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Coherent diffractive imaging microscope with a high-order harmonic source KHUONG BA DINH,* HOANG VU LE, PETER HANNAFORD,
AND
LAP VAN DAO
Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Vic 3122, Australia *Corresponding author: [email protected] Received 17 November 2014; revised 1 May 2015; accepted 5 May 2015; posted 6 May 2015 (Doc. ID 226904); published 3 June 2015
We report the generation of highly coherent extreme ultraviolet sources with wavelengths around 30 and 10 nm by phase-matched high-order harmonic generation (HHG) in a gas cell filled with argon and helium, respectively. We then perform coherent diffractive imaging (CDI) by using a focused narrow-bandwidth HHG source with wavelength around 30 nm as an illumination beam for two kinds of samples. The first is a transmission sample and the second is a absorption sample. In addition, we report the successful reconstruction of a complex absorption sample using a tabletop high-harmonic source. This will open the path to the realization of a compact soft x-ray microscope to investigate biological samples such as membrane proteins. © 2015 Optical Society of America OCIS codes: (110.0180) Microscopy; (110.1650) Coherence imaging; (140.7240) UV, EUV, and X-ray lasers. http://dx.doi.org/10.1364/AO.54.005303
1. INTRODUCTION Microscopy techniques have made many significant achievements with high-resolution imaging down to the nanometer scale. Scanning probe microscopy techniques such as atomic force microscopy have been developed with a resolution of the order of fractions of a nanometer [1]. However, they are limited to surface structures and are not able to allow us to make a morphological analysis. Electron microscopy has provided the resolution of crystalline structures at the atomic level by using a beam of electrons to illuminate a sample, but this technique is restricted to imaging thin samples [2]. Using extreme ultraviolet or soft x-ray radiation as a light source allows us to obtain high-resolution imaging of thick samples [3]. Imaging with extreme-ultraviolet or soft-x-ray radiation is usually performed with diffractive optical elements with very short focal lengths such as Fresnel zone plates, since conventional lenses have strong absorption of soft x rays. Unfortunately, at very high magnification, zone plates have a relatively short working distance and a small depth of focus leading to the potential for large chromatic aberration. Coherent x-ray diffractive imaging (CDI) using short wavelength light in the extreme ultraviolet or soft x-ray regions has emerged as a promising alternative approach for highresolution imaging of thick samples, especially for biological samples [4–6]. Instead of using optical elements, in CDI the sample to be investigated is illuminated with a coherent x-ray source, and the object’s image is reconstructed from the diffraction pattern by applying iterative phase-retrieval algorithms. This approach allows aberration-free imaging and offers a very 1559-128X/15/175303-06$15/0$15.00 © 2015 Optical Society of America
large depth of focus, since there is no physical lens used. The spatial reconstructed resolution is mainly limited by the wavelength of the radiation used for illumination and by the largest angle of scattering over which diffraction patterns are recorded. Short-wavelength sources based on large facilities such as synchrotrons and free-electron and x-ray lasers can be used as an illuminating source for CDI [7,8]. Besides these sources, tabletop soft x-ray sources based on high-order harmonic generation (HHG) have been used for this lensless imaging technique to enable small-scale microscopy, which provides high spatial resolution of nanometer-scale objects [6,9–11]. In addition, HHG produced by the interaction of an intense laser pulse with a gas medium can provide a high degree of spatial coherence [12–14]. Since iterative methods for image reconstruction normally require a monochromatic wave field, CDI is usually carried out with a single harmonic order of the harmonic spectrum, which is selected by using narrow bandwidth optical elements such as a monochromator. However, for the short-wavelength range (1 mm; therefore, the effective photon flux for illumination of a micrometer-scale sample was also low. Recently, CDI using a single harmonic beam selected by employing XUV focusing mirrors has been implemented to achieve a significant advance in imaging resolution and data-acquisition time [9,10,18,19]. The focusing mirror allows the illuminating
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beam to be confined to a smaller area ( 100) and coherent radiation of appropriate wavelength. The spatial coherence length needs to be larger than the product of the sample size and the linear oversampling factor. Second, the diffracted light pattern needs to be recorded with sufficient resolution to allow for the fact that the CCD detector only records an intensity pattern and loses the phase information required for simple Fourier transform reconstruction of the image. In addition, the photon flux of the radiation source needs to be high enough so that the high-angle diffractive signals are acquired. In order to record a far-field diffraction pattern and, thus satisfy the Fraunhofer approximation, the sample needs to be placed at a sufficiently long distance z from the detector, z ≫ D2 ∕λ, where D is the diameter of the sample or the diameter of the illumination area and λ is the wavelength of the illuminating radiation. For a successfully reconstructed image, the theoretical Rayleigh
spatial resolution can be estimated from δ 0.61λ∕NA, where NA is the numerical aperture. 3. EXPERIMENT Figure 1 shows our experimental configuration for tabletop coherent diffractive imaging. The laser pulses (∼2 mJ pulses with a duration of 30 fs centred at 810 nm) generated by a 1 kHz multistage multipass chirped-pulse amplifier system are focussed by a 300 mm focal length lens into a 150 mm long gas cell with a glass window at the entrance and an ∼0.1 mm pinhole at the exit. The effective peak intensity at the focus is approximately 2 × 1014 W∕cm2 . The XUV radiation is generated around the end of the gas cell. The high harmonic production and detection systems are described elsewhere [23]. Three pinholes (P1, P2, and P3) are used to reduce thermal impact on the ultrathin metal foil, which is installed to isolate the harmonic beam from the fundamental (200 nm thick aluminium for harmonics from argon or 300 nm thick zirconium for harmonics from helium) and scattering from the fundamental beam to the detector. The HHG radiation is reflected by an XUV plane mirror (M1) and is then focused by an XUV focusing mirror (M2) (commercial Optix Fab mirrors with 35% reflectivity for each mirror) in a Z configuration to reduce the reflection angle at the focusing mirror. In order to obtain a good focusing point, i.e., the astigmatism of the focusing mirror is minimized, the reflection angle is kept small (∼10°), while the HHG beam size (∼2 mm) is small and the focal length (∼10 cm) is not too short. The sample is mounted on a holder, which is placed on a linear stepper motor mounted on a set of x–y translation stages for precise control of the three directions (x, y, and z). A charge coupled device camera system with a 2048 × 2048 imaging array of 13 μm pixel size (Princeton Instruments PIXIS 2048 × 2048), which is cooled to −40°C to minimize thermal noise when taking diffraction data is placed 3.5 cm behind the sample to capture the sample’s diffraction pattern. Hence, the NA is measured to be ∼0.38, and a theoretical spatial resolution is estimated to be about 48 nm (Rayleigh criterion). The sample is now positioned at the appropriate coordinates so that the center of the diffraction pattern coincides with the center of the detector chip. The whole CDI apparatus downstream from the gas cell is placed inside a vacuum chamber, which is operated at a pressure of ∼10−5 Torr. Two 5 × 200 μm slits, which are placed in an x–y configuration, are also mounted on the sample holder to determine the HHG beam size at different positions relative to the focus point
Fig. 1. Experimental configuration for tabletop coherent diffractive imaging [18].
Research Article [18]. In our work, two kinds of samples are investigated. The first sample (3 μm × 3 μm SWIN sample) is fabricated on a 50 nm thick Si3 N4 membrane and the two sides are coated with 50 and 150 nm thick gold layers to ensure that the membrane is almost opaque to the illuminating beam. The SWIN pattern is milled using ion beam lithography with the smallest dimension ∼75 nm measured on the leg of the letter N [see Fig. 3(a)]. Therefore, this sample can be considered to be a transmission sample. The second sample is fabricated by doping 2 μm silica particles and a few 400 nm amino polystyrene nanoparticles on a 30 nm thick Si3 N4 membrane, which has a rather high transmission (∼40%) at this wavelength. All particles doped in the second sample are opaque to the incident beam at 30 nm; therefore, this sample can be considered to be an absorption sample. Scanning electron microscopy (SEM) images of these samples are shown in Figs. 3(a) and 4(a), respectively. The 2 μm silica particles cover ∼75% of the window area, and only a few 400 nm particles can be observed in the SEM image. The yellow arrow in Fig. 4(a) indicates one of the amino polystyrene nanoparticles. 4. RESULTS AND DISCUSSION A. Generation of the High-Order Harmonic Source
The number of effective harmonic orders and their relative weighting in the power spectrum can be controlled by the phase-matching parameters. By an appropriate choice of species of gas, gas pressure, effective interaction length, and aperture diameter, the harmonic emission can be phase-matched and confined to just a few harmonic orders. Variation of the macroscopic parameters influences the atomic density and the ionization fraction; therefore, macroscopic phase matching can be achieved by balancing the dispersion phase mismatch and the plasma phase mismatch. For argon, the laser focus is set close to the exit of the gas cell, and other experimental parameters such as the gas pressure and the aperture diameter are controlled so that the phase-matched and most intense harmonic orders (around four harmonics) around 30 nm shown in Fig. 2(a) are achieved because of the maximum reflectivity of the XUV mirror at 30 nm with 1 nm bandwidth. Under these experimental conditions, the argon pressure in the gas cell was measured to be ∼60 Torr, the laser energy was around 1.2 mJ, and the focus position was approximately 2 mm inside the gas cell. The inset of Fig. 2(a), which is measured by inserting a grazing incidence spectrometer (GIMS #4—Set Point, with a 300 grooves/mm grating) into the harmonic beam path, shows the harmonic source at around 30 nm (H27) after passing the focusing mirror (M2) to illuminate the sample. In this case, the ratio λ∕Δλ is ∼200, which is sufficiently large; thus, the condition of a reasonably narrow bandwidth is satisfied. Before conducting CDI experiments, the degree of spatial coherence of the source needs to be determined. Thus, we perform a Young’s double-slit (YDS) experiment to ensure that our harmonic source has a high degree of spatial coherence. The experimental setup for this measurement is similar to that used for the CDI experiment, except that the pair of mirrors (M1 and M2) and the CDI samples are not installed and the spectrometer is attached. We use a Young’s double slit consisting of two parallel 4 μm × 100 μm slits, with a spacing of
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Fig. 2. (a)–(c) Phase-matched harmonic spectra for argon before passing the focusing mirror with the most intense harmonic emission at ∼30 nm with the inset showing the reflected spectrum for illumination of the sample. Interference fringes for Young’s double-slit separation of 20 μm after being dispersed by the spectrometer. Intensity distribution of an interference fringe of H27. (d)–(f) For helium, with the most intense harmonic emission at ∼10 nm and the intensity distribution of an interference fringe of H81.
20 μm. The Young’s double slit is etched into a silicon wafer, which is mounted on a slit holder and placed at ∼60 cm from the CCD. By inserting a spectrometer into the beam path and mounting the YDS perpendicular to the slit of the spectrometer, the interference fringes of each harmonic observed along the X direction of the CCD are directly recorded in the Y direction. Based on the intensity distribution of the interference pattern shown in Fig. 2(c), the degree of spatial coherence of
Fig. 3. “SWIN” sample. (a) Scanning electron microscope image. (b) Diffraction image. (c) Zoom into the center of the diffraction image. (d) Zoom into the high-angle region of the diffraction image. (e) Reconstructed image. (f) Cross section of the leg of the letter N from the reconstructed image. All of the above results are obtained with the 30 nm focused harmonic source. (g) Diffraction image. (h) Zoom into the centre of the diffraction image. (i) Zoom into the high-angle region of the diffraction image obtained with the 10 nm focused harmonic source.
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the harmonic source generated from argon is ∼0.99, which indicates a very high spatial coherence of the HHG source. B. Imaging Results
First, we conduct the CDI experiment with the 30 nm focused harmonic source generated from argon. To simplify the reconstruction process, we considered that the FWHM beam size at the sample is much larger than the sample size, which allows the condition for a uniform illuminating field to be satisfied. Therefore, in order to determine the position to place the sample, a scanning slit method was implemented to measure the FWHM beam size at different distances from the focus point [18]. It was shown that at the focus, the FWHM beam size is ∼7 μm, and, at distances of 3.5 and 1.5 mm from the focus point, the FWHM beam size is ∼60 and ∼15 μm, respectively. With an exposure time of 8 s for the 3 μm × 3 μm SWIN sample and 30 s for the 13 μm × 13 μm Si3 N4 membrane sample doped with 2 μm plain silica particles and a few 400 nm amino polystyrene particles diffraction patterns with a rather high signal-to-noise (S/N) are obtained with the maximum dynamic range of our CCD (∼65; 000 counts) without any pixel being saturated. Figure 3(b) shows the diffraction image of the SWIN sample when it is placed 1.5 mm from the focus, and Fig. 4(b) shows the diffraction image of the doped particle sample when it is placed 3.5 mm from the focus. It is useful to recall that, at these large distances, since the FWHM beam size is more than four times larger than the sample size, leading to an intensity variation of the illuminating field over the sample of less than 5%, the condition for a uniform illuminating field is satisfied. The contribution of the harmonics (H25 and H29) to the diffraction image depends on the distance between the sample and the focus point of the mirror. When this distance is large enough, diffraction patterns from these harmonics can be seen on the CCD. In our previous paper [18], in order to measure the source’s spectrum, we placed the sample consisting of an array of pinholes relatively
Fig. 4. “Doped particle” sample. (a) Scanning electron microscope image. (b) Diffraction image. (c) Zoom into the center of the diffraction image. (d) Zoom into the high-angle region of the diffraction image. (e) Reconstructed image. (f) Cross section of the area marked by the dashed yellow line in the reconstructed image. (g) Zoom into the area marked by the dashed yellow rectangular in the reconstructed image. All of the above results are obtained with the 30 nm focused harmonic source.
Research Article far (∼7 mm) from the focus point. Consequently, the contribution of these harmonics was observed. However, in the present work, the sample-focus point distance is shorter in order to reduce the exposure time by improving the effective photon flux density at the sample spot. Therefore, the contribution of the harmonics H25 and H29 is negligible. This leads to the diffraction pattern of the sample resulting solely from the illumination of the strongest harmonic H27 on the sample. An iterative image reconstruction is performed by considering the Fraunhofer diffraction at the detector plane. The error reduction (ER) and hybrid input output (HIO) algorithms are used to recover the sample’s image, with a fixed support constraint [18]. Although the amplitude of the field can be uniform, the curved wavefront of the illuminating field needs to be taken into account via phase correction during the reconstruction process. The reconstructed images for the SWIN sample and the doped particle sample are shown in Figs. 3(e) and 4(e), respectively. To determine the resolution of the reconstructed images, a knife-edge test is performed [10]. A cross section of the leg of the letter N from the reconstructed image of the SWIN sample [see Fig. 3(f)] reveals a resolution of ∼45 nm (10%–90% of intensity profile) and a cross section of the transmission area marked with the dashed yellow line from the reconstructed image of the doped particle sample reveals a resolution of ∼250 nm [see Fig. 4(f)]. It is noted that the phase retrieval algorithm used in this study allows the transmission regions of the samples to be reconstructed. The reconstructed resolution for the SWIN sample matches the theoretical calculation based on the Rayleigh criterion (δ 0.61λ∕NA ∼ 48 nm) well. Here, we reiterate that, for the SWIN sample, high-angle diffraction data with the maximum dynamic range of the CCD can be seen clearly out to the edge of the CCD with a 2048 × 2048 imaging array of 13 μm × 13 μm pixels. On the other hand, for the doped particle sample, since the transmission of the 30 nm thick Si3 N4 membrane at ∼30 nm is rather high (∼40%), a high signal-to-noise image with a full dynamic range diffraction pattern is captured within an array 512 × 512 of the CCD leading to a NA of 0.095 and a theoretical resolution of the doped particle sample of 192 nm. A limitation of our reconstruction process is that, although the doped particle sample is absorbing and random, we are currently not able to include the complex absorption coefficient of the spherical particles, which is smoothly decreasing. Therefore, unlike a good match between the theoretical resolution and the reconstructed resolution of the SWIN sample, the reconstructed resolution (∼250 nm) of the doped particle sample obtained by the knife-edge test is large and significantly different from the theoretical resolution (∼192 nm). Figure 4(g) is a zoom into the area marked by the dashed yellow square in the reconstructed image in Fig. 4(e). With a resolution of ∼250 nm, the 400 nm amino polystyrene particles in the reconstructed image are likely to be visible [one of them is marked by the yellow arrow in Fig. 4(g)], though not clear as expected. In order to see these particles more clearly, the reconstructed resolution needs to be improved by acquisition of high-angle diffraction data with the help of a beam stop. The beam stop could allow the capture of diffraction patterns over a dynamic range that exceeds the maximum
Research Article dynamic range of the CCD. With this approach, first, an intense low-angle diffraction feature image is acquired with an appropriately short exposure time, which ensures that all pixels in the CCD are not saturated. After that, two beam stops (horizontal and vertical) are employed to capture high-angle diffraction feature images. Saturation of the center features is avoided by placing the beam stop over the center of the CCD. All three images are then normalized to each other and combined by image stitching in order to retain the high-angle diffraction data (with long exposure time) and the low-angle diffraction data (with short exposure time) with no information from any supporting material of the beam stops. However, use of beam stops would make the experimental design more complex. In this study, the most intense harmonic orders around 10 nm (H81) are generated from helium gas [see Fig. 2(d)]. For the spectrum in Fig. 2(d), the helium gas pressure was measured to be ∼700 Torr, a laser pulse energy of 1.9 mJ was applied, and the focus position was 2 mm inside the gas cell. The degree of spatial coherence of this source was measured to be ∼0.86, which is smaller than argon but is still relatively high for a CDI experiment. It is important to note that since helium gas has a very high ionization potential, even a small variation of the beam profile of the fundamental laser can cause a significantly unstable harmonic beam, leading to a lower degree of spatial coherence of the harmonic beam compared to that generated with argon. The motivation for this work is to achieve a higher resolution of reconstruction, since the resolution is inversely proportional to the incident wavelength, i.e., the shorter the wavelength of the illumination beam, the higher the resolution. In order to perform the CDI, two new mirrors, which allow a few harmonic orders around 10 nm to be selected and focused into the sample, are installed. With an exposure time of 1 min, a diffraction image with the maximum dynamics range of the CCD of the SWIN sample obtained with the 10 nm focused harmonic source is shown [Fig. 3(g)]. We should mention that, when the 10 nm high harmonic source is used as the illumination beam, there is no high-angle diffractive information to be observed beyond the 512 × 512 array of the CCD because of the limitation of the maximum dynamic range of the CCD (65,000 counts). In addition, from the zoom into the high-angle region of the diffraction images shown in Figs. 3(d) and 3(i), it is shown that the high-angle speckles at the edge of the CCD chip (2048 × 2048 array) generated with the 30 nm harmonic source based on argon gas has a higher signal-to-noise ratio than that within the 512 × 512 CCD array generated with the 10 nm harmonic source based on helium gas. We are currently not able to achieve a high-resolution reconstructed image in this case. It is useful to recall that, in the short-wavelength range (
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Coherent diffractive imaging microscope with a high-order harmonic source KHUONG BA DINH,* HOANG VU LE, PETER HANNAFORD,
AND
LAP VAN DAO
Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Vic 3122, Australia *Corresponding author: [email protected] Received 17 November 2014; revised 1 May 2015; accepted 5 May 2015; posted 6 May 2015 (Doc. ID 226904); published 3 June 2015
We report the generation of highly coherent extreme ultraviolet sources with wavelengths around 30 and 10 nm by phase-matched high-order harmonic generation (HHG) in a gas cell filled with argon and helium, respectively. We then perform coherent diffractive imaging (CDI) by using a focused narrow-bandwidth HHG source with wavelength around 30 nm as an illumination beam for two kinds of samples. The first is a transmission sample and the second is a absorption sample. In addition, we report the successful reconstruction of a complex absorption sample using a tabletop high-harmonic source. This will open the path to the realization of a compact soft x-ray microscope to investigate biological samples such as membrane proteins. © 2015 Optical Society of America OCIS codes: (110.0180) Microscopy; (110.1650) Coherence imaging; (140.7240) UV, EUV, and X-ray lasers. http://dx.doi.org/10.1364/AO.54.005303
1. INTRODUCTION Microscopy techniques have made many significant achievements with high-resolution imaging down to the nanometer scale. Scanning probe microscopy techniques such as atomic force microscopy have been developed with a resolution of the order of fractions of a nanometer [1]. However, they are limited to surface structures and are not able to allow us to make a morphological analysis. Electron microscopy has provided the resolution of crystalline structures at the atomic level by using a beam of electrons to illuminate a sample, but this technique is restricted to imaging thin samples [2]. Using extreme ultraviolet or soft x-ray radiation as a light source allows us to obtain high-resolution imaging of thick samples [3]. Imaging with extreme-ultraviolet or soft-x-ray radiation is usually performed with diffractive optical elements with very short focal lengths such as Fresnel zone plates, since conventional lenses have strong absorption of soft x rays. Unfortunately, at very high magnification, zone plates have a relatively short working distance and a small depth of focus leading to the potential for large chromatic aberration. Coherent x-ray diffractive imaging (CDI) using short wavelength light in the extreme ultraviolet or soft x-ray regions has emerged as a promising alternative approach for highresolution imaging of thick samples, especially for biological samples [4–6]. Instead of using optical elements, in CDI the sample to be investigated is illuminated with a coherent x-ray source, and the object’s image is reconstructed from the diffraction pattern by applying iterative phase-retrieval algorithms. This approach allows aberration-free imaging and offers a very 1559-128X/15/175303-06$15/0$15.00 © 2015 Optical Society of America
large depth of focus, since there is no physical lens used. The spatial reconstructed resolution is mainly limited by the wavelength of the radiation used for illumination and by the largest angle of scattering over which diffraction patterns are recorded. Short-wavelength sources based on large facilities such as synchrotrons and free-electron and x-ray lasers can be used as an illuminating source for CDI [7,8]. Besides these sources, tabletop soft x-ray sources based on high-order harmonic generation (HHG) have been used for this lensless imaging technique to enable small-scale microscopy, which provides high spatial resolution of nanometer-scale objects [6,9–11]. In addition, HHG produced by the interaction of an intense laser pulse with a gas medium can provide a high degree of spatial coherence [12–14]. Since iterative methods for image reconstruction normally require a monochromatic wave field, CDI is usually carried out with a single harmonic order of the harmonic spectrum, which is selected by using narrow bandwidth optical elements such as a monochromator. However, for the short-wavelength range (1 mm; therefore, the effective photon flux for illumination of a micrometer-scale sample was also low. Recently, CDI using a single harmonic beam selected by employing XUV focusing mirrors has been implemented to achieve a significant advance in imaging resolution and data-acquisition time [9,10,18,19]. The focusing mirror allows the illuminating
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beam to be confined to a smaller area ( 100) and coherent radiation of appropriate wavelength. The spatial coherence length needs to be larger than the product of the sample size and the linear oversampling factor. Second, the diffracted light pattern needs to be recorded with sufficient resolution to allow for the fact that the CCD detector only records an intensity pattern and loses the phase information required for simple Fourier transform reconstruction of the image. In addition, the photon flux of the radiation source needs to be high enough so that the high-angle diffractive signals are acquired. In order to record a far-field diffraction pattern and, thus satisfy the Fraunhofer approximation, the sample needs to be placed at a sufficiently long distance z from the detector, z ≫ D2 ∕λ, where D is the diameter of the sample or the diameter of the illumination area and λ is the wavelength of the illuminating radiation. For a successfully reconstructed image, the theoretical Rayleigh
spatial resolution can be estimated from δ 0.61λ∕NA, where NA is the numerical aperture. 3. EXPERIMENT Figure 1 shows our experimental configuration for tabletop coherent diffractive imaging. The laser pulses (∼2 mJ pulses with a duration of 30 fs centred at 810 nm) generated by a 1 kHz multistage multipass chirped-pulse amplifier system are focussed by a 300 mm focal length lens into a 150 mm long gas cell with a glass window at the entrance and an ∼0.1 mm pinhole at the exit. The effective peak intensity at the focus is approximately 2 × 1014 W∕cm2 . The XUV radiation is generated around the end of the gas cell. The high harmonic production and detection systems are described elsewhere [23]. Three pinholes (P1, P2, and P3) are used to reduce thermal impact on the ultrathin metal foil, which is installed to isolate the harmonic beam from the fundamental (200 nm thick aluminium for harmonics from argon or 300 nm thick zirconium for harmonics from helium) and scattering from the fundamental beam to the detector. The HHG radiation is reflected by an XUV plane mirror (M1) and is then focused by an XUV focusing mirror (M2) (commercial Optix Fab mirrors with 35% reflectivity for each mirror) in a Z configuration to reduce the reflection angle at the focusing mirror. In order to obtain a good focusing point, i.e., the astigmatism of the focusing mirror is minimized, the reflection angle is kept small (∼10°), while the HHG beam size (∼2 mm) is small and the focal length (∼10 cm) is not too short. The sample is mounted on a holder, which is placed on a linear stepper motor mounted on a set of x–y translation stages for precise control of the three directions (x, y, and z). A charge coupled device camera system with a 2048 × 2048 imaging array of 13 μm pixel size (Princeton Instruments PIXIS 2048 × 2048), which is cooled to −40°C to minimize thermal noise when taking diffraction data is placed 3.5 cm behind the sample to capture the sample’s diffraction pattern. Hence, the NA is measured to be ∼0.38, and a theoretical spatial resolution is estimated to be about 48 nm (Rayleigh criterion). The sample is now positioned at the appropriate coordinates so that the center of the diffraction pattern coincides with the center of the detector chip. The whole CDI apparatus downstream from the gas cell is placed inside a vacuum chamber, which is operated at a pressure of ∼10−5 Torr. Two 5 × 200 μm slits, which are placed in an x–y configuration, are also mounted on the sample holder to determine the HHG beam size at different positions relative to the focus point
Fig. 1. Experimental configuration for tabletop coherent diffractive imaging [18].
Research Article [18]. In our work, two kinds of samples are investigated. The first sample (3 μm × 3 μm SWIN sample) is fabricated on a 50 nm thick Si3 N4 membrane and the two sides are coated with 50 and 150 nm thick gold layers to ensure that the membrane is almost opaque to the illuminating beam. The SWIN pattern is milled using ion beam lithography with the smallest dimension ∼75 nm measured on the leg of the letter N [see Fig. 3(a)]. Therefore, this sample can be considered to be a transmission sample. The second sample is fabricated by doping 2 μm silica particles and a few 400 nm amino polystyrene nanoparticles on a 30 nm thick Si3 N4 membrane, which has a rather high transmission (∼40%) at this wavelength. All particles doped in the second sample are opaque to the incident beam at 30 nm; therefore, this sample can be considered to be an absorption sample. Scanning electron microscopy (SEM) images of these samples are shown in Figs. 3(a) and 4(a), respectively. The 2 μm silica particles cover ∼75% of the window area, and only a few 400 nm particles can be observed in the SEM image. The yellow arrow in Fig. 4(a) indicates one of the amino polystyrene nanoparticles. 4. RESULTS AND DISCUSSION A. Generation of the High-Order Harmonic Source
The number of effective harmonic orders and their relative weighting in the power spectrum can be controlled by the phase-matching parameters. By an appropriate choice of species of gas, gas pressure, effective interaction length, and aperture diameter, the harmonic emission can be phase-matched and confined to just a few harmonic orders. Variation of the macroscopic parameters influences the atomic density and the ionization fraction; therefore, macroscopic phase matching can be achieved by balancing the dispersion phase mismatch and the plasma phase mismatch. For argon, the laser focus is set close to the exit of the gas cell, and other experimental parameters such as the gas pressure and the aperture diameter are controlled so that the phase-matched and most intense harmonic orders (around four harmonics) around 30 nm shown in Fig. 2(a) are achieved because of the maximum reflectivity of the XUV mirror at 30 nm with 1 nm bandwidth. Under these experimental conditions, the argon pressure in the gas cell was measured to be ∼60 Torr, the laser energy was around 1.2 mJ, and the focus position was approximately 2 mm inside the gas cell. The inset of Fig. 2(a), which is measured by inserting a grazing incidence spectrometer (GIMS #4—Set Point, with a 300 grooves/mm grating) into the harmonic beam path, shows the harmonic source at around 30 nm (H27) after passing the focusing mirror (M2) to illuminate the sample. In this case, the ratio λ∕Δλ is ∼200, which is sufficiently large; thus, the condition of a reasonably narrow bandwidth is satisfied. Before conducting CDI experiments, the degree of spatial coherence of the source needs to be determined. Thus, we perform a Young’s double-slit (YDS) experiment to ensure that our harmonic source has a high degree of spatial coherence. The experimental setup for this measurement is similar to that used for the CDI experiment, except that the pair of mirrors (M1 and M2) and the CDI samples are not installed and the spectrometer is attached. We use a Young’s double slit consisting of two parallel 4 μm × 100 μm slits, with a spacing of
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Fig. 2. (a)–(c) Phase-matched harmonic spectra for argon before passing the focusing mirror with the most intense harmonic emission at ∼30 nm with the inset showing the reflected spectrum for illumination of the sample. Interference fringes for Young’s double-slit separation of 20 μm after being dispersed by the spectrometer. Intensity distribution of an interference fringe of H27. (d)–(f) For helium, with the most intense harmonic emission at ∼10 nm and the intensity distribution of an interference fringe of H81.
20 μm. The Young’s double slit is etched into a silicon wafer, which is mounted on a slit holder and placed at ∼60 cm from the CCD. By inserting a spectrometer into the beam path and mounting the YDS perpendicular to the slit of the spectrometer, the interference fringes of each harmonic observed along the X direction of the CCD are directly recorded in the Y direction. Based on the intensity distribution of the interference pattern shown in Fig. 2(c), the degree of spatial coherence of
Fig. 3. “SWIN” sample. (a) Scanning electron microscope image. (b) Diffraction image. (c) Zoom into the center of the diffraction image. (d) Zoom into the high-angle region of the diffraction image. (e) Reconstructed image. (f) Cross section of the leg of the letter N from the reconstructed image. All of the above results are obtained with the 30 nm focused harmonic source. (g) Diffraction image. (h) Zoom into the centre of the diffraction image. (i) Zoom into the high-angle region of the diffraction image obtained with the 10 nm focused harmonic source.
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Vol. 54, No. 17 / June 10 2015 / Applied Optics
the harmonic source generated from argon is ∼0.99, which indicates a very high spatial coherence of the HHG source. B. Imaging Results
First, we conduct the CDI experiment with the 30 nm focused harmonic source generated from argon. To simplify the reconstruction process, we considered that the FWHM beam size at the sample is much larger than the sample size, which allows the condition for a uniform illuminating field to be satisfied. Therefore, in order to determine the position to place the sample, a scanning slit method was implemented to measure the FWHM beam size at different distances from the focus point [18]. It was shown that at the focus, the FWHM beam size is ∼7 μm, and, at distances of 3.5 and 1.5 mm from the focus point, the FWHM beam size is ∼60 and ∼15 μm, respectively. With an exposure time of 8 s for the 3 μm × 3 μm SWIN sample and 30 s for the 13 μm × 13 μm Si3 N4 membrane sample doped with 2 μm plain silica particles and a few 400 nm amino polystyrene particles diffraction patterns with a rather high signal-to-noise (S/N) are obtained with the maximum dynamic range of our CCD (∼65; 000 counts) without any pixel being saturated. Figure 3(b) shows the diffraction image of the SWIN sample when it is placed 1.5 mm from the focus, and Fig. 4(b) shows the diffraction image of the doped particle sample when it is placed 3.5 mm from the focus. It is useful to recall that, at these large distances, since the FWHM beam size is more than four times larger than the sample size, leading to an intensity variation of the illuminating field over the sample of less than 5%, the condition for a uniform illuminating field is satisfied. The contribution of the harmonics (H25 and H29) to the diffraction image depends on the distance between the sample and the focus point of the mirror. When this distance is large enough, diffraction patterns from these harmonics can be seen on the CCD. In our previous paper [18], in order to measure the source’s spectrum, we placed the sample consisting of an array of pinholes relatively
Fig. 4. “Doped particle” sample. (a) Scanning electron microscope image. (b) Diffraction image. (c) Zoom into the center of the diffraction image. (d) Zoom into the high-angle region of the diffraction image. (e) Reconstructed image. (f) Cross section of the area marked by the dashed yellow line in the reconstructed image. (g) Zoom into the area marked by the dashed yellow rectangular in the reconstructed image. All of the above results are obtained with the 30 nm focused harmonic source.
Research Article far (∼7 mm) from the focus point. Consequently, the contribution of these harmonics was observed. However, in the present work, the sample-focus point distance is shorter in order to reduce the exposure time by improving the effective photon flux density at the sample spot. Therefore, the contribution of the harmonics H25 and H29 is negligible. This leads to the diffraction pattern of the sample resulting solely from the illumination of the strongest harmonic H27 on the sample. An iterative image reconstruction is performed by considering the Fraunhofer diffraction at the detector plane. The error reduction (ER) and hybrid input output (HIO) algorithms are used to recover the sample’s image, with a fixed support constraint [18]. Although the amplitude of the field can be uniform, the curved wavefront of the illuminating field needs to be taken into account via phase correction during the reconstruction process. The reconstructed images for the SWIN sample and the doped particle sample are shown in Figs. 3(e) and 4(e), respectively. To determine the resolution of the reconstructed images, a knife-edge test is performed [10]. A cross section of the leg of the letter N from the reconstructed image of the SWIN sample [see Fig. 3(f)] reveals a resolution of ∼45 nm (10%–90% of intensity profile) and a cross section of the transmission area marked with the dashed yellow line from the reconstructed image of the doped particle sample reveals a resolution of ∼250 nm [see Fig. 4(f)]. It is noted that the phase retrieval algorithm used in this study allows the transmission regions of the samples to be reconstructed. The reconstructed resolution for the SWIN sample matches the theoretical calculation based on the Rayleigh criterion (δ 0.61λ∕NA ∼ 48 nm) well. Here, we reiterate that, for the SWIN sample, high-angle diffraction data with the maximum dynamic range of the CCD can be seen clearly out to the edge of the CCD with a 2048 × 2048 imaging array of 13 μm × 13 μm pixels. On the other hand, for the doped particle sample, since the transmission of the 30 nm thick Si3 N4 membrane at ∼30 nm is rather high (∼40%), a high signal-to-noise image with a full dynamic range diffraction pattern is captured within an array 512 × 512 of the CCD leading to a NA of 0.095 and a theoretical resolution of the doped particle sample of 192 nm. A limitation of our reconstruction process is that, although the doped particle sample is absorbing and random, we are currently not able to include the complex absorption coefficient of the spherical particles, which is smoothly decreasing. Therefore, unlike a good match between the theoretical resolution and the reconstructed resolution of the SWIN sample, the reconstructed resolution (∼250 nm) of the doped particle sample obtained by the knife-edge test is large and significantly different from the theoretical resolution (∼192 nm). Figure 4(g) is a zoom into the area marked by the dashed yellow square in the reconstructed image in Fig. 4(e). With a resolution of ∼250 nm, the 400 nm amino polystyrene particles in the reconstructed image are likely to be visible [one of them is marked by the yellow arrow in Fig. 4(g)], though not clear as expected. In order to see these particles more clearly, the reconstructed resolution needs to be improved by acquisition of high-angle diffraction data with the help of a beam stop. The beam stop could allow the capture of diffraction patterns over a dynamic range that exceeds the maximum
Research Article dynamic range of the CCD. With this approach, first, an intense low-angle diffraction feature image is acquired with an appropriately short exposure time, which ensures that all pixels in the CCD are not saturated. After that, two beam stops (horizontal and vertical) are employed to capture high-angle diffraction feature images. Saturation of the center features is avoided by placing the beam stop over the center of the CCD. All three images are then normalized to each other and combined by image stitching in order to retain the high-angle diffraction data (with long exposure time) and the low-angle diffraction data (with short exposure time) with no information from any supporting material of the beam stops. However, use of beam stops would make the experimental design more complex. In this study, the most intense harmonic orders around 10 nm (H81) are generated from helium gas [see Fig. 2(d)]. For the spectrum in Fig. 2(d), the helium gas pressure was measured to be ∼700 Torr, a laser pulse energy of 1.9 mJ was applied, and the focus position was 2 mm inside the gas cell. The degree of spatial coherence of this source was measured to be ∼0.86, which is smaller than argon but is still relatively high for a CDI experiment. It is important to note that since helium gas has a very high ionization potential, even a small variation of the beam profile of the fundamental laser can cause a significantly unstable harmonic beam, leading to a lower degree of spatial coherence of the harmonic beam compared to that generated with argon. The motivation for this work is to achieve a higher resolution of reconstruction, since the resolution is inversely proportional to the incident wavelength, i.e., the shorter the wavelength of the illumination beam, the higher the resolution. In order to perform the CDI, two new mirrors, which allow a few harmonic orders around 10 nm to be selected and focused into the sample, are installed. With an exposure time of 1 min, a diffraction image with the maximum dynamics range of the CCD of the SWIN sample obtained with the 10 nm focused harmonic source is shown [Fig. 3(g)]. We should mention that, when the 10 nm high harmonic source is used as the illumination beam, there is no high-angle diffractive information to be observed beyond the 512 × 512 array of the CCD because of the limitation of the maximum dynamic range of the CCD (65,000 counts). In addition, from the zoom into the high-angle region of the diffraction images shown in Figs. 3(d) and 3(i), it is shown that the high-angle speckles at the edge of the CCD chip (2048 × 2048 array) generated with the 30 nm harmonic source based on argon gas has a higher signal-to-noise ratio than that within the 512 × 512 CCD array generated with the 10 nm harmonic source based on helium gas. We are currently not able to achieve a high-resolution reconstructed image in this case. It is useful to recall that, in the short-wavelength range (
