Abstract

Here we present multiple-wavelength digital holographic interferometry with a wide measurement range using laser diodes. Small wavelength differences can be easily realized by the wavelength tuning of laser diodes with injection current controls. A contour map of an object with a wide measurement range and a high sensitivity is demonstrated by combining a few contour maps with several measurement sensitivities. Synthetic wavelengths are calibrated using a known height difference. This alleviates the need to have high precise knowledge of the recording wavelengths. The synthetic wavelengths ranged from 3mm for high measurement sensitivity to 4cm for wide measurement range. An rms error of 35μm for a 1cm height measurement is shown. The measured profile of holographic interferometry agrees with a standard stylus instrument.

© 2008 Optical Society of America

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References

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2006

2004

2003

2001

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417-428 (2001).

2000

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79-85 (2000).

1999

1998

1991

1985

1984

1976

1969

L. O. Heflinger and R. F. Wuerker, “Holographic contouring via multifrequency lasers,” Appl. Phys. Lett. 15, 28 (1969).
[CrossRef]

1967

Appl. Opt.

Appl. Phys. Lett.

L. O. Heflinger and R. F. Wuerker, “Holographic contouring via multifrequency lasers,” Appl. Phys. Lett. 15, 28 (1969).
[CrossRef]

J. Opt. Soc. Am.

Opt. Eng.

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79-85 (2000).

Opt. Lasers Eng.

I. Yamaguchi, S. Ohta, and J. Kato, “Surface contouring by phase-shifting digital holography,” Opt. Lasers Eng. 36, 417-428 (2001).

Opt. Lett.

Other

Y. Ishii, Progress in Optics, Chap. Laser-diode interferometry, (Elsevier, 2004), vol. 46, pp. 243-309.

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Figures (9)

Fig. 1
Fig. 1

Geometry of holographic interferometry.

Fig. 2
Fig. 2

Hologram recording setupDOSA: optical spectrum analyzer; FC: fiber coupler; HM: half mirror; OL1: × 10 objective lens; OL2: 5 × objective lens; L1: lens ( f = 60 mm ); L2: lens ( f = 70 mm ); L3: lens ( f = 170 mm ); L4: lens ( f = 60 mm ).

Fig. 3
Fig. 3

Image reconstructed from a hologram. (a) The entire image. (b) Closeup in a first-order diffracted image.

Fig. 4
Fig. 4

Plot of the wavelength as a function of the injection current.

Fig. 5
Fig. 5

Phase differences Δ Φ n . (a)  Δ Φ 1 , λ 1 = 783.24 nm . (b)  Δ Φ 2 , λ 2 = 783.26 nm . (c)  Δ Φ 3 , λ 3 = 783.30 nm . (d)  Δ Φ 4 , λ 4 = 783.38 nm . (e)  Δ Φ 5 , λ 5 = 783.41 nm .

Fig. 6
Fig. 6

Plots of the phase differences in (a) and (b) extracted from white lines designated by Figs. 5a, 5e, respectively, as a function of lateral positions.

Fig. 7
Fig. 7

An object profile calculated from Δ ϕ 5 ( Λ 5 = 3.2 mm )D (a) Gray scale of an entire distribution. (b) Plot of the object height along a white line in (a) as a function of lateral positions.

Fig. 8
Fig. 8

An object profile calculated from Δ ϕ 5 ( Λ 5 = 3.2 mm )DMedian filter was applied to the measurement profile. (a) Gray scale of an entire distribution. (b) Plot of the object height along a white line in (a) as a function of lateral positions.

Fig. 9
Fig. 9

Height measurements by present holographic and mechanical stylus methods.

Tables (1)

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Table 1 Synthetic Wavelengths ( λ 0 = 783.23 nm )

Equations (27)

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u r ( x , y , z ) = 1 z exp ( i π x 2 + y 2 λ z ) ,
u o ( x , y , z ) = d x d y u o ( x , y , 0 ) z exp [ i π ( x x ) 2 + ( y y ) 2 λ z ] = 1 z exp ( i π x 2 + y 2 λ z ) d x d y u o ( x , y , 0 ) exp ( i π x 2 + y 2 λ z ) exp ( i 2 π x x + y y λ z ) .
u o ( x , y ) = u o ( x , y , 0 ) exp ( i π x 2 + x 2 λ z ) ,
U o ( f x , f y ) = F ( u o ) = d x d y u o ( x , y ) exp [ i 2 π ( f x x + f y y ) ] .
u o ( x , y , z ) = 1 z exp ( i π x 2 + y 2 λ z ) U o ( x λ z , y λ z ) .
I ( x , y , z ) = | u r ( x , y , z ) + u o ( x , y , z ) | 2 = | u r | 2 + | u o | 2 + u r * u o + u r u o * = 1 z 2 { 1 + | U o ( x λ z , y λ z ) | 2 + U o ( x λ z , y λ z ) + U o * ( x λ z , y λ z ) } = 1 z 2 { 1 + | U o ( f x , f y ) | 2 + U o ( f x , f y ) + U o * ( f x , f y ) } .
u rec ( x , y ) = F 1 { I ( x , y , z ) } = F 1 { I ( λ z f x , λ z f y , z ) } = d f x d f y I ( λ z f x , λ z f y , z ) exp [ i 2 π ( f x x + f y y ) ] = λ 2 { δ ( x , y ) λ 2 z 2 + u o ( x , y ) u o * ( x , y ) + u o ( x , y ) + u o * ( x , y ) } ,
u rec ( s Δ x , t Δ y ) = p = N x / 2 N x / 2 1 q = N y / 2 N y / 2 1 I ( p Δ x , q Δ y , z ) exp { i 2 π ( p Δ x λ z s Δ x + q Δ y λ z t Δ y ) } ,
u rec ( s Δ x , t Δ y ) = p = N x / 2 N x / 2 1 q = N y / 2 N y / 2 1 I ( p Δ x , q Δ y , z ) exp { i 2 π ( p s N x + q t N y ) } ,
Δ x = λ z Δ x N x , Δ y = λ z Δ y N y ,
N x / 2 s < N x / 2 , N y / 2 t < N y / 2 .
ϕ ( x , y ) = 2 π λ { L + x 2 + y 2 2 z } ,
L = ( 1 + cos θ ) h ( x , y ) x sin θ .
Δ ϕ n ( x , y ) = ϕ n ϕ 0 2 π Λ n L ,
Λ n = λ 0 λ n λ n λ 0 λ ¯ n 2 Δ λ n ,
λ ¯ n = λ 0 + λ n 2 , Δ λ n = λ n λ 0 .
Δ Φ n = tan 1 Im ( u o n u o 0 * ) Re ( u o n u o 0 * ) .
Δ Φ n = Δ ϕ n 2 π NINT ( Δ ϕ n 2 π ) ,
Δ ϕ n = Δ Φ n + 2 π NINT ( α n Δ ϕ n 1 Δ Φ n 2 π ) ,
α n = Λ n 1 Λ n .
Δ L r = ( 1 + cos θ ) { h ( x 1 , y 1 ) h ( x 2 , y 2 ) } ( x 1 x 2 ) sin θ .
Λ 1 = 2 π Δ ϕ 1 ( x 1 , y 1 ) Δ ϕ 1 ( x 2 , y 2 ) Δ L r .
Λ n = λ ¯ n 2 Δ λ n ,
ϕ n = Δ Φ n + 2 π NINT ( α n Δ ϕ n 1 Δ Φ n 2 π ) ,
α n = Λ n 1 Λ n .
Λ n = 2 π Δ ϕ n ( x 1 , y 1 ) Δ ϕ n ( x 2 , y 2 ) Δ L r .
h = Λ n Δ ϕ n 4 π

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