Abstract

By use of a superresolution pupil filtering technique to achieve a lateral optical superresolution and a differential confocal microscopy technique to achieve an axial resolution at the nanometer level, we propose a high spatial resolution bipolar absolute differential confocal approach for the ultraprecision measurement of three-dimensional microstructures. The feasibility of the proposed approach has been proved by use of a shaped annular beam differential confocal microscopy system. The experimental results indicate that the lateral and axial resolutions of the shaped annular beam differential confocal system are better than 0.2 μm and 2 nm, respectively, when λ=632.8 nm, ε=0.5, uM=6.95, and with a 0.85 numerical aperture.

© 2004 Optical Society of America

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References

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Acta Phys.

L. Liu, X. Deng, and G. Wang, �??Phase-only optical pupil filter for improving axial resolution in confocal microscopy,�?? Acta Phys. Sin. 50, 48�??51 (2001).

Chin. J. Lasers

X. Deng, G. Wang, and Z. Xu, �??3D superresolution pupil filter,�?? Chin. J. Lasers 28, 459�??462 (2001).

J. Opt. Soc. Am. A

Meas. Sci. Technol.

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, �??Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,�?? Meas. Sci. Technol. 11, 305�??314 (2000).
[CrossRef]

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, �??Characterization of surface topography by confocal microscopy: II. The micro and macro surface irregularities,�?? Meas. Sci. Technol. 11, 315�??329 (2000).
[CrossRef]

L. Yang, G. Wang, J. Wang, and Z. Xu, �??Surface profilometry with a fibre optical confocal scanning microscope,�?? Meas. Sci. Technol. 11, 1786�??1791 (2000).
[CrossRef]

Opt. Acta

R. W. Gerchberg, �??Superresolution through error energy reduction,�?? Opt. Acta 21, 709�??720 (1974).
[CrossRef]

Opt. Commun.

C. H.Lee and J. P. Wang, �??Noninterferometric differential confocal microscopy with 2-nm depth resolution,�?? Opt. Commun. 135, 233�??237 (1997).
[CrossRef]

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, and M. Kowalczyk, �??Three-dimensional superresolution by annular binary filters,�?? Opt. Commun. 165, 267�??278 (1999).
[CrossRef]

Opt. Eng.

H. Wang and F. Gan, �??New approach to superresolution,�?? Opt. Eng. 40, 851�??855 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

F. Wang, J. Tan, and W. Zhao, �??Optical probe using differential confocal technique for surface profile measurement,�?? in Process Control and Inspection for Industry, S. Zhang and W. Gao, eds., Proc. SPIE 4222, 194�??197 (2000).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Block diagram of the differential confocal approach to higher spatial resolution.

Fig. 2.
Fig. 2.

Response curves with axial offset of a pinhole.

Fig. 3.
Fig. 3.

Block diagram of the shaped annular beam differential confocal measurement.

Fig. 4.
Fig. 4.

Lateral response curves for different ε

Fig. 5.
Fig. 5.

Axial response curves for different uM .

Fig. 6.
Fig. 6.

Variations of gradient curves k(0,0,uM ) with uM .

Fig. 7.
Fig. 7.

Schematic diagram for shaping a Gaussian beam into an annular beam.

Fig. 8.
Fig. 8.

Actual axial intensity response curves.

Fig. 9.
Fig. 9.

Measurements of a standard step scanned with an AFM.

Fig. 10.
Fig. 10.

Measurements of a standard step for different ε.

Equations (11)

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

I 3 v u u M = [ 2 0 1 P ( ρ ) · e ( ju ρ 2 ) 2 J 0 ( ρv ) ρdρ ] 2 ×
( [ 2 0 1 P ( ρ ) · e j ρ 2 ( u u M ) 2 J 0 ( ρv ) ρdρ ] 2 [ 2 0 1 P ( ρ ) · e j ρ 2 ( u + u M ) 2 J 0 ( ρv ) ρdρ ] 2 )
P ( ρ ) = j = 1 N t j · e i φ j
{ I ( r ) = 0 0 r ε I ( r ) = A 2 ε r 1
E = 2 π ε 1 A 2 rdr 2 π ε 1 rdr
A = 1 1 ε 2
I 3 v u u M = 2 ε 1 A e ( ju ρ 2 ) 2 J 0 ( ρv ) ρdρ 2 × ( 2 ε 1 A e j ρ 2 ( u u M ) 2 J 0 ( ρv ) ρdρ 2 2 ε 1 A e j ρ 2 ( u + u M ) 2 J 0 ( ρv ) ρdρ 2 )
= 1 ( 1 ε 2 ) 2 · 2 ε 1 e ( j 2 ) 2 J 0 ( ρv ) ρdρ 2 × ( 2 ε 1 e j ρ 2 ( u u M ) 2 J 0 ( ρv ) ρdρ 2 2 ε 1 e j ρ 2 ( u + u M ) 2 J 0 ( ρv ) ρdρ 2 )
k 0 u u M = ( 1 ε 2 ) 2 · sin c [ u M ( 1 ε 2 ) 4 π ] × { { ( 2 u u M ) ( 1 ε 2 ) 4 } · cos { ( 2 u u M ) ( 1 ε 2 ) 4 } sin ( 2 u u M ) ( 1 ε 2 ) 4 { ( 2 u u M ) ( 1 ε 2 ) 4 } 2 }
( 1 ε 2 ) 2 · sin c [ u M ( 1 ε 2 ) 4 π ] × { { ( 2 u + u M ) ( 1 ε 2 ) 4 } · cos { ( 2 u + u M ) ( 1 ε 2 ) 4 } sin ( 2 u + u M ) ( 1 ε 2 ) 4 { ( 2 u + u M ) ( 1 ε 2 ) 4 } 2 }
k 0, 0 u M = 2 × ( 1 ε 2 ) 2 · sin c [ u M 4 π ( 1 ε 2 ) ] × { { u M ( 1 ε 2 ) 4 } · cos { u M ( 1 ε 2 ) 4 } sin { u M ( 1 ε 2 ) 4 } { u M ( 1 ε 2 ) 4 } 2 }

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