Abstract

A noncontact optical technique for the measurement of surface profile is described, which has a height sensitivity of the order of 1 Å. It is based on a common path heterodyne interferometer in which two orthogonally polarized beams of slightly different frequency are focused on the surface to be measured. One focal point acts as a reference as the other point circularly scans the surface. The phase of the beat frequency of the interfering return beams is directly proportional to the surface height. The results of a surface measurement include graphical displays of the surface profile, autocovariance function, spectral density function, stability, and repeatability. Comparison with other instruments is also discussed.

© 1981 Optical Society of America

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References

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  1. J. M. Bennett, Appl. Opt. 15, 2705 (1976).
    [CrossRef] [PubMed]
  2. S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon, Oxford, 1948).
  3. B. P. Hildebrand, R. L. Gordon, E. V. Allen, Appl. Opt. 13, 177 (1974).
    [CrossRef] [PubMed]
  4. J. C. Stover, Appl. Opt. 14, 1796 (1975).
    [CrossRef] [PubMed]
  5. J. M. Elson, J. M. Bennett, J. Opt. Soc. Am. 69, 31 (1979).
    [CrossRef]
  6. H. E. Bennett, J. O. Porteus, J. Opt. Soc. Am. 51, 123 (1961).
    [CrossRef]
  7. H. E. Bennett, J. Opt. Soc. Am. 53, 1389 (1963).
    [CrossRef]
  8. J. O. Porteus, J. Opt. Soc. Am. 53, 1394 (1963).
    [CrossRef]
  9. G. Breitweiser, J. Vac. Sci. Technol. 11, 101 (1974).
    [CrossRef]
  10. C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
    [CrossRef]
  11. This beam splitter has a BK-7 substrate with three dielectric layers (SiO2, TiO2, SiO2) to give 9% reflection for s and p polarizations at 45° angle of incidence.
  12. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
    [CrossRef]

1979 (1)

1976 (1)

1975 (2)

J. C. Stover, Appl. Opt. 14, 1796 (1975).
[CrossRef] [PubMed]

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

1974 (2)

1963 (2)

1961 (1)

1941 (1)

Allen, E. V.

Bennett, H. E.

Bennett, J. M.

Breitweiser, G.

G. Breitweiser, J. Vac. Sci. Technol. 11, 101 (1974).
[CrossRef]

Christensen, J.

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

Elson, J. M.

Gordon, R. L.

Hildebrand, B. P.

Jerner, R. C.

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

Jones, R. C.

Peavey, J. H.

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

Pellerin, C. J.

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

Porteus, J. O.

Stover, J. C.

Tolansky, S.

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon, Oxford, 1948).

Appl. Opt. (3)

J. Opt. Soc. Am. (5)

J. Vac. Sci. Technol. (2)

G. Breitweiser, J. Vac. Sci. Technol. 11, 101 (1974).
[CrossRef]

C. J. Pellerin, J. Christensen, R. C. Jerner, J. H. Peavey, J. Vac. Sci. Technol. 12, 496 (1975).
[CrossRef]

Other (2)

This beam splitter has a BK-7 substrate with three dielectric layers (SiO2, TiO2, SiO2) to give 9% reflection for s and p polarizations at 45° angle of incidence.

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Clarendon, Oxford, 1948).

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Figures (12)

Fig. 1
Fig. 1

Schematic of optical system.

Fig. 2
Fig. 2

Zeeman split He–Ne laser and stabilization controls.

Fig. 3
Fig. 3

Detail of interferometer.

Fig. 4
Fig. 4

Detail of phase detection.

Fig. 5
Fig. 5

Beam path geometry in the interferometer.

Fig. 6
Fig. 6

Optical heterodyne surface profile measurement system.

Fig. 7
Fig. 7

View of optical system.

Fig. 8
Fig. 8

Analysis of three surfaces prepared by different methods: (a) vitreous carbon; (b) BK-7; (c) fused silica.

Fig. 9
Fig. 9

Stability test of system.

Fig. 10
Fig. 10

Repeatability test of system.

Fig. 11
Fig. 11

Optical arrangement for producing a variable phase bias.

Fig. 12
Fig. 12

Local slope effect on beam path in the interferometer.

Tables (2)

Tables Icon

Table I Comparison of the Magnitude of the Individual Phase Contributions in Eq. (9) for Typical Parametic Values and Variations

Tables Icon

Table II Comparison of rms Heights, rms Slopes, and First Zero Crossings of the Autocovariance Function for Surfaces Measured Optically and with a Stylus Instrument

Equations (23)

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V = V + + V - = exp [ i ( k + z + - ω + t ) ] + exp [ i ( k - z - - ω - t ) ] ,
S r = exp [ i ( k + z r - ω + t - 2 θ ) ] + exp [ i ( k - z r - ω - t + 2 θ ) ] 2 = 2 [ 1 + cos [ ( k + - k - ) z r - ω t - 4 θ ] ] ,
S m = exp { i [ k + ( z m + z / 2 ) - ω + t ] } + exp { i [ k - ( z m - z / 2 ) - ω - t ] } 2 = 2 { 1 + cos [ ( k + - k - ) z m + ( k + + k - ) 2 z - ω t ] } ,
ϕ = ( k + - k - ) ( z m - z r ) + ( k + + k - ) 2 z + 4 θ .
k = ω / c and ω = 2 π f ,
k + = 2 π c ( f + f / 2 )             k - = 2 π c ( f - f / 2 ) ,
k + - k - = 2 π c f             k + + k - 2 = 2 π c f .
ϕ = 2 π c [ f ( z m - z r ) + f z ] + 4 θ = 2 π c ( f z + f z ) + 4 θ ,
Δ ϕ = 2 π c ( z Δ f + f Δ z + z Δ f + f Δ z ) + 4 Δ θ .
Δ ϕ = 2 π c f Δ z = 2 π λ Δ z ,
Δ z = 2 Δ h cos β + .
β ± = tan - 1 [ b ± ( d - f ) tan α ± f ] ,
Δ h = λ b 2 + f 2 4 π f Δ ϕ .
Δ h = λ 8 π N . A . 2 + 4 Δ ϕ .
A ( m s ) = n = 1 N n [ ( n + m ) s ] h ( n s ) n = 1 N h 2 ( n s ) ,
S ( u ) = | n = 1 N W ( n s ) exp ( - 2 π i n s u λ ) | 2 n = 1 N W ( n s ) 2 ,
W ( n s ) = R exp [ - 2 i k h ( n s ) ] = R exp [ - 4 π i h ( n s ) λ ] ,
V = exp [ i ( k + z + - ω + t ) ] [ 1 0 ] + exp [ i ( k - z - - ω - t ) ] [ 0 1 ] ,
V = T P T HWP T QWP V ,
T QWP = 1 2 [ 1 - i - i 1 ] , T HWP = - i [ cos 2 θ sin 2 θ sin 2 θ - cos 2 θ ] , T p = 1 2 [ 1 - 1 - 1 1 ] .
V = - ( 1 + i ) 2 2 { exp [ i ( k + z r - ω + t - 2 θ ) ] + exp [ i ( k - z r - ω - t + 2 θ ) ] } [ 1 - 1 ] .
I = V V = 1 2 [ 1 + cos ( k + - k - ) z r - ( ω + - ω - ) t - 4 θ ] ,
2 b = γ 2 ( N . A . 2 + 4 N . A . ) ,

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