Abstract

An analytical model has been developed and applied to explore the limits in the design of a highly miniaturized planar optical microspectrometer based on an imaging diffraction grating. This design tool has been validated as providing the smallest possible dimensions while maintaining acceptable spectral resolution. The resulting planar spectrometer is composed of two parallel glass plates, which contain all components of the device, including a reflective slit and an imaging diffraction grating. Fabrication is based on microelectromechanical system technology and starts with a single glass wafer; IC-compatible deposition and lithography are applied to realize the parts in aluminum, which makes the microspectrometer highly tolerant for component mismatch. The fabricated spectrometer was mounted directly on top of an image sensor and takes up a volume of only 50mm3. The measured spectral resolution of 6nm (FWHM) in the 100nm operating wavelength range (600700nm) is in agreement with a model calculation.

© 2008 Optical Society of America

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References

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2007 (1)

2006 (2)

2005 (2)

S.-H. Kong and R. F. Wolffenbuttel, “Spectral performance of a micromachined infrared spectrum analyzer in silicon,” IEEE Trans. Instrum. Meas. 54, 264-267 (2005).
[CrossRef]

R. F. Wolffenbuttel, “MEMS-based optical mini- and microspectrometers for the visible and infrared spectral range,” J. Micromech. Microeng. 15, S145-S152 (2005).
[CrossRef]

2003 (1)

2001 (2)

S. Ura, T. Sasaki, and H. Nishihara, “Combination of grating lenses for color splitting and imaging,” Appl. Opt. 40, 5819-5824 (2001).
[CrossRef]

D. Sander and J. Muller, “Selffocusing phase transmission grating for an integrated optical microspectrometer,” Sens. Actuators A, Phys. 88, 1-9 (2001).
[CrossRef]

1999 (1)

M. Testorf and J. Jahns, “Imaging properties of planar-integrated micro-optics,” J. Opt. Soc. Am. 16, 1175-1183(1999).
[CrossRef]

1996 (1)

D. Rossberg, “Optical properties of the integrated infrared sensor,” Sens. Actuators A, Phys. 54, 793-797(1996).
[CrossRef]

1994 (1)

C. Palmer and W. R. McKinney, “Imaging theory of plane-symmetric varied line-space grating systems,” Opt. Eng. 33, 820-829 (1994).
[CrossRef]

1992 (1)

T. A. Kwa and R. F. Wolffenbuttel, “Integrated grating/detector array fabricated in silicon using micromachining techniques,” Sens. Actuators A, Phys. 31, 259-266(1992).
[CrossRef]

1990 (1)

1987 (1)

1981 (1)

1974 (1)

Appl. Opt. (5)

IEEE Trans. Instrum. Meas. (1)

S.-H. Kong and R. F. Wolffenbuttel, “Spectral performance of a micromachined infrared spectrum analyzer in silicon,” IEEE Trans. Instrum. Meas. 54, 264-267 (2005).
[CrossRef]

J. Micromech. Microeng. (1)

R. F. Wolffenbuttel, “MEMS-based optical mini- and microspectrometers for the visible and infrared spectral range,” J. Micromech. Microeng. 15, S145-S152 (2005).
[CrossRef]

J. Opt. Soc. Am. (2)

M. Testorf and J. Jahns, “Imaging properties of planar-integrated micro-optics,” J. Opt. Soc. Am. 16, 1175-1183(1999).
[CrossRef]

H. Noda, T. Namioka, and M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031-1036 (1974).
[CrossRef]

Opt. Eng. (1)

C. Palmer and W. R. McKinney, “Imaging theory of plane-symmetric varied line-space grating systems,” Opt. Eng. 33, 820-829 (1994).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Sens. Actuators A, Phys. (3)

D. Rossberg, “Optical properties of the integrated infrared sensor,” Sens. Actuators A, Phys. 54, 793-797(1996).
[CrossRef]

T. A. Kwa and R. F. Wolffenbuttel, “Integrated grating/detector array fabricated in silicon using micromachining techniques,” Sens. Actuators A, Phys. 31, 259-266(1992).
[CrossRef]

D. Sander and J. Muller, “Selffocusing phase transmission grating for an integrated optical microspectrometer,” Sens. Actuators A, Phys. 88, 1-9 (2001).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Cambridge, 2002).

zemax optical design program user's guide, version 9.0 (Focus Software, 2000).

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic of a diffraction grating imaging point A in to point B and (b) principal design of an imaging grating-based spectrometer.

Fig. 2
Fig. 2

Dependence of spectral resolution on angle of incidence and input aperture.

Fig. 3
Fig. 3

Dependence of the resolution within a 100 nm bandwidth on the angle of incidence and size (the distance from the entrance slit to the grating) of a spectrometer. The results are for the grating period 1 μm and 2 μm with (a) input aperture 0.1 and (b) input aperture 0.05.

Fig. 4
Fig. 4

Design of the planar microspectrometer.

Fig. 5
Fig. 5

Part of the mask used for the lithographic fabrication of the grating. The spacing between curved lines varied from 1.5 to 2.8 μm along the mask.

Fig. 6
Fig. 6

Experimental setup. The spectrometer is visible as two glass rectangles on top of the image sensor. The diffraction grating is visible as an ellipse on the lower rectangle. Light is fed into the spectrometer from the fiber tip shown in the upper left corner.

Fig. 7
Fig. 7

Spectrum of a Ne lamp produced with the planar spectrometer and registered with the CCD image sensor.

Fig. 8
Fig. 8

Spectrum of a Ne lamp obtained with the microspectrometer.

Equations (9)

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F ( λ , y , z ) = A P B A O B + m λ N ( y , z ) ,
F ( λ , y , z ) = i = 0 j = 0 F i j y i z j = i = o j = 0 ( M i j + m λ N i j ) y i z j .
N i j = M i j m λ 0 = 1 i ! j ! m λ 0 [ i + j ( A P B A O B ) y i z j ] ( 0 , 0 ) .
s aberr = F y | y = y 1 + F y | y = y 2 .
s diffr = 2 λ y 2 y 1 .
s slit = cos ( α ) cos ( β ) × s 0 r ,
Δ λ = Δ λ ( λ , λ 0 , α , r , β , r , γ , ψ ) = f × ( s slit + s aberr + s diffr ) .
f = d 0 × cos ( β ) .
Δ λ w g = f × ( s aberr + s diffr ) ,

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