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Imaging interferometric microscopy–approaching the linear systems limits of optical resolution

Yuliya Kuznetsova, Alexander Neumann, and S. R. J. Brueck

Open Access Open Access

Abstract

The linear systems optical resolution limit is a dense grating pattern at a λ/2 pitch or a critical dimension (resolution) of λ/4. However, conventional microscopy provides a (Rayleigh) resolution of only ~ 0.6λ/NA, approaching λ/1.67 as NA → 1. A synthetic aperture approach to reaching the λ/4 linear-systems limit, extending previous developments in imaging-interferometric microscopy, is presented. Resolution of non-periodic 180-nm features using 633-nm illumination (λ/3.52) and of a 170-nm grating (λ/3.72) is demonstrated. These results are achieved with a 0.4-NA optical system and retain the working distance, field-of-view, and depth-of-field advantages of low-NA systems while approaching ultimate resolution limits.

©2007 Optical Society of America

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Figures (13)
Fig. 1.
Fig. 1. Optical arrangement for imaging interferometric microscopy: α = sin-1(NA), β is the incident beam angle of incidence, and βref is the angle of the reference beam onto the image plane.

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Fig. 2.
Fig. 2. (a). Manhattan geometry pattern used for image resolution exploration consisting of five nested “ells” and a large box. The lines and spaces of the “ells” are 240 nm. (b). intensity Fourier space components of the pattern, mapped onto the frequency space coverage of the imaging system.

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Fig. 3.
Fig. 3. Experimental setup for off-axis images and interferometric reconstruction.

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Fig. 4.
Fig. 4. (a). Low-frequency and (b) reconstructed images with the high frequency images taken at an offset illumination of 53, (c) reconstructed image with high frequency images taken at 53° and 80° without filtering, and d) reconstructed image using electronic spatial filtering.

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Fig. 5.
Fig. 5. Optical arrangement using a tilted object (with respect to the objective image plane) to enhance the frequency space information.

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Fig. 6.
Fig. 6. Frequency space coverage with tilted mask, a) for 180-nm CD structure, b) location of high frequency spectral components for a 170-nm CD structure.

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Fig. 7.
Fig. 7. Range of captured frequencies versus tilt mask angle, β = 80°. The vertical dashed line corresponds to the present experiment. The shaded region is the accessible frequency space coverage along the tilt direction.

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Fig. 8.
Fig. 8. Mapping between spatial frequencies in tilted/offset image and actual object spatial frequencies. Curves correspond to the indicated spatial frequencies in the y-direction. The decreasing extent of the curves with increasing transverse wave vector is a result of the circular aperture of the objective.

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Fig. 9.
Fig. 9. Experiment for a 180-nm CD: a) reconstructed image, b) reconstructed model

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Fig. 10.
Fig. 10. Comparison of cross cuts for the experiment (reconstructed total image) and a Fourier optics model (along the line indicated line in Fig. 8).

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Fig. 11.
Fig. 11. Reconstructed images of: a) a 170-nm CD structure; b) a 170-nm CD grating, obtained using multiple partial images including one with a tilted object plane.

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Fig. 12.
Fig. 12. Experiment (a, c) and simulation (b, d) results showing the impact of the frequency restoration on the high frequency partial image. The dotted lines are visual guides showing the significant shift of the out-of-focus object (left) in the laboratory frame.

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Fig. 13.
Fig. 13. Reconstructed image, 180- and 170-nm structures illustrating the restoration of the field of view achieved by transforming the laboratory frame spatial frequencies to the image frame.

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Tables (1)

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Table I: Scalability of resolution including immersion microscopy

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Equations (2)

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f y = f y ′
f x = f x ′ cos ⁡ θ tilt + 1 − f x ′2 − f y ′2 sin ⁡ θ tilt
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