living size. Data are same as for the Fig. 4 but the grating is moved parallel in its plane during exposure. Note that shadow of lines of grating and aliasing moiré are washed away.

Fig. 6
Fig. 6

Contour line system of a mannequin taken by shadow-free illumination. s0 = 1.0 mm, lE = lS1 = lS2 = 200 cm, d1 = d2 = 50 cm, Δh ≈ 4.0 mm, moving grating.

Fig. 7
Fig. 7

Contour line system of a living body, s0 = 1.0 mm, lE = lS = l = 200 cm, d = 40 cm, Δh ≈ 5.0 mm, moving grating.

Fig. 8
Fig. 8

Subtractively engaged two contour line systems of back of a living body. Each of the contour line systems is taken with right arm in raised and lowered positions. Note the moiré running near backbone on right shoulder.

Fig. 9
Fig. 9

Graphically drawn contour line system of same depth difference of the back of a living body. Δh ≈ 2.0 mm.

Equations (12)

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T Q = 1 2 [ 1 + cos 2 π ( + y ) / s 0 ] ,
I s = 1 2 { 1 + cos 2 π [ ( + y Q ) / s 0 + ξ / s ] I 0 } ,
ξ = ( y y R ) cos θ ( x x R ) sin θ .
I M = { 1 + cos 2 π [ ( + y Q ) / s 0 + ( y y R ) cos θ / s ( x x R ) sin θ / s ] + cos 2 π ( + y ) / s 0 + cos 2 π 1 2 [ ( y Q y R ) / s 0 + ( y y R ) ( cos θ / s 1 / s 0 ) ( x x R ) sin θ / s ] + cos 2 π { [ ( 2 + y Q + y R ) / s 0 + ( y y R ) ( cos θ / s + 1 / s 0 ) ( x x R ) sin θ / s ] / 2 } I 0 / 4 .
I p = 1 8 [ 1 + cos 2 π ( y Q y R ) / s 0 ] I 0 .
y Q y R = [ l E d ( l E l s ) y R ] h / l E ( l s + h ) ,
y Q y R = h d / ( l + h ) ,
h = l N / ( d / s 0 N ) .
h l s 0 N / d .
h = s 0 N cot φ ,
f 1 ( x , y ) = I Δ h f 2 ( x , y ) = J Δ h } ,
f ( x , y ) = [ f 2 ( x , y ) f 1 ( x , y ) ] = K Δ h ,

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