Submitted at Applied Physics Supervisor Univ.-Prof. Dr. Thomas A. Klar Supervisor
Assoc. Prof. PhD. J¨org Bewersdorf
April 2018
JOHANNES KEPLER UNIVERSITY LINZ Altenbergerstraße 69
Adaptive Optics in
Two-Photon Microscopy and
Two-Photon Lithography
Master Thesis
to obtain the academic degree of
Diplom-IngenieurIn
in the Master’s Program
I declare that I have authored this thesis independently, that I have not used other than the declared sources/resources, and that I have explicitly indicated all material which has been quoted either literally or by content from the sources used. The text document uploaded online is identical to the present master‘s thesis.
Two-photon microscopy has become an indispensable tool in biological re-search allowing imaging of intracellular structures especially deep in tissue. Due to its capability of three-dimensional (3D) fabrication in lithography, two-photon excitation is also an essential tool for nanofabrication. However, both two-photon microscopy and two-photon lithography suffer from aberra-tions that are introduced by spatial variaaberra-tions in the refractive index of the specimen, leading to compromised image and structure quality. Specimen-induced aberrations can be compensated by adaptive optics. In this thesis, I propose a new correction scheme for two-photon microscopy and two-photon lithography adaptive optics, namely poke mode aberration correction. This new scheme simplifies the communication between the wavefront sensor and the deformable mirror, therefore eliminating the need for multiple conversions and in turn the potential to minimize the amount of error introduced during analysis. Using this new control system, we demonstrate that test aberrations can be reliably compensated using the developed feedback loop. In addition, aberrations induced by biological tissue, e.g. a 50 µm and 85 µm thick section
and image quality. Furthermore, preliminary two-photon lithography fabri-cated structures illustrate the potential of smoother structure surfaces when aberration correction is conducted with the new control system.
Firstly, I would like to express my gratitude to my advisors Univ. Prof. Dr. Thomas A Klar and Assoc. Prof. PhD. Joerg Bewersdorf for the useful com-ments, remarks and engagement through the learning process of this master thesis. Moreover, I would like to thank them for supporting me making it possible to conduct my research work abroad.
My sincere thanks also go to Ph.D. Xiang Hao who has provided me extensive personal and professional guidance.
Furthermore, I want to express my special thanks to Mary Grace Velasco for providing me with unfailing support and continuous encouragement through-out the process of researching.
University for making my research stay as delightful as it was.
Thanks also go to Dr. Jaroslaw Jacak who supported me during the prepa-ration for my research work abroad and for his guidance during my education.
Further thanks also go to the Lithography Group in the Applied Physics Department at JKU.
Abstract v
Acknowledgements vii
1. Introduction 1
2. Background 5
2.1. Two-Photon Microscopy and Lithography . . . 5
2.1.1. Fluorescence Microscopy . . . 6 2.1.2. Optical Lithography . . . 11 2.1.3. Two-Photon Excitation . . . 14 2.1.4. Two-Photon Microscopy . . . 16 2.1.5. Two-Photon Lithography . . . 17 2.2. Adaptive Optics . . . 18
2.2.1. Adaptive Optics Background . . . 19
2.2.2. Adaptive Optics Systems . . . 21
2.2.4. Sensor-less Adaptive Optics . . . 26
2.2.5. Adaptive Optics in Microscopy and Lithography . . . . 27
3. System Design 29 4. Characterization 33 4.1. The Implemented Adaptive Optics System . . . 33
4.1.1. Theory of the Modes from Wavefront Slopes . . . 34
4.1.2. Implementation of the Adaptive Optics System . . . 37
4.2. Adaptive Optics System Simulation . . . 42
4.2.1. Simulation of the Combined System . . . 43
4.2.2. Simulation Results . . . 46
4.3. Adaptive Optics System Testing . . . 47
4.3.1. Linearity of the Adaptive Optics Element . . . 48
4.3.2. Stability of the Adaptive Optics Element . . . 51
4.3.3. Calibration Testing . . . 52
4.3.4. Aberration Correction of Artificial Aberrations . . . 54
5. Preliminary Applications 61 5.1. Adaptive Optics in Microscopy . . . 61
5.1.1. Sample Preparation . . . 62
5.1.2. System Calibration . . . 62
5.1.3. Imaging through 50 µm and 85 µm Mouse Brain Tissue 63 5.1.4. Discussion . . . 66
5.2. Adaptive Optics in Lithography . . . 67
5.2.2. Sample Preparation . . . 68 5.2.3. Fabrication of 30 µm Polymer Lines . . . 69 5.2.4. Discussion . . . 70
6. Conclusion and Outlook 73
Bibliography 79
A. Sample preparation 89
A.1. Photoresist . . . 89 A.2. Sample Preparation Microscopy . . . 90 A.3. Sample Preparation Lithography . . . 90
2.1. Jabłonski Diagram . . . 8
2.2. Confocal Microscope . . . 11
2.3. Radical Polymerization . . . 12
2.4. Polymer Conversion Threshold . . . 13
2.5. Jablonski Diagram for Two-Photon Absorption . . . 15
2.6. Single-Photon Excitation vs. Two-Photon Excitation . . . 15
2.7. Adaptive Optics Principle . . . 21
2.8. Deformable Mirror . . . 23
2.9. Shack-Hartmann Wavefront Sensor . . . 25
3.1. Two-Photon Excitation Stimulated Emission Depletion Setup . 31 4.1. Sensor-less Adaptive Optics Correction . . . 39
4.2. Control Loop for Closed-Loop Aberration Correction . . . 41
4.3. Simulation - Calibration Steps . . . 45
4.4. Simulation - Example . . . 46
4.6. Characterization - System Stability . . . 51
4.7. Characterization - Poke Matrix Height Determination . . . 54
4.8. Artificial Aberrations - Poke Aberration Correction . . . 56
4.9. Artificial Aberrations - Deformable Mirror Shapes . . . 57
4.10. Artificial Aberrations - Shack-Hartmann Spot Diagrams . . . . 58
4.11. Artificial Aberrations - Analysis of Random DM Pattern 1 . . . 59
4.12. Artificial Aberrations - Analysis of Random DM Pattern 2 . . . 60
5.1. Microscopy - Sample Sketch . . . 62
5.2. Microscopy - Bead Image through 50 µm Mouse Brain Tissue . 64 5.3. Microscopy - Bead Image through 85 µm Mouse Brain Tissue . 65 5.4. Lithography - Photoresist’s Chemical Structures . . . 68
5.5. Lithography - Sample Sketch . . . 68
3D three-dimensional
AO adaptive optics
AOM acousto-optic modulator
AOS adaptive optics system
DM deformable mirror
EOM electro-optic modulator
FITC fluorescein
FOV field of view
IR infrared
NIR near infrared
NIV normalized influence vector
NL-GS nonlinear guide-star PBS phosphate-buffered-saline
PSF point spread function
ROI region of interest
SHWFS Shack-Hartmann wavefront sensor SLM spatial light modulator
SNR signal-to-noise ratio
SPE single-photon excitation
SPP single-photon polymerization
STED stimulated emission depletion
SVD singular value decomposition
TPA two-photon absorption
TPE two-photon excitation
TPM Two-photon microscopy
TPP two-photon polymerization
UV ultraviolet
Fluorescence microscopy is an indispensable tool in biological investigations, allowing imaging of intracellular structures [1], [2]. A wide variety of labeling techniques enables the visualization of structures of interest in biological systems, thus leading to a better understanding of biological processes [2], [3]. The invention of confocal [4] and multiphoton microscopes [5] improved the acquisition of 3D information of the studied specimen, hence, enabling studies of new 3D cellular complexes and their mechanisms. Through the 3D sectioning capabilities of these two methods, deep tissue imaging is also pushed forward.
Deep tissue imaging, even with the improvement of confocal or two-photon excitation, is prone to a reduction in signal, contrast and resolution. Spatial variations in the refractive index of the specimens lead to a compromise in image quality. These specimen-induced aberrations can be corrected by the introduction of adaptive optics (AO) [6], [7]. Traditionally, AO has been used in the field of astronomy to address the aberrating effects of atmospheric turbulence during imaging [7]. To apply this technique to microscopy, an
adaptive element is implemented into the optical system. This adaptive ele-ment corrects for specimen-induced aberrations, restores the image quality and therefore allows imaging deeper into the specimen [8].
Optical systems are also central to optical fabrication techniques such as opti-cal lithography enabling nanofabrication. Feature sizes with sub-wavelength sizes (<100 nm) can be achieved through the use of nonlinear, thresholded
op-tical processes [9]. As in microscopy, these methods are detrimentally affected by aberrations introduced by refractive index mismatches in the specimen, which compromises the efficiency and accuracy of the fabrication process. AO is also applicable here and can be used to maintain the focal spot quality [7].
AO correction for sample-induced aberrations is performed in several ways [8]. In this thesis, a new control loop for a sensor-based adaptive optics system (AOS) is discussed. This new control mechanism minimizes the number of conversions used in more traditional control schemes. Furthermore, the new control loop has an easy in situ calibration implemented, which allows immediate recalibration after changes in the optical system. The overall goal of this thesis is to improve the image quality in deep tissue imaging as well as the structure fabrication in two-photon polymerization (TPP) with an easy implementation of an AOS.
This thesis comprises the following chapters. Chapter 2 presents an overview of microscopy, lithography and adaptive optics, especially focusing on the techniques used in this thesis. Chapter 3 describes the microscopy setup with the implemented AOS. Chapter 4 focuses on the AOS, starting with a
de-limit and testing the AOS. Examples of aberration correction of user-induced artificial aberrations via the deformable mirror (DM) complete this chapter. Chapter 5 illustrates first preliminary applications in microscopy and lithogra-phy using the implemented AOS with the new control loop scheme. Chapter 6 concludes this thesis, discussing the observed results and providing an outlook on further research.
2.1. Two-Photon Microscopy and Lithography
Fluorescence microscopy is a vital tool in the life sciences, enabling the visual-ization of small structures in biological specimens. In particular, fluorescence microscopy allows the investigation of cellular processes in living specimens [10], including processes beyond the diffraction-limit of light [11]. Some mi-croscopy techniques can also be used for optical lithography allowing structure fabrication in the nanometer range. Nanostructurization leads to a huge range of applications in microelectronics [9].
In this section two-photon microscopy and two-photon lithography are briefly discussed. First, an overview of fluorescence microscopy starting from fluores-cence, the basic principle of fluorescence microscopy to confocal microscopy will be given. Then a brief history of optical lithography and its techniques is described. Afterwards an introduction to two-photon absorption is provided.
At the end, two-photon excitation (TPE) in microscopy and lithography is discussed.
2.1.1. Fluorescence Microscopy
Fluorescence
Fluorescence is the spontaneous emission of light by a fluorescent molecule called fluorophore after excitation by an external source [12, 13]. Alexander Jabłonski was the first to summarize the absorption and emission process of a photon in a fluorophore and illustrated the process in the Jabłonski diagram, see Figure 2.1 [13].
The horizontal lines depict the electronic energy levels, singlet ground state (S0), first excited state (S1) and second excited state (S2), with their correspond-ing vibrational energy levels 0, 1, 2.1 An external light source, e.g. a laser, with an appropriate excitation energy excites a fluorophore from its ground state S0 to a vibrational mode of the excited state S1 or S2 (purple or blue line). The fluorophore usually undergoes internal conversion - a non-radiative transition - (dashed lines) to the lowest vibrational level of S1 in less than 10 12s. Fluorescent emission occurs by the transition of the fluorophore from
1Typically, a fluorophore has more than three vibrational energy levels. To simplify the
its first excited state S1 to a vibrational level of the electronic ground-state (green lines). The average lifetime of the first excited state is referred to as the fluorescence lifetime, which is of the order of nanoseconds. After emitting light the molecule relaxes in the time range of 10 12s via internal conversion to the thermal equilibrium [12, 13]. In contrast to a fluorescence transition, the fluorophore can also undergo intersystem crossing (orange line) by spin conversion into the so-called first triplet state T1. The resulting emission from the transition of the first triplet state T1 to the singlet ground state S0, called phosphorescence, is spin forbidden and hence, has a slower emission rate with lifetimes of up to milliseconds or seconds (red lines). The energy difference for phosphorescence is smaller than for fluorescence, resulting in a larger wavelength [12, 13].
Noticeable is that the photon absorption energy is typically higher than the emission energy, which is caused by the energy loss during internal conversion before and after emission. Thus, the fluorescence wavelength is longer than the absorption wavelength. This effect is called Stokes shift [13].
Figure 2.1.: Jabłonski Diagram. A fluorophore is excited from the ground state S0to a vibra-tional state of an excited state Si such as the first excited state S1 or the second excited state S2and lowers its energy through internal conversion to the first singlet
state S1. Fluorescence emission occurs by the transition of the excited state to the ground state. However, the fluorophore can undergo intersystem crossing to a triplet state and therefore phosphorescence will occur by the transition from the triplet state to the ground state.
Fluorescence Microscopy
Fluorescence microscopes take advantage of the emission of fluoresence light by fluorophores [13]. Within a specimen, structures of interest get labeled with selective fluorophores to allow their visualization. After excitation with a light source at a suitable wavelength, which is coupled into the objective lens by a dichroic mirror, the fluorophore emits light at a longer wavelength.
The emitted light is then collected by the objective lens. After filtering the collected light from the scattered background light and the backscattered excitation light with appropriate filters, the emitted fluorescence is detected by a detector, for example the eye or a camera. Thus, the labeled structures can be reconstructed [10]. Multiple targets can be imaged simultaneously if different labeling strategies as well as the right fluorophores for the imple-mented excitation laser and the appropriate emission filters are combined [14]. The capability to resolve two target organelles as distinct is determined by the resolution of the microscope. The resolution is defined as the shortest distance between two objects at which a specified contrast is achieved [15]. A major drawback of wide-field illumination, where the whole specimen in the beam path is exposed, is the lack of optical sectioning due to the simultaneous emission of fluorophores located in several image planes. This leads to high background in images and consequently reduces the image quality. In 1961, M. Minsky addressed this challenge by introducing confocal imaging [4].
Confocal Microscopy
In confocal microscopy, optical sectioning is achieved by using a point-like illumination source (e.g. a laser focus) and a pinhole in front of the detector, see Figure 2.2. The pinhole in front of the illumination source reduces the illu-mination to a point-like illuillu-mination of the specimen. Consequently, scanning
of the specimen is inevitable. The additional pinhole in front of the detector suppresses out-of-focus light. Thus, light originating from the focus is imaged by the microscope objective in such a way that it freely passes the pinhole, whereas out-of-focus light is largely blocked by the detection pinhole. Since the pinholes reduce the amount of scattered light, the resolution improves. These modifications lead to an enhancement in lateral resolution by a factor of
⇠0.7 [16, 17]. The axial resolution amounts to approximately an order of one wavelength. While the resolution improves due to these modifications, the specimen has to be scanned and the detected signal intensity decreases due to the detection pinhole. To compensate for the lower signal intensity, the power of the point-like illumination source can be increased [13]. In deep tissue imaging scattering will prevail, leading to a smaller signal-to-noise ratio (SNR) in confocal microscopy. Thus, pushing TPE as the method of choice since it shows its benefits to the fullest by minimizing scattering in the sample, see section 2.1.4 [18, 19].
Figure 2.2.: Confocal Microscopy. The conjugated illumination and detection pinholes reduce the excitation and detection volume. Thus, only signal from the focal volume (green) is detected. Out of focus light (red) will be blocked by the detection pinhole. This enables optical sectioning in axial direction.
2.1.2. Optical Lithography
Optical lithography refers to photopolymerization induced by light in the ultraviolet (UV), visible or infrared (IR) spectral region. Photopolymerization is the process of using light as an energy source to induce the conversion of small unsaturated molecules in the liquid state to solid macromolecules through a polymerization reaction [9]. The starting material, called photoresist, consists of at least two components, a monomer and a photoinitiator [20]. Photopolymerization typically proceeds when a chromophore, a photoinitiator, absorbs a photon and subsequently generates active centers that initiate the
polymerization reaction [21, 22], see Figure 2.3. After initiation (2.3 A), chain propagation follows (2.3 B). The produced active centers at the monomer, which were generated through the active centers of the photoinitiator, combine with new monomers and so on; leading to a chain reaction. This chain reaction terminates (2.3 C) through the binding of two active centers or the stabilization of the active center with impurities [9, 23].
Since optical lithography, similar to fluorescence microscopy, takes advantage of the absorption of light, the same setup can be used for both.
Figure 2.3.: Radical polymerization. A A photoinitiator absorbs light and subsequently gen-erates active centers that initiate the polymerization reaction. B The active center cross-links to a monomer and creates an active center at the monomer. C This cross-linking step is carried on until termination through another active center or an impurity occurs. Figure from [24].
The photoresist’s behavior under light irradiation is described by a threshold model, see Figure 2.4. Regions that are exposed with at least the threshold value will change their functionality, whereas regions exposed below the threshold will remain unaffected. Therefore, polymer structures will only withstand the development process when the exposure dose reaches a certain
threshold. Smaller features can be achieved by lowering either the irradiation intensity or the exposure time [21, 25]. In this manner, arbitrarily small features in lateral direction can be reached [25]. However, the contrast between the conversion of the gelled, insoluble material and the ungelled, soluble material is reduced. This results in loosely cross-linked, unstable structures unable to withstand the solvent processing that is necessary for device fabrication. Furthermore, the axial resolution is typically in the micrometer-scale for single-photon polymerization (SPP) limiting the fabrication of smaller layers [21]. The emergence of a new technology in 1997, TPP [26], has addressed this challenge realizing the fabrication of 3D nanostructures with feature sizes below the diffraction limit [9, 21].
Figure 2.4.: Polymer conversion over illumination cross section. The peak conversion g quanti-fies the mechanical stability at the feature center. The width after development is determined by the gelation threshold. Photoresist above the threshold is insoluble after conversion. The rest of the photoresist remains liquid. When the illumination power is decreased (g!0) smaller features with less stability will result. In theory, arbitrarily small structures can be obtained. Figure from [21]
2.1.3. Two-Photon Excitation
In 1931, Maria G¨oppert-Mayer proposed the simultaneous absorption and emission of two photons in an atom [27]. A simplified Jabłonski diagram of the two-photon absorption (TPA) process is shown in Figure 2.5. TPE is a nonlinear process where its absorption rate depends on the square of the light intensity. The intensity of a focused laser is highest at the focus and drops off approximately quadratically with the axial distance from the focus. As a result, excitation almost exclusively occurs in a diffraction limited focal volume, see Figure 2.6 b [13, 19]. Depending on the numerical aperture of the objective and the wavelength, the two-photon volume can be as small as
⇠0.1 µm3 or⇠100 attoliters [17].
The number of absorbed photons N per second by TPE is given by
N=s2I2 (2.1)
whit s2 the absorption coefficient for TPE and I the intensity [13]. The absorp-tion coefficient in TPE is, compared to single-photon excitaabsorp-tion (SPE), rather small. Therefore, ultra short pulsed lasers are used for TPE.
Figure 2.5.: Simplified Jabłonski diagram of a two-photon absorption process. A fluorophore is excited from the ground state S0to the first excited state S1by the simultaneous absorption of two photons. The figure illustrates the simplest version of Maria G¨oppert-Mayer’s theoretical prediction in fact the simultaneous absorption of two photons with the same wavelength.
Figure 2.6.: Single-photon vs. two-photon excitation. (a) Single-photon excitation (l=488 nm) of fluorescein. (b) Two-photon excitation (l=960 nm). Both beams are focused through a 0.16 NA objective. At two-photon excitation, in comparison to one-photon excitation, only localized excitation of the fluorescein solution is shown. Figure from [17]
2.1.4. Two-Photon Microscopy
Denk et al. demonstrated the practical realization of a two-photon laser scan-ning microscope in 1990 [5]. Two-photon microscopy (TPM) uses the simplest version of Maria G¨oppert-Mayer’s theoretical prediction. An excitation equiv-alent to the absorption of a single photon possessing twice the energy is produced by two photons of about equal energy from the same laser which then interact simultaneously with a molecule [17]. Due to the fact that in TPM fluorophores are only excited in the rather small TPE focus volume, photo-bleaching and photo-damage along the axial direction are reduced [17, 19, 28].
TPE, compared to one-photon techniques, provides three advantages for microscopy in scattering specimens leading to improved live-cell or deep tissue imaging with TPM. First, NIR radiation penetrates tissue better due to reduced scattering. Second, scattered excitation photons are too dilute to cause perceptible TPE fluorescence. This holds true even deep in tissue where most of the photons are scattered. Third, all fluorescence photons, even scattered photons, contribute to useful signal if they are detected since practically all originate from the laser focus. Thus, TPM provides optical sectioning without a pinhole resulting in a simpler detection path because de-scanning is redundant [19]. These enhancements thus enable imaging deeper in the specimen.
Quality and Resolution of Two-Photon Microscopy
Using two-photon instead of one-photon excitation of fluorophores can enable 3D resolution comparable to confocal microscopy without intensity loss due to a pinhole [5]. This intensity preservation can lead to better images, because there is no actual fluorescence degradation which decreases the contrast in non-confocal fluorescence microscopy [13, 28]. In deep tissue imaging, the effective resolution of TPE compared to confocal microscopy seems improved although the wavelength is approximately doubled [17].
2.1.5. Two-Photon Lithography
TPP with visible light was introduced by Maruo et al. in 1997 [26]. As indicated by the name, two photons at longer wavelengths are absorbed simultaneously reducing the effective exposure volume to a small volume, called voxel, in the focal region [25]. This enables the fabrication of 3D structures. Therefore, TPP has a large variety of applications in micro-electronics [9].
TPP has two advantages compared to single-photon absorption. First, near infrared (NIR) absorption is negligible in common polymers enabling struc-turization deep in the photoresist with negligible crosslinking of the material outside of the photoresist. Secondly, 3D spatial resolution is enabled [9].
2.2. Adaptive Optics
Adaptive optics (AO) is used to improve the performance of an optical signal by using information about the environment which it passes [29]. In 1953, Babcock proposed a method for improving the performance of a telescope by compensating for atmospheric distortions using a deformable optical element which is driven by a wavefront sensor (WFS) [30]. In the early 2000s, AO methods were adapted for microscopy to compensate for specimen-induced aberrations instead of atmospheric turbulence [7].
This section will describe the overall principle of adaptive optics in microscopy and lithography. Starting from the source of aberrations, the basic principle of AO is explained. Afterwards a brief overview of AOSs with a focus on devices used in the system’s implementation is provided. Then the two common methods for AO, namely sensor-based AO and sensor-less AO, are discussed. At the end, a brief overview of the development and state of the art of AO is reviewed.
Aberrations
A microscope’s resolving power is limited by the phenomenon of the diffrac-tion of light [31, 32]. However, in practice deviadiffrac-tions in the optical system and the specimen cause distortion of the focus from the diffraction-limit. These
de-viations are known as aberrations. Aberrations in microscopy and lithography have at least three main causes. First, the intrinsic optical element’s quality and their misalignment [6, 7, 8, 33]. Second, one of the most studied specimen geometries, a planar refractive index mismatch when passing from the objec-tive to the immersion media to the cover glass [34]. Third, a more significant challenge, the complex aberration introduced by the optically inhomogeneous structure of biological specimens [8, 6, 7, 33]. Small but measurable refractive indices variations of biological materials and organelles have been found in measurements [35]. These variations induce significant aberrations in thick samples, especially during deep tissue imaging [7]. In addition, scattering of specimens also reduces the image quality [33, 36]. These aberrations lead to a spreading of the focus in the sample, both in axial and lateral directions, decreasing the contrast of the microscope images [6, 8, 37]. As a consequence, the resolution and the intensity reduces, ultimately limiting the depth at which imaging is practical [7, 33, 38]. The induced aberrations can be removed by the introduction of the opposite phase aberration into the optical path, which is done dynamically by AO [6, 38].
2.2.1. Adaptive Optics Background
AO is a technique to optimize and in the best case restore the optimum resolution of an optical system.
be determined. To do so, a WFS for measuring the phase of the distorted wavefront is usually implemented. This approach is called sensor-based AO. Another approach for measuring the aberrated wavefront is an indirect process, which is called sensor-less AO. Both methods will be discussed in detail in the following sections. Compensation is then performed with an adaptive optical element. This adaptive element introduces an equal but opposite aberration to that measured in the optical path. As the sum of these two aberrations is zero, un-aberrated operation, in principle, is restored. The adaptive optics system is driven by a control, typically a computer [7, 39].
Figure 2.7 shows the principle of a conventional closed-loop AOS. Light from the guide star in the region of interest (ROI) is captured by an objective and sampled by the WFS. The control computer then calculates the necessary compensation and applies it to the corrector.
Figure 2.7.: A conventional closed-loop adaptive optics system. The non-linear guide star from the ROI is captured by an objective and imaged onto a wavefront sensor. The control computer calculates the compensation and applies it to the corrector. Figure adapted from [39]
2.2.2. Adaptive Optics Systems
Adaptive optics system (AOS) have been developed for many different appli-cations, each taking into consideration the microscope type (e.g. wide-field, confocal, two-photon etc.), as well as the excitation lasers used and the spec-imens being probed. In a TPM for example, aberration correction has to be applied just in the excitation beam path. Aberrations induced in the emission path do not affect image quality due to large area detectors, which act as fluorescent light collectors [6, 33, 40]. In confocal microscopy, on the other
hand, both excitation and collected beams need to be compensated because of the confocal aperture [33, 40, 41].
Adaptive Optics Elements
Aberrations can in principle be removed in the form of static correction plates, such as binary phase plates [42]. However, aberrations vary among specimens and even among different regions of the same specimen. Thus, dynamic correction elements such as spatial light modulators (SLMs) or deformable mirrors (DMs) are preferable [8].
Liquid Crystal Spatial Light Modulator SLMs modulate the incident light corresponding to optical or electronic properties, performing a modulation of phase and intensity [43]. SLMs are highly motivated by their compactness, high density (e.g.: panel resolution⇠4000x2100, pixel pitch 4 µm) and low cost. Therefore, SLMs have been employed in several AOSs [6, 44, 45]. However, SLMs liquid crystal devices are polarization and wavelength dependent, which is not compatible with fluorescence microscopy.
Deformable Mirror In microelectromechanical DMs, a reflective membrane is positioned between a transparent electrode and a series of individual elec-trodes, also called actuators, at the back of the mirror, as shown in Figure
2.8. When no voltage is applied, the membrane is assumed to remain flat. When a voltage is applied to the electrodes, the electrostatic attraction be-tween the electrodes deforms the membrane into the desired shape [43]. DMs have their advantages in the wavelength and polarization independence and additionally ensure high optical efficiency with low optical losses [7]. Further-more, subnanometer positioning precision, repeatability and stability have been demonstrated, which has made them very attractive for high-contrast microscopy applications [46].
Figure 2.8.: Implementation of a deformable mirror. A deformable mirror consists of multiple actuators, which are arranged in a grid pattern. When applying a voltage to the several actuators, the shape of the reflective membrane changes. Figure from [43]
Wavefront Sensors
Before aberration correction can be performed in a sensor-based AOS, the wavefront needs to be sensed to measure the induced aberration. Several types of wavefront sensing have been developed for sensor-based AO, the most
prominent being interferometric sensors and the Shack-Hartmann wavefront sensor (SHWFS) [7, 47]. Since a SHWFS detecting a non-linear guide star is incorporated in the implemented AOS, both will be discussed in more detail.
Non-linear guide star In order to determine the aberration introduced by a sample, a light source needs to be present in the ROI enabling its wavefront detection with a wavefront sensor for sensor-based AO. Since TPE provides a small confined volume, the excited fluorescence can be used as an incoherent secondary light source, called nonlinear guide-star (NL-GS), for wavefront sensing. The key point for the NL-GS concept is that fluorescence is an incoherent process and thus does not contain information about the aberration gained by the excitation beam. Therefore, a single pass aberration scheme, where the light source for aberration detection passes the aberrating medium only once, can be implemented with a NL-GS [33, 48].
Shack-Hartmann Wavefront Sensor A SHWFS consists of a lenslet array, which is an aperture with small lenses, so called microlenses, and a camera, shown in Figure 2.9. The impinging wavefront is focused by the lenslet array onto the camera generating a so-called spot diagram. Thus, the wavefront slope in each subaperture is measured by the deflection of the focused spot, as displayed on the left. When a planar wavefront enters the SHWFS, the wavefront, case B in figure 2.9, in each subaperture is parallel to each lenslet’s
lateral axis. Therefore, each plane wavefront will be focused on the lenslet’s center. However, when an aberrated wavefront impinges onto the SHWFS, the wavefront at some subapertures will have a tip/tilt regarding to the lenslet’s lateral axis resulting in a displacement of these focal spots, see case A [47, 49].
Figure 2.9.: Principle of a Shack-Hartmann wavefront sensor. The impinging wavefront is sampled by a lenslet array, which focuses the wavefront onto a CCD camera. On the left the front few of the CCD camera is shown. When an aberrated wavefront impinges onto the lenslet array, the spots will be displaced on the camera in regard to the lenslet’s center positions, see case A (red). However, if a planar wavefront impinges, the lenslets will focus the wavefront in their centers and no displacements are present, see case B (green).
2.2.3. Sensor-based Adaptive Optics
In sensor-based AO, the correction is performed by an explicit determination of the optical aberrations through a sensing device such as an interferometer or WFS. These methods need a point-like reference source in the ROI to detect a well-defined wavefront [7, 49]. Several reference sources have been developed for wavefront sensing. In some AOS, beads are placed within the specimen either using microinjection needles or negative pressure protocols to create the reference source. However, this is prone to cause sample damage and therefore limiting its potential for in vivo imaging [33, 50]. As another reference source reflected or scattered light is used. This can cause ambiguity in the wavefront measurement due to coherent interaction between the incident and reflected light [7, 51]. In nonlinear microscopy the guide star concept is adopted from astronomy. Thus, the WFS (e.g. SHWFS etc.) can measure the specimen aberrations by the use of a fluorescent guide star excited by TPE [33].
2.2.4. Sensor-less Adaptive Optics
Another common aberration sensing technique is called sensor-less AO. This is an indirect approach, which, in contrast to sensor-based AO, never measures the explicit wavefront. More precisely, it optimizes the photodetector signal via a sequence of images using optimization schemes. Although optimized
algorithms to reduce specimen exposure have been reported, the ROI still has to be exposed a considerable number of times, which might not be feasible for some applications [7, 49].
2.2.5. Adaptive Optics in Microscopy and Lithography
Since the adoption of AO from astronomy to microscopy in the early 2000s, AO has progressed tremendously in microscopy. One of the first implementations of AO in microscopy was a tip/tilt correction in a transmission confocal microscope [52]. A DM for aberration correction in a confocal fluorescence microscope was successfully implemented in 2002 [53]. As TPM is normally used for imaging thick specimens, AO was also implemented in TPM early on and is still advancing [6, 54]. Newer approaches use NL-GSs as source for wavefront sensing. Since TPE naturally produces a small confined volume, this is utilized in the guide star concept as an incoherent secondary light source. The key is that fluorescence is an incoherent process and does not contain information about the aberrations gained by the excitation beam [33]. Thus, the WFS (e.g. SHWFS etc.) can measure the specimen aberrations by the use of a fluorescent guide star excited by TPE. The latest approaches in TPM minimize bleaching of the WFS signal and correct for an averaged aberration by scanning the ROI during wavefront sensing. Consequently, WFS signal collection is conducted via a de-scanned signal collection [55]. Since the most widely used optical microscopes for high-resolution biomedical imaging are
scanning confocal and two-photon microscopes, AO was in the beginning mainly developed for scanning microscopes. However, more recent research in AO is also focusing on camera-based microscopes [8]. AOS for widefield, structured illumination, light sheet microscopes and micro-endoscopy are reported [56, 57, 58]. Even AOSs for the expanding field of super-resolution microscopes are studied, enabling better image quality with resolution in the nanometer range [45]. Due to the higher complexity of super-resolution microscopes more elaborate AOSs are developed [59]. In stimulated emission depletion (STED) microscopy, for example, a dual adaptive optics scheme was developed. The scheme makes use of the combination of a sensor-based AOS and a sensor-less AOS, both based on Zernike polynomials, to conduct aberration correction and consequently restore image quality [60].
AO also expanded its horizon from microscopy to other optical and engineer-ing techniques. These techniques include data storage, optical trappengineer-ing and micro/nanofabrication [61, 62]. As in microscopy, these methods also suffer from aberrations. Thus, AO can be used to compensate for the induced aber-rations and restore the focal spot quality even when focusing at depth [7, 63]. In optical lithography, for example, introduces the refractive index mismatch between the immersion medium, the coverslip and the photoresist mainly spherical aberrations. These introduced aberrations will reduce the focal inten-sity and thus limit the use of the nonlinear, thresholded optical process [61]. Recent developments in AO for ultra UV lithography use multiple-mirror AO to correct for thermally induced aberrations [64].
The microscopy and lithography setup is based on a custom built confocal microscope. A sketch of the setup is shown in Figure 3.1. Multiphoton mi-croscopy and lithography are conducted with a titanium:sapphire (Ti:S) laser (MaiTai HP, Spectra-Physics), whose excitation wavelength can be tuned from 690 nm to 1040 nm. Stimulated emission depletion (STED) is performed with a picosecond-pulsed laser (Katana HP, OneFive GmbH) at 775 nm. The excita-tion laser power is tuned by an electro-optic modulator (EOM), whereas the STED laser power is regulated by an acousto-optic modulator (AOM). Coarse sample adjustment is performed by manually driven stages in 3D. Precision positioning can be conducted by a 3D piezo-driven stage (P-733.3DD, Physik Instrumente). Scanning of the field of view (FOV) is done by beam scanning with a two-rotating-mirror scanning system (EOPC), which includes a reso-nant scanner in x-direction with a frequency of⇠10 kHz and a galvo scanner in y-direction. A 25x, 1.05 NA water dipping objective lens (XLPLN25XWMP2, Olympus) is used for focusing into the sample. Aberration correction is ex-ecuted in closed-loop configuration using a deformable mirror (Multi-5.5,
Boston Micromachines Corporation) and a SHWFS (custom-made: lenslet-array (#64-483, Edmund Optics), EMCCD camera (iXon ultra, Andor)), which are both conjugated to the back focal plane as are the two scanning mirrors. The wavefront sensor signal from the non-linear guide star is directed to the SHWFS by a dichroic mirror. It has to be emphasized that the adaptive optics element is a DM even though SLMs are more accurate. This is due to the simultaneous correction of the excitation and depletion point spread func-tion (PSF) in STED mode and the fact that in the closed-loop operafunc-tion the DM is also located in the wavefront sensing path and reflects the non-polarized fluorescence light. Although both excitation and depletion wavelengths are in close proximity to each other, a SLM would not be applicable to correct for all wavelengths simultaneously because of the narrow wavelength bandwidth of the SLM.
780 nm and 810 nm. STED wavelength is 775 nm. Coarse sample adjustment is conducted by a manual 3D stage, whereas precision positioning is performed by a 3D motorized stage. Scanning of the FOV is executed by two rotating mirrors.
Several AOS have been invented for different microscopes. To optimize specif-ically for their application great importance has to be attached to the selection of the AOS components. In this chapter, the implemented system is explained in detail, especially focusing on the compensation theory of the implemented AOS and the specific implementation. Afterwards a simulation of the com-bined system is outlined to determine the system’s compensation limitations. Then the combined system is characterized and calibration enhancements are tested. The last section of the chapter will show first results of correcting manually introduced aberrations.
4.1. The Implemented Adaptive Optics System
As described in chapter 3, aberration correction is applied by detecting the aberrated wavefront with a SHWFS and adding the equal but opposite sign
aberration to the DM.
The interaction between the SHWFS and the DM can be realized in several ways. The two basic types of wavefront information are either zonal, where the wavefront is expressed over a small spatial area, or modal, when the wave-front is expressed in terms of mode coefficients of a polynomial expansion over the entire pupil [43]. A common approach in microscopy is a modal method, where the deflections of the SHWFS’ spot diagram are transformed into Zernike polynomials [65]. The linear combination of the Zernike poly-nomials producible by the DM are then applied with a negative sign. This optical path length adjustment is canceling out whilst the excitation wave travels through the aberrated specimen resulting in a diffraction limited PSF [66]. In theory, however, any number of basis sets with the conditions of linear independence and completeness can be used for wavefront representation in the modal approach [66]. Therefore, in our system’s implementation the eigenmodes of the adaptive optics element, the DM, are taken as the basis, hence, limiting our AOS to the actual hardware limitations.
4.1.1. Theory of the Modes from Wavefront Slopes
The theory of an AOS is based on a linear equation system, because most of the adaptive optics operate in a linear regime. Thus, straightforward methods
of linear algebra are sufficient.
A wavefront phase F at a position (x,y) in the pupil plane is described by a polynomial expansion F(x, y) = K
Â
k=1 akZk(x, y) (4.1)with the coefficients ak, the polynomial basis functions Zk, also called modes, and K the total number of modes.
A SHWFS measures the wavefront slopes in two directions at m lenslet posi-tions. Assume that the wavefront slopes in x and in y direction are measured at position m. Hence, the number of total measurements M is 2xm, with m in x direction and m in y direction. The corresponding set of linear equation is given by ∂F(x, y) ∂x m = K
Â
k=1 ak∂Zk(x, y) ∂x (4.2) ∂F(x, y) ∂y m = KÂ
k=1 ak∂Zk(x, y) ∂y (4.3)where m implies the evaluation at the coordinates (xm, ym). These two equa-tions, eq. (4.2) and eq. (4.3), can be rewritten as the matrix equation
with [B] = 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 ∂Z(x,y)1 ∂x 1 ∂Z(x,y)2 ∂x 1 · · · ∂Z(x,y)K ∂x 1 ∂Z(x,y)1 ∂x 2 ∂Z(∂x,yx )2 2 · · · ∂Z(∂x,yx )K 2 ... ... ∂Z(x,y)1 ∂x M 2 ∂Z(x,y)2 ∂x M 2 · · · ∂Z(x,y)K ∂x M 2 ∂Z(x,y)1 ∂y 1 ∂Z(x,y)2 ∂y 1 · · · ∂Z(x,y)K ∂y 1 ... ... ∂Z(x,y)1 ∂y M 2 ∂Z(x,y)2 ∂y M 2 · · · ∂Z(x,y)K ∂y M 2 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 (4.5)
as the so called control matrix. B contains the influence of every mode Zk on every lenslet at position m.
As mentioned earlier, in theory, a number of basis sets can be used for wavefront representation with linear independence and completeness as their only requirement [66]. In the implemented control system the eigenmodes of the DM, called poke modes, are used. Because the eigenmodes of the DM are spanned by the set of actuators, the poke modes are equivalent to the actuators and the mode coefficients are equivalent to the actuator heights from the reference plane. This poke mode approach allows direct transformation from deflections on the SHWFS to actuator heights on the DM and thus bypassing transformations in other basis as is necessary with Zernike modes. During a calibration, the control matrix B is generated. In that process a certain height is applied to every actuator iteratively, the resulting spot diagram is detected by the SHWFS and the deflections for each lenslet are calculated and stored in the control matrix column-wise. After calibration, when an
aberrated wavefront is measured with a SHWFS the deflections s are obtained. Thus, the poke mode coefficients can be determined by solving the linear equation system eq. (4.4). Due to our system’s composition, consisting of 144 actuators - where approximately 44 are discarded because these are located out of the pupil- and 145 illuminated lenslets, it has to be emphasized that the control matrix is a rectangular matrix. Hence, a pseudo inversion [67] is necessary for matrix inversion to solve for the mode coefficients. For our overdetermined system singular value decomposition (SVD) is implemented as pseudo inversion.
4.1.2. Implementation of the Adaptive Optics System
In the implemented AOS a SHWFS is used for wavefront sensing of a two-photon-induced guide star that can either average the aberrations over the FOV by scanning it during wavefront determination or measures the aberration just in a single focal volume where the beam is parked. The control method for wavefront correction is based on slope measurements, which will be discussed briefly.
Before aberration correction can be conducted, the control system has to be calibrated by creating the control matrix B. Prior to the calibration, the system aberrations are corrected using a sensor-less AOS to minimize initial aberrations.
Sensor-less AOS The implemented sensor-less AOS is based on Zernike polynomials with pixel intensity as their metric. This sensor-less AOS is in this thesis mainly used for the elimination of aberrations introduced by the system, called “flatten the system”. The “flatten the system” process iterates through a user-specified amount of Zernike polynmials. Every Zernike polynomial is applied to the DM iteratively in a user-specified coefficient range. An image of the ROI for every Zernike polynomial with a specific coefficient is captured and the pixel with highest intensity is stored. When iterating through the given coefficient range for a Zernike polynomial a parabola-shaped curve, see Figure 4.1, for the corresponding pixel intensities will result. The discrete intensity values M for every coefficient a are then fitted with a parabola and the coefficient value for the maximum intensity of the fit is extracted. This procedure is conducted for all inserted Zernike polynomials leading to a vector of Zernike coefficients with the enhanced image intensity. Therefore, a linear combination of the Zernike polynomials with the extracted coefficients gives an optimized system flat pattern minimizing the initial aberrations when applied to the DM. This procedure is conducted prior to every AOS calibration to ensure minimized initial system aberrations and to optimize the PSF before imaging.
Figure 4.1.: Example of a sensor-less AO correction for one Zernike polynomial. When iterating through a given coefficient range {0,+x, x},see first three graphs from the left, a parabola-shaped curve for the corresponding pixel intensities {M0, M+, M }
will result. The discrete intensity values for every coefficient are then fitted with a parabola and the coefficient value acorrfor the maximum intensity x of the fit is
extracted, see right graph. Figure from [68].
Calibration After minimizing the initial system aberrations, the AOS calibra-tion is conducted. For the AOS calibracalibra-tion a spot diagram is captured and defined as the reference or non-aberrated spot diagram and the center position of the focal spot from every lenslet is determined and stored in a vector. This will be the reference vector for aberration correction. After the center positions of the focal spots are determined, the calibration of the control matrix can be carried out. As described previously, for control matrix determination an actuator is poked with a certain height and the corresponding SHWFS spot diagram is recorded. This spot diagram is then analyzed immediately by determining the center position of the focal spot for each lenslet. Spots corresponding to lenslets that are conjugate to the poked actuator will be deflected by the applied poke. Thus, these spots will be displaced depending on the applied poke height. When subtracting the reference spot positions by
the poke aberrated spot position, deflections will result for lenslets, which were affected by the aberrations. These deflections are then stored in the column of the control matrix, which the actuator corresponds to. This is done for every actuator resulting in matrix B of eq. (4.4). After calibration, artificial-or specimen-induced aberrations can be measured as described below.
Closed-loop control To maximize aberration correction, closed-loop con-trolled aberration correction is implemented. The closed-loop control for aberration measurement is shown in Figure 4.2. A SHWFS spot diagram is recorded and then analyzed as mentioned above to determine the x- and y-deflection of each focal spot. The resulting vector is s in eq. (4.4). Thus, the actuator compensation can be easily calculated by solving eq. (4.4) with the use of a pseudo inversion for B. In theory, simply the negative of the recon-structed actuator heights can be applied to the deformable mirror to correct for the measured aberration. However, pseudo inversion introduces large ac-tuator heights for non-contributing acac-tuators, the acac-tuators, which lie outside the DM aperture. Thus, compensation is adjusted by an influence vector. As mentioned above, the control matrix also contains information regarding the influence of every actuator on all the lenslets. Hence, the control matrix is used to determine the influence vector. The influence vector is calculated from the control matrix as following
niv(k) = q ÂmM=1B2m,k max (4.6) with max=maximum( v u u t
Â
M m=1 B2 m,k) (4.7)Figure 4.2.: Control loop for closed-loop aberration correction. In a closed-loop aberration correction, first the spot diagram of the aberrated wavefront is captured. Then the correction is calculated and applied to the DM using the control computer. Then another spot diagram of the previously corrected wavefront is captured and analyzed again. When the calculated correction factors are smaller than the user-set threshold an aberration corrected image is acquired. Else another aberration correction iteration is conducted.
Before applying the reconstructed actuator heights, the normalized influence vector (NIV) is multiplied weighing the contribution of each actuator. Hence,
actuators on the outside of the pupil with less influence on the spot diagram will have less contribution on the correction. Additionally, the reconstructed actuator heights for outer rim actuators are set to 0, because these have, according to experimental observation, no significant contribution to the aberration correction. Finally, the negative of the recalculated actuator heights, multiplied with the NIV and after setting the outer rim actuators to 0, are added to the deformable mirror for compensation. Because a closed-loop approach is implemented, aberration correction is done iteratively. However, if the maximum closed-loop compensation iteration is set to one, aberration correction terminates here. Otherwise it starts again until the actuator heights for the current iteration step is lower than an expected user-set value, or the maximum compensation iteration is exceeded.
4.2. Adaptive Optics System Simulation
The testing of the combined system via simulations was carried out to de-termine the system’s aberration detection and reconstruction accuracy. To do so, the same steps as in an actual measurement are conducted. First, a calibration for the control matrix generation is simulated. Then a simulated aberration is generated and the corresponding poke mode coefficients are calculated. These are then used to reconstruct the simulated aberration. As simulated aberrations, Zernike polynomials were chosen since these are both well-known in the optics field and are usually implemented in control loops
for a SHWFS/DM based AOS. The reconstruction quality is determined by the subtraction of the reconstructed wavefront from the inserted wavefront. Simulated aberration correction is determined successful, when the resulting subtracted wavefront is smaller than l
10, which is the flatness of a regular commercially available mirror.
4.2.1. Simulation of the Combined System
The combined system simulation consists of two parts, a calibration and an aberration reconstruction. In the calibration, the simulated control matrix (see eq. 4.5) is calculated. Afterwards in the aberration reconstruction step the simulated control matrix is used to reconstruct the simulated aberrations, which were in form of Zernike polynomials.
Calibration In the calibration step, measured interferometric poke data, see Figure 4.3 A, of pokes from every actuator were collected by poking each actuator of the DM with a specific height. To eliminate any measuring artifacts each poke mode wavefront is simulated. The simulated poke mode wavefront was determined from the measured poke modes by fitting. Multiple fits were tested resulting in a Gaussian fit as being the best. Thus, each poke mode wavefront is fitted successively with a Gaussian at every actuator center position. The Gaussian-fitted poke of the poke mode in Figure 4.3 A is shown
in Figure 4.3 B. The negative values, which resulted from the fitted offset, of each poke mode wavefront are set to zero. Comparing Figure 4.3 A and Figure 4.3 B illustrates that fitting the poke modes with Gaussian gives also just an approximation of the actual wavefront as a visual difference can be observed. After Gaussian fitting, a binary mask representing the lenslet array with the corresponding lenslet size is created, see Figure 4.3 C, and mapped on top of each fitted poke mode wavefront. The Zernike mode tip and tilt values, which are related to the deflections, are calculated for each lenslet and stored in a tip/tilt vector with the tilt values concatenated to the tip values for each poke mode. Hence, the control matrix, see eq. 4.5, is generated with the tip/tilt values for each poke mode in a new column. Figure 4.3 D illustrates the control matrix displaying the response of every lenslet to all actuators.
Figure 4.3.: Simulation of the calibration steps. A shows an example of a poke mode captured with an interferometer. B illustrates the same poke mode after Gaussian fitting. C displays the binary lenslet array. D shows the control matrix, hence, illustrating the response of every lenslet to all actuators.
Reconstruction After calibration, aberration measurement and reconstruc-tion can be conducted. The reconstrucreconstruc-tion execureconstruc-tion is displayed in Figure 4.4. The aberrated input (Figure 4.4 A), in this example Zernike polynomial Z4
6, is measured by mapping the lenslet array on top (Figure 4.4 B) and cal-culating the tip/tilt values for each lenslet which are stored in the s vector. Reconstruction of the aberrated wavefront is performed by first calculating the poke mode coefficients with eq. (4.4) and then summing over all modes using eq. (4.1). The subtraction of the reconstructed image from the inserted aberration, displayed in Figure 4.4 A, is shown in Figure 4.4 C.
Figure 4.4.: Illustration of the simulation reconstruction steps. A displays the inserted aber-ration, Zernike polynomial Z4
6. B displays the same aberration with the mapped
lenslets. C displays the subtracted image of the reconstructed aberration from the inserted aberration. The scale bar illustrates radiants.
4.2.2. Simulation Results
Aberrations in terms of Zernike polynomials up to radial degree 9 were mea-sured and reconstructed in the simulation. The reconstruction of all Zernike polynomials of radial degree 6 (mode 22-28) except Zernike polynomial Z0 6 (mode 25) meet the defined flatness constraint of l
10 for the subtraction of the reconstructed wavefront from the input wavefront. For Zernike polynomials of radial degree 7 and Zernike polynomial Z0
6reconstruction with less than 1% of pixels exceeding the constraint is achieved. Higher modes resulted in less flat subtraction wavefronts. The main reason for this observation is most likely due to the limited shape capability of a continuous surface DM [69]. However, according to experimental observations, aberration correction for low order Zernike polynomials, up to mode 21 (Z5
quality improvement [40]. Since the simulated combined system can detect and reconstruct up to mode 21 and even higher within the defined flatness constraint of l
10, the simulation data indicates that the currently installed AO components can perform sufficient wavefront sensing and aberration correc-tion. Thus, no adjustments of hardware components are required.
An example for an input aberration in form of Zernike polynomial Z4
6 (A) and a subtracted wavefront (C) is illustrated in Figure 4.4
4.3. Adaptive Optics System Testing
In this section the combined adaptive optics system is tested before aberration correction of user-induced artificial aberrations. Afterwards specimen-induced aberrations are corrected with the combined adaptive optics system. First, the linearity of the DM is tested on the system. Thereafter the system stability is tested. Then the in situ calibration is investigated. Afterwards, user-induced poke aberrations are applied and reconstructed on the system to validate the aberration correction capabilities of the AOS. At the end, arbitrary poke heights are manually applied on the DM and compensated iteratively.
4.3.1. Linearity of the Adaptive Optics Element
To test whether the DM is behaving linearly throughout its full stroke capacity, the deflections on the lenslets were measured over the complete range of each actuator. The measurement is carried out by poking a specific actuator through its full range of 3500 nm. In the actuator control system the actuator zero position is set to⇠3500 nm /2 to allow negative and positive strokes and the controlling input is converted to [-1, 1]. Therefore, in the measurement a specific actuator is poked through its full range [-1, 1] by a step size of 0.01 and a spot diagram is captured for each step. The deflection of each spot is then calculated and stored. This is repeated 100 times to create an average. To test the linearity of the adaptive optics element, a FITC solution sample is prepared to collect spot diagrams via a two-photon induced guide star. Prior to the data collection, compensation for initial system aberrations has been conducted via the implemented sensor-less AOS to minimize initial aberrations and therefore optimize the PSF prior to any experiment. This procedure is called “flatten the system”.
Figure 4.5 A illustrates an overlay of multiple spot diagrams taken at various step heights, -1, -0.5, 0, 0.5 and 1, of actuator 65; an actuator in the central region. It is apparent that a single actuator affects just some lenslets of the lenslet array, which are highlighted by the red square. Noticeable is the single spot of the center lenslet within the red square. For this lenslet only one spot is visible, whereas for the other lenslets within the affected region multiple spots corresponding to the step heights are apparent. This is because the
poked actuator is situated almost directly at the same position in the optical system as this lenslet. Consequently, this focal spot is shifted by the poking actuator mostly in axial direction and is therefore not focused on the camera chip anymore for higher poke heights.
Figure 4.5.: Adaptive optics system testing - linearity. A illustrates an overlay of five spot diagrams recorded at a step size of -1, -0.5, 0, 0.5 and 1. A zoom out of the red bordered area is shown in the white highlighted box. B shows the x- and y-deflections at every step size of the purple highlighted lenslet. An average over 100 iterations is taken.
As mentioned earlier, only the red highlighted lenslets show a substantial response to the poked actuator. Thus, only affected lenslets are considered for the linearity analysis.
Figure 4.5 B shows the mean x- and y- deflections with their standard devia-tions for each step size when poking actuator 65 from [-1, 1] for the purple
highlighted lenslet in Figure 4.5 A. The deflections illustrate a linear response in the actuator height region of [⇠ 0.7, ⇠0.7]. However, beyond that region a saturation is apparent. One reason for this effect is likely a programming error in the DM manufaturer’s driver software which prevents the use of the whole actuator stroke of the DM. This was clarified by Boston machine during the final stage of this thesis. Another reason might be the fact that the implemented DM consists of a membrane, which results in actuator crosstalk and becomes primarily apparent when poking only one actuator. Nonethe-less, this saturation effect does not limit the compensation capability, because sample induced-aberrations are not expected to occur at these height regimes. We limit our linearity analysis to within 60 % of each DM actuator stroke ([-0.6 to 0.6]) which corresponds to⇠ ±1, 050 nm. Experimental observations indicate that the expected correction region is within this range, as beyond this range, aberration effects in the actual spot diagram become apparent and the actuators in the DM no longer follow a linear response when a certain bias voltage is given. The residuum of the deflections of the red highlighted lenslets in Figure 4.5 A is lower than 5% except for the center lenslet. This is, however, due to vanishing spots at a certain step size as mentioned earlier. The linear response of the actuators can be confirmed for the actuators of the deformable mirror, which have significant influence on aberration correction. Linearity analysis for actuators located outside of the pupil was not conducted, since no significant deflections could be measured in the spot diagram.
4.3.2. Stability of the Adaptive Optics Element
In this section, the system stability is investigated. To determine the system stability, poke experiments are conducted over a span of 10 hours. Prior to the calibration the system was flattened. It has to be noted that before calibration and before the measurement, the sample had time to settle down to avoid influence of a stage drift. In the experiment, actuator 65 is repeatedly poked through its full range. Meanwhile, a spot diagram (collected from a FITC solution) of the flat mirror is captured approximately every 10 minutes for this amount of time and the deflection of lenslet 86 is analyzed and plotted in Figure 4.6. A linear fit is conducted and the slope is within the standard error of the estimate for all influenced lenslets. Thus, no detectable drift can be distinguished within this time span.
Figure 4.6.: Drift curve example of the deflection of a lenslet over 10 hours. The figure illustrates the measured deflection of a certain lenslet with a flat DM mirror surface for every hour.
4.3.3. Calibration Testing
According to eq. (4.4), the aberration correction calculation is based on the control matrix B, which is acquired during the calibration step. To ensure optimal aberration correction data acquisition for control matrix generation is investigated. During testing, emphasis is placed on the ideal step size for control matrix generation.
To test different control matrix settings, a FITC solution sample was prepared to collect spot diagrams via a two-photon induced guide star. Prior to the data collection, the system was flattened to minimize initial aberrations.
Poke Height Determination
To determine the best poke height for control matrix generation, multiple control matrices were tested in a step size range from 0.05 to 0.5. The lower limit of 0.05 is selected, because it is the lowest step size detectable by eye. Thus, this step size should be detectable by the wavefront sensor. The upper limit of 0.5 is chosen because beyond this poke height, aberrating effects on the affected spots become apparent and localization precision degrades when spots deviate from the expected round shape.
with the same poke aberration of 0.25 are collected after calibration. The deflections for the 100 spot diagrams of a certain poke height were averaged. Then the reconstructed actuator heights are calculated and plotted in Figure 4.7. The red inset shows a zoom in on the recalculated poke heights for the specific actuator and the respective control matrix. When comparing the different reconstructed images in the red highlighted box of Figure 4.7 it can be seen that a step size of 0.3 and 0.4 perform best by reconstruction. This is most likely, because this step size is above the detection accuracy of the system and the spots do not show significant aberrations, which are already visible by eye for a step size of 0.5. Since 0.3 performs slightly better than 0.4, a step height of 0.3 is selected for control matrix generation.
Figure 4.7.: Reconstructed step heights of different control matrices between 0.05 and 0.5 are shown. The red highlighted box illustrates a zoom in on the reconstructed actuator. It can be seen that a control matrix of 0.3 performs best.
4.3.4. Aberration Correction of Artificial Aberrations
In this section the aberration correction capabilities of the AOS using poke modes is validated. This is conducted by introducing artificial aberrations into the optical system by manually applying deformations onto the DM. First, only a single actuator is poked with several heights and reconstruction is performed. Then two random patterns, one between the stroke height of [-0.1,
0.1] and another one between [-0.2, 0.2], are applied to the DM and corrected iteratively.
For testing, a FITC solution sample is prepared to collect spot diagrams via a two-photon induced guide star. Prior to data collection the system was flattened via sensorless AO to minimize initial aberrations. Then a control matrix with a step size of 0.3 is generated for aberration correction.
Single-Poke Compensation
Artificial aberrations are added to the optical system by manually poking one actuator, in this case actuator 65, with a certain height. From the collected spot diagram, which was collected 100 times, the compensation is calculated using the control matrix, which was collected once before correction. During this experiment, several poke heights are tested, namely 0.2 , 0.25 and 0.35. These are applied to the DM successively. The reconstructed actuator heights for the different applied poke aberrations are plotted in Figure 4.8. The vertical axis’ maximum is set to the applied poke height on the DM. Thus, actuator 65 should have a reconstructed height of the vertical axis’ maximum, whereas the remaining actuators should be 0.
As illustrated in Figure 4.8 the reconstructed actuators show the expected behavior of one peak at actuator 65 for all applied aberrations. However, it
is obvious that none of the reconstructed actuator heights reach exactly their desired value of the applied aberration. There are several reasons for this. First, when reconstructing the actuator heights, the pseudo inversion uses a linear least square approximation, which induces inaccuracies in the solution. Furthermore, after reconstruction of the actuator heights, the normalized influence vector reduces the recalculated actuator heights except for the actuator which has an influence of 1. In this experiment, however, actuator 65 does not have the most influence on the spot diagram and thus will always be underestimated due to the influence vector. Finally, the coupling between two or more actuators controlling the DM membrane may also be playing a role. Actuator coupling in DM devices is a well-known, and widely discussed phenomenon in the AO community [46]. The noise in the side actuators is most likely introduced by the control matrix, since it was collected only once during control matrix calibration.
Figure 4.8.: Poke aberration correction of different poke heights. The applied poke height and thus the targeted reconstruction height is the y axis’ maximum. Hence, it can be seen that each poke aberration calculation underestimates the applied aberration.
