axial scanning in confocal microscopy employing adaptive ... · this is due to defocus and...

Axial scanning in confocal microscopy employing adaptive lenses (CAL)

Nektarios Koukourakis,1,* Markus Finkeldey,2 Moritz Stürmer,3 Christoph Leithold,1 Nils C. Gerhardt,2 Martin R. Hofmann,2 Ulrike Wallrabe,3 Jürgen W. Czarske,1

and Andreas Fischer1 1Laboratory for Measurement and Testing Techniques, Technische Universität Dresden, Helmholtzstr. 18, 01062

Dresden, Germany 2Photonics and Terahertz-Technology, Ruhr-University Bochum, Universitätsstr. 150, 44801 Bochum, Germany

3Department of Microsystems Engineering-IMTEK Laboratory for Microactuators, University of Freiburg, Georges-Köhler-Allee 102, 79110 Freiburg, Germany

*[email protected]

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

OCIS codes: (180.1790) Confocal microscopy; (110.1085) Adaptive imaging; (220.1000) Aberration compensation.

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#205312 - $15.00 USD Received 23 Jan 2014; revised 27 Feb 2014; accepted 27 Feb 2014; published 6 Mar 2014(C) 2014 OSA 10 March 2014 | Vol. 22, No. 5 | DOI:10.1364/OE.22.006025 | OPTICS EXPRESS 6025

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1. Introduction

Confocal microscopy (CM) was originally invented by Minsky in 1957 [1] on his search to overcome limitations of traditional wide-field fluorescence microscopes. The technique achieved its breakthrough as confocal laser scanning microscopy (CLSM) [2] which is mainly used in life-sciences for imaging cells or tissues that are marked with fluorescent probes [3, 4]. The key advantage of CM is introduced by the illumination using a strongly confined diffraction-limited spot and pinhole-based detection, which effectively reduces out-of focus light to reach the detector. This leads to an enhanced depth-discrimination capability compared to conventional microscopes. In case of fluorescent samples this means that the fluorescence excited across the beam propagation path in out-of focus regions does not contribute to the image. This results in an improved axial resolution. Additionally, as this spatial filtering represses side-lobes, the effective lateral resolution is also improved [5]. These capabilities opened up further applications in material science e.g. in profilometry or semiconductor characterization [6–8].

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] and adapted by several others, the sample was moved across the focus in all three dimensions [9, 10]. 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]. This is not practical for the usage at biological samples [11]. 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) [12–14]. 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].

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]. 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 [17–20]. Especially the latter have undergone a rapid development in the last years [20–22], which led to several applications like e.g. in extended depth-of-field imaging [23], in fast axial focusing in two-photon microscopy [24], optical coherence microscopy [25, 26] and light-sheet microscopy [27]. This list can be extended by a huge number of potential application areas such as phase retrieval [28], flow measurements [29] and shape measurements [30]. 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] 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]. 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]. 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, 35]. 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]. 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) 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]. 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.

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.

2.2. Fabrication

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

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)]. 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.

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.

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). 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.

Fig. 3. Confocal microscope employing adaptive lenses (CAL) in the illumination and the detection path.

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.

Fig. 4. a) Block diagram of the setup. b) Test-chart.

The pinhole used has a diameter of dpinhole = 10 µm, which corresponds to about 0.6 airy units (AU). The efficiency of the system, i.e. the ratio of the intensity in focus and the integrated intensity in the pinhole, is simulated to be ~10%. Read-out of the intensity at the set position is performed as shown in Fig. 4(a). Applying voltage to AL1 allows shifting the focus axially. In the experiments described in the next section we just use positive electrical voltages for UAL1. Thus the focus of the lens shifts between fU = 0 V = −800 mm and fU = + 40 V = + 150 mm. The lateral scan in our case is implemented using stage-scanning. A


Newport LTA-HL (M-MVN80) is used for axial and two Newport LTA-HS (M-462) for lateral high-precision positioning, to move the sample through the focus in three dimensions.

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].

4.1. Tuning the focal volume with AL1

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.

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]. For clarity, we call the stage-based scan A-scan. The results are shown in Fig. 5.

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]:

2

2 20.67 1 4 .z AU µm

n n NA

λΔ = + ≈− −

(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].

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

r kNA

λΔ = ⋅ (2)

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].

A commonly used value for the constant is k = 0.51, for AU = 1 [43]. The lateral resolution can be even improved by more than 40% compared to the Abbe limit for very small pinholes (AU<0.1) [43]. 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 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 function ( )P θ , i.e. the wave-front at the pinhole, has a

constant phase. In presence of aberration the pupil function can be expressed as:

1 1( , ) exp( ( , )).AL AL ALP U j Uρ ρ= Φ (3)

ALΦ is the phase at the exit pupil and ρ is 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.

Fig. 7. Scheme of the simulated aberrated focal volume.

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]. The spherical aberration can be expressed as

4 21 1 1( , ) ( ) ( )AL S AL D ALU A U B Uρ ρ ρΦ = + , where SA is the coefficient of spherical aberration of

the wave-front and DB is the defocus coefficient [45]. 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 as 28 SF AΔ = , where F is the focal ratio of

the image-forming light cone [45]. Both F and SA change with 1ALU . At the CoC the

spherical wave-front aberration is minimum and the Strehl ratio maximum [46]. 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 as 4 2

1( , ) ( )bal AL SU Aρ ρ ρΦ = − , with S DA B= − .


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). 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 ( )ρΦ can be expressed as the weighted sum of Zernike polynomials

Z using:

1 ,( ) .

AL

f fU n nn f

c ZρΦ = Σ (4)

The defocus, the primary and secondary spherical aberrations are given by Eqs. (5a) to (5c) [46].

0 22 ( ) 2 1Z ρ ρ= − (5a)

0 4 24 ( ) 6 6 1Z ρ ρ ρ= − + (5b)

0 6 4 26 ( ) 20 30 12 1.Z ρ ρ ρ ρ= − + − (5c)

Here the Zernike expansion coefficients 20c , 40c and 60c are 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 1 0ALU V= the 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.

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.

With increasing voltage the observation plane shifts away from the CoC and both defocus and primary spherical aberrations increase [Fig. 8(a)]. 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, 48]. 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

2ALU . 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.

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.

The results are summarized in Fig. 9. 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.

At UAL2 = −8 V both peaks start melting together resulting in the perfect overlap for UAL2 = 0 V which has the smallest FWHM and the highest intensity. Further increasing UAL2 shifts the confocal peak away from the focal volume and the second peak appears again [Fig. 9(d)]. Applying a voltage detunes the system and the increasing FWHM deteriorates the axial resolution. The detuning also leads to a drop of the intensity as the confocal plane is tuned away from the CoC. Figure 10(a) shows simulated results on the detuning from the CoC. It is evident that just small changes of voltage detune the observation plane which is accompanied by increasing aberration influences [Fig. 10(b)]. But it also follows that AL2 indeed allows shifting the observation plane. The aberrations introduced by AL2 itself are negligible in comparison to the ones induced by the illumination lens system. Still AL2 has a strong impact as tuning 2ALU shifts the confocal plane and selects which aberrations reach the pinhole.

Hence, it should be possible to balance the changing spherical aberrations during the z-scan employing AL2. This will be discussed in the next section.

Fig. 10. Simulated detuning of the initially aligned setup. a) and b) Increasing 2ALU shifts the

observation plane away of the CoC. This consequently increases the influence of the aberrations.

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) 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.

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.

Experimental results are plotted in [Fig. 12(a)]. 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.

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.


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] or a comprehensive volumetric design introduced in [50] 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]. Defocussing techniques [51, 52] 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.


axial scanning in confocal microscopy employing adaptive ... · this is due to defocus and...

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