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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 9, Iss. 5 — Apr. 29, 2014
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Axial scanning in confocal microscopy employing adaptive lenses (CAL)

Nektarios Koukourakis, Markus Finkeldey, Moritz Stürmer, Christoph Leithold, Nils C. Gerhardt, Martin R. Hofmann, Ulrike Wallrabe, Jürgen W. Czarske, and Andreas Fischer  »View Author Affiliations


Optics Express, Vol. 22, Issue 5, pp. 6025-6039 (2014)
http://dx.doi.org/10.1364/OE.22.006025


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Abstract

In this paper we analyze the capability of adaptive lenses to replace mechanical axial scanning in confocal microscopy. The adaptive approach promises to achieve high scan rates in a rather simple implementation. This may open up new applications in biomedical imaging or surface analysis in micro- and nanoelectronics, where currently the axial scan rates and the flexibility at the scan process are the limiting factors. The results show that fast and adaptive axial scanning is possible using electrically tunable lenses but the performance degrades during the scan. This is due to defocus and spherical aberrations introduced to the system by tuning of the adaptive lens. These detune the observation plane away from the best focus which strongly deteriorates the axial resolution by a factor of ~2.4. Introducing balancing aberrations allows addressing these influences. The presented approach is based on the employment of a second adaptive lens, located in the detection path. It enables shifting the observation plane back to the best focus position and thus creating axial scans with homogeneous axial resolution. We present simulated and experimental proof-of-principle results.

© 2014 Optical Society of America

1. Introduction

CM is generally based on point by point image acquisition. Hence, scanning in three dimensions is required to obtain three-dimensional object information. Different approaches have been used to implement this scanning. In the original method used by Minsky [1

1. M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10(4), 128–138 (1988). [CrossRef]

] and adapted by several others, the sample was moved across the focus in all three dimensions [9

9. J. Benschop and G. van Rosmalen, “Confocal compact scanning optical microscope based on compact disc technology,” Appl. Opt. 30(10), 1179–1184 (1991). [CrossRef] [PubMed]

, 10

10. A. E. Dixon, S. Damaskinos, and M. R. Atkinson, “Transmission and double-reflection scanning stage confocal microscope,” Scanning 13(4), 299–306 (1991). [CrossRef]

]. This stage scanning technique employs an optically simple setup and is thus not that vulnerable to aberrations as other more complex implementations. A major drawback is that stage scanning is too slow, and needs some seconds to record one frame [5

5. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59(3), 427–471 (1996). [CrossRef]

]. This is not practical for the usage at biological samples [11

11. B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum. 80(7), 073706 (2009). [CrossRef] [PubMed]

]. Furthermore, scanning the sample may be prohibited depending on its size and movability.

Alternatively laser scanning techniques have been developed, where the laser is scanned laterally across a static sample. There are several types of methods which are either optimized for speed or resolution, like scanning using galvanometric mirrors, rotating Nipkow Discs or digital micromirror devices (DMD) [12

12. M. Rajadhyaksha, R. R. Anderson, and R. H. Webb, “Video-rate confocal scanning laser microscope for imaging human tissues in vivo,” Appl. Opt. 38(10), 2105–2115 (1999). [CrossRef] [PubMed]

14

14. L.-C. Chen, H.-W. Li, and Y.-W. Chang, ”Full-field chromatic confocal surface profilometry employing DMD correspondence for minimizing lateral cross talks,” Proc. Of SPIE Vol. 832120, Symp. on Precision Eng. (2011). [CrossRef]

]. The need of mechanical scanning is not only a problem of CM. All imaging modalities that are based on laser-scanning techniques have to address this task. The lateral-scanning rates commonly achieved are up to 100-500 Hz [15

15. B. F. Grewe, D. Langer, H. Kasper, B. M. Kampa, and F. Helmchen, “High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision,” Nat. Methods 7(5), 399–405 (2010). [CrossRef] [PubMed]

].

Aside from the lateral scans additional axial z-scans are required to obtain 3D images. This is usually achieved by moving the objective, e.g. using a piezoelectric device, but there are also stage scanning based approaches that move the sample through the focus.

Typically the axial scanning is the limiting factor for the achievable 3D sampling rate that amounts to about 10 Hz [16

16. W. Göbel and F. Helmchen, “New angles on neuronal dendrites in vivo,” J. Neurophysiol. 98(6), 3770–3779 (2007). [CrossRef] [PubMed]

]. Speeding-up this value is a hurdle, as fast moving objectives aggravate the performance and accuracy due to the inertia which lead to overshoots and oscillations. For further improving the acquisition speed of CMs it is desirable to circumvent mechanical scanning and to create a system without moving parts. This may open up new applications, especially for microscopy of cellular or neuronal activity or for following fast reactions e.g. in chemistry. Often such measurements require real-time imaging that are beyond the typical time-scales achieved today. Supported by the technological progress in recent years a variety of approaches came up that overcome these limitations by using adaptive optical elements to implement the axial scan or to change the focus position, including deformable mirrors and tunable lenses [17

17. W. Amir, R. Carriles, E. E. Hoover, T. A. Planchon, C. G. Durfee, and J. A. Squier, “Simultaneous imaging of multiple focal planes using a two-photon scanning microscope,” Opt. Lett. 32(12), 1731–1733 (2007). [CrossRef] [PubMed]

20

20. H. Oku, K. Hashimoto, and M. Ishikawa, “Variable-focus lens with 1-kHz bandwidth,” Opt. Express 12(10), 2138–2149 (2004). [CrossRef] [PubMed]

]. Especially the latter have undergone a rapid development in the last years [20

20. H. Oku, K. Hashimoto, and M. Ishikawa, “Variable-focus lens with 1-kHz bandwidth,” Opt. Express 12(10), 2138–2149 (2004). [CrossRef] [PubMed]

22

22. B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000). [CrossRef]

], which led to several applications like e.g. in extended depth-of-field imaging [23

23. S. Liu and H. Hua, “Extended depth-of-field microscopic imaging with a variable focus microscope objective,” Opt. Express 19(1), 353–362 (2011). [CrossRef] [PubMed]

], in fast axial focusing in two-photon microscopy [24

24. K. S. Lee, P. Vanderwall, and J. P. Rolland, “Two-photon microscopy with dynamic focusing objective using a liquid lens,” Proc. SPIE 7569, 756923 (2010). [CrossRef]

], optical coherence microscopy [25

25. S. Murali, K. P. Thompson, and J. P. Rolland, “Three-dimensional adaptive microscopy using embedded liquid lens,” Opt. Lett. 34(2), 145–147 (2009). [CrossRef] [PubMed]

, 26

26. S. Murali, P. Meemon, K.-S. Lee, W. P. Kuhn, K. P. Thompson, and J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (2010). [CrossRef] [PubMed]

] and light-sheet microscopy [27

27. F. O. Fahrbach, F. F. Voigt, B. Schmid, F. Helmchen, and J. Huisken, “Rapid 3D light-sheet microscopy with a tunable lens,” Opt. Express 21(18), 21010–21026 (2013). [CrossRef] [PubMed]

]. This list can be extended by a huge number of potential application areas such as phase retrieval [28

28. L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001). [CrossRef]

], flow measurements [29

29. J. König, K. Tschulik, L. Büttner, M. Uhlemann, and J. Czarske, “Analysis of the Electrolyte Convection inside the concentration boundary layer during structured electrodeposition of Copper in high magnetic gradient fields,” Anal. Chem. 85(6), 3087–3094 (2013). [CrossRef] [PubMed]

] and shape measurements [30

30. P. Günther, R. Kuschmierz, T. Pfister, and J. Czarske, “Distance measurement technique using tilted interference fringe systems and receiving optic matching,” Opt. Lett. 37(22), 4702–4704 (2012). [CrossRef] [PubMed]

]. Adaptive lenses allowed achieving axial scan-rates up to 500 fps and thus promise to be an appropriate alternative for fast axial scanning. Although such axial scan rates can also be achieved by nowadays fastest mechanical scanners, the approach using adaptive lenses bears the possibility for further improvements. The progress of adaptive lenses in terms of image quality and speed will surely carry on.

In this paper we investigate the usage of adaptive lenses to overcome the need for mechanical axial scanning in confocal microscopy. A comparable approach has been introduced in [31

31. L. Yang, A. Mac Raighne, E. M. McCabe, L. A. Dunbar, and T. Scharf, “Confocal microscopy using variable-focal-length microlenses and an optical fiber bundle,” Appl. Opt. 44(28), 5928–5936 (2005). [CrossRef] [PubMed]

] that used a micro lens array combined with an optical fiber bundle to create a confocal setup. Although this configuration elegantly overcame any need for scanning, the performance of this approach is strongly degraded by inhomogeneous focusing of the micro lenses and by inhomogeneous axial responses of the fibers.

We instead use a single adaptive lens in the illumination path in combination with a lens of high numerical aperture and a pinhole based detection. The fastest adaptive lens reported so far is an acoustic gradient-index lens that achieves switching times of 1 µs enabling axial scan rates of several hundred kHz. This lens could be inserted to the proposed setup enabling ultrafast axial scanning [32

32. A. Mermillod-Blondin, E. McLeod, and C. B. Arnold, “High-speed varifocal imaging with a tunable acoustic gradient index of refraction lens,” Opt. Lett. 33(18), 2146–2148 (2008). [CrossRef] [PubMed]

]. However, the imaging performance is a major issue whenever adaptive lenses are used. Very recently axial scanning using a single adaptive lens in CM was reported [33

33. J. M. Jabbour, B. H. Malik, C. Olsovsky, R. Cuenca, S. Cheng, J. A. Jo, Y.-S. L. Cheng, J. M. Wright, and K. C. Maitland, “Optical axial scanning in confocal microscopy using an electrically tunable lens,” Biomed. Opt. Express 5(2), 645–652 (2014). [CrossRef] [PubMed]

]. Though the presented results are promising, the imaging quality degraded during the lens based axial scanning procedure.

In this paper we analyze the impact of axial scanning with adaptive lenses on the imaging quality in greater depth. The results show that our Confocal microscopy with Adaptive Lenses (CAL) system enables axial scanning without any moving parts. But the axial resolution strongly degrades during the scan. This is due to aberrations that increase during the tuning as the imaging capabilities of the lens system change with the lens driving voltage, rather than quality restrictions of the adaptive lenses. To address the inhomogeneous axial-resolution the influence of aberrations has to be minimized. Commonly aberrations in confocal microscopy are compensated employing deformable mirrors [34

34. M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002). [CrossRef] [PubMed]

, 35

35. O. Albert, L. Sherman, G. Mourou, T. B. Norris, and G. Vdovin, “Smart microscope: an adaptive optics learning system for aberration correction in multiphoton confocal microscopy,” Opt. Lett. 25(1), 52–54 (2000). [CrossRef] [PubMed]

]. Though the deformable mirrors have more capabilities concerning aberration correction they offer a small stroke. Furthermore the potentially ultrafast scans possible with adaptive lenses would require ultrafast balancing, which is beyond their capabilities.

We introduce and characterize a novel design including a second lens located in the detection path to balance the aberrations. Experimental and simulated proof of principle results show that it this approach is sufficient to create a homogeneous axial resolution.

2. Adaptive fluid-membrane lenses with integrated piezo actuation

Tunable lenses offer a variety of advantages to common lens systems, such as compactness, high tuning speeds, as well as setups free of mechanical components. There are two general methods for tuning the focal power of a lens: controlling the lens curvature on the one hand and controlling the refractive index of the lens material on the other hand. The latter is usually achieved with liquid crystal materials that change their refractive index upon application of an electric field, e.g. in [36

36. B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with focal length variable from negative to positive values,” Photonics Technol. Lett. IEEE 18(1), 79–81 (2006). [CrossRef]

]. While this method is limited to small changes of the refractive power, varying the lens curvature allows for large tuning ranges.

2.1. Design

Our lens design is based on the fluid-membrane working principle. We employ a transparent Polydimethylsiloxan (PDMS) membrane (thickness ~300 µm) into which an annular piezo bending actuator is embedded as it is depicted in Fig. 1(a)
Fig. 1 Cross-section view of the device design in a) unactuated and b) actuated state. c) Schematic bimorph actuator configuration. d) Sketch of the assembly procedure with integrated filling and bonding and photographs of the components.
and 1(b). The actuator is bimorph so that large deflections in both directions are possible. It is composed of two active piezo sheets with parallel oriented polarization [Fig. 1(c)] and just one driving voltage is needed to act on both layers. However, one of the layers is driven against polarization direction with this configuration. Hence, the voltage needs to be limited in order to stay well below the coercive field strength to avoid any damage of the piezo electric material. The actuator is supported on a soft ring made from PDMS. This ensures that upon actuation the resulting deflection is spherical and maximal because it is not constricted by any boundary clamping. Further, this support ring acts as a spacer to the glass substrate. The integrated actuators allow for a small overall thickness of the device of about 1.5 mm. The cavity between substrate and membrane is filled with an incompressible, transparent fluid. When actuated, the bending actuators displace the fluid underneath which generates a pressure inside the lens and therefore the membrane gets deflected. Since all piezo actuators suffer from hysteresis it is necessary to compensate for this behavior. One method is to use a feedback signal of a strain sensor to control the piezo deflection. For our lens we found that the membrane deflection and therefore the refractive power has a good linear dependency on the pressure inside the lens chamber [37

37. J. Draheim, T. Burger, and R. Kamberger, “Closed-loop pressure control of an adaptive single chamber membrane lens with integrated actuation,” in International Conference on Optical MEMS and Nanophotonics, 47–48 (2011). [CrossRef]

]. Therefore, we integrate a pressure sensor into the lens chamber to use the pressure as a control variable. This increases the reliability and accuracy of the lens and thus of the whole CM.

2.2. Fabrication

For fabrication of the lenses we use a prototyping process which is similar to a procedure we have introduced earlier [38

38. F. Schneider, J. Draheim, R. Kamberger, P. Waibel, and U. Wallrabe, “Optical characterization of adaptive fluidic silicone-membrane lenses,” Opt. Express 17(14), 11813–11821 (2009). [CrossRef] [PubMed]

]. The piezo actuators are commercially available PZT sheets with silver electrodes (Ekulit GmbH, thickness ~100 µm) which are glued together with epoxy. The outer contour of the actuator is laser cut. Subsequently the actuator is cast in a transparent PDMS (Momentive RTV 615) in a machined brass mold to form the membrane and the support ring. The optical surfaces in the lens area as well, as a precisely controlled membrane thickness are achieved by silicon insets in the mold. It is important to cure the silicone at room temperature, in order to avoid high shrinkage and therefore a pre-stress in the membrane. A platinum catalyst is added to enhance curing. Float glass wafers are used for the glass substrate and are cut to a round shape with a UV laser. Further, a trench is laser machined to the glass in this process step. It provides a rough surface which improves adhesion to the lens chamber. Gold pads are deposited onto the glass substrate by evaporation. A commercial absolute pressure sensor (Epcos C33) is manually glued to the substrate and contacted to the gold pads by wire bonding. The contacts and the pressure sensor are then covered with a droplet of PDMS to protect them from damage. In a final step the lens chamber which consists of actuator, support ring, and membrane is bonded onto the substrate and filled with the lens fluid at the same time, as depicted in Fig. 1(d). A small amount of PDMS is filled into the trench on the substrate and cured inside a container filled with the lens liquid. Filling the lens in situ with its assembly avoids the need for a separate filling step and reduces the risk of trapping air bubbles inside the device. A perfluoropolyether (Zeiss Immersol W2010, refractive index n ~1.33) is used as an optical liquid since it avoids PDMS swelling and does not evaporate through the membrane, which is usually considered to be a limitation of silicone membranes [39

39. J. N. Lee, C. Park, and G. M. Whitesides, “Solvent compatibility of poly(dimethylsiloxane)-based microfluidic devices,” Anal. Chem. 75(23), 6544–6554 (2003). [CrossRef] [PubMed]

].

2.3. Characterization

The mechanical properties of the prototypes were characterized by scanning the lens surface with a laser triangulation sensor (Keyence LK-G32) while varying the actuation voltage which means that the lens is operated in open-loop mode. The refractive power was calculated from the curvature under the assumption that the refractive effect of the lens is only achieved by the refraction of the lens fluid [Fig. 2(a)
Fig. 2 a) Stack of line-scans across the profiles obtained with the triangulation sensor. The curvature was used to calculate the refractive power at each voltage. b) Refractive power as a function of rising voltage. For UAL = 40 V the focal length is about f = 150 mm. At UAL = 0 V the membrane has a pre-deflection induced by fabrication tolerances.
]. The curvature is obtained by a regression of the measured surface profile. For the regression an aperture diameter of half the membrane diameter was assumed in order to stay within an area of good agreement with the spherical membrane shape. Figure 2(b) shows the refractive power obtained for the lens used in this work. A larger membrane diameter reduces the tuning range. This is a consequence of the decreased deflection of a smaller piezo actuator and a decreased pumping volume. The shift of the offset refractive power, i.e. the pre-deflection of the membrane in the unactuated state, can be attributed to fabrication tolerances. The focus of our lens can be tuned from fU = −40 V = −150 mm to fU = + 40 V = + 150 mm. The switching times achieved using this lens design, are in the order of 10 ms.

3. Experimental setup

We use a 80 fs Ti:Sapphire laser at 800 nm as light source, coupled into a single-mode fiber. The light is collimated by a large beam collimator and propagates towards a beam splitter that reflects the light into the illumination-arm of the CM. As the numerical aperture of liquid lenses in general is low (~0.017) we use a combination of the adaptive lens 1 (AL1) with an aspherical lens (L1) of high numerical aperture (NA = 0.55, f = 4.51) to create an adequate high-quality tunable system (Fig. 3
Fig. 3 Confocal microscope employing adaptive lenses (CAL) in the illumination and the detection path.
). The distance d between AL1 and L1 amounts to d = 4.5 cm. We measured the power in the focus to be P = 750 µW. The light backscattered by a sample located in the focal plane passes the illumination-objective and reaches the detection-objective that consists of the second adaptive lens, which we from now on call ‘AL 2’, and a second lens L2 with an effective numerical aperture of NA = 0.065.

AL2 introduces a further degree of freedom, as it allows shifting the observation plane. Both adaptive lenses used have a membrane diameter of 10 mm. The tuning behavior shown in Fig. 2 belongs to AL1, while AL2 shows a comparable performance. The exit pupil of the system is placed at the focus of the detection lens system. A Si photodiode completes the confocal setup detecting the light passing the pinhole.

Nevertheless, CAL principally could be easily extended to a laser scanning technique which will be part of future work. The sample used in our experiment is a plasma-etched Si-substrate that contains small features that have a depth of around 40 nm. Vertical and horizontal lines and dots are the smallest that correspond to lateral resolutions between 1 µm and 500 nm, as marked in Fig. 4(b). The lateral fabrication error amounts to ± 35 nm.

4. Experiments and simulations

In order to provide a better understanding of the experiment a simulation of the CAL system was accomplished by Matlab. Each interface in the beam-path is computed and described separately according to data of the particular manufacturer. The surface curvature of the adaptive lenses is implemented using the surface profiles shown in Fig. 2(a). Using this data we solve the scalar Helmholtz equation in cylindrical coordinates with rotation symmetry by means of a coordinate-adapted angular spectrum method to propagate the wave through the optical system. The angular spectrum method is commonly used in cartesian coordinates with two-dimensional fourier transforms for the lateral axes. Due to the coordinate transformation from cartesian to cylindrical those 2D-Fourier transforms are changed to one-dimensional Hankel transforms and evaluated with the quasi fast Hankel transform [40

40. A. E. Siegman, “Quasi fast Hankel transform,” Opt. Lett. 1(1), 13–15 (1977). [CrossRef] [PubMed]

].

4.1. Tuning the focal volume with AL1

In the initial condition the system is ideally aligned for UAL1 = 0 V and UAL2 = 0 V. Tuning UAL1 changes the focal length of AL1 and thus changes the effective focal length of the illumination lens system. This scans the focus in the axial direction, called z-scan. In order to analyze the behavior of the system, we perform the scan step-wise. For each voltage-step we drive the sample in the z-direction using the stage and acquire the intensity that reaches the detector through the pinhole. This allows scanning the focus and tracking the changes occurring for each voltage step. The full-width half maximum (FWHM) of the detected intensity distribution is commonly seen as the axial resolution [5

5. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59(3), 427–471 (1996). [CrossRef]

]. For clarity, we call the stage-based scan A-scan. The results are shown in Fig. 5
Fig. 5 a) The experimentally measured A-scans show that the focus is tuned with the driving voltage of the lens UAL1. b) The shift of the peak position of the experimentally measured and simulated A-scans agree very well. The tuning range amounts to about 380 µm. c) The FWHM increases, which means that the axial resolution decreases with voltage. d) The peak intensity also decreases with voltage. The behavior can be explained by aberrations introduced to the system by the adaptive lens.
.

With increasing the voltage UAL1 from 0V up to 40 V, three results can be observed:

The focus is tuned with the driving voltage UAL1. The mean slope of the focus shift is 63 µm per 10 V. As can be seen in Figs. 5(a) and 5(b) at voltages of > 25 V, the tuning becomes non-linear leading to measured tuning range-values of 380 µm. The simulations show a very good agreement to the experimentally measured behavior [Figs. 5(b) and 5(c)].

The axial performance degrades. The FWHM of the A-scans [Fig. 5(c)], which can be seen as a measure for the axial resolution of the setup, amounts to FWHM0V = 9 µm at UAL1 = 0 V initially. This value is too big for the applied configuration with the pinhole of 0.6 airy units. The expected resolution can be estimated after [41

41. T. Wilson, “Resolution and optical sectioning in the confocal microscope,” J. Microsc. 244(2), 113–121 (2011). [CrossRef] [PubMed]

]:
Δz=0.67λnn2NA21+AU24µm.
(1)
The difference can be attributed to aberrations introduced by the lens tuning, that add to the aberrations already present in the system. The peak-intensity of the A-scans drops by 10% during the scan. Furthermore the axial resolution deteriorates by a factor 2.33 with increasing voltage, as the FWHM increases up to 20 µm. This is verified with the simulated results (factor 2.55) that are in good agreement to the measured ones. Simultaneously the shape of the A-scan undergoes a change and becomes strongly asymmetrical, which is a further hint that especially spherical aberrations are present [42

42. C. J. R. Sheppard, M. Gu, K. Brain, and H. Zhou, “Influence of spherical aberration on axial imaging of confocal reflection microscopy,” Appl. Opt. 33(4), 616–624 (1994). [CrossRef] [PubMed]

].

The lateral resolution is not affected. The experiments show that the aberrations have a small impact on the lateral resolution. The lateral resolution in CM benefits from the side-lobe suppression by the pinhole [5

5. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59(3), 427–471 (1996). [CrossRef]

]. It can be calculated from the numerical aperture (NA) of the microscope objective and the wavelength λ using:

Δr=kλNA
(2)

A commonly used value for the constant is k = 0.51, for AU = 1 [43

43. J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd-Edition (Springer Science + Business Media, 2006).

]. The lateral resolution can be even improved by more than 40% compared to the Abbe limit for very small pinholes (AU<0.1) [43

43. J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd-Edition (Springer Science + Business Media, 2006).

]. To analyze the lateral resolution we use the stage to scan the sample laterally across the focus and acquire 2D en-face images of our test sample. As shown in Fig. 6
Fig. 6 The stage is positioned at z = 0. There the sample is out of focus. Using UAL1 allows shifting the focus to the depth of the sample. Further increasing the voltage shifts the focus too far and the sample is out of focus again. At UAL1 = 10 V the 500 nm element of the sample is resolved as can be expected for a pinhole with 0.6 AU [43].
we perform the scans at the stage-position z = 0. Using UAL1 allows shifting the focus through the sample. At UAL1 = 10 V the 3rd element can be resolved, which corresponds to 500 nm lateral resolution, which is in the expected magnitude for the used implementation of AU = 0.6. This shows that the lateral resolution of our system is not noticeably affected by the aberrations.

4.2. Theoretical problem description

In an aberration-free CM the pupil functionP(θ), i.e. the wave-front at the pinhole, has a constant phase. In presence of aberration the pupil function can be expressed as:
P(ρ,UAL1)=exp(jΦAL(ρ,UAL1)).
(3)
ΦAL is the phase at the exit pupil andρis a radial variable. The main origin of the aberrations in the CAL system is the usage of the lens system necessary to address the low NA of the adaptive lenses. Commonly the front lenses (in our case the aspheric lens L1) are designed to be illuminated with collimated plane wave beams at full-illumination. When AL1 is tuned, the illumination angle of L1 is changed, and amounts up to 10° for UAL1 = 40 V. This has two consequences: First, L1 is illuminated by spherical wave fronts rather than plane waves. Secondly, the illuminated area of the microscope objective L1 decreases by about 30% compared to collimated illumination. As the setup strongly deviates from the optimal illumination conditions with increasing voltage, the aberrations of the system also increase and add to the present aberrations.

In CM systems the main aberrations are spherical and defocus aberrations, which lead to an extended and blurred effective focus. This is due to different foci created by beams crossing the centre and the edges of the lens-aperture. These are the axially separated paraxial focus and marginal focus respectively [44

44. R. R. Shannon and J. C. Wyant, Applied Optics and Optical Engineering (Academic Press Inc., 1992), Chapter 1.

]. The spherical aberration can be expressed as Φ(ρ,UAL1)=AS(UAL1)ρ4+BD(UAL1)ρ2, where ASis the coefficient of spherical aberration of the wave-front and BDis the defocus coefficient [45

45. V. N. Mahajan, “Strehl ratio of a Gaussian beam,” J. Opt. Soc. Am. A 22(9), 1824–1833 (2005). [CrossRef] [PubMed]

]. At an axial position between these two foci there is the best focus at which the blurred focal spot has minimal lateral dimensions and highest intensity, also known as the circle of least confusion (CoC). The distance Δ between the CoC and the paraxial focus can be expressed asΔ=8F2AS, where Fis the focal ratio of the image-forming light cone [45

45. V. N. Mahajan, “Strehl ratio of a Gaussian beam,” J. Opt. Soc. Am. A 22(9), 1824–1833 (2005). [CrossRef] [PubMed]

]. Both Fand ASchange with UAL1. At the CoC the spherical wave-front aberration is minimum and the Strehl ratio maximum [46

46. G. Martial, “Strehl ratio and aberration balancing,” J. Opt. Soc. Am. A 8(1), 164–170 (1991). [CrossRef]

]. It is well known that the spherical aberrations can be balanced by defocus. This is equivalent to shifting the observation plane from the paraxial focus to the CoC. The balance condition can be given asΦbal(ρ,UAL1)=AS(ρ4ρ2), withAS=BD.

Compared to aberrations in common CMs CAL is more difficult to handle, as the scanning tunes also the aberrations. Thus the properties of L1 and AL1 have a strong impact on the behaviour of the system. Choosing L1 with higher NA and adaptive lenses with higher-refractivity should increase the influence of aberrations.

The observation plane in CM is chosen and defined by the pinhole position. We call it confocal plane (Fig. 7
Fig. 7 Scheme of the simulated aberrated focal volume.
). At this plane the system has the highest coupling efficiency. For clarity, we call the axial extent of the focus focal volume.

In general the phase Φ(ρ) can be expressed as the weighted sum of Zernike polynomials Z using:
ΦUAL1(ρ)=Σn,fcnfZnf.
(4)
The defocus, the primary and secondary spherical aberrations are given by Eqs. (5a) to (5c) [46

46. G. Martial, “Strehl ratio and aberration balancing,” J. Opt. Soc. Am. A 8(1), 164–170 (1991). [CrossRef]

].
Z20(ρ)=2ρ21
(5a)
Z40(ρ)=6ρ46ρ2+1
(5b)
Z60(ρ)=20ρ630ρ4+12ρ21.
(5c)
Here the Zernike expansion coefficients c20,c40 and c60are equal to the corresponding wave-front variance. To understand the aberrations in CAL we simulate the phase at the exit pupil for different voltages and use Zernike polynomials expansion up to the sixth order. The sample in our simulation is a mirror with 100% reflectivity, which is axially scanned, mimicking an A-scan. In the initial configuration for UAL1=0Vthe observation plane and the CoC overlap, thus the CoC is imaged onto the pinhole. In this configuration, the spherical aberrations are balanced by defocus. This means that c20 = 0.

With increasing voltage the observation plane shifts away from the CoC and both defocus and primary spherical aberrations increase [Fig. 8(a)
Fig. 8 a) Zernike polynomial expansion for the simulated wave fronts reaching the pinhole. Initially the spherical aberrations are balanced. But they increase with increasing voltage as the system gets detuned from the CoC. b) The detuning of observation plane is determined by comparison of the peak position of the A-scans and the position with balanced aberrations, which corresponds to the CoC.
]. The Zernike coefficients are computed for several voltages at the peak of the A-scan and the axial positions of balanced aberrations (i.e. the CoC) are extracted. Taking the distance between the axial position of the peak intensity of the A-scan and the CoC position allows tracking the detuning as plotted in Fig. 8(b). This shows that the loss of axial resolution with increasing voltage is introduced by detuning of the system which increases the influence of the aberrations. As the aberrations in CAL change with voltage, an adaptive adjustment of the confocal plane is necessary to balance the aberrations. Note that when the aberrations are balanced, this does not mean that they are completely compensated but their influence is reduced. There have been suggestions addressing spherical aberrations in common confocal systems by introducing a movable correcting lens into the detection arm [47

47. C. J. R. Sheppard and M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30(25), 3563–3568 (1991). [CrossRef] [PubMed]

, 48

48. C. J. R. Sheppard and C. J. Cogswell, “Effects of aberrating layers and tube length of confocal imaging properties,” Optik (Stuttg.) 87, 34–38 (1991).

]. We use a comparable approach and apply the second adaptive lens AL2 in the detection path in order to have an adaptive element that is capable of balancing the spherical aberrations. In the following section we will analyze the impact of AL2 on the behavior of the system both experimentally and employing simulations in more detail.

4.3. Tuning the confocal plane with AL2

A-scans are recorded to obtain the depth dependent intensity distribution for different voltages UAL2. In the initial stage, the focal plane and the confocal plane are overlapping which leads to the best axial resolution and the highest peak intensity. It can be assumed, that for UAL2 = 0V the spherical aberrations are minimal. Thus tuning of AL2 leads to a detuning of the system.

The results are summarized in Fig. 9
Fig. 9 a) Experimentally measured A-scans as a function of UAL2. The confocal plane (green dots) scans the z-axis and shifts across the focal volume (orange dots). b) Peak position of the A-scans in dependency of UAL2. At large detuning, the A-scans appear to have two peaks, corresponding to both focal and confocal planes. c) and d) The confocal peak shifts across the focal peak. At UAL2 = 0 V both planes perfectly overlap leading to the highest intensity and smallest FWHM. At higher voltages the confocal peak passed the focal volume.
. In a completely detuned system, the backscattered intensity coupled through the pinhole during an A-scan is highest for two configurations, which leads to two peaks in the intensity-distribution. The first one is created when the sample crosses the focal volume, as in this case the highest intensity propagates through the system, leading to a comparably high intensity value although the coupling efficiency is low. Secondly, another peak will occur at the depth, which corresponds to the optimal coupling through the pinhole, i.e. the confocal plane, even if the intensity in this case is relatively low [Figs. 9(a) and 9(b)]. At UAL2 = −15 V the confocal and the focal peaks can be clearly distinguished [Fig. 9(c)]. Increasing UAL2 shifts the confocal peak across the z-axis.

4.4. Balancing aberrations with AL2

We use simulations to analyze the impact of driving AL2, on the degradation of axial resolution by a factor of ~2.4 during the z-scan. Figure 11(a)
Fig. 11 a) The shift between the CoC and the peak of the A-scan shows that at higher voltages UAL1, the shift becomes zero for higher negative voltages UAL2. b) The Zernike coefficient for defocus increases with UAL1. At c20 = 0 the spherical aberrations are balanced. c) Balancing the system minimizes the FWHM. d) The re-tuning is at the cost of tuning range which is nearly halved.
depicts the shift between the CoC and the peak of the A-scan. When the shift is zero the aberrations are balanced. Starting with an adjusted setup at UAL2 = 0V (black lines), it is detuned with increasing UAL1 leading to a rising shift. As described this happens due to increasing spherical aberrations as can be seen in Fig. 11(b). These lead to deterioration of the axial resolution [Fig. 11(c)]. At UAL2 = −1.6 V (red line) the shift for UAL1 = 0 is negative. With increasing UAL1 the peak of the A-scan shifts to the CoC where the spherical aberrations are balanced. At this constellation the axial resolution is nearly unchanged by the scan. Further increase of UAL1 requires further reduction of UAL2. As shown, when the setup starts detuning for UAL2 = −1.6 V, using UAL2 = −3.2 V (green line) reduces the shift again. Hence the FWHM and aberrations are again reduced. But the re-tuning also leads to a smaller tuning range as shown in [Fig. 11(d)]. To keep the aberrations balanced up to UAL1 = 40 V, UAL2 has to be driven up to UAL2 = −5 V (cyan line). Thus the tuning range for CAL with homogeneous axial resolution is halved to ~200 µm. These results should be seen as a proof of principle, as we just use a couple of electrical voltages. In order to implement a fast high-quality axial scanning both lenses have to be driven simultaneously in a calibrated way, that AL2 always keeps the observation plane on the best focus to keep the aberrations balanced. Furthermore, the curves in Figs. 11(a) and 11(b) show discontinuous behavior for voltages between UAL1 = 10 V and 25 V. This is due to the change of curvature of AL1 in this voltage region and the dependence of the CoC-position on both the aberrations and the focal length.

Experimental results are plotted in [Fig. 12(a)
Fig. 12 a) The experimentally measured FWHM proves that driving UAL2 with negative voltage allows retuning the confocal plane to the CoC. b) Exemplary A-scans. Increasing the voltage from UAL1 = 0 V to UAL1 = 20 V at UAL2 = 0 V increases the FWHM by 20%. Applying UAL2 = −2 V re-tunes the setup and the FWHM decreases.
]. Although there are discrepancies in the overall behavior at high and low voltages, the simulated data agree in the main point very well to the measurements. The results prove that the deterioration of the axial resolution during the z-scan can be compensated by the usage of negative UAL2. Both lenses have to be driven simultaneously, so that the axial resolution does not change by the scan.

Figure 12(b) exemplarily shows the A-scans for UAL1 = 0 V and UAL1 = 20 V both at UAL2 = 0 V. The FWHM increases from FWHM0V-0V = 9.1 µm to FWHM20V-0V = 11.2 µm, as the observation plane is still optimized for 0 V. Repositioning of the observation plane at the CoC leads to FWHM20V-(−2)V = 9.4 µm and to a slight increase of the peak intensity. Both simulations and experiments show that the usage of a second adaptive lens in the CAL setup allows balancing the aberrations, as it enables shifting the confocal plane to the CoC.

5. Conclusions

We analyzed the potential of adaptive lenses in confocal microscopes both experimentally and in simulations using the Hankel transform. The results prove that it is possible to replace mechanical axial scanning by using a piezo-electronically tunable adaptive lens in combination with a high NA objective. The tuning range of our setup is about 380 µm as both experiments and simulations show. But the axial resolution strongly degrades during the scan by a factor of 2.3, which makes the configuration suboptimal. The main factors responsible for this deterioration are spherical aberrations that are introduced by the lens-system. Tuning the adaptive lens AL1 leads to deviation of the ideal illumination of the front lens L1 and consequently to an increase of spherical aberrations leading to a blurred focal volume. During the scan the confocal plane and the circle of least confusion (CoC) detune. Employing a second adaptive lens AL2 in the detection path allows shifting the confocal plane back to the CoC. This enables to perform z-scans with a more homogeneous axial resolution but at the cost of tuning range, which halves (~200 µm) when this approach is used.

There are several advantages that make it worth characterizing and improving the performance of CAL. Although the response times of common adaptive lenses are currently in the time-scale of mechanical scans, the progress of the last years promises that CAL will enable ultrafast axial scans in the range of hundreds kHz, e.g. using an acoustic gradient-index lens. This could enable performing ultrafast 1D-scans for surface analysis, e.g. in assembly lines, or in microelectronics. Principally CAL can be extended with laser-scanning to enable fast 3D scans in biological samples, e.g. in fluorescence measurements of living or motile cells. Moreover, spectrally encoded lateral illumination [49

49. G. J. Tearney, R. H. Webb, and B. E. Bouma, “Spectrally encoded confocal microscopy,” Opt. Lett. 23(15), 1152–1154 (1998). [CrossRef] [PubMed]

] or a comprehensive volumetric design introduced in [50

50. D. K. Kang, H. Yoo, P. Jillella, B. E. Bouma, and G. J. Tearney, “Comprehensive volumetric confocal microscopy with adaptive focusing,” Biomed. Opt. Express 2(6), 1412–1422 (2011). [CrossRef] [PubMed]

] could be used to circumvent lateral scanning, enabling confocal microscopy in 3D, without any mechanically moving elements. Beside the speed, CAL offers maximal flexibility for the practical implementation. It allows adjusting the scan properties, like scan range or scan speed to the requirement of each application [33

33. J. M. Jabbour, B. H. Malik, C. Olsovsky, R. Cuenca, S. Cheng, J. A. Jo, Y.-S. L. Cheng, J. M. Wright, and K. C. Maitland, “Optical axial scanning in confocal microscopy using an electrically tunable lens,” Biomed. Opt. Express 5(2), 645–652 (2014). [CrossRef] [PubMed]

]. Defocussing techniques [51

51. M. Martínez-Corral, M. Kowalczyk, C. J. Zapata-Rodríguez, and P. Andrés, “Tunable optical sectioning in confocal microscopy by use of symmetrical defocusing and apodization,” Appl. Opt. 37(29), 6914–6921 (1998). [CrossRef] [PubMed]

, 52

52. C. J. R. Sheppard and D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta (Lond.) 31(6), 723–727 (1984). [CrossRef]

] can be easily implemented or detuning due to chromatic errors, which e.g. may arise when the emission wavelength is not known accurately in photoluminescence measurements, can be corrected.

Future work will concentrate on CAL with high NA immersion lenses. These could be used for applications in multi plane lithography.

The usage of adaptive lenses in CMs bears a huge potential for creating fast, flexible and powerful microscopic devices and will surely attract attention in future applications.

Acknowledgments

We thank M.Sc. Joeren von Pock from the chair for Electronic Materials and Nanoelectronics in Bochum for the preparation of the test sample. We also thank Julia Schmidt for her helping hand in the lab and Daniel Haufe for his gentle support.

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R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59(3), 427–471 (1996). [CrossRef]

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R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, “„Triggered polarization entangled photon pairs from a single quantum dot up to 30 K,” New J. Phys. 9(9), 315 (2007). [CrossRef]

7.

D. A. Lange, H. M. Jennings, and S. P. Shah, “Analysis of surface roughness using confocal microscopy,” J. Mater. Sci. 28(14), 3879–3884 (1993). [CrossRef]

8.

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000). [CrossRef]

9.

J. Benschop and G. van Rosmalen, “Confocal compact scanning optical microscope based on compact disc technology,” Appl. Opt. 30(10), 1179–1184 (1991). [CrossRef] [PubMed]

10.

A. E. Dixon, S. Damaskinos, and M. R. Atkinson, “Transmission and double-reflection scanning stage confocal microscope,” Scanning 13(4), 299–306 (1991). [CrossRef]

11.

B. S. Chun, K. Kim, and D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum. 80(7), 073706 (2009). [CrossRef] [PubMed]

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M. Rajadhyaksha, R. R. Anderson, and R. H. Webb, “Video-rate confocal scanning laser microscope for imaging human tissues in vivo,” Appl. Opt. 38(10), 2105–2115 (1999). [CrossRef] [PubMed]

13.

M. Petran, M. Hadravsky, M. D. A. V. I. D. Egger, and R. O. B. E. R. T. Galambos, “Tandem-scanning reflected-light microscope,” J. Opt. Soc. Am. 58(5), 661–664 (1968). [CrossRef]

14.

L.-C. Chen, H.-W. Li, and Y.-W. Chang, ”Full-field chromatic confocal surface profilometry employing DMD correspondence for minimizing lateral cross talks,” Proc. Of SPIE Vol. 832120, Symp. on Precision Eng. (2011). [CrossRef]

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18.

Y. Yasuno, S. Makita, T. Yatagai, T. F. Wiesendanger, A. K. Ruprecht, and H. J. Tiziani, “Non-mechanically-axial-scanning confocal microscope using adaptive mirror switching,” Opt. Express 11(1), 54–60 (2003). [CrossRef] [PubMed]

19.

L. Büttner, C. Leithold, and J. Czarske, “Interferometric velocity measurements through a fluctuating Gas-Liquid interface employing Adaptive Optics,” Opt. Express 21(25), 30653–30663 (2013). [CrossRef] [PubMed]

20.

H. Oku, K. Hashimoto, and M. Ishikawa, “Variable-focus lens with 1-kHz bandwidth,” Opt. Express 12(10), 2138–2149 (2004). [CrossRef] [PubMed]

21.

B. H. W. Hendricks, S. Kuiper, M. A. J. Van As, C. A. Renders, and T. W. Tukker, “Electrowetting-based variable-focus lens for miniature systems,” Opt. Rev. 12(3), 255–259 (2005). [CrossRef]

22.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000). [CrossRef]

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S. Liu and H. Hua, “Extended depth-of-field microscopic imaging with a variable focus microscope objective,” Opt. Express 19(1), 353–362 (2011). [CrossRef] [PubMed]

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K. S. Lee, P. Vanderwall, and J. P. Rolland, “Two-photon microscopy with dynamic focusing objective using a liquid lens,” Proc. SPIE 7569, 756923 (2010). [CrossRef]

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S. Murali, P. Meemon, K.-S. Lee, W. P. Kuhn, K. P. Thompson, and J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (2010). [CrossRef] [PubMed]

27.

F. O. Fahrbach, F. F. Voigt, B. Schmid, F. Helmchen, and J. Huisken, “Rapid 3D light-sheet microscopy with a tunable lens,” Opt. Express 21(18), 21010–21026 (2013). [CrossRef] [PubMed]

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47.

C. J. R. Sheppard and M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30(25), 3563–3568 (1991). [CrossRef] [PubMed]

48.

C. J. R. Sheppard and C. J. Cogswell, “Effects of aberrating layers and tube length of confocal imaging properties,” Optik (Stuttg.) 87, 34–38 (1991).

49.

G. J. Tearney, R. H. Webb, and B. E. Bouma, “Spectrally encoded confocal microscopy,” Opt. Lett. 23(15), 1152–1154 (1998). [CrossRef] [PubMed]

50.

D. K. Kang, H. Yoo, P. Jillella, B. E. Bouma, and G. J. Tearney, “Comprehensive volumetric confocal microscopy with adaptive focusing,” Biomed. Opt. Express 2(6), 1412–1422 (2011). [CrossRef] [PubMed]

51.

M. Martínez-Corral, M. Kowalczyk, C. J. Zapata-Rodríguez, and P. Andrés, “Tunable optical sectioning in confocal microscopy by use of symmetrical defocusing and apodization,” Appl. Opt. 37(29), 6914–6921 (1998). [CrossRef] [PubMed]

52.

C. J. R. Sheppard and D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta (Lond.) 31(6), 723–727 (1984). [CrossRef]

OCIS Codes
(180.1790) Microscopy : Confocal microscopy
(220.1000) Optical design and fabrication : Aberration compensation
(110.1085) Imaging systems : Adaptive imaging

ToC Category:
Microscopy

History
Original Manuscript: January 23, 2014
Revised Manuscript: February 27, 2014
Manuscript Accepted: February 27, 2014
Published: March 6, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Nektarios Koukourakis, Markus Finkeldey, Moritz Stürmer, Christoph Leithold, Nils C. Gerhardt, Martin R. Hofmann, Ulrike Wallrabe, Jürgen W. Czarske, and Andreas Fischer, "Axial scanning in confocal microscopy employing adaptive lenses (CAL)," Opt. Express 22, 6025-6039 (2014)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-5-6025


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References

  1. M. Minsky, “Memoir on inventing the confocal scanning microscope,” Scanning 10(4), 128–138 (1988). [CrossRef]
  2. C. Cremer, T. Cremer, “Considerations on a laser-scanning-microscope with high resolution and depth of field,” Microsc. Acta 81(1), 31–44 (1978). [PubMed]
  3. J. G. White, W. B. Amos, “Confocal microscopy comes of age,” Nature 328(6126), 183–184 (1987). [CrossRef]
  4. J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105(1), 41–48 (1987). [CrossRef] [PubMed]
  5. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59(3), 427–471 (1996). [CrossRef]
  6. R. Hafenbrak, S. M. Ulrich, P. Michler, L. Wang, A. Rastelli, O. G. Schmidt, “„Triggered polarization entangled photon pairs from a single quantum dot up to 30 K,” New J. Phys. 9(9), 315 (2007). [CrossRef]
  7. D. A. Lange, H. M. Jennings, S. P. Shah, “Analysis of surface roughness using confocal microscopy,” J. Mater. Sci. 28(14), 3879–3884 (1993). [CrossRef]
  8. G. Udupa, M. Singaperumal, R. S. Sirohi, M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000). [CrossRef]
  9. J. Benschop, G. van Rosmalen, “Confocal compact scanning optical microscope based on compact disc technology,” Appl. Opt. 30(10), 1179–1184 (1991). [CrossRef] [PubMed]
  10. A. E. Dixon, S. Damaskinos, M. R. Atkinson, “Transmission and double-reflection scanning stage confocal microscope,” Scanning 13(4), 299–306 (1991). [CrossRef]
  11. B. S. Chun, K. Kim, D. Gweon, “Three-dimensional surface profile measurement using a beam scanning chromatic confocal microscope,” Rev. Sci. Instrum. 80(7), 073706 (2009). [CrossRef] [PubMed]
  12. M. Rajadhyaksha, R. R. Anderson, R. H. Webb, “Video-rate confocal scanning laser microscope for imaging human tissues in vivo,” Appl. Opt. 38(10), 2105–2115 (1999). [CrossRef] [PubMed]
  13. M. Petran, M. Hadravsky, M. D. A. V. I. D. Egger, R. O. B. E. R. T. Galambos, “Tandem-scanning reflected-light microscope,” J. Opt. Soc. Am. 58(5), 661–664 (1968). [CrossRef]
  14. L.-C. Chen, H.-W. Li, and Y.-W. Chang, ”Full-field chromatic confocal surface profilometry employing DMD correspondence for minimizing lateral cross talks,” Proc. Of SPIE Vol. 832120, Symp. on Precision Eng. (2011). [CrossRef]
  15. B. F. Grewe, D. Langer, H. Kasper, B. M. Kampa, F. Helmchen, “High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision,” Nat. Methods 7(5), 399–405 (2010). [CrossRef] [PubMed]
  16. W. Göbel, F. Helmchen, “New angles on neuronal dendrites in vivo,” J. Neurophysiol. 98(6), 3770–3779 (2007). [CrossRef] [PubMed]
  17. W. Amir, R. Carriles, E. E. Hoover, T. A. Planchon, C. G. Durfee, J. A. Squier, “Simultaneous imaging of multiple focal planes using a two-photon scanning microscope,” Opt. Lett. 32(12), 1731–1733 (2007). [CrossRef] [PubMed]
  18. Y. Yasuno, S. Makita, T. Yatagai, T. F. Wiesendanger, A. K. Ruprecht, H. J. Tiziani, “Non-mechanically-axial-scanning confocal microscope using adaptive mirror switching,” Opt. Express 11(1), 54–60 (2003). [CrossRef] [PubMed]
  19. L. Büttner, C. Leithold, J. Czarske, “Interferometric velocity measurements through a fluctuating Gas-Liquid interface employing Adaptive Optics,” Opt. Express 21(25), 30653–30663 (2013). [CrossRef] [PubMed]
  20. H. Oku, K. Hashimoto, M. Ishikawa, “Variable-focus lens with 1-kHz bandwidth,” Opt. Express 12(10), 2138–2149 (2004). [CrossRef] [PubMed]
  21. B. H. W. Hendricks, S. Kuiper, M. A. J. Van As, C. A. Renders, T. W. Tukker, “Electrowetting-based variable-focus lens for miniature systems,” Opt. Rev. 12(3), 255–259 (2005). [CrossRef]
  22. B. Berge, J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3(2), 159–163 (2000). [CrossRef]
  23. S. Liu, H. Hua, “Extended depth-of-field microscopic imaging with a variable focus microscope objective,” Opt. Express 19(1), 353–362 (2011). [CrossRef] [PubMed]
  24. K. S. Lee, P. Vanderwall, J. P. Rolland, “Two-photon microscopy with dynamic focusing objective using a liquid lens,” Proc. SPIE 7569, 756923 (2010). [CrossRef]
  25. S. Murali, K. P. Thompson, J. P. Rolland, “Three-dimensional adaptive microscopy using embedded liquid lens,” Opt. Lett. 34(2), 145–147 (2009). [CrossRef] [PubMed]
  26. S. Murali, P. Meemon, K.-S. Lee, W. P. Kuhn, K. P. Thompson, J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (2010). [CrossRef] [PubMed]
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