November 15, 2013 / Vol. 38, No. 22 / OPTICS LETTERS
4801
Wavefront sensorless modal deformable mirror correction in adaptive optics: optical coherence tomography S. Bonora1,* and R. J. Zawadzki2 1 2
CNR-Institute of Photonics and Nanotechnology, via Trasea 7, 35131 Padova, Italy
Vision Science and Advanced Retinal Imaging Laboratory (VSRI) and Department of Ophthalmology & Vision Science, UC Davis, 4860 Y Street, Ste. 2400, Sacramento, California 95817, USA *Corresponding author: [email protected] Received September 19, 2013; accepted October 3, 2013; posted October 7, 2013 (Doc. ID 197957); published November 13, 2013
We present a method for optimization of optical coherence tomography images using wavefront sensorless adaptive optics. The method consists of systematic adjustment of the coefficients of a subset of the orthogonal Zernike bases and application of the resulting shapes to a deformable mirror, while optimizing using image sharpness as a merit function. We demonstrate that this technique can compensate for aberrations induced by trial lenses. Measurements of the point spread function before and after compensation demonstrate near diffraction limit imaging. © 2013 Optical Society of America OCIS codes: (110.4500) Optical coherence tomography; (170.4470) Ophthalmology; (220.1000) Aberration compensation; (110.1080) Active or adaptive optics. http://dx.doi.org/10.1364/OL.38.004801
Optical coherence tomography (OCT) is an imaging modality allowing acquisition of micrometer-resolution, three-dimensional images of scattering materials (e.g., biological tissue) [1]. OCT is based on detection of the interference of light backscattered from the sample with light reflected from a reference mirror; it is an optical analogue of ultrasound. OCT systems may employ Michelson or Mach–Zehnder interferometers. OCT has many applications in biology and medicine and can be treated as a type of noninvasive optical biopsy [2]. One of the interesting features of OCT is that, unlike in most optical imaging techniques, the axial and lateral resolutions are decoupled, thus allowing for independent control of each. The axial resolution Δz is determined by the roundtrip coherence length of the light source and can be calculated from the central wavelength λ0 and the FWHM Δλ of the light source via [3] Δz
2 ln 2 λ20 : π ΔλFWHM
The lateral resolution (Δx) in OCT is defined as in confocal scanning laser ophthalmoscopy (cSLO), since OCT is based on a confocal imaging scheme. In many imaging systems, however, the confocal aperture exceeds the size of the Airy disc, which degrades resolution to the transverse resolution known from microscopy, e.g., Δx 1.22λ
f : D
Therefore, similar to standard microscopy, adaptive optics (AO)-enhanced devices might be necessary to achieve diffraction-limited transverse resolution if optical aberrations are present in imaging system. As a result, only a combination of OCT with AO has the potential to achieve diffraction limited volumetric resolution [4]. The use of broadband light sources that are necessary for 0146-9592/13/224801-04$15.00/0
OCT, combined with the inherent complexity of both AO and OCT, makes their combination challenging [5]. In general, any AO-OCT instrument can be divided into two subsystems: an AO subsystem (with wavefront sensing and wavefront correction) and an OCT subsystem. All the optical elements of the AO subsystem are located in the sample arm of the OCT interferometer. Indeed, there is no need to have AO correction in the reference arm because aberrations introduced within this part of the system will not influence the transverse resolution of the image. In most AO-OCT systems, a Shack–Hartmann wavefront sensor is used to measure aberrations and provide feedback (residual error) to the closed control loop, which in turn supplies commands to the deformable mirror. Many reports of sensorless aberration correction exist in the literature, which use, for example, techniques, such as genetic algorithms [6,7], simplex algorithms, simulated annealing, ant colonies, etc. [8]. All of them follow the principle of the maximization of the value of a merit function. Since deformable mirrors have a large number of actuators, ranging from about 20–90, and the number of actuators determines the dimensionality of the optimization search space, the convergence time may be high. For example, convergence time is on the order of tens of seconds (which corresponds to 800 iterations for [6,8]), depending on the DM and acquisition speed. Other techniques for sensorless optimization search a reduced space defined by an orthogonal wavefront basis such as Zernike or Lukosz in order to reduce convergence time [9,10]. Such modal correction techniques may converge after as few as three iterations. This approach is facilitated by the recent introduction of a modally controlled DM [11]. An interesting feature of the modal electrostatic deformable mirror (MDM) is that it can generate low-order modal corrections, spherical aberration correction, coma and their combinations with just nine actuators, thereby reducing the hardware © 2013 Optical Society of America
4802
OPTICS LETTERS / Vol. 38, No. 22 / November 15, 2013 Table 1. Peak to Valley Amplitude of the Modal Corrections that the MDM Can Generate Modal Correction Defocus Astigmatism Coma Spherical aberration
Peak to Valley (μm) 7 2.5 0.7 1
consisting of an Air Force Test target with a 70 μm thick polymer layer glued to its front side and a cylindrical trial lens (0.5D) in front of the imaging objective. We were able to improve image resolution by using the following merit function S [13] on the OCT en face projection images, Z S
complexity and cost of the system. The performance of the MDM is summarized in Table 1. This DM consists of a set of graphite actuators that exert electrostatic forces on a metallized membrane mounted 50 μm away [11]. The membrane has a clear aperture of 19 mm and the DM is optimized to have an active area of 10 mm that is biased to half of the maximum voltage (V max 260 V) through the use of a voltage divider. Each of the two external rings has four contacts. The outer ring is used to generate astigmatism, the intermediate ring is used to generate coma, whereas defocus and spherical aberration are generated with a combination of the intermediate and inner rings. Details of the voltage patterns that generate the desired aberrations can be found in [11]. The algorithm corrects modes in the following order: defocus, astigmatism, spherical aberration, and coma, one at a time. The effectiveness of this DM and sequential optimization was demonstrated by improving laser focalization using the photon flux as fitness function [12]. For imaging systems various fitness functions can be used, as described in detail in [13]. In this Letter, we demonstrate that sensorless correction using the MDM can be implemented in an AO-OCT system in order to compensate aberrations without the use of a wavefront sensor. Figure 1 shows a schematic representation of the sensorless AO-OCT system used in the experiments. The details of the OCT system can be found in [4]. Briefly, we used a superluminescent diode (848 μm, 112 nm bandwidth), a spectrometer incorporating a Basler Sprint camera (2048 pixels), and we acquired 512 B-scans each consisting of 512 A-scans, at a line acquisition rate of 50 kHz. To test the performance of our sensorless AO-OCT system, we evaluated the image quality of the sample,
Fig. 1. Schematic of sensorless AO-OCT system. The far field camera (FF) is used to monitor improvement in focal spots. Quality of the OCT image is used to search for DM shapes that optimally compensate for aberrations.
I 2 x; ydxdy;
where Ix; y is the intensity in the OCT en face image. The algorithm drives the DM through a control vector: c fd; a0 ; a45 ; s; c0 ; c90 g, where d: 0 < d < 1 is the defocus value, a0 : − 1 < a0 < 1 is the astigmatism 0° control value, a45 : − 1 < a45 < 1 is the astigmatism 45° control value, S: − 1 < S < 1 is the amount of spherical aberration, and c0 , c90 : − 1 < c0 ; c90 < 1 are the coma 0° and 90° control value. The algorithm steps are the following: Set the DM to flat c f0; 0; 0; 0; 0; 0g Scan the defocus d: 0 < d < 1 Find the max value dm and set c fdm ; 0; 0; 0; 0; 0g Scan a0 : − 1 < a0 < 1 and set the best value a0m : c fdm ; a0m ; 0; 0; 0; 0g 5. Scan a45 : − 1 < a45 < 1 and set the best value a45 : c fdm ; a0m ; a45m ; 0; 0; 0g 6. Scan S: − 1 < S < 1 and set the best value S m : c fdm ; a0m ; a45m ; S m ; 0; 0g 7. Scan c0 : − 1 < c0 < 1 and set the best value C 0m : c fdm ; a0m ; a45m ; S m ; C 0m ; 0g 8. Scan c90 : − 1 < c90 < 1 and set the best value C 90m : c fdm ; a0m ; a45m ; S m ; C 0m ; C 90m g
1. 2. 3. 4.
Each modal correction scan samples the image sharpness for several coefficients of the mode. The resulting sharpness values are B-spline interpolated to find the optimum value (Fig. 2). Correcting astigmatism generated by the trial lens required, as expected, adjustment of just defocus and astigmatism (see Fig. 2). The best images after defocus, astigmatism, spherical aberration, and coma optimization are shown in Fig. 3. The image sequence clearly shows an improvement of the sharpness of the image. In addition, the visibility
Fig. 2. Merit function during the optimization process. Square markers indicate measured sharpness; dashed lines show B-spline interpolations.
November 15, 2013 / Vol. 38, No. 22 / OPTICS LETTERS
4803
Fig. 4. Far field images during the optimization process with the cross section of the spots. (a) After the insertion of a 0.5D astigmatic lens, (b) after defocus correction, (c) after Ast 0° correction, and (d) after Ast 45° correction.
Fig. 3. En face view of the target during the sequential optimization process. (a) Before the optimization, (b) after defocus correction, (c) after Ast 0°, and (d) after Ast 45° correction.
of the polymer tape stack on the top of the Air Force target improves as well. To confirm the optimization performance, we placed a CMOS camera (3.6 μm pixels) in the far field, used to monitor the system’s lateral point spread function (PSF). Figure 4(a) shows that the inserted astigmatic lens generates significant aberrations and degrades (broadens) the PSF. At the end of the process, the PSF improves up to a FWHM of 14.4 μm (4 pixels), close to its diffraction limit value of about 10 μm. In conclusion, we demonstrated that optimizationbased sensorless AO can be implemented successfully in OCT systems using sequential modal correction and a modal deformable mirror. This technique could be extended to in vivo imaging of the human eye. Ideally, for such an application, the stroke of the modal deformable mirror should be increased by a factor of 4, which means that the driving voltage has to be increased by a factor of two. Recently, Hofer et al. reported on successful sensorless AO applied to the human in vivo retinal imaging with a confocal AO scanning laser ophthalmoscope [14]. In that case, a stochastic parallel gradient descent (SPGD)
algorithm that directly optimizes the mean intensity of retinal images was used, allowing continuous (dynamic) AO correction during imaging. One limitation of that method was the large number of iterations (several hundred) required to achieve image quality comparable to that achieved with sensor-based AO correction. For comparison, our method allows correction of static aberrations with just 30–40 iterations. Potentially, a combination of both search algorithms could result in improved performance: fast modal correction of low-order aberrations coupled with SPGD correction of high-order aberrations. Such an approach may be ideal for in vivo applications. This project was financed in part by the National Eye Institute (EY 014743) and Research to Prevent Blindness (R. J. Zawadzki). The authors would like to acknowledge the kind support of professor John S. Werner and Dr. Ravi S. Jonnal (Vision Science and Advanced Retinal Imaging Laboratory (VSRI), UC Davis Eye Center). The authors acknowledge the assistance of Adaptica Srl, which supplied part of the experimental equipment. References 1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science, New Series 254, 1178 (1991). 2. A. F. Fercher, Zeitschrift für Medizinische Physik 20, 251 (2010). 3. A. F. Fercher and C. K. Hitzenberger, Progress in Optics, E. Wolf, ed. (Elsevier, 2002), Vol. 44, pp. 215–302. 4. R. J. Zawadzki, S. Jones, S. Olivier, M. Zhao, B. Bower, J. Izatt, S. Choi, S. Laut, and J. Werner, Opt. Express 13, 8532 (2005). 5. M. Pircher and R. J. Zawadzki, Expert Rev. Ophthalmol. 2, 1019 (2007).
4804
OPTICS LETTERS / Vol. 38, No. 22 / November 15, 2013
6. P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, Opt. Lett. 29, 207 (2004). 7. E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, Opt. Lett. 25, 587 (2000). 8. M. Minozzi, S. Bonora, A. V. Sergienko, G. Vallone, and P. Villoresi, Opt. Lett. 38, 489 (2013). 9. D. Debarre, M. J. Booth, and T. Wilson, Opt. Express 15, 8176 (2007).
10. M. J. Booth, Opt. Lett. 32, 5 (2007). 11. S. Bonora, Opt. Commun. 284, 3467 (2011). 12. S. Bonora, F. Frassetto, S. Coraggia, C. Spezzani, M. Coreno, M. Negro, M. Devetta, C. Vozzi, S. Stagira, and L. Poletto, Appl. Phys. B 106, 905 (2012). 13. R. A. Muller and A. Buffington, J. Opt. Soc. Am. 64, 1200 (1974). 14. H. Hofer, N. Sredar, H. Queener, C. Li, and J. Porter, Opt. Express 19, 14160 (2011).
4801
Wavefront sensorless modal deformable mirror correction in adaptive optics: optical coherence tomography S. Bonora1,* and R. J. Zawadzki2 1 2
CNR-Institute of Photonics and Nanotechnology, via Trasea 7, 35131 Padova, Italy
Vision Science and Advanced Retinal Imaging Laboratory (VSRI) and Department of Ophthalmology & Vision Science, UC Davis, 4860 Y Street, Ste. 2400, Sacramento, California 95817, USA *Corresponding author: [email protected] Received September 19, 2013; accepted October 3, 2013; posted October 7, 2013 (Doc. ID 197957); published November 13, 2013
We present a method for optimization of optical coherence tomography images using wavefront sensorless adaptive optics. The method consists of systematic adjustment of the coefficients of a subset of the orthogonal Zernike bases and application of the resulting shapes to a deformable mirror, while optimizing using image sharpness as a merit function. We demonstrate that this technique can compensate for aberrations induced by trial lenses. Measurements of the point spread function before and after compensation demonstrate near diffraction limit imaging. © 2013 Optical Society of America OCIS codes: (110.4500) Optical coherence tomography; (170.4470) Ophthalmology; (220.1000) Aberration compensation; (110.1080) Active or adaptive optics. http://dx.doi.org/10.1364/OL.38.004801
Optical coherence tomography (OCT) is an imaging modality allowing acquisition of micrometer-resolution, three-dimensional images of scattering materials (e.g., biological tissue) [1]. OCT is based on detection of the interference of light backscattered from the sample with light reflected from a reference mirror; it is an optical analogue of ultrasound. OCT systems may employ Michelson or Mach–Zehnder interferometers. OCT has many applications in biology and medicine and can be treated as a type of noninvasive optical biopsy [2]. One of the interesting features of OCT is that, unlike in most optical imaging techniques, the axial and lateral resolutions are decoupled, thus allowing for independent control of each. The axial resolution Δz is determined by the roundtrip coherence length of the light source and can be calculated from the central wavelength λ0 and the FWHM Δλ of the light source via [3] Δz
2 ln 2 λ20 : π ΔλFWHM
The lateral resolution (Δx) in OCT is defined as in confocal scanning laser ophthalmoscopy (cSLO), since OCT is based on a confocal imaging scheme. In many imaging systems, however, the confocal aperture exceeds the size of the Airy disc, which degrades resolution to the transverse resolution known from microscopy, e.g., Δx 1.22λ
f : D
Therefore, similar to standard microscopy, adaptive optics (AO)-enhanced devices might be necessary to achieve diffraction-limited transverse resolution if optical aberrations are present in imaging system. As a result, only a combination of OCT with AO has the potential to achieve diffraction limited volumetric resolution [4]. The use of broadband light sources that are necessary for 0146-9592/13/224801-04$15.00/0
OCT, combined with the inherent complexity of both AO and OCT, makes their combination challenging [5]. In general, any AO-OCT instrument can be divided into two subsystems: an AO subsystem (with wavefront sensing and wavefront correction) and an OCT subsystem. All the optical elements of the AO subsystem are located in the sample arm of the OCT interferometer. Indeed, there is no need to have AO correction in the reference arm because aberrations introduced within this part of the system will not influence the transverse resolution of the image. In most AO-OCT systems, a Shack–Hartmann wavefront sensor is used to measure aberrations and provide feedback (residual error) to the closed control loop, which in turn supplies commands to the deformable mirror. Many reports of sensorless aberration correction exist in the literature, which use, for example, techniques, such as genetic algorithms [6,7], simplex algorithms, simulated annealing, ant colonies, etc. [8]. All of them follow the principle of the maximization of the value of a merit function. Since deformable mirrors have a large number of actuators, ranging from about 20–90, and the number of actuators determines the dimensionality of the optimization search space, the convergence time may be high. For example, convergence time is on the order of tens of seconds (which corresponds to 800 iterations for [6,8]), depending on the DM and acquisition speed. Other techniques for sensorless optimization search a reduced space defined by an orthogonal wavefront basis such as Zernike or Lukosz in order to reduce convergence time [9,10]. Such modal correction techniques may converge after as few as three iterations. This approach is facilitated by the recent introduction of a modally controlled DM [11]. An interesting feature of the modal electrostatic deformable mirror (MDM) is that it can generate low-order modal corrections, spherical aberration correction, coma and their combinations with just nine actuators, thereby reducing the hardware © 2013 Optical Society of America
4802
OPTICS LETTERS / Vol. 38, No. 22 / November 15, 2013 Table 1. Peak to Valley Amplitude of the Modal Corrections that the MDM Can Generate Modal Correction Defocus Astigmatism Coma Spherical aberration
Peak to Valley (μm) 7 2.5 0.7 1
consisting of an Air Force Test target with a 70 μm thick polymer layer glued to its front side and a cylindrical trial lens (0.5D) in front of the imaging objective. We were able to improve image resolution by using the following merit function S [13] on the OCT en face projection images, Z S
complexity and cost of the system. The performance of the MDM is summarized in Table 1. This DM consists of a set of graphite actuators that exert electrostatic forces on a metallized membrane mounted 50 μm away [11]. The membrane has a clear aperture of 19 mm and the DM is optimized to have an active area of 10 mm that is biased to half of the maximum voltage (V max 260 V) through the use of a voltage divider. Each of the two external rings has four contacts. The outer ring is used to generate astigmatism, the intermediate ring is used to generate coma, whereas defocus and spherical aberration are generated with a combination of the intermediate and inner rings. Details of the voltage patterns that generate the desired aberrations can be found in [11]. The algorithm corrects modes in the following order: defocus, astigmatism, spherical aberration, and coma, one at a time. The effectiveness of this DM and sequential optimization was demonstrated by improving laser focalization using the photon flux as fitness function [12]. For imaging systems various fitness functions can be used, as described in detail in [13]. In this Letter, we demonstrate that sensorless correction using the MDM can be implemented in an AO-OCT system in order to compensate aberrations without the use of a wavefront sensor. Figure 1 shows a schematic representation of the sensorless AO-OCT system used in the experiments. The details of the OCT system can be found in [4]. Briefly, we used a superluminescent diode (848 μm, 112 nm bandwidth), a spectrometer incorporating a Basler Sprint camera (2048 pixels), and we acquired 512 B-scans each consisting of 512 A-scans, at a line acquisition rate of 50 kHz. To test the performance of our sensorless AO-OCT system, we evaluated the image quality of the sample,
Fig. 1. Schematic of sensorless AO-OCT system. The far field camera (FF) is used to monitor improvement in focal spots. Quality of the OCT image is used to search for DM shapes that optimally compensate for aberrations.
I 2 x; ydxdy;
where Ix; y is the intensity in the OCT en face image. The algorithm drives the DM through a control vector: c fd; a0 ; a45 ; s; c0 ; c90 g, where d: 0 < d < 1 is the defocus value, a0 : − 1 < a0 < 1 is the astigmatism 0° control value, a45 : − 1 < a45 < 1 is the astigmatism 45° control value, S: − 1 < S < 1 is the amount of spherical aberration, and c0 , c90 : − 1 < c0 ; c90 < 1 are the coma 0° and 90° control value. The algorithm steps are the following: Set the DM to flat c f0; 0; 0; 0; 0; 0g Scan the defocus d: 0 < d < 1 Find the max value dm and set c fdm ; 0; 0; 0; 0; 0g Scan a0 : − 1 < a0 < 1 and set the best value a0m : c fdm ; a0m ; 0; 0; 0; 0g 5. Scan a45 : − 1 < a45 < 1 and set the best value a45 : c fdm ; a0m ; a45m ; 0; 0; 0g 6. Scan S: − 1 < S < 1 and set the best value S m : c fdm ; a0m ; a45m ; S m ; 0; 0g 7. Scan c0 : − 1 < c0 < 1 and set the best value C 0m : c fdm ; a0m ; a45m ; S m ; C 0m ; 0g 8. Scan c90 : − 1 < c90 < 1 and set the best value C 90m : c fdm ; a0m ; a45m ; S m ; C 0m ; C 90m g
1. 2. 3. 4.
Each modal correction scan samples the image sharpness for several coefficients of the mode. The resulting sharpness values are B-spline interpolated to find the optimum value (Fig. 2). Correcting astigmatism generated by the trial lens required, as expected, adjustment of just defocus and astigmatism (see Fig. 2). The best images after defocus, astigmatism, spherical aberration, and coma optimization are shown in Fig. 3. The image sequence clearly shows an improvement of the sharpness of the image. In addition, the visibility
Fig. 2. Merit function during the optimization process. Square markers indicate measured sharpness; dashed lines show B-spline interpolations.
November 15, 2013 / Vol. 38, No. 22 / OPTICS LETTERS
4803
Fig. 4. Far field images during the optimization process with the cross section of the spots. (a) After the insertion of a 0.5D astigmatic lens, (b) after defocus correction, (c) after Ast 0° correction, and (d) after Ast 45° correction.
Fig. 3. En face view of the target during the sequential optimization process. (a) Before the optimization, (b) after defocus correction, (c) after Ast 0°, and (d) after Ast 45° correction.
of the polymer tape stack on the top of the Air Force target improves as well. To confirm the optimization performance, we placed a CMOS camera (3.6 μm pixels) in the far field, used to monitor the system’s lateral point spread function (PSF). Figure 4(a) shows that the inserted astigmatic lens generates significant aberrations and degrades (broadens) the PSF. At the end of the process, the PSF improves up to a FWHM of 14.4 μm (4 pixels), close to its diffraction limit value of about 10 μm. In conclusion, we demonstrated that optimizationbased sensorless AO can be implemented successfully in OCT systems using sequential modal correction and a modal deformable mirror. This technique could be extended to in vivo imaging of the human eye. Ideally, for such an application, the stroke of the modal deformable mirror should be increased by a factor of 4, which means that the driving voltage has to be increased by a factor of two. Recently, Hofer et al. reported on successful sensorless AO applied to the human in vivo retinal imaging with a confocal AO scanning laser ophthalmoscope [14]. In that case, a stochastic parallel gradient descent (SPGD)
algorithm that directly optimizes the mean intensity of retinal images was used, allowing continuous (dynamic) AO correction during imaging. One limitation of that method was the large number of iterations (several hundred) required to achieve image quality comparable to that achieved with sensor-based AO correction. For comparison, our method allows correction of static aberrations with just 30–40 iterations. Potentially, a combination of both search algorithms could result in improved performance: fast modal correction of low-order aberrations coupled with SPGD correction of high-order aberrations. Such an approach may be ideal for in vivo applications. This project was financed in part by the National Eye Institute (EY 014743) and Research to Prevent Blindness (R. J. Zawadzki). The authors would like to acknowledge the kind support of professor John S. Werner and Dr. Ravi S. Jonnal (Vision Science and Advanced Retinal Imaging Laboratory (VSRI), UC Davis Eye Center). The authors acknowledge the assistance of Adaptica Srl, which supplied part of the experimental equipment. References 1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Science, New Series 254, 1178 (1991). 2. A. F. Fercher, Zeitschrift für Medizinische Physik 20, 251 (2010). 3. A. F. Fercher and C. K. Hitzenberger, Progress in Optics, E. Wolf, ed. (Elsevier, 2002), Vol. 44, pp. 215–302. 4. R. J. Zawadzki, S. Jones, S. Olivier, M. Zhao, B. Bower, J. Izatt, S. Choi, S. Laut, and J. Werner, Opt. Express 13, 8532 (2005). 5. M. Pircher and R. J. Zawadzki, Expert Rev. Ophthalmol. 2, 1019 (2007).
4804
OPTICS LETTERS / Vol. 38, No. 22 / November 15, 2013
6. P. Villoresi, S. Bonora, M. Pascolini, L. Poletto, G. Tondello, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, and S. De Silvestri, Opt. Lett. 29, 207 (2004). 7. E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, Opt. Lett. 25, 587 (2000). 8. M. Minozzi, S. Bonora, A. V. Sergienko, G. Vallone, and P. Villoresi, Opt. Lett. 38, 489 (2013). 9. D. Debarre, M. J. Booth, and T. Wilson, Opt. Express 15, 8176 (2007).
10. M. J. Booth, Opt. Lett. 32, 5 (2007). 11. S. Bonora, Opt. Commun. 284, 3467 (2011). 12. S. Bonora, F. Frassetto, S. Coraggia, C. Spezzani, M. Coreno, M. Negro, M. Devetta, C. Vozzi, S. Stagira, and L. Poletto, Appl. Phys. B 106, 905 (2012). 13. R. A. Muller and A. Buffington, J. Opt. Soc. Am. 64, 1200 (1974). 14. H. Hofer, N. Sredar, H. Queener, C. Li, and J. Porter, Opt. Express 19, 14160 (2011).
