Abstract

Recently, the development of motion-free 3D microscopy utilizing focus tunable lenses (FTL) has been rapid. However, the downgrade of optical performance due to FTL and its gravity effect are rarely discussed in detail. Also, color dispersion is usually maintained purely depending on the FTL material without further correction. In this manuscript, we provide a quantitative evaluation of the impact of FTL on the optical performance of the microscope. The evaluation is based on both optical ray tracing simulations and lab experiments. In addition, we derive the first order conditions to correct axial color aberration of FTL through its entire power tuning range. Secondary spectrum correction is also possible and an apochromatic motion-free 3D microscope with 2 additional doublets is demonstrated. This study will serve a guidance in utilizing FTL as a motion-free element for 3D microscopy.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

2018 (4)

2017 (4)

2015 (1)

H. Li, X. Cheng, and Q. Hao, “An electrically tunable zoom system using liquid lenses,” Sensors 16(1), 45 (2015).
[Crossref]

2013 (3)

2011 (2)

2006 (1)

2005 (1)

2001 (1)

C. Quilliet and B. Berge, “Electrowetting: a recent outbreak,” Curr. Opin. Colloid Interface Sci. 6(1), 34–39 (2001).
[Crossref]

1998 (1)

1979 (1)

S. Sato, “Liquid-Crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[Crossref]

Alacoque, L.

Aldaba, M.

P. F. Sanabria, F. Diaz-Douton, M. Aldaba, and J. Pujol, “Spherical refractive correction with an electro-optical liquid lens in a double-pass system,” J. Europ. Opt. Soc. Rap. Public. 8, 13062 (2013).
[Crossref]

Annibale, P.

Aschwanden, M.

M. Blum, M. Bueler, C. Gratzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” in SPIE Optical Systems Design (ISOP, 2011), paper 81670W

Augustyniak, E.

Barber, P.

Bathe-Peters, M.

Berge, B.

C. Quilliet and B. Berge, “Electrowetting: a recent outbreak,” Curr. Opin. Colloid Interface Sci. 6(1), 34–39 (2001).
[Crossref]

Berge, Bruno

Jerome Crassous, Claude Gabay, Gaetan Liogier, and Bruno Berge, “Liquid lens based on electrowetting: a new adaptive component for imaging applications in consumer electronics,” Proc. SPIE5639, Adaptive Optics and Applications III (2004).

Blum, M.

M. Blum, M. Bueler, C. Gratzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” in SPIE Optical Systems Design (ISOP, 2011), paper 81670W

Brock, N.

Bueler, M.

M. Blum, M. Bueler, C. Gratzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” in SPIE Optical Systems Design (ISOP, 2011), paper 81670W

Cheng, X.

H. Li, X. Cheng, and Q. Hao, “An electrically tunable zoom system using liquid lenses,” Sensors 16(1), 45 (2015).
[Crossref]

Chung, E.

Cooper, E. A.

N. Padmanaban, R. Konrad, T. Stramer, E. A. Cooper, and G. Wetzstein, “Gaze-contingent focus displays for virtual reality,” Proc. Natl. Acad. Sci. U. S. A. 114(9), 2183–2188 (2017).
[Crossref]

Crassous, Jerome

Jerome Crassous, Claude Gabay, Gaetan Liogier, and Bruno Berge, “Liquid lens based on electrowetting: a new adaptive component for imaging applications in consumer electronics,” Proc. SPIE5639, Adaptive Optics and Applications III (2004).

Creath, K.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), pp. 1–53.

de la Tocnaye, J. d. B.

Diaz-Douton, F.

P. F. Sanabria, F. Diaz-Douton, M. Aldaba, and J. Pujol, “Spherical refractive correction with an electro-optical liquid lens in a double-pass system,” J. Europ. Opt. Soc. Rap. Public. 8, 13062 (2013).
[Crossref]

Dupret, A.

Emberger, S.

Eom, T.

Fahrbach, F.

Fraval, N.

Gabay, Claude

Jerome Crassous, Claude Gabay, Gaetan Liogier, and Bruno Berge, “Liquid lens based on electrowetting: a new adaptive component for imaging applications in consumer electronics,” Proc. SPIE5639, Adaptive Optics and Applications III (2004).

Gao, W.

J. Sasian, W. Gao, and Y. Yan, “Method to design apochromat and superachromat objectives,” Opt. Eng. 56(10), 1 (2017).
[Crossref]

Gopinath, J.

Gratzel, C.

M. Blum, M. Bueler, C. Gratzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” in SPIE Optical Systems Design (ISOP, 2011), paper 81670W

Grewe, B.

Guralnik, I.

Hao, Q.

H. Li, X. Cheng, and Q. Hao, “An electrically tunable zoom system using liquid lenses,” Sensors 16(1), 45 (2015).
[Crossref]

Hayes, J.

Helmchen, F.

Huisken, J.

Jo, S.-H.

Kim, C.-S.

Kim, J. W.

Kim, W.

Konrad, R.

N. Padmanaban, R. Konrad, T. Stramer, E. A. Cooper, and G. Wetzstein, “Gaze-contingent focus displays for virtual reality,” Proc. Natl. Acad. Sci. U. S. A. 114(9), 2183–2188 (2017).
[Crossref]

Lavrentovich, O.

Lee, B. H.

Lee, K.

Lee, S.

Li, H.

H. Li, X. Cheng, and Q. Hao, “An electrically tunable zoom system using liquid lenses,” Sensors 16(1), 45 (2015).
[Crossref]

Liang, R.

Liebetraut, P.

Liogier, Gaetan

Jerome Crassous, Claude Gabay, Gaetan Liogier, and Bruno Berge, “Liquid lens based on electrowetting: a new adaptive component for imaging applications in consumer electronics,” Proc. SPIE5639, Adaptive Optics and Applications III (2004).

Lohse, M.

Loktev, M.

Mader, D.

Millerd, J.

Naumov, A.

Niederriter, R.

North-Morris, M.

Novak, M.

Padmanaban, N.

N. Padmanaban, R. Konrad, T. Stramer, E. A. Cooper, and G. Wetzstein, “Gaze-contingent focus displays for virtual reality,” Proc. Natl. Acad. Sci. U. S. A. 114(9), 2183–2188 (2017).
[Crossref]

Park, S.-C.

Pau, S.

Pishnyak, O.

Pujol, J.

P. F. Sanabria, F. Diaz-Douton, M. Aldaba, and J. Pujol, “Spherical refractive correction with an electro-optical liquid lens in a double-pass system,” J. Europ. Opt. Soc. Rap. Public. 8, 13062 (2013).
[Crossref]

Quilliet, C.

C. Quilliet and B. Berge, “Electrowetting: a recent outbreak,” Curr. Opin. Colloid Interface Sci. 6(1), 34–39 (2001).
[Crossref]

Sanabria, P. F.

P. F. Sanabria, F. Diaz-Douton, M. Aldaba, and J. Pujol, “Spherical refractive correction with an electro-optical liquid lens in a double-pass system,” J. Europ. Opt. Soc. Rap. Public. 8, 13062 (2013).
[Crossref]

Sasian, J.

J. Sasian, W. Gao, and Y. Yan, “Method to design apochromat and superachromat objectives,” Opt. Eng. 56(10), 1 (2017).
[Crossref]

Sato, S.

Schmid, B.

Seifert, A.

Siemens, M.

Smart, S.

Spires, O.

Stramer, T.

N. Padmanaban, R. Konrad, T. Stramer, E. A. Cooper, and G. Wetzstein, “Gaze-contingent focus displays for virtual reality,” Proc. Natl. Acad. Sci. U. S. A. 114(9), 2183–2188 (2017).
[Crossref]

Tian, X.

Tu, X.

Tullis, I.

Vallis, K.

van’t Hoff, M.

Vdovin, G.

Voigt, F.

Vojnovic, B.

Volpi, D.

Waibel, P.

Wetzstein, G.

N. Padmanaban, R. Konrad, T. Stramer, E. A. Cooper, and G. Wetzstein, “Gaze-contingent focus displays for virtual reality,” Proc. Natl. Acad. Sci. U. S. A. 114(9), 2183–2188 (2017).
[Crossref]

Wyant, J.

Wyant, J. C.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), pp. 1–53.

Yan, Y.

J. Sasian, W. Gao, and Y. Yan, “Method to design apochromat and superachromat objectives,” Opt. Eng. 56(10), 1 (2017).
[Crossref]

Yoo, H.

Zappe, H.

Zhang, J.

Appl. Opt. (4)

Biomed. Opt. Express (2)

Curr. Opin. Colloid Interface Sci. (1)

C. Quilliet and B. Berge, “Electrowetting: a recent outbreak,” Curr. Opin. Colloid Interface Sci. 6(1), 34–39 (2001).
[Crossref]

Curr. Opt. Photon. (1)

J. Europ. Opt. Soc. Rap. Public. (1)

P. F. Sanabria, F. Diaz-Douton, M. Aldaba, and J. Pujol, “Spherical refractive correction with an electro-optical liquid lens in a double-pass system,” J. Europ. Opt. Soc. Rap. Public. 8, 13062 (2013).
[Crossref]

Jpn. J. Appl. Phys. (1)

S. Sato, “Liquid-Crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[Crossref]

Opt. Eng. (1)

J. Sasian, W. Gao, and Y. Yan, “Method to design apochromat and superachromat objectives,” Opt. Eng. 56(10), 1 (2017).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Proc. Natl. Acad. Sci. U. S. A. (1)

N. Padmanaban, R. Konrad, T. Stramer, E. A. Cooper, and G. Wetzstein, “Gaze-contingent focus displays for virtual reality,” Proc. Natl. Acad. Sci. U. S. A. 114(9), 2183–2188 (2017).
[Crossref]

Sensors (1)

H. Li, X. Cheng, and Q. Hao, “An electrically tunable zoom system using liquid lenses,” Sensors 16(1), 45 (2015).
[Crossref]

Other (3)

Jerome Crassous, Claude Gabay, Gaetan Liogier, and Bruno Berge, “Liquid lens based on electrowetting: a new adaptive component for imaging applications in consumer electronics,” Proc. SPIE5639, Adaptive Optics and Applications III (2004).

M. Blum, M. Bueler, C. Gratzel, and M. Aschwanden, “Compact optical design solutions using focus tunable lenses,” in SPIE Optical Systems Design (ISOP, 2011), paper 81670W

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), pp. 1–53.

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Figures (8)

Fig. 1.
Fig. 1. Light propagation through infinite conjugate microscope objectives. a) A conventional infinite conjugate objective with a fixed focus plane. b) A conventional infinite conjugate objective pairs with an FTL with a tuning range from negative to positive focal length to image the specimen at different depth.
Fig. 2.
Fig. 2. Simulation setup in Zemax. “Black box” models provided by Thorlabs were used as the objective lenses. An OL is paired with FTL to expand its focus tuning range.
Fig. 3.
Fig. 3. Experiment setups. a) A Twyman-Green interferometer to measure the spherical aberration and chromatic focal shift of the 3D microscopy setup in vertical direction. b) Measure the image contrast with a USAF 1951 target to evaluate system resolution. Illumination system shares the common path with imaging system to provide same NA. c) Measure aberration and contrast of the 3D microscopy setup in horizontal direction to exam gravity effect.
Fig. 4.
Fig. 4. On-axis MTF of the FTL and OL paired with a) Thorlabs 2X refractive objective, b) Thorlabs 4X refractive objective, c) Thorlabs 15X reflective objective and d) Thorlabs 40X reflective objective at different FTL power setting. Performance of the systems without FTL are provided as reference.
Fig. 5.
Fig. 5. Chromatic aberration evaluation from the simulation. a) Chromatic focal shifts between F-line and C-line (blue bar) and between F-line and d-line (orange bar) for 4 chosen objectives with FTL and OL. b) Chromatic focal shifts for the 2 refractive objectives without and 4 objectives with FTL. Note the scale of refractive objectives after attaching FTL is 10X of the original objectives without FTL. The reflective objectives without FTL has no chromatic aberration due to their reflective natures, thus the curves are not shown.
Fig. 6.
Fig. 6. Optical performance evaluation of 3D microscopy setup in vertical direction. a) Spherical aberration by evaluate Zernike coefficient Z8 at different FTL power setting. b) Chromatic focal shift between 488 nm and 633 nm (blue bar), and between 488 nm and 543 nm (orange bar). c) Image of USAF1951 resolution target at different FTL settings. d) Contrast of group 7 element 1 of the resolution chart image.
Fig. 7.
Fig. 7. Optical performance evaluation of 3D microscopy setup in horizontal direction. a) Spherical aberration and coma by evaluate Zernike coefficient Z6, Z7 and Z8 at different FTL power setting. b) Wavefront map from interferometer shows strong coma. Coma direction departures from gravity direction by about 6 degrees c) Image of USAF1951 resolution target at different FTL settings. d) Contrast of group 7 element 1 of the resolution chart image.
Fig. 8.
Fig. 8. Chromatic aberration correction for FTL. a) Initial setup for equation derivation. b) Achromatic FTL system with 2 thin doublets c) Apochromatic 3D microscopy system. d) Chromatic focal shift for the chromatic FTL system. Maximum plot scale is 100 µm. e) Chromatic focal shift for the apochromatic 3D microscopy system. Maximum plot scale is 2 µm. f) On-axis MTF performance for the apochromatic 3d microscopy system

Tables (1)

Tables Icon

Table 1. Comparison between Zemax solution and derived conditions. Condition 1 from Eq. 18 is highlighted in red and condition 2 from Eq. 21 is highlighted in green.

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

W ( ρ , θ ) f o c u s = ρ 2 ( 2 Z 3 6 Z 8 ± Z 4 2 + Z 5 2 ) .
Φ t o t a l = ( Φ 1 + Φ 2 ) + Φ 3 ( Φ 1 + Φ 2 ) Φ 3 t
B F D = 1 Φ t o t a l + d
d = Φ 1 + Φ 2 Φ t o t a l t
Φ n C = Φ n F Φ n d V n
Φ F t o t a l = ( Φ 1 F + Φ 2 F ) + Φ 3 F ( Φ 1 F + Φ 2 F ) Φ 3 F t
Φ C t o t a l = ( Φ 1 C + Φ 2 C ) + Φ 3 C ( Φ 1 C + Φ 2 C ) Φ 3 C t
Φ C t o t a l = [ ( Φ 1 F Φ 1 d V 1 ) + ( Φ 2 F Φ 2 d V 2 ) ] + ( Φ 3 F Φ 3 d V 3 ) [ ( Φ 1 F Φ 1 d V 1 + Φ 2 F Φ 2 d V 2 ) ( Φ 3 F Φ 3 d V 3 ) t ]
d F = Φ 1 F + Φ 2 F Φ F t o t a l t
d C = Φ 1 C + Φ 2 C Φ C t o t a l t
B F D F = 1 Φ F t o t a l Φ 1 F + Φ 2 F Φ F t o t a l t = 1 ( Φ 1 F + Φ 2 F ) t Φ F t o t a l = 1 ( Φ 1 F + Φ 2 F ) t ( Φ 1 F + Φ 2 F ) + Φ 3 F ( Φ 1 F + Φ 2 F ) Φ 3 F t
B F D C = 1 Φ C t o t a l Φ 1 C + Φ 2 C Φ C t o t a l t = 1 ( Φ 1 C + Φ 2 C ) t Φ C t o t a l = 1 ( Φ 1 F + Φ 2 F Φ 1 d V 1 Φ 2 d V 2 ) t ( Φ 1 F + Φ 2 F ) + Φ 3 F ( Φ 1 F + Φ 2 F Φ 1 d V 1 Φ 2 d V 2 ) ( Φ 3 F Φ 3 d V 3 ) t Φ 1 d V 1 Φ 2 d V 2 Φ 3 d V 3
Δ B F D = B F D F B F D C = Φ 3 d [ ( Φ 2 d V 1 t α ) + ( Φ 1 d V 2 t α ) ( V 1 V 2 α 2 ) ] Φ 2 d V 1 V 3 Φ 1 d V 2 V 3 D
α = 1 + Φ 1 F t + Φ 2 F t
D = [ Φ 3 F + Φ 1 F ( 1 + Φ 3 F ) + Φ 2 F ( 1 + Φ 3 F ) ] { Φ 2 d V 1 ( Φ 3 d t + V 3 Φ 3 F t V 3 ) + Φ 1 d V 2 ( Φ 3 d t + V 3 Φ 3 F t V 3 ) V 1 V 2 [ Φ 3 d α + V 3 ( Φ 1 F + Φ 2 F + Φ 3 F Φ 1 F Φ 3 F t Φ 2 F Φ 3 F t ) ] }
Φ 2 d V 1 V 3 + Φ 1 d V 2 V 3 = 0
Φ 2 d V 1 t α + Φ 2 d V 1 t α V 1 V 2 α 2 = 0
Φ 2 d = Φ 1 d V 2 V 1
V 1 V 2 + V 1 V 2 Φ 1 F t + V 1 V 2 Φ 2 F t = 0
Φ 2 d Φ 2 F Φ 1 d Φ 1 F
Φ 1 d t = V 1 V 1 V 2
B F D d = 1 Φ d t o t a l Φ 1 d + Φ 2 d Φ d t o t a l t = 1 ( Φ 1 d + Φ 2 d ) t ( Φ 1 d + Φ 2 d ) + Φ 3 d ( Φ 1 d + Φ 2 d ) Φ 3 d t
B F D d = 1 ( Φ 1 d Φ 1 d V 2 V 1 ) t ( Φ 1 d Φ 1 d V 2 V 1 ) + Φ 3 d ( Φ 1 d Φ 1 d V 2 V 1 ) Φ 3 d t = 1 Φ 1 d t ( 1 V 2 V 1 ) Φ 1 d ( 1 V 2 V 1 ) + Φ 3 d ( 1 Φ 1 d + Φ 1 d V 2 V 1 t )
B F D d = 1 V 1 V 1 V 2 ( 1 V 2 V 1 ) Φ 1 d ( 1 V 2 V 1 ) + Φ 3 d ( 1 V 1 V 1 V 2 + V 1 V 1 V 2 V 2 V 1 ) = 1 V 1 V 2 V 1 V 2 Φ 1 d ( 1 V 2 V 1 ) + Φ 3 d ( 1 V 2 V 1 V 1 V 2 ) = 0