Abstract

When an asymmetric triangle voltage signal is applied to drive an electro-optic modulator, interference signals with two groups of periodic sinusoidal segments with different frequencies are obtained. An improved method is proposed to fit these two groups of segments, and their associated phases can be determined. The absolute phase can be obtained by subtracting the initial phase from the phases of these two groups. This technique is applied to all pixels, and the full-field absolute phase measurements can be achieved. The validity of this method is demonstrated.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. L. Chen and D. C. Su, “Method for determining full-field absolute phases in the common-path heterodyne interferometer with an electro-optic modulator,” Appl. Opt. 47, 6518–6523 (2008).
    [CrossRef] [PubMed]
  2. N. A. Massie, R. D. Nelson, and S. Holly, “High-performance real-time heterodyne interferometry,” Appl. Opt. 18, 1797–1803 (1979).
    [CrossRef] [PubMed]
  3. R. Dandliker, R. Thalmann, and D. Prongue, “Two-wavelength laser interferometry using superheterodyne detection,” Opt. Lett. 13, 339–341 (1988).
    [CrossRef] [PubMed]
  4. E. Gelmini, U. Minoni, and F. Docchio, “Tunable, double-wavelength heterodyne detection interferometer for absolute-distance measurements,” Opt. Lett. 19, 213–215 (1994).
    [CrossRef] [PubMed]
  5. C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
    [CrossRef]
  6. T. Tkaczyk and R. Jozwicki, “Full-field heterodyne interferometer for shape measurement: experimental characteristics of the system,” Opt. Eng. 42, 2391–2399 (2003).
    [CrossRef]
  7. M. C. Pitter, C. W. See, and M. G. Somekh, “Full-field heterodyne interference microscope with spatially incoherent illumination,” Opt. Lett. 29, 1200–1202 (2004).
    [CrossRef] [PubMed]
  8. P. Egan, M. J. Connely, F. Lakestani, and M. P. Whelan, “Random depth access full-field heterodyne low-coherence interferometry utilizing acousto-optic modulation and a complementary metal-oxide semiconductor camera,” Opt. Lett. 31, 912–914 (2006).
    [CrossRef] [PubMed]
  9. M. Akiba, K. P. Chan, and N. Tanno, “Full-field optical coherence tomography by two-dimensional heterodyne detection with a pair of CCD cameras,” Opt. Lett. 28, 816–818 (2003).
    [CrossRef] [PubMed]
  10. Y. L. Lo, H. W. Chih, C. Y. Yeh, and T. C. Yu, “Full-field heterodyne polariscope with an image signal processing method for principal axis and phase retardation measurements,” Appl. Opt. 45, 8006–8012 (2006).
    [CrossRef] [PubMed]
  11. IEEE, “Standard for terminology and test methods for analog to digital converters,” IEEE Std 1241-2000, 25–29 (2001).

2008

2006

2004

2003

M. Akiba, K. P. Chan, and N. Tanno, “Full-field optical coherence tomography by two-dimensional heterodyne detection with a pair of CCD cameras,” Opt. Lett. 28, 816–818 (2003).
[CrossRef] [PubMed]

T. Tkaczyk and R. Jozwicki, “Full-field heterodyne interferometer for shape measurement: experimental characteristics of the system,” Opt. Eng. 42, 2391–2399 (2003).
[CrossRef]

2001

IEEE, “Standard for terminology and test methods for analog to digital converters,” IEEE Std 1241-2000, 25–29 (2001).

1997

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

1994

1988

1979

Akiba, M.

Chan, K. P.

Chang, J. G.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Chang, M.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Chen, Y. L.

Chih, H. W.

Chou, C.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Connely, M. J.

Dandliker, R.

Docchio, F.

Egan, P.

Feng, C. M.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Gelmini, E.

Holly, S.

Huang, Y. C.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Jozwicki, R.

T. Tkaczyk and R. Jozwicki, “Full-field heterodyne interferometer for shape measurement: experimental characteristics of the system,” Opt. Eng. 42, 2391–2399 (2003).
[CrossRef]

Lakestani, F.

Lo, Y. L.

Massie, N. A.

Minoni, U.

Nelson, R. D.

Pitter, M. C.

Prongue, D.

See, C. W.

Somekh, M. G.

Su, D. C.

Tanno, N.

Thalmann, R.

Tkaczyk, T.

T. Tkaczyk and R. Jozwicki, “Full-field heterodyne interferometer for shape measurement: experimental characteristics of the system,” Opt. Eng. 42, 2391–2399 (2003).
[CrossRef]

Whelan, M. P.

Yeh, C. Y.

Yu, T. C.

Appl. Opt.

Opt. Commun.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314–321(1997).
[CrossRef]

Opt. Eng.

T. Tkaczyk and R. Jozwicki, “Full-field heterodyne interferometer for shape measurement: experimental characteristics of the system,” Opt. Eng. 42, 2391–2399 (2003).
[CrossRef]

Opt. Lett.

Other

IEEE, “Standard for terminology and test methods for analog to digital converters,” IEEE Std 1241-2000, 25–29 (2001).

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 (7)

Fig. 1
Fig. 1

Schematic diagram for the full-field common-path heterodyne interferometer: LS, linearly polarized laser source; EO, electro-optic modulator; FG, function generator; LVA, linear voltage amplifier; MO, microscopic objective; PH, pinhole; CL, collimating lens; AN, analyzer; IL, imaging lens; C, CMOS camera; PC, personal computer.

Fig. 2
Fig. 2

(a) Asymmetric triangle voltage signal is used to drive the EO. (b)–(j) Theoretical interference signals as ϕ is changed from 180 ° to 180 ° in steps of 45 ° .

Fig. 3
Fig. 3

Sampled data divided into two groups: group A (symbol *) with f = 3 / 2 T and group B (symbol ○) with f = 3 / T .

Fig. 4
Fig. 4

Processes to obtain associated sinusoidal signals: (a) the sampled data of group A; (b) the odd segments in (a) are shifted a π phase; (c) the associated sinusoidal signals (solid line) of (b); (d) the sampled data of group B; (e) the associated sinusoidal signals (solid line) of (d).

Fig. 5
Fig. 5

Flow chart for the whole process.

Fig. 6
Fig. 6

Intensities of the sampled signals at the pixel ( + 100 , + 100 ) .

Fig. 7
Fig. 7

Measured full-field phase retardation distribution of the quarter-wave-plate.

Equations (16)

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

Γ = π V π V z .
V Z = 3 V π T [ ( t t 0 ) m T ] V π , m T t t 0 ( m + 2 / 3 ) T ;
V Z = 6 V π T [ ( t t 0 ) ( m + 1 ) T ] V π , ( m + 2 / 3 ) T t t 0 ( m + 1 ) T ,
Γ = 3 π t t 0 T ( m + 1 ) π , m T t t 0 ( m + 2 / 3 ) T ;
Γ = 6 π t t 0 T π , ( m + 2 / 3 ) T t t 0 ( m + 1 ) T .
I ( t ) = 1 2 [ 1 + cos ( 3 π t T ϕ 0 + ϕ m π ) ] , m T t t 0 ( m + 2 / 3 ) T ;
I ( t ) = 1 2 [ 1 + cos ( 6 π t T 2 ϕ 0 ϕ ) ] , ( m + 2 / 3 ) T t t 0 ( m + 1 ) T ,
ϕ = ( 2 ψ 1 ψ 2 ) 3 .
I A ( t ) = 1 2 [ 1 + cos ( 3 π t T + ψ 1 ) ] = A 1 · cos ( 3 π t T ) + B 1 · sin ( 3 π t T ) + C 1 , if     m   is   even ;
I A ( t ) = 1 2 [ 1 + cos ( 3 π t T + ψ 1 + π ) ] = A 1 · cos ( 3 π t T ) + B 1 · sin ( 3 π t T ) + C 1 , if     m   is   odd .
I A ( t ) = ( I A ( m = 0 , t = 0 ) I A ( m = 0 , t = Δ t ) : I A ( 1 , k Δ t ) I A ( 1 , ( k + 1 ) Δ t ) : I A ( 2 , ( k + T f c ) Δ t ) : ) = ( cos ( 3 π 0 T ) sin ( 3 π 0 T ) 1 cos ( 3 π Δ t T ) sin ( 3 π Δ t T ) 1 : : : cos ( 3 π k Δ t T ) sin ( 3 π k Δ t T ) 1 cos ( 3 π ( k + 1 ) Δ t T ) sin ( 3 π ( k + 1 ) Δ t T ) 1 : : : cos ( 3 π ( k + T f c ) Δ t T ) sin ( 3 π ( k + T f c ) Δ t T ) 1 : : : ) × ( A 1 B 1 C 1 ) = M 1 × ( A 1 B 1 C 1 ) ,
( A 1 B 1 C 1 ) = ( M 1 t M 1 ) 1 M 1 t I A ,
I B ( t ) = 1 2 [ 1 + cos ( 6 π t T + ψ 2 ) ] = A 2 · cos ( 6 π t T ) + B 2 · sin ( 6 π t T ) + C 2 ,
ψ 1 = tan 1 ( B 1 A 1 ) ,
ψ 2 = tan 1 ( B 2 A 2 ) .
I c = 1 2 [ 1 + cos ( 2 π V V π T t + ψ ) ] ,

Metrics