Abstract

An improved interferometric method is described for measuring plotting errors of desk-top computer plotters used to make computer-generated holograms. The plotting errors are measured using moiré fringes formed using Young’s fringes and straight lines drawn by the plotters. The Young’s fringes are produced by laser beams originating from two single-mode optical fibers. Using this method, plotting errors of Hewlett-Packard 7225A and 7470A plotters are measured.

© 1984 Optical Society of America

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References

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  1. A. J. MacGovern, J. C. Wyant, “Computer Generated Holograms for Testing Optical Elements,” Appl. Opt. 10, 619 (1971).
    [CrossRef] [PubMed]
  2. J. C. Wyant, P. K. O’Neill, A. J. MacGovern, “Interferometric Method of Measuring Plotter Distortion,” Appl. Opt. 13, 1541 (1974).
    [CrossRef]
  3. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

1974 (1)

1971 (1)

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Figures (8)

Fig. 1
Fig. 1

Optical setup of interferometric method.

Fig. 2
Fig. 2

Interferogram taken by the setup shown in Fig. 1.

Fig. 3
Fig. 3

Optical setup of improved interferometric method.

Fig. 4
Fig. 4

Model pattern of interference fringes.

Fig. 5
Fig. 5

Optical schematic of Young’s interference.

Fig. 6
Fig. 6

Distortion of Young’s fringes.

Fig. 7
Fig. 7

Interferograms with fringes parallel to CGH lines.

Fig. 8
Fig. 8

Interferograms with fringes perpendicular to CGH lines.

Tables (5)

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Table I Conditions for Taking Interferograms

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Table II Straightness of CGH Lines

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Table III Difference of Plotter’s Scale Deviation From 7225A X-Axis Scale

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Table IV Maximum Distortion

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Table V Line Space Fluctuation

Equations (22)

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ɛ ( X , Y ) = δ ( x , y ) P f · P c 2 N ,
S 1 A n - S 2 A n = n λ a X + d l X 2 + Y 2 + l 2 ,
P y = λ l a ,
A x n + d l X n 2 + Y n 2 + l 2 = a X n + d l X n 2 + l 2
a X n + d l X n 2 + Y n 2 + l 2 = a ( X n - Δ X ) + d l ( X n - Δ X ) 2 + l 2 .
Δ X = ( X n + d a l ) Y n 2 2 ( l 2 - d a X n l ) .
Δ X = ( X n + d a l ) Y n 2 2 l 2 .
f ( X , Y ) = X 2 + Y 2 - R 2 = 0 ,
Δ X ( X , Y ) X f ( X , Y ) Y - Δ X ( X , Y ) Y f ( X , Y ) X = 0.
X = - 1 3 d l a + 1 3 d 2 a 2 l 2 + 3 R 2 , Y 2 = 2 3 R 2 - 2 9 d 2 a 2 l 2 + 2 9 d a l × d 2 a 2 l 2 + 3 R 2             when d > 0 ;
X = - 1 3 d l a - 1 3 d 2 a 2 l 2 + 3 R 2 , Y 2 = 2 3 R 2 - 2 9 d 2 a 2 l 2 - 2 9 d a l × d 2 a 2 ; l 2 + 3 R 2             when d < 0.
Δ X max = | 1 3 d a l R 2 - 1 27 d 3 a 3 l | + ( 1 27 d 2 a 2 + 1 9 R 2 l 2 ) × d 2 a 2 l 2 + 3 R 2
a = λ l P y = 3.17 × 10 - 3 l ,
Δ X max = 1.12 × 10 5 l 2 .
P y n = X n + 1 - X n , X n + 1 = X n + P y n .
a X n + 1 + d l X n + 1 2 + Y n 2 + l 2 - a X n + d l X n 2 + Y n 2 + l 2 = λ
a ( X n + P y n + d l ) ( X n + P y n ) 2 + Y n 2 + l 2 - a X n + d l X n 2 + Y n 2 + l 2 = λ .
P y n = λ X n 2 + Y n 2 + l 2 a + λ X n ( a X n + d l ) a 2 l .
Δ P y = P y n - P y = λ a ( 3 X n 2 + Y n 2 ) + 2 λ d X n l 2 a 2 l .
Δ P y max = 0.0003 mm = 0.3 μ m .
D = 2 R ( 1 P f - 1 P f ) P c 2 N = 150 × ( 1 30 - 1 35 ) × 0.2 = 0.14 mm .
Δ P c = ( θ max - θ min ) P c 2 2 N .

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