High-resolution [JH1] soft x-ray digital in-line holographic microscopy

Abstract: A scheme of sHigh-spatial-resolution soft x-ray digital in-line holographic microscopy was developed. to achieve high spatial resolution. ItThe scheme usesd partially coherent and highly divergenting[JH2]  lights, which were generated by a combination of a Fresnel zone plate (FZP) and a pinhole with a radius of 200 nm radius, when thewith incidence incoherent lights were tightly focused on the pinhole. At a wavelength of 2.38 nm, objectives such as a two objects, a carbon powder particle and a a gold -pattern, were imaged withto a spatial resolution of ~150 nm. The scheme overcamesuperseded the achievable resolution, (i.e. the pinhole’s radius), of typical pinhole-based holographic microscopy.


OCIS codes: (090.0090) Hh[JH3] olography; (090.1995) digital holography; (110.2960) image analysis; (110.7440) x-ray imaging; (340.6720) synchrotron radiation; (340.7460) x-ray microscopy


1. Introduction


Lensless x-ray holography has been ofattracted interest for the pastin recent years for its utility toin obtaining complex field information withat a high spatial resolution. Since Gabor’s invention in 1948 innovation [1], holography has been proved asto be a powerful technique that offerings 3D sample information of a sample from a single 2D hologram. Soft x-ray holography with aof sub-100 nm resolution, has been demonstrated throughin the forms of both Fourier transform holography (FTH) [2, 4] and Gabor holography (or in-line holography) [3]., has been demonstrated. In the reported FTH, [2, 4], a delicate pinhole was fabricated inon the sample plane in order to generate a coherent and divergenting reference wave. High-resolution imaging withto 50 nm resolution was reported withfor a scheme that usedthat uses a Fresnel zone plate (FZP) to generate a reference wave and a mask-sample structure [2]. In the setup, the pinhole size limited the resolution and the CCD detector’s dimensions limited the magnification. The inherent problem ofwith the FTH is theits limited brightness due to athe nanoscale pinhole size. Recently, more intense holograms have been acquiredachieved by replacing the pinhole withsubstituting multiple pinholes [5] for the single one orand by means of binary uniformly redundant arrays (URAs) [6]. The main drawback of those reportedthese FTH schemes, however, is that one hasthe need to fabricatedrill a pinhole(s) or fabricate URAs near the sample atin or on the same substrate, which limits practical applications forto diverse samples and/or in-situ experiments.

In a[JH4]  typical x-ray digital in-line holography setup [7-10] which uses a spherical reference wave, a pinhole, an object, and a CCD are positioned in series inon different planes. in series. If the magnification is sufficiently large, enough, then[JH5]  the resolution is determined by the radius of the pinhole. The highest spatial resolution by the pinhole-based digital in-line holography reported to date[JH6]  is ~400 nm [7]. One may obtain aA high-NA (numerical aperture) (NA) coherent light also can be obtained without a pinhole, by using spherical mirrors with extreme ultraviolet (EUV) radiation [11-12]. However, the resolution is limited by the longer wavelength of the EUV. limited the resolution. One may also overcome theThis limitation of NA can be overcome by recording holograms with a high-resolution photoresist nearby a sample [3]. AlthoughDespite the high- resolution was achieved, the method required a post-process tohologram digitizatione  the hologram by use of an atomic force microscopy is required, limiting the capability [JH7] of in-situ investigation.

Fully coherent reference waves, specifically low-NA undulator radiation or long-wavelength EUV radiation,  have been used forwith the above described methods to illuminate the entire CCD or resist;. undulator radiation of low NA or a EUV radiation of long wavelength. A Ffew researchesstudies werehave reported on the resolution of the in-line holography using a partially coherent light. OneTwo of them showed through calculations that, although the highly coherent light produces a high-resolution image, there is no need to pursue very high, coherence more than abeyond-the-criterion coherence [13, 14]. In fact, Iit was provedn that a partially coherent source doeshas not significantly lowerdeleterious effect on[JH8]  the resolution [15]. TheThis result has stimulatedmotivated ourthe present studyinvestigation withof a rather incoherent x-ray source.

In this study, we presentreport a high-resolution soft x-ray digital in-line holographic microscopy by usemeans of a spatial filter composed of an FZP and pinhole. The pinhole with a radius of 200 nm radius generates highly divergenting and partially coherent lights [JH9] when incidence incoherent lights are tightly focused by the FZP on the pinhole. TheThis combination results in a relatively high NA reference wave, even with a short wavelength of 2.38 nm. AA  ccarbon powder particle and a gold- pattern were imaged withto a spatial resolution of ~150 nm. This is the highest resolution ever reported withfor digital in-line holographic microscopy. The scheme overcamesuperseded the achievable resolution, (i.e. the pinhole’s radius), of typical pinhole-based in-line holographic microscopy.


2. Experiment


The experiments were carried out with a modified TXM of ~50 nm spatial resolution [16] that was newly developed aton the 7B1 beamline at Pohang Light Source (PLS). The spatial resolution of the TXM was ~50 nm. Figure 1 showsis a thumbnail view of the experimental setup. In the experiment, 2.38 nm sSoft x-rays (520 eV) of 2.38 nm wavelength withand a  1000X resolving power (EE) of 1000 were used. The rays have a temporal coherence length (l2l) of ~2 mm, which limits the observable region of interference in in-line holography. The spatial filter is composed of an FZP and a pinhole. It has 4600 zones and is made out of 140 nm thick gold on a silicon nitride membrane. The focal length (f) of the 1st-order diffraction of the FZP is 92 mm, and the range of the NA is 0.005 ~ 0.01 at the wavelength of 2.38 nm wavelength. The expected efficiency of the 1st-order diffraction’s expected efficiency is ~10 %. Because the FZP has the central beam stop, the beam’s profile on any plane excepting on the focal plane, the beam’s profile on any plane  is of an annular shape. The minimum size of the focused beam, which isas determined by the beamline geometry, is ~1 μm in the vertical direction and more than 10 μm in the horizontal direction. The ZP’s depth of focus (DOF) is ~20 μm. The pinhole, withof radius R=200 nm, was drilled on a 3 mm-thick nickel plate by focused ion beam (FIB) milling.




           Fig. 1. Schematic layout of the experiment and conceptual enlargement of the illumination angle.


If we assume that the illumination beam is a highly collimated plane wave and that the FZP is a combination of an annular pupil and a thin lens, then the field distribution at the focal plane is proportional to the Fourier transform of the annular flattop beam. The Fourier transform provides a 2D spatial spectrum of the beam. The pinhole functions as a low-pass filter, which passes smaller allowing spatial frequencies smaller than the cutoff frequency to pass and blockings higher frequencies ofon the spectrum. Thus the pinhole effectively excludes the edge[JH10]  of the annular disk and passestakes in the global distribution of the beam. Figure 1’s Cconceptual figuresdepictions of a line’s intensity profiles beforein front of[JH11]  and afterbehind[JH12]  the pinhole, as is shown in Fig. 1, show that the width (from minima to minima[JH13] ) of the latter became much wider than that of the former, effectively increasing the NA. In this experiment,[JH14]  forAs regards the converging incidence beam, with an angle of 0.005 rad., the diverging[JH15]  angle of the beam afterbehind[JH16]  the 200 nm-radius pinhole became ~0.018 rad. ian[JH17] . The pinhole, Iin addition to its spatial filtering function, the pinhole defines athe spatial coherence. Even though the pinhole size does not satisfy the condition for coherent light, R=λ/4πθ, the transmitted lights have[JH18]  a partial coherence. As a result, the spatial filter generates partially coherent and highly divergenting soft x-rays. It should be noted that the wavelength is the shortest and the corresponding NA is rather high, as everalways[JH19]  reported inof the digital in-line x-ray holography. The sample is placed at ~3 mm from the pinhole. As is described in Ref. 16, the pinhole and the sample are located in an atmospheric pressure, helium-ambient environment. with helium-ambient. The holographic image is recorded on an in-vacuum back-illuminated 16-bits CCD detector (1024 x 1024 pixels, 13 μm pixel size) placedpositioned at 1040 mm downstream of the sample. In order to characterize the imaging performance of the in-line holography, two samples were imaged.. The samples, each of which was placed on a 100 nm-thick silicon nitride membrane, One is a included a random-shaped carbon powder particle withof a few microns sizesdiameter.  The other is and a gold pattern ‘160’, made of gold with of 160 nm thickness. The samples were on a silicon nitride membrane of 100 nm thickness.

The nNumerical reconstruction of the hologram, back-propagation of the hologram to the object plane with illumination of the reference wave, was doneperformed by a convolution approach [17]: where is a complex object field aton the object plane,  is a hologram aton the CCD plane, is a reference wave aton the hologram plane,  is the impulse response function: , r is the distance between a point in the hologram and a point inon the reconstruction plane,  is the wave number: , and is a 2D Fourier transform of the . The reference wave  aton the hologram plane isis assumed asas a plane wave, which is simply a constant. Because the hologram is produced by a spherical wave, the magnified object field is obtained at a reconstruction distance , where A is the pinhole-sample distance, B is the sample-CCD distance, and M is the magnification of the system.


3. Results


                                   Fig. 2. Holograms of a carbon powder particle with respect to various

                                   pinhole sizes, with a radiius of (a) 700, (b) 500, (c) 400, and (d) 200 nm.


Holograms of a a carbon powder particle with different pinhole sizes were obtained with different pinhole sizes to verify the enhancement of the spatial coherence and the numerical apertureNA of the spatial filter. Figures 2(a) ~[JH20]   (d) show the holograms by use ofand the pertinent pinholes withof radiius  R=700 nm, 500 nm, 400 nm and 200 nm, respectively. The hHolograms 2(a)-2(c) were acquired for 180 s, and 2(d), for 300 s. Because of the limited detector size, we used a part of the annular ring of the FZP’s 1st-order diffraction, which is more clearly noticeable in 2(a). As the pinhole’s size decreased, the visibility of the fringes increased and the high spatial frequencies of the object field were revealed. In spite of the intensity’s decrease, the interference region expanded as the pinhole size decreased. When using the pinhole withof R=200 nm, the interference fringes extended to almost the full area of the CCD.

Figure 3 shows images of the fishlike carbon powder particle. To compare the reconstructed holographic image with the real object,,  as shown in Fig. 3(a), we imaged the powder[JH21]  with the TXM that is described in Ref. 16 (Fig. 3(a))[JH22] . The figureimage was obtained at the same photon energy (520 eV) with an exposure time of 60 s. Figure 3(b) shows the hologram of the powder by use offor the R=200 nm pinhole, with an exposure time of 300 s and with a338X magnification. of 338. The reconstructed amplitude image 3(c) shows particle detailsed image such as a bump, of the particle that is indicated by the red arrow. In this image, the reconstructed distance lies at the focus of the bump[JH23] , and some parts of the edges awayoutside from the field of focus are blurred. Figure 3(d) showsis a reconstructed phase image.



Fig. 3. Images of a fishlike carbon powder particle. (a) TXM’s absorption contrast image. (b) Image of hologram.

       (c) Reconstructed amplitude image. (d) Reconstructed phase image. The Rreconstructed images werewere enlarged..


To accurately quantify the spatial resolution of the reconstructed image, a gold pattern ‘160’ made of gold withof 160 nm thickness was imaged. The pattern hashad morea sharper edge than the carbon powder particle. The Hhologram image and the reconstructed amplitude image are shown in Figs. 4(a) and 4(b). A line profile of the magnified image 4(c) was obtained, and is plotted in Fig. 4(d). The 10% to 90% contrast change (knife-edge-criterion) in the line profile hads a width of 150 nm. This is the highest resolution so far reported inof digital in-line holographic microscopy; andit overcomessupersedes the criterion that the best resolution is defined by the pinhole radius size. In our geometry, assuming coherent illumination, the CCD size limits the resolution. The estimated resolution is ~160 nm (considering the CCD diagonal length: 18.8 mm), which matches to our measured resolution within the experimental error. This therefore implies that partially coherent light also resulted in the same theoretically expected resolution based on coherent illumination, and that the resolution depends only on the effective NA when the coherencey of the illumination is moregreater than athe criterion.




Fig. 4. Images of 160 nm-thick gold pattern ‘160’. made of gold with 160 nm thickness. (a) Hologram image. (b) Reconstructed amplitude image. (c) Magnified image of (b). (d) A lLine profile of the line indicated in (c).


4. Conclusions

We presented a high-resolution soft x-ray digital in-line holographic microscopy usingthat uses highly divergenting short wavelength lights that were generated by a spatial filter composed of an FZP and a pinhole. At a 2.38 nm wavelength of 2.38 nm provided by incoherent synchrotron radiation, samples were imaged withto a spatial resolution of ~150 nm. ItThis overcamesuperseded the resolution limit of typical pinhole-illuminated in-line holography. The method described here hasallows more rooms to enhance thefor further resolution enhancement. For example, the CCD’s area and the FZP’s NA, are rather small in thisthe present experimentation, were rather small and low. Thus, uUsing a high-NA’s FZP to enlarge the illumination angle, and using a large-area CCD to detect more lights, one could enhance the resolution could be enhanced. Moreover, Tthe exposure time ofin our case iswas rather long, due to the limited flux of the source. Thus, using a brighter source maymight[JH24]  decrease the exposure time and may reduce blurring of the finest fringes, resulting in higher resolution images. An effective method withfor a limited-flux source is to replace the gold-patterned FZP towith a nickel-patterned FZP. ItThis substitution giveswould provide moreapproximately double the photon flux about a factor of 2 at a wavelength of 2.8 nm. We expect that, using this method, one can obtain a highresolution holographic images down toof sub-100 nm resolution and better, sooner or later, will be achieved. sooner or later. This scheme maycould also be effectively applied forto hard x-rays toin investigationse of low-Z comprising materials, which showing relatively low absorption contrasts.



We acknowledge the financial support of the Basic Science Research Program administered by the National Research Foundation of Korea (NRF) and funded by the Ministry of eEducation, Science and Technology (Ggrant Nno. R15-2008-006-03002-0).

 [JH1]Not “High-spatial-resolution” -?


**--throughout the paper, be sure to substitute “high spatial resolution” for “high resolution” wherever necessary

 [JH2]“Diverging” would be ok too, but the “~ent” version balances better with “coherent.”

 [JH3]… just for consistency

 [JH4]OR (if there is only one typical setup): the



 [JH7]OR (alternative meaning): applicability / OR (if preferred): applications

 [JH8]OR (if you prefer): {Undo this change.}

 [JH9](?) Make sure that either the singular or the plural form is used appropriately for the context.

 [JH10]OR: edges

 [JH11]*OR: before


 [JH12]*OR: after




 [JH15]Here, “diverging” is necessary (not "divergent").

 [JH16]* (again—see Comments above)

 [JH17]… just for consistency

 [JH18]**(?) Should this be “light has” -?


(1) commonly

(2) typically

(3) usually

 [JH20]… just for consistency

 [JH21]here ok

 [JH22]*OR (alternative meaning): “with the real object shown in Fig. 3(a), we imaged … Ref. 16”


 [JH24]OR: could