Abstract

We describe a signal-processing method for determining the center position of a white-light fringe signal. This is achieved in two steps. First, the center of gravity of the signal power is calculated to better than half a fringe period. Second, a synchronous sampling with four samples per fringe period is used to calculate the phase of the zero fringe. The theoretical analysis and experimental results show that the proposed signal processing is simple to operate, fast, accurate, and extremely noise resistant.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Koch, R. Ulrich, Sensors Actuators A 25–27, 201 (1991).
  2. S. Chen, A. J. Rogers, B. T. Meggit, Opt. Lett. 16, 761 (1991).
    [Crossref] [PubMed]
  3. B. S. Lee, T. C. Strand, Appl. Opt. 29, 3784 (1990).
    [Crossref] [PubMed]
  4. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969), p. 59.

1991 (2)

A. Koch, R. Ulrich, Sensors Actuators A 25–27, 201 (1991).

S. Chen, A. J. Rogers, B. T. Meggit, Opt. Lett. 16, 761 (1991).
[Crossref] [PubMed]

1990 (1)

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969), p. 59.

Chen, S.

Koch, A.

A. Koch, R. Ulrich, Sensors Actuators A 25–27, 201 (1991).

Lee, B. S.

Meggit, B. T.

Rogers, A. J.

Strand, T. C.

Ulrich, R.

A. Koch, R. Ulrich, Sensors Actuators A 25–27, 201 (1991).

Appl. Opt. (1)

Opt. Lett. (1)

Sensors Actuators A (1)

A. Koch, R. Ulrich, Sensors Actuators A 25–27, 201 (1991).

Other (1)

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969), p. 59.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Typical white-light fringe signal s(x) with Gaussian noise as described by Eq. (1).

Fig. 2
Fig. 2

Experimental setup. PH, pinhole; GTP, Glan–Thomson polarizer.

Fig. 3
Fig. 3

Fringe signal s(x) obtained from the photodiode array (SNR ≅ 63 dB).

Fig. 4
Fig. 4

Center position of the white-light signal versus SBC retardation for SNR ≅ 31 dB: squares, center of gravity xs1 circles, center of gravity xs2 (after one iteration); crosses, zero fringe position xΦ (phase).

Fig. 5
Fig. 5

Statistical reproducibility of the center position xs2 [curve (a)] and the phase Φ [curve (b)] as a function of the SNR.

Tables (1)

Tables Icon

Table 1 Theoretical Values of the Relative Systematic Error Δxs/xs and the Statistical Error δxs (Pixels) for a Gaussian Envelope of Width Δx = 35 Pixels

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

s ( x ) = s dc + s ac ( x ) = s dc + f ( x - x s ) cos [ 2 π ( x - x s ) Λ ] + g ( x , σ ) ,
A = n [ s ac ( x n ) ] 2 ,             B = n n [ s ac ( x n ) ] 2 , x s 1 = B / A .
x s 1 x s - ( N + 1 ) σ 2 A f x s = x s + Δ x s ,
δ x s 2 σ A f A f + ( N + 1 ) σ 2 × [ Δ x s 2 + 12 ( N + 1 ) x s 2 + N ( N + 1 ) ( N + 2 ) 24 × σ 2 A f + C f 0 A f ] 1 / 2 ,
f ( x ) = m exp [ - ( x / Δ x ) 2 ] ,
A f = n f n 2 m 2 Δ x 2 π 2 , C f 0 = n n 2 f n 2 Δ x 2 4 A f .
S n = ½ ( s n - 1 - s n + 1 ) , C n = ½ [ s n - ½ ( s n + 2 + s n - 2 ) ] .
Φ n = arg [ ( - i ) n ( C n + i S n ) ] .

Metrics