Field of the Invention
The present invention relates to microscopy and other forms of imaging using coherent light. In particular, the present invention relates to coherent diffractive imaging (CDI) with an arbitrary angle of incidence.
Discussion of Related Art
Coherent diffractive imaging (CDI), for example ptychography, is an emerging technique that enables wavelength- and diffraction-limited imaging.
The fact that conventional CDI is limited to the above configurations brings several disadvantages: 1) it limits the freedom of the imaging geometry; 2) for reflection CDI, it results in a narrow range of scattering available for detection, leading to low resolution in the reconstructed image; 3) the reflectivity of objects might be low at near-zero degrees incidence. A need remains in the art for methods and apparatus to enable CDI with arbitrary angle of incidence and efficient computation.
An object of the present invention is to provide apparatus and methods for efficient CDI with arbitrary angle of incidence.
The invention includes the development of practical techniques for microscopy and other forms of imaging using coherent light. In particular, the use of coherent diffractive imaging techniques in conjunction with short-wavelength deep-UV, vacuum ultraviolet (VUV), extreme ultraviolet (EUV), and soft x-ray (SXR) sources allows for new methodologies for diffraction-limited imaging, with the numerical aperture depending only on the solid-angle of collected light. In the VUV-EUV-SXR regions of the spectrum, obviating the need for an imaging optic dramatically improves the prospects for imaging with high-NA; i.e. near wavelength-limited resolution.
Embodiments of the present invention provide a fast numerical method for processing the measured scattering pattern, so it is amenable for use with Fast Fourier transform (FFT) in the reconstruction of the image.
Embodiments of the present invention provide methods and apparatus to image objects at arbitrary angles of incidence both in reflection and transmission.
Embodiments of the present invention provide methods and apparatus to image objects with multi-wavelength illumination at an arbitrary angle of choice.
Embodiments of the present invention provide methods and apparatus to image a dynamic process with high NA.
A method of fast remapping of a detected diffraction intensity from a detector pixel array (initial grid) to a uniform spatial frequency grid (final grid) allows for FFT on the final grid. This is accomplished by remapping the initial grid to an intermediate grid chosen to result in a final grid that is linear in spatial frequency. The initial grid is remapped (generally by interpolation) to the intermediate grid that is calculated to correspond to the final grid. In general, the initial grid (x,y) is uniform in space, the intermediate grid ({tilde over (x)},{tilde over (y)}) is non-uniform in spatial frequency, and the final grid ({tilde over (f)}x,{tilde over (f)}y) is uniform in spatial frequency.
The present invention may be used in image reconstruction for any high NA diffractive imaging configuration, including a) the normal incidence configuration and b) the non-normal incidence configurations for which the remapping includes what is termed “tilted plane correction” in prior art (Gardner, D. F. et al., Opt. Express 20, 19050-9, 2012).
An imaging instrument capable of imaging samples at arbitrary angle of incidence consists of a) a radiation source; b) focusing optic(s) to condense the light onto the sample; and c) scanning ptychography. This instrument could have a light source from high-order harmonic upconversion of a driving laser. It could operate in a transmission mode configuration or a reflection mode configuration.
The instrument could use a vacuum iris far upstream of the focusing element, instead of positioning it close to the sample, to create well-confined illumination without decreasing the working distance of the microscope.
The focusing optic might be an off-axis or grazing incidence focusing optic (typically an ellipsoidal mirror or a toroidal mirror). The focusing optics may employ a concave EUV multilayer mirror.
The high-order harmonic conversion can be of any polarization state, including linear, circular and elliptical polarization, for magnetic imaging. Imaging can be done performing hyperspectral ptychography imaging of samples at arbitrary incidence angle using a comb of high-order harmonics, or other multi-wavelength illumination.
A comb of harmonics may be used for hyperspectral imaging
The illumination spectrum may be tailored for coherent imaging using a combination of high-harmonic generation, spectral filters such as thin-film EUV filters, a zero-dispersion stretcher with spectrum modulation in the spectrum plane, and multilayer or grazing incidence reflection to obtain an optimum spectrum for illumination, which may include one or more wavelengths or a well-defined continuous bandwidth.
A method of using ptychography obtains information on the illumination wavefront at the sample, then subsequently uses keyhole imaging that makes use of the obtained wavefront.
Stroboscopic imaging uses scanning reflection mode ptychography.
The following table of elements and reference numbers is provided for convenience.
In the prior art, first the spatial frequency grid (fx,fy) 302 that corresponds to the detector grid is calculated. (fx,fy) 302 turns out to be non-uniform due to the nonlinear relationship with (x,y) 27. Then the Fourier transform magnitude is remapped from non-uniform grid (fx,fy) 302 to uniform grid ({tilde over (f)}x,{tilde over (f)}y) 202, which is a time consuming process, because remapping from a non-uniform to a uniform grid typically involves triangulation.
In the implementation of the present invention, we first calculate the intermediate non-uniform spatial grid ({tilde over (x)},{tilde over (y)}) 29 that corresponds to eventual desired grid ({tilde over (f)}x,{tilde over (f)}y) 202, in step 206. Then the Fourier transform magnitude 44 is remapped from initial uniform grid (x,y) 27 to intermediate non-uniform grid ({tilde over (x)},{tilde over (y)}) 29 in step 34. Remapping from a uniform grid to a non-uniform one, instead of the other way around, is fast. The key is to choose an appropriate coordinate transform that enables the eventual usage of Fast Fourier transform, similar to what has been done in holographic microscopes (for example, see Kreuzer, U.S. Pat. No. 6,411,406 B1).
Without losing generality, any coordinate system may be chosen but for this example we select one for which the xy-plane is on the sample plane and for which the xz-plane is parallel to the incident wave vector {right arrow over (k)}0, such as coordinate system 210 in
where Σ is the sample plane, is the wavelength of the incident radiation, k=2π/λ is the angular wave number, R=√{square root over ((x−x′)2+(y−y′)2+z2)} is the distance from a sample point (x′, y′, 0) to (x, y, z). Notice that we explicitly write out the linear phase in the field for the non-normal incidence case. Assuming |{right arrow over (r)}|>>max [|{right arrow over (r)}′|, λ] and the far field condition |{right arrow over (r)}|>>D2/λ, (D is the physical size of the sample) then equation (1) can be approximated with a 2D Fourier transform:
where:
and
is the normalized incident wave vector.
Assume zds is the distance from the sample to the detector plane 211, {right arrow over (n)}det is the normal vector of the detector plane, then any point {right arrow over (r)}′=(x, y, z) on the detector satisfy:
{right arrow over (n)}det·{right arrow over (r)}=zds (5)
With equation (2), from the measured diffraction field magnitude on detector |EDet(x, y, z)| 212, the magnitude of the Fourier transform of the sample-plane E field |F[ESmp]|f
To allow for the use of fast Fourier transform (FFT) in CDI reconstructions, we need to use the E-field Fourier transform magnitude on a uniform grid of frequencies ({tilde over (f)}x,{tilde over (f)}y), instead of on a uniform grid of detector pixel coordinates which correspond to a non-uniform grid of frequencies (fx,fy). The most straightforward way to obtain |E({tilde over (f)}x,{tilde over (f)}y)| from |E(x, y, z)| is as following: first, calculate (fx,fy) for all pixel coordinates (x, y, z) using equation (3) and (4), resulting in a non-uniform grid; secondly, interpolate E magnitude from non-uniform (fx,fy) grid onto the uniform grid ({tilde over (f)}x,{tilde over (f)}y). This way is intuitive, but interpolation from a non-uniform to uniform grid is time-consuming as it typically involves triangulation methods. Instead, we use a different and much faster approach. Assume ({circumflex over (f)}x, {circumflex over (f)}x)=λ({tilde over (f)}x,{tilde over (f)}y) is the chosen uniform frequency grid 202 normalized by 1/λ. First we calculate the coordinates ({tilde over (x)},{tilde over (y)}) 29 corresponding to the uniform grid ({tilde over (f)}x,{tilde over (f)}y) of choice 202 from equations (3), (4) and (5) using the measured distance zds 211 and angle θi 17:
Then, in step 34, we interpolate |F[ESmp]|f
In summary, the steps of performing fast reforming 34 are as following:
As seen from equations (7) and (8), the fast remapping is wavelength-independent making it suitable for hyperspectral imaging in which the incident radiation contains multiple wavelengths.
Although the distortion in the diffraction looks more obvious with non-normal incidence, for any diffraction measured with wide collecting angle, or high numerical aperture (NA), even for normal-incidence, it may be advisable to perform the remapping. The remapping results in a better result for any high-NA configuration simply because the spatial-frequency coordinates have a non-linear relationship with the detector pixel coordinates. An alternative to the remapping would be to use a Non-uniform FFT.
As an example, we used the imaging instrument of the present invention to image a test object, which is composed of titanium of about 30 nm thickness deposited on a silicon wafer. The fast remapping is performed on each diffraction pattern in the ptychography scan, which is composed of approximately 200 diffraction patterns. The fast remapping algorithms is beneficial for practical implementation of the microscope reconstruction step.
The microscope according to the invention has potential for applications including inspection of masks for lithography, semiconductor metrology, and general surface profilometry. It also has applications for magnetic imaging.
Imaging using multiple colors in the EUV can be done sequentially; however, it is often more convenient to illuminate the sample with several colors simultaneously, then to use a ptychographic reconstruction to obtain a separate image for each illumination wavelength.
With the probe reconstructed from ptychography, keyhole CDI technique can be employed to reconstruct the sample from a single diffraction pattern.
Due to the ultrashort pulse nature of the HHG light source, embodiments of a microscope of the invention are capable of imaging ultrafast dynamics (changing in time), with temporal resolution of up to femtosecond or even attosecond.
While the embodiments of the present invention have been described hereinabove by way of example with particularity, those skilled in the art will appreciate various modifications, additions, and applications other than those specifically mentioned, which are within the scope of this invention. For example, the fast remapping is applicable not only ptychography CDI, but also other types of CDI.
Number | Name | Date | Kind |
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6411406 | Kreuzer | Jun 2002 | B1 |
20120105744 | Maiden | May 2012 | A1 |
20150108352 | Maiden | Apr 2015 | A1 |
20160154301 | Ekinci | Jun 2016 | A1 |
Entry |
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Harada et al., Phase Imaging of Extreme-Ultraviolet Mask Using Coherent Extreme-Ultraviolet Scatterometry Microscope, Japanese Journal of Applied Physics 52, 2013. |
Gardener et al., High numerical aperture reflection mode coherent diffraction microscopy using off-axis apertured illumination, Optics Express, vol. 20, No. 16, Aug. 13, 2012. |
Seaberg et al., Tabletop nanometer extreme ultraviolet imaging in an extended reflection mode using coherent Fresnel ptychography, Optica vol. 1 No. 1, Jul. 2014. |
Number | Date | Country | |
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20160187849 A1 | Jun 2016 | US |
Number | Date | Country | |
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62043132 | Aug 2014 | US |