Abstract

A scanning and rotating nanoslit is used to measure submicrometer features in focused spot distributions. Using a filtered backprojection technique, a highly accurate reconstruction is demonstrated. Experimental results are confirmed by simulating the scanning slit technique using a physical optics simulation program. Analysis of various error mechanisms is reported, and the reconstruction algo rithm is determined to be very resilient. The slit is 125nm wide and 50μm long and is fabricated on a 120nm thick layer of aluminum. The size of the image field is 15μm, and simulations indicate that 200nm Rayleigh resolution is possible with an infinitely narrow slit.

© 2011 Optical Society of America

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References

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2010 (1)

2007 (1)

2001 (1)

J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).
[CrossRef]

1997 (2)

1995 (2)

S. Samson and A. Korpel, “Two-dimensional operation of a scanning optical microscope by vibrating knife-edge tomography,” Appl. Opt. 34, 285–289 (1995).
[CrossRef] [PubMed]

T. D. Milster and C. L. Vernold, “Technique for aligning optical and mechanical axes based on a rotating linear grating,” Opt. Eng. 34, 2840–2845 (1995).
[CrossRef]

1993 (1)

1990 (1)

1984 (1)

1980 (1)

Barrett, H. H.

M. A. Kujoory, E. L. Miller, H. H. Barrett, G. R. Gindi, and P. N. Tamura, “Coded aperture imaging of γ-ray sources with an off-axis rotating slit,” Appl. Opt. 19, 4186–4195 (1980).
[CrossRef] [PubMed]

H. H. Barrett and W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, 1981), Vol.  2, pp. 413–417.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), p. 371.

Byer, R. L.

Chen, L.

J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).
[CrossRef]

George, A.

Gindi, G. R.

Gureyev, T. E.

Herman, G. T.

G. T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections, 2nd ed. (Springer, 2009).

Hertz, H. M.

Korpel, A.

Kujoory, M. A.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley-Interscience, 1992), p. 465.

Martin, M.

McCally, R. L.

Miller, E. L.

Milster, T. D.

A. George and T. D. Milster, “Characteristics of a scanning nano-slit image sensor for line-and-space patterns,” Appl. Opt. 49, 3821–3830 (2010).
[CrossRef] [PubMed]

T. D. Milster and C. L. Vernold, “Technique for aligning optical and mechanical axes based on a rotating linear grating,” Opt. Eng. 34, 2840–2845 (1995).
[CrossRef]

Nesterets, Y. I.

Pavlov, K. M.

Rendon, M.

Samson, S.

Soto, J.

Sun, H.

H. Sun, “Measurement of laser diode astigmatism,” Opt. Eng. 36, 1082–1087 (1997).
[CrossRef]

Swindell, W.

H. H. Barrett and W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, 1981), Vol.  2, pp. 413–417.

Tamura, P. N.

Vernold, C. L.

T. D. Milster and C. L. Vernold, “Technique for aligning optical and mechanical axes based on a rotating linear grating,” Opt. Eng. 34, 2840–2845 (1995).
[CrossRef]

Wang, Q.

J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).
[CrossRef]

Wilkins, S. W.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), p. 371.

Zhang, X.

J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).
[CrossRef]

Zhao, S.

J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).
[CrossRef]

Zheng, J.

J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).
[CrossRef]

Appl. Opt. (6)

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

H. Sun, “Measurement of laser diode astigmatism,” Opt. Eng. 36, 1082–1087 (1997).
[CrossRef]

T. D. Milster and C. L. Vernold, “Technique for aligning optical and mechanical axes based on a rotating linear grating,” Opt. Eng. 34, 2840–2845 (1995).
[CrossRef]

Opt. Laser Technol. (1)

J. Zheng, S. Zhao, Q. Wang, X. Zhang, and L. Chen, “Measurement of beam quality factor (M2) by slit-scanning method,” Opt. Laser Technol. 33, 213–217 (2001).
[CrossRef]

Opt. Lett. (1)

Other (11)

http://www.thorlabs.us/NewGroupPage9.cfm?ObjectGroup_ID=2421

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999), p. 371.

http://www.photon-inc.com/products/nanoscan/nanoscan.html

http://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=804

http://www.dataray.com/pdf/BSDataSh.pdf

https://www.cvilaser.com/products/Documents/Catalog/Measurement_of_Beam_Profiles.pdf

G. T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections, 2nd ed. (Springer, 2009).

H. H. Barrett and W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, 1981), Vol.  2, pp. 413–417.

http://www.optics.arizona.edu/Milster/optiscan/OptiScan_MENU_PAGE.htm

http://www.zemax.com

D. Malacara, Optical Shop Testing (Wiley-Interscience, 1992), p. 465.

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Figures (11)

Fig. 1
Fig. 1

(a) Top view and (b) cross-sectional profile of the slit. The slit is fabricated using a FIB. The slit is 50 μm long and 125 nm wide at the aluminum-mask/glass-substrate interface. The aluminum mask is 120 nm thick. The slit has a smooth cross-sectional profile and an 85 nm deep etching into the glass substrate. The cross-sectional SEM view is obtained from a test slit fabricated with identical FIB parameters to that of the final slit.

Fig. 2
Fig. 2

Schematic for the method employed in reconstructing a spot irradiance distribution. Shown are the irradiance distribution and two random projections, P m ( ρ , θ ) and P n ( ρ , θ ) , at angles θ m and θ n , respectively. Multiple projections are arranged to form a sinogram, which is then analyzed with an inverse Radon transform to recreate the irradiance distribution. The technique is similar to that used in CAT [14].

Fig. 3
Fig. 3

The experimental setup for the first experiment, showing the laser beam focused onto a 125 nm wide nanoslit. The section view shows the slit assembly mounted on a rotary table. For the second experiment, the lens is replaced with a microscope objective and a 500 μm half-pitch grating at its entrance pupil.

Fig. 4
Fig. 4

(a) Experimental sinogram showing all 180 measured projections. An inverse Radon transform of the sinogram provides the reconstructed spot irradiance distribution shown in (b). The sinogram and spot are for a 20 μm defocus from the best focus position. The power level in the sinogram is normalized to the maximum pixel power among all sinograms obtained. The power level in the reconstructed spot is normalized to the maximum pixel power among all the reconstructed spots.

Fig. 5
Fig. 5

(a) Simulated spot obtained from a physical optics program using known experimental parameters. (b) Sinogram obtained after simulating the effect of a scanning and rotating slit on the image shown in (a). (c) Reconstructed spot after performing the inverse Radon transform on the sinogram shown in (b).

Fig. 6
Fig. 6

Simulated sinograms that have (a) 25% error from DC shift in projections Δ P DC , (b) 25% error in angular position Δ θ , and (c) 25% error in scanning slit data point position Δ ρ . Δ P DC is the dominant cause of sinogram error.

Fig. 7
Fig. 7

Reconstructed spots after performing the inverse Radon transform on the simulated sinogram shown in Fig. 5. (a) 5% error from Δ P DC , (b) 25% error in Δ θ , (c) 25% error in Δ ρ . Δ ρ is the dominant cause of reconstruction error.

Fig. 8
Fig. 8

(a) Plot showing the RMS error in the simulated sinogram for errors in various measurement parameters. The parameters include the error in the DC shift between projections, the error in angular position, and the error in the slit scan data point position. (b) Plot showing the RMS error in the reconstructed image for errors of various measurement parameters. Both plots are normalized with respect to the maximum pixel power.

Fig. 9
Fig. 9

Reconstructed spot from the first experiment [shown in (a) and (c)] and simulation [shown in (b) and (d)] at best focus and + 20 μm from best focus. The experimental and simulated reconstructions for the 20 μm defocus spot are shown in Figs. 4b, 5c, respectively.

Fig. 10
Fig. 10

(a) Sinogram of a focused diffraction pattern with the 0, + 1 , and 1 orders. (b) Reconstruction of the focused diffraction pattern. The simulated sinogram and reconstruction are shown in (c) and (d). The power levels in all figures are normalized to the maximum pixel power in the sinogram.

Fig. 11
Fig. 11

(a) Irradiance profiles to be measured—two 100 nm wide features with varying separations between them. (b) Measured profiles normalized to the maximum irradiance value. The Rayleigh resolution criteria states that the irradiance of the central dip between two resolvable features should be no more than 0.81% of the peak irradiance values [22]. Using this criteria, features separated by 260 and 220 nm are easily resolvable. For those separated by 200 nm , the central dip is 0.75% of the irradiance. It is thus very close to the resolution limit. Features separated by less than 200 nm are unresolvable.

Equations (7)

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SNR Slit = SNR laser SNR Knife-Edge ,
I ( x , y ) = 0 2 π d θ 0 ρ d ρ P ( ρ , θ ) exp [ j 2 π ρ ( cos θ + sin θ ) ] ,
ρ sample w ,
θ sample = ρ sample / a ,
N ρ = 2 a / ρ sample ,
N θ = π / θ sample ,
RMS Error = j = 1 M k = 1 N ( I j , k I j , k ' ) 2 / N × M ,

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