Abstract

We have experimentally investigated the enhancement in spatial resolution by image subtraction in mid-infrared central solid-immersion lens (c-SIL) microscopy. The subtraction exploits a first image measured with the c-SIL point-spread function (PSF) realized with a Gaussian beam and a second image measured with the beam optically patterned by a silicon π-step phase plate, to realize a centrally hollow PSF. The intense sides lobes in both PSFs that are intrinsic to the SIL make the conventional weighted subtraction methods inadequate. A spatial-domain filter with a kernel optimized to match both experimental PSFs in their periphery was thus developed to modify the first image prior to subtraction, and this resulted in greatly improved performance, with polystyrene beads 1.4 ± 0.1 µm apart optically resolved with a mid-IR wavelength of 3.4 µm in water. Spatial-domain filtering is applicable to other PSF pairs, and simulations show that it also outperforms conventional subtraction methods for the Gaussian and doughnut beams widely used in visible and near-IR microscopy.

© 2017 Optical Society of America

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References

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2016 (3)

N. Liu, M. Kumbham, I. Pita, Y. Guo, P. Bianchini, A. Diaspro, S. A. Tofail, A. Peremans, and C. Silien, “Far-field subdiffraction imaging of semiconductors using nonlinear transient absorption differential microscopy,” ACS Photonics 3(3), 478–485 (2016).
[Crossref]

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C. J. Sheppard, A. Diaspro, and P. Bianchini, “Intensity Weighted Subtraction Microscopy Approach for Image Contrast and Resolution Enhancement,” Sci. Rep. 6(1), 25816 (2016).
[Crossref] [PubMed]

M. Kumbham, S. Daly, K. O’Dwyer, R. Mouras, N. Liu, A. Mani, A. Peremans, S. M. Tofail, and C. Silien, “Doubling the far-field resolution in mid-infrared microscopy,” Opt. Express 24(21), 24377–24389 (2016).
[Crossref] [PubMed]

2015 (3)

Z. Rong, C. Kuang, Y. Fang, G. Zhao, Y. Xu, and X. Liu, “Super-resolution microscopy based on fluorescence emission difference of cylindrical vector beams,” Opt. Commun. 354, 71–78 (2015).
[Crossref]

Y. Fang, C. Kuang, Y. Ma, Y. Wang, and X. Liu, “Resolution and contrast enhancements of optical microscope based on point spread function engineering,” Front. Optoelectron. 8(2), 152–162 (2015).
[Crossref]

N. Tian, L. Fu, and M. Gu, “Resolution and contrast enhancement of subtractive second harmonic generation microscopy with a circularly polarized vortex beam,” Sci. Rep. 5(1), 13580 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (4)

2012 (2)

C. Silien, N. Liu, N. Hendaoui, S. A. Tofail, and A. Peremans, “A framework for far-field infrared absorption microscopy beyond the diffraction limit,” Opt. Express 20(28), 29694–29704 (2012).
[Crossref] [PubMed]

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

2009 (1)

O. Haeberlé and B. Simon, “Saturated structured confocal microscopy with theoretically unlimited resolution,” Opt. Commun. 282(18), 3657–3664 (2009).
[Crossref]

2001 (1)

G. Carr, “Resolution limits for infrared microspectroscopy explored with synchrotron radiation,” Rev. Sci. Instrum. 72(3), 1613–1619 (2001).
[Crossref]

2000 (1)

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

1990 (1)

S. M. Mansfield and G. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2616 (1990).
[Crossref]

Antipov, A.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C. J. Sheppard, A. Diaspro, and P. Bianchini, “Intensity Weighted Subtraction Microscopy Approach for Image Contrast and Resolution Enhancement,” Sci. Rep. 6(1), 25816 (2016).
[Crossref] [PubMed]

Bianchini, P.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C. J. Sheppard, A. Diaspro, and P. Bianchini, “Intensity Weighted Subtraction Microscopy Approach for Image Contrast and Resolution Enhancement,” Sci. Rep. 6(1), 25816 (2016).
[Crossref] [PubMed]

N. Liu, M. Kumbham, I. Pita, Y. Guo, P. Bianchini, A. Diaspro, S. A. Tofail, A. Peremans, and C. Silien, “Far-field subdiffraction imaging of semiconductors using nonlinear transient absorption differential microscopy,” ACS Photonics 3(3), 478–485 (2016).
[Crossref]

Birge, B.

B. Birge, “PSOt-a particle swarm optimization toolbox for use with Matlab,”in Proceeding of the 3rd IEEE Swarm Intelligence Symposium (IEEE, 2003), pp. 973–990.
[Crossref]

Bullkich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Carr, G.

G. Carr, “Resolution limits for infrared microspectroscopy explored with synchrotron radiation,” Rev. Sci. Instrum. 72(3), 1613–1619 (2001).
[Crossref]

Cohen, O.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Cohen-Hyams, T.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Côté, D.

Daly, S.

Dana, H.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Daradich, A.

De Koninck, Y.

Dehez, H.

Diaspro, A.

N. Liu, M. Kumbham, I. Pita, Y. Guo, P. Bianchini, A. Diaspro, S. A. Tofail, A. Peremans, and C. Silien, “Far-field subdiffraction imaging of semiconductors using nonlinear transient absorption differential microscopy,” ACS Photonics 3(3), 478–485 (2016).
[Crossref]

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C. J. Sheppard, A. Diaspro, and P. Bianchini, “Intensity Weighted Subtraction Microscopy Approach for Image Contrast and Resolution Enhancement,” Sci. Rep. 6(1), 25816 (2016).
[Crossref] [PubMed]

Eldar, Y. C.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Fang, Y.

Z. Rong, C. Kuang, Y. Fang, G. Zhao, Y. Xu, and X. Liu, “Super-resolution microscopy based on fluorescence emission difference of cylindrical vector beams,” Opt. Commun. 354, 71–78 (2015).
[Crossref]

Y. Fang, C. Kuang, Y. Ma, Y. Wang, and X. Liu, “Resolution and contrast enhancements of optical microscope based on point spread function engineering,” Front. Optoelectron. 8(2), 152–162 (2015).
[Crossref]

Fu, L.

N. Tian, L. Fu, and M. Gu, “Resolution and contrast enhancement of subtractive second harmonic generation microscopy with a circularly polarized vortex beam,” Sci. Rep. 5(1), 13580 (2015).
[Crossref] [PubMed]

Gasecka, A.

Gazit, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Ge, J.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref] [PubMed]

Gu, M.

N. Tian, L. Fu, and M. Gu, “Resolution and contrast enhancement of subtractive second harmonic generation microscopy with a circularly polarized vortex beam,” Sci. Rep. 5(1), 13580 (2015).
[Crossref] [PubMed]

Gu, Z.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref] [PubMed]

Guo, Y.

N. Liu, M. Kumbham, I. Pita, Y. Guo, P. Bianchini, A. Diaspro, S. A. Tofail, A. Peremans, and C. Silien, “Far-field subdiffraction imaging of semiconductors using nonlinear transient absorption differential microscopy,” ACS Photonics 3(3), 478–485 (2016).
[Crossref]

Gustafsson, M. G.

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

Haeberlé, O.

O. Haeberlé and B. Simon, “Saturated structured confocal microscopy with theoretically unlimited resolution,” Opt. Commun. 282(18), 3657–3664 (2009).
[Crossref]

Hao, X.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref] [PubMed]

Hendaoui, N.

Kino, G.

S. M. Mansfield and G. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2616 (1990).
[Crossref]

Kley, E. B.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Korobchevskaya, K.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C. J. Sheppard, A. Diaspro, and P. Bianchini, “Intensity Weighted Subtraction Microscopy Approach for Image Contrast and Resolution Enhancement,” Sci. Rep. 6(1), 25816 (2016).
[Crossref] [PubMed]

Kozawa, Y.

Kuang, C.

Z. Rong, C. Kuang, Y. Fang, G. Zhao, Y. Xu, and X. Liu, “Super-resolution microscopy based on fluorescence emission difference of cylindrical vector beams,” Opt. Commun. 354, 71–78 (2015).
[Crossref]

Y. Fang, C. Kuang, Y. Ma, Y. Wang, and X. Liu, “Resolution and contrast enhancements of optical microscope based on point spread function engineering,” Front. Optoelectron. 8(2), 152–162 (2015).
[Crossref]

S. You, C. Kuang, Z. Rong, and X. Liu, “Eliminating deformations in fluorescence emission difference microscopy,” Opt. Express 22(21), 26375–26385 (2014).
[Crossref] [PubMed]

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref] [PubMed]

Kumbham, M.

Li, H.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref] [PubMed]

Li, S.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref] [PubMed]

Li, Z.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C. J. Sheppard, A. Diaspro, and P. Bianchini, “Intensity Weighted Subtraction Microscopy Approach for Image Contrast and Resolution Enhancement,” Sci. Rep. 6(1), 25816 (2016).
[Crossref] [PubMed]

Liu, N.

Liu, W.

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref] [PubMed]

Liu, X.

Y. Fang, C. Kuang, Y. Ma, Y. Wang, and X. Liu, “Resolution and contrast enhancements of optical microscope based on point spread function engineering,” Front. Optoelectron. 8(2), 152–162 (2015).
[Crossref]

Z. Rong, C. Kuang, Y. Fang, G. Zhao, Y. Xu, and X. Liu, “Super-resolution microscopy based on fluorescence emission difference of cylindrical vector beams,” Opt. Commun. 354, 71–78 (2015).
[Crossref]

S. You, C. Kuang, Z. Rong, and X. Liu, “Eliminating deformations in fluorescence emission difference microscopy,” Opt. Express 22(21), 26375–26385 (2014).
[Crossref] [PubMed]

C. Kuang, S. Li, W. Liu, X. Hao, Z. Gu, Y. Wang, J. Ge, H. Li, and X. Liu, “Breaking the diffraction barrier using fluorescence emission difference microscopy,” Sci. Rep. 3, 1441 (2013).
[Crossref] [PubMed]

Ma, Y.

Y. Fang, C. Kuang, Y. Ma, Y. Wang, and X. Liu, “Resolution and contrast enhancements of optical microscope based on point spread function engineering,” Front. Optoelectron. 8(2), 152–162 (2015).
[Crossref]

Mani, A.

Mansfield, S. M.

S. M. Mansfield and G. Kino, “Solid immersion microscope,” Appl. Phys. Lett. 57(24), 2615–2616 (1990).
[Crossref]

Mouras, R.

O’Dwyer, K.

Osherovich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Peremans, A.

Peres, C.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C. J. Sheppard, A. Diaspro, and P. Bianchini, “Intensity Weighted Subtraction Microscopy Approach for Image Contrast and Resolution Enhancement,” Sci. Rep. 6(1), 25816 (2016).
[Crossref] [PubMed]

Piché, M.

Pita, I.

N. Liu, M. Kumbham, I. Pita, Y. Guo, P. Bianchini, A. Diaspro, S. A. Tofail, A. Peremans, and C. Silien, “Far-field subdiffraction imaging of semiconductors using nonlinear transient absorption differential microscopy,” ACS Photonics 3(3), 478–485 (2016).
[Crossref]

I. Pita, N. Hendaoui, N. Liu, M. Kumbham, S. A. Tofail, A. Peremans, and C. Silien, “High resolution imaging with differential infrared absorption micro-spectroscopy,” Opt. Express 21(22), 25632–25642 (2013).
[Crossref] [PubMed]

Rong, Z.

Z. Rong, C. Kuang, Y. Fang, G. Zhao, Y. Xu, and X. Liu, “Super-resolution microscopy based on fluorescence emission difference of cylindrical vector beams,” Opt. Commun. 354, 71–78 (2015).
[Crossref]

S. You, C. Kuang, Z. Rong, and X. Liu, “Eliminating deformations in fluorescence emission difference microscopy,” Opt. Express 22(21), 26375–26385 (2014).
[Crossref] [PubMed]

Sato, S.

Segawa, S.

Segev, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Shechtman, Y.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Sheppard, C. J.

K. Korobchevskaya, C. Peres, Z. Li, A. Antipov, C. J. Sheppard, A. Diaspro, and P. Bianchini, “Intensity Weighted Subtraction Microscopy Approach for Image Contrast and Resolution Enhancement,” Sci. Rep. 6(1), 25816 (2016).
[Crossref] [PubMed]

Shoham, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Sidorenko, P.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Silien, C.

Simon, B.

O. Haeberlé and B. Simon, “Saturated structured confocal microscopy with theoretically unlimited resolution,” Opt. Commun. 282(18), 3657–3664 (2009).
[Crossref]

Steiner, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Szameit, A.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11(5), 455–459 (2012).
[Crossref] [PubMed]

Tian, N.

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Figures (4)

Fig. 1
Fig. 1 (a) Mid-IR c-SIL scanning microscope. M: mirror; F1 and F2: near-IR filters; L1 and L2: beam expander/collimation; ChW: mechanical chopper wheel; LP: linear polarizer; BS: pellicle beam splitter; S: beam shutter (blocking the Gaussian beam path as shown or used to block the half-moon beam path); TP: thin plate; π-PP: π-step phase plate; Pol: linear polarization axis; MCT: mid-IR MCT detectors; L: lens; OBJ: reflective objective; SIL: silicon central solid immersion lens; SPL: sample with specimen frontside immersed in water; NDF: neutral density filter. (b) Images of a single 1 µm PS bead recorded with the Gaussian beam. Sale bar 5 µm. The double-tipped arrow marks the direction of polarization. The image was normalized to a background of 1. (c) Same as (b) with the half-moon beam. (d) Line profiles extracted from (b) and (c).
Fig. 2
Fig. 2 (a) Gaussian image of 1 µm PS beads. Scale bar 10 µm. (b) Same with half-moon beam. (c) Line profiles (i) and (ii) extracted from (a) and (b) showing that 2 nearby beads are observed as 3 depressions with the half-moon beam (see arrows). (d) Line profiles (iii) and (iv) extracted from (a) and (b) showing that 2 beads unresolved with the Gaussian beam are also observed as 3 depressions with the half-moon beam (see arrows).
Fig. 3
Fig. 3 (a) Line profiles of simulated Gaussian (blue, unbroken) and doughnut (orange) PSFs, with spatial-domain filtered Gaussian (blue, dashed) after optimization of the kernel. (b) Evolution of the error function with the number of PSO iterations, with the optimized kernel shown in inset. (c) Line profiles of Gaussian and subtracted images for a specimen made of one isolated pixel object and 3 adjacent pixel objects, all 4 objects being aligned (thick black dashed line): (i) shows Gaussian image (orange, dashed), (ii) shows I K (orange), (iii) shows I IWS (blue), and (iv) shows I α (black). The profiles are offset for clarity with a tick marking the zero. Dashed lines mark the maximum intensity measured across the isolated pixel object for each profiles, normalized to 1 at the centre of the isolated pixel object. (d) Same as (c) for a specimen made of 1-pixel wide objects elongated to 50 pixels in the direction normal to the profiles.
Fig. 4
Fig. 4 (a) Mid-IR c-SIL image of PS beads recorded with the Gaussian beam. Scale bar 5 µm. (b) Same as (a) with the half-moon beam. (c) Reconstruction of the sample using the method presented in [17]. (d) Gaussian image after application of the spatial-domain filter. (e) Subtraction image IK. (f) Subtraction image IIWS. (g) Subtraction image Iα. (h) Line profiles measured across the PS beads identified by the blue and orange arrows: (i) for Gaussian image (a) (ii) for IK image (e), (iii) for IIWS image (f), and (iv) for Iα image (g).

Equations (4)

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ROI = ||PS F g KPS F d | | 2 2
I K = I g K I d
I IWS = I g I g I d +1 2 .× I d
I α = I g α I d

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