Abstract

We propose an optical corrective element with zooming capability to convert nonlinear sinusoidal scanning into linear scanning. Such a device will be useful for linearizing the angular scan of a resonant mirror scanner. The design methodology is to create a graded index of refraction device as the reference design, with its index of refraction parameters based on the propagation of an electromagnetic field in inhomogeneous media. The algorithm for converting this refractive element to the corresponding binary diffractive version is also presented. Design and simulation data are shown.

© 2006 Optical Society of America

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References

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  1. J. Khoury, C. L. Woods, B. Haji-saeed, D. Pyburn, S. K. Sengupta, and J. Kierstead, "A mapping approach for image correction and processing for bidirectional resonant scanners," Opt. Eng. (to be published).
  2. GSI Lumonics CRS scanner manual, available for download at http://www.gsilumonics.com/process_download_open/01_optical_scanning/resources/7om025_CRS.pdf.
  3. C. L. Confer and G. J. Burrer, "Linear resonant approach to scanning," in Beam Deflection and Scanning Technologies, L. Beiser and G. F. Marshall, eds., Proc. SPIE 1454 , 215-222 (1991).

1991 (1)

C. L. Confer and G. J. Burrer, "Linear resonant approach to scanning," in Beam Deflection and Scanning Technologies, L. Beiser and G. F. Marshall, eds., Proc. SPIE 1454 , 215-222 (1991).

Burrer, G. J.

C. L. Confer and G. J. Burrer, "Linear resonant approach to scanning," in Beam Deflection and Scanning Technologies, L. Beiser and G. F. Marshall, eds., Proc. SPIE 1454 , 215-222 (1991).

Confer, C. L.

C. L. Confer and G. J. Burrer, "Linear resonant approach to scanning," in Beam Deflection and Scanning Technologies, L. Beiser and G. F. Marshall, eds., Proc. SPIE 1454 , 215-222 (1991).

Haji-saeed, B.

J. Khoury, C. L. Woods, B. Haji-saeed, D. Pyburn, S. K. Sengupta, and J. Kierstead, "A mapping approach for image correction and processing for bidirectional resonant scanners," Opt. Eng. (to be published).

Khoury, J.

J. Khoury, C. L. Woods, B. Haji-saeed, D. Pyburn, S. K. Sengupta, and J. Kierstead, "A mapping approach for image correction and processing for bidirectional resonant scanners," Opt. Eng. (to be published).

Kierstead, J.

J. Khoury, C. L. Woods, B. Haji-saeed, D. Pyburn, S. K. Sengupta, and J. Kierstead, "A mapping approach for image correction and processing for bidirectional resonant scanners," Opt. Eng. (to be published).

Pyburn, D.

J. Khoury, C. L. Woods, B. Haji-saeed, D. Pyburn, S. K. Sengupta, and J. Kierstead, "A mapping approach for image correction and processing for bidirectional resonant scanners," Opt. Eng. (to be published).

Sengupta, S. K.

J. Khoury, C. L. Woods, B. Haji-saeed, D. Pyburn, S. K. Sengupta, and J. Kierstead, "A mapping approach for image correction and processing for bidirectional resonant scanners," Opt. Eng. (to be published).

Woods, C. L.

J. Khoury, C. L. Woods, B. Haji-saeed, D. Pyburn, S. K. Sengupta, and J. Kierstead, "A mapping approach for image correction and processing for bidirectional resonant scanners," Opt. Eng. (to be published).

Proc. SPIE 1454 (1)

C. L. Confer and G. J. Burrer, "Linear resonant approach to scanning," in Beam Deflection and Scanning Technologies, L. Beiser and G. F. Marshall, eds., Proc. SPIE 1454 , 215-222 (1991).

Other (2)

J. Khoury, C. L. Woods, B. Haji-saeed, D. Pyburn, S. K. Sengupta, and J. Kierstead, "A mapping approach for image correction and processing for bidirectional resonant scanners," Opt. Eng. (to be published).

GSI Lumonics CRS scanner manual, available for download at http://www.gsilumonics.com/process_download_open/01_optical_scanning/resources/7om025_CRS.pdf.

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Figures (5)

Fig. 1
Fig. 1

(Color online) Ray diagram of resonant scanner with refractive–diffractive corrective element.

Fig. 2
Fig. 2

(Color online) Linearized scanning geometries with FOV greater than, equal to, or less than that for the sinusoidal scanner.

Fig. 3
Fig. 3

(Color online) Calculated index variations as a function of distance from the optical axis, y, at A, B, and C constant dimension, variable g / ω , and A , B , C variable dimension, constant g∕ω.

Fig. 4
Fig. 4

Binarized diffractive element for A and B, constant g / ω , variable dimension y 0 = 0.5 and 1, respectively.

Fig. 5
Fig. 5

Binarized diffractive element for A, B, C constant dimension, variable g / ω = 0.5 , 1, and 2, respectively.

Equations (28)

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Tan θ 1 = h Z 1 ,
h = Z 1 Tan θ 1 ;
Tan θ 2 = h 2 Z 2 ,
h 2 = Z 2 Tan θ 2 .
Tan θ 3 = h - h 2 Z 1 - Z 2 = Z 1 Tan θ 1 - Z 2 Tan θ 2 Z 1 - Z 2 ,
θ 3 = h - h 2 Z 1 - Z 2 = Z 1 θ 1 - Z 2 θ 2 Z 1 - Z 2 .
θ 2 = θ 20 sin ω t = y Z 2 ,
t = 1 ω sin - 1 y Z 2 θ 20 .
θ 1 = gt ,
θ 1 = g ω sin - 1 ( y Z 2 θ 20 ) .
Tan θ 3 θ 3 = Z 1 g ω sin - 1 ( y Z 2 θ 20 ) - Z 2 y Z 2 ( Z 1 - Z 2 )
= g Z 1 sin - 1 ( y Z 2 θ 20 ) - y ω ( Z 1 - Z 2 ) ω ,
d d s ( n d r d s ) = n ,
n d 2 r d z 2 = n y .
d 2 r d z 2 = 1 n n y = ln ( n ) y .
d r d z = θ = ln ( n ) y z + c 1 ,
θ 2 = d r ( Z 2 ) d z = y Z 2 = ln ( n ) y ( Z 2 ) + c ,
θ 3 = d r ( Z 2 + l ) d z = g Z 1 sin - 1 ( y Z 2 θ 20 ) - y ω ω ( Z 1 - Z 2 ) = ln ( n ) y ( Z 2 + l ) + c .
ln [ n ( Z 2 + l ) ] y ln [ n ( Z 2 ) ] y .
θ 3 - θ 2 = g Z 1 sin - 1 ( y Z 2 θ 20 ) - y ω ω ( Z 1 - Z 2 ) - y Z 2 = l [ ln ( n ) y ] .
ln ( n ) = 1 l ( Z 1 Z 1 - Z 2 ) { g ω [ y sin - 1 ( y Z 2 θ 20 ) + Z 2 2 θ 20 2 - y 2 ] - y 2 2 Z 2 } .
y 0 = Z 2 θ 20 .
ln ( n ) = 1 l ( Z 1 Z 1 - Z 2 ) { g ω [ y sin - 1 ( y y 0 ) + y 0 2 - y 2 ] - y 2 2 Z 2 } .
ln ( n ) = 1 l { g ω [ y sin - 1 ( y y 0 ) + y 0 2 - y 2 ] - y 2 2 Z 2 } ,
n off = e ( g / l ω ) y 0
n = λ l Floor [ ln off λ ] .
T = { 2 ( m - 1 ) π < 2 π λ nl < 2 m π = 0 ( 2 m - 1 ) π < 2 π λ nl < ( 2 m + 1 ) π = 1 ,
T = { 2 ( m - 1 ) π < 2 π λ nl < 2 m π = −1 ( 2 m - 1 ) π < 2 π λ nl < ( 2 m + 1 ) π = 1.

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