Experiments performed at the Laboratory for Laser Energetics with a continuous-wave (cw) x-ray source and on the OMEGA and OMEGA EP Laser Systems [Boehly et al., Opt. Commun. 133, 495 (1997) and Waxer et al., Opt. Photonics News 16, 30 (2005)] have utilized a Fresnel zone plate (FZP) to obtain x-ray images with a spatial resolution as small as ∼1.5 μm. Such FZP images were obtained with a charge-coupled device or a framing camera at energies ranging from 4.5 keV to 6.7 keV using x-ray line emission from both the cw source and high-intensity, laser-beam–illuminated metal foils. In all cases, the resolution test results are determined from patterns and grids backlit by these sources. The resolutions obtained are shown to be due to a combination of the spectral content of the x-ray sources and detector resolution limited by the magnification of the images (14× to 22×). High-speed framing cameras were used to obtain FZP images with frame times as short as ∼30 ps. Double-shell implosions on OMEGA were backlit by laser-irradiated Fe foils, thus obtaining a framing-camera–limited, FZP-image resolution of ∼3 μm–4 μm.

In this paper, we report on the development of, along with the results from, the use of Fresnel zone plates (FZP’s) to image x rays emitted by laser-generated plasmas on the University of Rochester’s OMEGA and OMEGA EP Laser Systems.1,2 As first suggested by Baez,3 FZP’s are in ubiquitous use in research conducted at synchrotron facilities around the world and have been extended to resolution limits approaching 10 nm (Ref. 4). FZP’s have been used in early laser fusion research such as that performed by Ceglio et al.5 and Ceglio and Smith6 at Lawrence Livermore National Laboratory. More recently, modern FZP’s, manufactured by e-beam lithography, have been used to image x rays emitted by laser-produced plasmas at LULI20007–9 and on GEKKO-XII.10 This work reports on the use of FZP’s to image x rays on both the OMEGA and OMEGA EP Laser Systems.

Pinholes and pinhole arrays are in widespread use on OMEGA and OMEGA EP, allowing imaging of either plasma self-emission or emission from a backlighter used to radiograph objects evolving due to ablation, shock compression, or implosions by high-intensity laser beams. These pinholes are used in conjunction with framing cameras, streak cameras, charged-coupled devices (CCD’s), and simpler recording media such as film and image plate. FZP images have been obtained by positioning a single zone plate inside the OMEGA and OMEGA EP target chambers and by using x-ray emission from laser-beam–irradiated metal foils to backlight test subjects.

Unlike pinholes, whose imaging resolution is in general limited to the pinhole diameter, FZP’s are diffraction limited to a resolution of δ ≈ 1.22Δrn, where Δrn is the width of the outermost zone of the FZP.11 Since outer zones of modern FZP’s can approach dimensions of ∼10 nm, the diffraction-limited resolution can be achieved only if the sampling resolution is at least 2× smaller. This is typically achieved by magnifying the image by 2000× to 10 000×, allowing CCD’s with pixels ranging from 9 μm to 13.5 μm in size to have sufficient resolution to approach the 10-nm limit. While possible in laser-plasma research, these very high magnifications are typically impractical. In this work, imaging with FZP’s has been performed with magnifications ranging from 14× to 22×. When the detector resolution δdet becomes the limiting resolution element of the system, the inferred resolution at the object then becomes δobjδdet/M, where M is the magnification. With these modest magnifications along with well-developed image-recording methods, it is straightforward to approach 1-μm spatial resolution, as will be shown in this paper.

To obtain useful x-ray images with an FZP, the focusing properties and contributions from the various orders must be properly taken into account. In the case of the undiffracted zeroth-order component, as will be shown, this includes both the magnitude of the component and the spatial distribution thereof.

The well-known FZP focal length f is given by11 

F=rn2nλ=Dn24nλ=Dn2E4nhc,
(1)

where rn is the radius and Dn is the diameter of the nth zone, and λ is the wavelength. Alternatively, one can calculate f from the x-ray line energy E, Planck’s constant h, and the speed of light c. When alternating zones are opaque to the incident x rays, then constructive interference occurs. The effect of partially transparent zones yielding phase shifting by the bars of the FZP is described in Sec. II C.

The paraxial-approximation focus equation for the FZP is given by11 

1f=1p+1q,
(2)

where f is the focal length, p is the distance from the object to the FZP, and q is the distance from the FZP to the image plane (Fig. 1). The case of magnification M = q/p ≈ 1 is shown. In this work, the object at O is backlit by a source just behind it at B. The image at I is inverted and surrounded by an undiffracted contribution (zeroth order), indicated by the larger yellow region surrounding the image. The relative contributions of the two important orders (first and zeroth) are described later in this section.

FIG. 1.

The FZP focus condition. A first-order image of an object at O is formed at I1st, where p and q obey the focus equation. In this work, the x rays are emitted from a backlighter behind the object at B. The zeroth-order I0th or undiffracted contribution diverges from O and surrounds the image. The extent of the zeroth-order contribution is indicated by the blue dashed lines. A central block CB may be used to reduce the zeroth-order contribution as described later in this paper. Additional higher positive and negative orders are not shown.

FIG. 1.

The FZP focus condition. A first-order image of an object at O is formed at I1st, where p and q obey the focus equation. In this work, the x rays are emitted from a backlighter behind the object at B. The zeroth-order I0th or undiffracted contribution diverges from O and surrounds the image. The extent of the zeroth-order contribution is indicated by the blue dashed lines. A central block CB may be used to reduce the zeroth-order contribution as described later in this paper. Additional higher positive and negative orders are not shown.

Close modal

A practical use of this equation is for a fixed distance L from the object to image given by L = p + q. Solving for p yields

p=12LL24fL.
(3)

A pointer can be used to align the zone plate at a distance p from the object to be imaged.

An FZP manufactured by Applied Nanotools, Inc.12 with no central block (CB) was used for all experiments described in this work. The FZP specifications are a 284.9-μm outer diameter, 512 zones, a 140-nm outermost zone width, and a resulting focal length of 151.86 mm for an energy of 4.750 keV (Ti Heα resonance line). The FZP zone bars consisted of 1.3-μm-thick Au bars on a 1.0-μm-thick Si3N4 support membrane. For an example distance from the object to image of L = 3708.4 mm, Eq. (3) yields p = 158.65 mm, from which q = 3549.75 mm, and M = 22.37.

At best focus, for a single-line energy, the FZP resolution is given by the diffraction limit δ = 1.22Δrn, where Δrn is the width of the outermost zone.11 For the above example FZP, this implies a best single-line resolution of 171 nm. However, since the focus of the FZP is a function of energy, if the spectrum of x rays passing through the FZP is other than monoenergetic, then different energies will focus at different positions. Taking the derivative of Eq. (3) with respect to f from Eq. (2), re-expressed in terms of p/q = 1/M and E, substituting Δf/f = ΔE/E, keeping only to first order in 1/M (i.e., 1/M2 ≪ 1), the variation of p with E is found to be

Δpp=1+1MΔEE.
(4)

As an example for the case of the Ti Heα resonance and intercombination lines at 4.750 keV and 4.727 keV, respectively, the two lines differ by 0.49% in energy. Their focal lengths will differ by the same fraction, and the variation in object distance will then be given by Eq. (4). The out-of-focus line will be defocused by an amount δ given approximately by

δ=ΔppD.
(5)

In this case, for the above values of D, ΔE/E, and M, Δp/p = 0.51% and δ = 1.4 μm. If both lines are equal in strength, the limit of focus would be δ = 0.7 μm if the focus is set between the lines. An alternative is to use a monochromator, such as a crystal or multilayer diffractor, thereby further minimizing or eliminating contributions from defocused x rays.7–9 

In either case, some defocus over and above the diffraction limit is to be expected depending on the spectral content of the illuminating radiation. It should be noted that beneficial defocusing of the backlighter will occur since it is placed behind the object being radiographed. Equation (5) also applies to this situation, where in this case Δp will correspond to the distance from the object to backlighter. A typical case would be with Δp = 10 mm, and with p = 158.65 mm, D = 284.9 μm as in the case above, a backlighter defocus of δ = 18 μm would occur. This defocus can be used to smooth out small-scale structure of the backlighter emission.

A range of possible resolutions are obtainable, limited not by the FZP, or by the spectral content, but further by the resolution at the image plane. As an example, for a magnification of ∼20, the best obtainable with a CCD having 13.5-μm pixels is when the feature can be discerned by only two pixels (Nyquist limit), yielding a resolution limit of δ(CCD) ≈ 27 μm/20 = 1.35 μm. Other example detector resolutions of those used on OMEGA and OMEGA EP are δ (film) ≈ 10 μm–20 μm, δ (image plate) ≈90 μm, and δ (framing camera) ≈50 μm–60 μm. The higher the magnification, the better for these cases since all can severely compromise the resolution obtained at low magnification. The film limit quoted is that imposed on the image results by scanning the film using a microdensitometer, the two best scanning resolutions being 5-μm and 10-μm pixel spacing, hence having Nyquist limits of 10 μm and 20 μm, respectively. The image plate resolution is that found to be typical for Fuji image plate scanned images.13 The framing-camera resolution is that typical for film recorded framed x-ray images14 but expected to be similar if the recording medium is a CCD at the framing-camera output.

The fluence in photons per unit area at the first-order image plane of an FZP is given by

F1(x,y)=ε1EΔΩFZPM2s(x,y)Tfilter,
(6)

where ε1E is the first-order efficiency, ΔΩ is the solid angle, s is the surface fluence in energy or photons per unit area per unit solid angle, and Tfilter is the filter transmission. Positions in the image x′, y′ are magnified such that x = x′/M and y = y′/M, and the choice of origin is arbitrary. The collection solid angle of the FZP is given by

ΔΩFZP=πD24p2.
(7)

For the example zone plate dimensions mentioned above, the area of the FZP compared to that of a 10-μm-diam pinhole is ∼800× larger. The FZP efficiency in first order can vary from ∼10% to 35%, dependent on photon energy and FZP thickness. When multiplied by an assumed efficiency of 25%, the effective collecting area of the FZP is ∼200× that of the pinhole. This can be used to advantage by either increasing the distance to the source or increasing the magnification, thereby obtaining either a similar fluence level or, if desired, a greater one as compared to that obtainable with a pinhole.

The FZP can have a collection solid angle that is also greater than that of a Kirkpatrick–Baez (KB) microscope. Examples of KB microscopes are two that are in use on OMEGA.15,16 The KB optic in the instrument known as the GMXI15 has four mirror pairs with ΔΩKB = 4 × 10−7 sr each, while the instrument KBFRAMED16 has 16 mirror pairs with ΔΩKB = 9 × 10−8 sr each. For the example FZP and positions p, q, and L given above, ΔΩFZP = 2.5 × 10−6 sr, which is ∼6× and ∼28× greater than the two example OMEGA KB optics given above. Being reflective systems, the KB optics focus all wavelengths to the same distance unlike the FZP, so the solid angles themselves are not the only things to consider when comparing the two.

The values of the diffraction-order efficiencies are calculated from the atomic scattering factors of the zone bars. The zeroth and mth-order efficiencies are given by7,17,18

ε0=141+2cos2πδtλ×exp2πβtλ+exp4πβtλ,
(8)
εm=1(πm)212cos2πδtλ×exp2πβtλ+exp4πβtλ,
(9)
δ=reλ2ρNA2πMzF1(λ),
(10)
β=reλ2ρNA2πMzF2(λ),
(11)
re=e2mc2,
(12)

where δ and β are the real and imaginary parts of the equation for the index of refraction n = 1 − δ + , t is the zone thickness, F1 and F2 are the real and imaginary parts of the atomic scattering factors, ρ is the mass density, NA is Avogadro’s constant, Mz is the molar mass, and re is the classical electron radius. Equations (8) and (9) apply only to perfectly rectangular zone bars of the given thickness t, which is the only case considered in this work. Note that x-ray FZP’s and x-ray gratings have identical order efficiencies in the case where the grating bars and gaps are equal.17,18 Furthermore, in both cases, the even orders are identically zero. The calculated zeroth- and first-order efficiencies are shown in Fig. 2(a) for the case of the above-mentioned FZP. The atomic scattering factors used were those published by Henke et al.19 The ratio ε1/ε0 is shown in Fig. 2(b); it has a narrow peak at ∼7 keV with a value >9.

FIG. 2.

FZP-order diffraction efficiency: (a) calculated zeroth- and first-order efficiencies for the FZP described in this work and (b) the ratio of the first- to the zeroth-order values in (a).

FIG. 2.

FZP-order diffraction efficiency: (a) calculated zeroth- and first-order efficiencies for the FZP described in this work and (b) the ratio of the first- to the zeroth-order values in (a).

Close modal

There is a range of energies where ε1, the effect of phase, gives a value greater than an opaque FZP (i.e., >1/π2 ∼ 0.1) but with a subsequently larger zeroth order. Note also that the support membrane and any filter used will reduce both zeroth and first orders equally so will have no effect on the ratio. The simplest method of minimizing the zeroth order relative to the first order is by finding where the ratio ε1/ε0 is a maximum. This is accomplished graphically by finding the maximum of the ratio as a function of E (or λ) for a given choice of zone material and thickness.

A subtlety of using FZP’s is the fact that finite amounts of undiffracted (zeroth-order) x rays pass through the FZP, arriving at the image plane in addition to the first-order image. It is assumed in this discussion that all x rays are blocked at the FZP for regions outside the outermost bar. The zeroth order simply diverges through the open aperture of the FZP and falls onto the first-order image as an unfocused contribution. Higher-order contributions are neglected in this work because they are (1/m)2 smaller and greatly defocused. An expression for this zeroth-order contribution is given by

F0x,y=ε0ΔΩM+12sx,ycircxx,yydxdy,
(13)

where circ(x, y) is the circular aperture function20 

circ(x,y)=1,x2+y2RFZP=0,x2+y2>RFZP.
(14)

In the simple case when the source distribution is a uniform region of size equal to the FZP, the convolution yields the function chat(x, y) (Ref. 20),

chat(x,y)=circ(x,y)*circ(x,y),
(15)

where (*) denotes convolution and is shown as curve “a” in Fig. 3. Dimensions are scaled back to the object plane. This simplified result applies in the limit when M ≫ 1 since the zero point of the function will extend to a slightly larger value of R/RFZP for finite M. The radial extent of this region R0th in the simple case of a circular source size is given by

R0th=M+1RFZP+MRBM,
(16)

with RFZP and RB as the radius of the FZP and backlighter, respectively, and the region size is scaled to the object plane. If the source diameter is 1/2 that of the FZP, the resulting zeroth-order distribution is curve “b” in Fig. 3; the fluence of the zeroth order will be 1/4 of that from a source of twice that diameter, whereas the first-order fluence will be unchanged. The use of a so-called central block (CB) (Fig. 1) can further reduce or eliminate the zeroth-order throughout.7,9 An example of the zeroth-order distribution when using a CB is shown as curve “c” in Fig. 3. The case is where the central 3/4-diam region of the FZP is covered with an opaque block, and the source region diameter is 1/2 the FZP. In this case, the region at the image plane corresponding to 1/2 the source diameter has no zeroth-order contribution. The first-order throughput would also be reduced by a factor 1 − (3/4)2 = 0.44.

FIG. 3.

The spatial distribution of the undiffracted x rays (zeroth-order) scaled to the object plane for M ≫ 1. The cases shown are described in the text.

FIG. 3.

The spatial distribution of the undiffracted x rays (zeroth-order) scaled to the object plane for M ≫ 1. The cases shown are described in the text.

Close modal

Experiments were performed with both e-beam–generated cw x rays and laser-plasma x-ray emission. The FZP assembly was tested for throughput and focus with the e-beam source before deploying on the OMEGA and OMEGA EP target chambers. The FZP is placed in an assembly otherwise used for pinholes and pinhole arrays and is commonly used on the OMEGA and OMEGA EP target chambers in front of pinhole cameras imaged with solid-state detectors and framing cameras. A 25-μm-thick Ta foil with a laser-cut aperture 10 μm less in diameter than the outermost FZP zones is coaligned to the FZP to within 10 μm. This blocks the uncovered region around the FZP, which would otherwise contribute to an undiffracted background. When used in the OMEGA and OMEGA EP target chambers, a 100-μm-thick Be foil is also placed in the assembly, acting as a blast shield, protecting the FZP from laser-plasma blowoff and debris generated in pulsed laser experiments.

The FZP was placed in a vacuum chamber containing a cw e-beam–generated x-ray source. The length of this vacuum chamber is close to the radii of the OMEGA and OMEGA EP target chambers (∼1.7 m). In this way, the FZP was tested at a distance close to that required in the target chambers. Figure 4(a) shows an exposure taken with the FZP focused on x rays passing through a custom star pattern, also manufactured by Applied Nanotools, Inc. Images were obtained with a Spectral Instruments SI800 CCD having 13.5-μm pixels.21 The e-beam impinged on a Ti target, producing a spectrum containing principally Ti Kα x rays (4.51 keV) but with some (∼15%) Ti Kβ x rays (4.93 keV). The FZP was focused for Ti Kα with the resulting calculated focal length of f = 144.12 mm. The distance from the resolution grid to the image plane was L = 2353 mm, from which is calculated p = 152.72 mm, q = 2200.28 mm, and M = 14.41 mm. The FZP was positioned to an accuracy of ∼20 μm using a pointer adjusted to this accuracy. The original pattern as imaged by an electron microscope is shown in Fig. 4(b). The pattern is such that the radial bars (spokes) are 20 μm wide at the outer diameter, decreasing to 10 μm at the first gap, 3 μm wide at the second gap, and 1 μm wide at the third gap (not visible). The pattern consists of 32 spokes and equal gaps with an outer diameter of 407 μm. The innermost spoke widths are 0.2 μm, and the spokes consist of 7-μm-thick Au supported by a 1-μm-thick Si3N4 membrane.

FIG. 4.

Images of a custom star pattern: (a) the FZP image, (b) an electron microscope image of the star pattern, and (c) a 10-μm-diam pinhole image.

FIG. 4.

Images of a custom star pattern: (a) the FZP image, (b) an electron microscope image of the star pattern, and (c) a 10-μm-diam pinhole image.

Close modal

In order to obtain good x-ray exposures, the following experimental conditions were used: A 101.6-μm-thick Be foil was placed over the star pattern to protect it from e-beam–generated debris. Both the star pattern and the FZP were in the vacuum region. A 12.7-μm-thick Be vacuum window allowed x rays to pass out of the chamber to the CCD, entering the CCD through a 25.4-μm-thick Be window. The intervening path was flushed with He gas, eliminating further signal loss. A 13.5-μm-thick Ti foil was also placed in the path to act as a notch filter greatly reducing the x-ray flux above the Ti K-edge at 4.966 keV. The exposure lasted for 1 h and consisted of 12 exposures of 5 min each. The multiple exposures allowed for observation of any drift of the image, which after initial heating of the star pattern holder caused by infrared emission from the e-beam was not detectable in the individual images to the resolution of the CCD camera. Vibrations of the vacuum chamber containing the FZP and e-beam were well below 0.1 μm in amplitude, and the CCD was positioned on an optical table with equally good vibration isolation.

For comparison, an image taken with a 10-μm-diam pinhole replacing the FZP is shown in Fig. 4(c). This exposure was a net 2-h exposure using a Cu target and contained x rays from 2 keV to 14 keV, dominated by Cu Kα line emission at 8.0 keV. No notch filter was used for this exposure. The reduced resolution obtainable with the 10-μm-diam pinhole is clearly evident. The pinhole resolves bars to bar widths of ∼10 μm, consistent with a resolution of the same. The FZP image in Fig. 4(a) is seen to resolve features smaller than 3 μm with spokes resolved from the surrounding gaps down to ∼2-μm width. The Nyquist limit due to the CCD pixel size is 27 μm/14.41 = 1.9 μm, so it is expected that bar visibility will be limited to this scale size. Further analysis of the star pattern images will be the subject of a forthcoming paper. Other factors aside, higher magnification should allow higher resolution to be obtained. Magnifications of up to 22.37 were accessible for experiments on the OMEGA Laser Systems, and the corresponding results are described below.

Experiments have been performed on both the OMEGA1 and OMEGA EP2 Laser Systems. The FZP assembly was positioned by a ten-inch-manipulator (TIM) remote positioner, placing the FZP at the focus position to an accuracy of ∼20 μm well within the accuracy needed to insure that detector-limited resolution only is obtained, as will be shown. The images were recorded with either an SI800 CCD or a framing camera recording on Kodak TMAX 400 film. The image planes were at the back of the TIM’s (L = 3708 mm on OMEGA EP, L = 3647 mm on OMEGA).

A resolution grid test was performed on the OMEGA EP target chamber using the same FZP assembly. The FZP was positioned to be focused on a grid placed at the target chamber center, with a Ti foil 5 mm behind the grid. A pulsed OMEGA EP beam with 1 kJ of UV (351-nm) light in a 0.5-ns pulse was used to generate Ti Heα x rays. The magnification of the arrangement was M = 22.37, with L = 3708.4 mm, p = 158.65 mm, q = 3549.8 mm, and f = 151.86 mm, respectively, corresponding to the focus for the Ti Heα resonance line (4.75 keV). The grid consisted of 6-μm-wide by 20-μm-thick Au bars, spaced by 25-μm. The grids are manufactured by SPI Supplies, Inc.,22 and are known as TEM grids. The dimensions are considered to be effectively perfect compared to the spatial resolution being investigated in this work. The grid was covered by a 25-μm-thick Ta foil into which a 100-μm-diam aperture (mask) was laser cut. A 13.5-μm-thick Ti foil notch filter was placed in front of the CCD. Figure 5(a) shows the grid image obtained with an SI800 CCD. A lineout through the image is shown in Fig. 5(b); Fig. 5(c) shows the line spread function (LSF) calculated by taking the derivative of the lineout. When averaging over eight edges, the width of the features implies an LSF full width at half maximum (FWHM) of 1.62 ± 0.31 μm. In this case, the Nyquist limit is 27 μm/22.39 = 1.19 μm, implying that the resolution obtained is partly detector limited and partly by spectral content, as the error in focus positioning (∼20 μm) was a negligible contributor. The relative strength of the zeroth-order contribution is reduced since the Ta foil mask restricts the emitting region to ∼1/2 the diameter of the FZP, a case similar to curve “b” in Fig. 2. The right-hand side of Fig. 5(b) samples the image out to the spatial extent of the zeroth-order image, which extends outward from the image by ∼RFZP, i.e., 100 μm, as expected [Eq. (16)].

FIG. 5.

FZP image of a backlit grid obtained on OMEGA EP shot 30 382 using a Ti-foil backlighter (4.75 keV): (a) CCD image of the grid with a 100-μm-diam mask over the grid, (b) lineout through the grid showing the grid bar shadows, and (c) LSF (derivative) from which the resolution of 1.62 ± 0.31 μm is inferred.

FIG. 5.

FZP image of a backlit grid obtained on OMEGA EP shot 30 382 using a Ti-foil backlighter (4.75 keV): (a) CCD image of the grid with a 100-μm-diam mask over the grid, (b) lineout through the grid showing the grid bar shadows, and (c) LSF (derivative) from which the resolution of 1.62 ± 0.31 μm is inferred.

Close modal

A second grid resolution experiment with the same type TEM grid was performed on OMEGA EP using a vanadium (V) foil as a backlighter. This time the grid was masked by a 300-μm-diam aperture also in a 25-μm-thick Ta foil (Fig. 6). A 9-μm-thick V notch filter was placed in front of the CCD. Three pulsed OMEGA EP beams with a total of 300 J of UV (351-nm) light in a 1-ns pulse were used to generate V Heα x rays. The principal emission line is the V Heα resonance line at 5.207 keV. In this case, f = 166.41 mm, p = 174.63 mm, q = 3533.77 mm, and M = 20.24 mm. A similar LSF FWHM of 1.54 ± 0.16 μm is obtained from the measured lineouts (averaged over ten edges). In this case, the Nyquist limit is 27 μm/20.24 = 1.33 μm. Similar to the Ti backlighter result, the resolution obtained is partly detector limited and partly by spectral content. The relative contributions of the zeroth- and first-order images are different, however, as a consequence of the size of the backlit grid region. A lineout through the image is shown in Fig. 6(b). The zeroth order approaches the first-order signal level for this grid image and should be ∼4× larger in the center in Fig. 6(b) as is curve “a” to curve “b” in Fig. 3.

FIG. 6.

FZP image of a backlit grid obtained on OMEGA EP shot 31 019 using a Ti-foil backlighter (5.70 keV): (a) CCD image of the grid with a 300-μm-diam mask over the grid, (b) lineout through the grid showing the grid bar shadows, and (c) LSF (derivative) from which the resolution of 1.54 ± 0.16 μm is inferred.

FIG. 6.

FZP image of a backlit grid obtained on OMEGA EP shot 31 019 using a Ti-foil backlighter (5.70 keV): (a) CCD image of the grid with a 300-μm-diam mask over the grid, (b) lineout through the grid showing the grid bar shadows, and (c) LSF (derivative) from which the resolution of 1.54 ± 0.16 μm is inferred.

Close modal

A third grid resolution experiment (also with a TEM grid) was performed on the OMEGA target chamber with a high-speed framing camera23 at the image plane in the back of a TIM, with 20 beams of OMEGA incident onto a Ti foil. The same grid type was used, and the mask was a 500-μm-diam aperture also in a 25-μm-thick Ta foil. Both sides of the foil were illuminated with seven beams on the side toward the grid and FZP and 13 on the back. The beams were defocused to illuminate a 750-μm-diam region with 9 kJ of UV in a 1-ns square pulse. For this case, L = 3647 mm, p = 158.78 mm, q = 3487.82 mm, and M = 21.97 mm. The framing camera was triggered near the middle of the pulse, and all strips were co-timed. The single image that was obtained impinged on two of the four anode strips [Fig. 7(a)].

FIG. 7.

Framed FZP image of a backlit grid obtained on OMEGA shot 94 697 using a Ti-foil backlighter (4.75 keV): (a) film-recorded framing camera image of the grid with a 500-μm-diam mask over the grid and (b) lineout through the inferred intensity values in the image compared to a 3.5-μm blurred grid bar and gap pattern. The blur determination uncertainty is ∼0.5 μm; therefore, ∼3 μm to 4 μm-blurring is inferred.

FIG. 7.

Framed FZP image of a backlit grid obtained on OMEGA shot 94 697 using a Ti-foil backlighter (4.75 keV): (a) film-recorded framing camera image of the grid with a 500-μm-diam mask over the grid and (b) lineout through the inferred intensity values in the image compared to a 3.5-μm blurred grid bar and gap pattern. The blur determination uncertainty is ∼0.5 μm; therefore, ∼3 μm to 4 μm-blurring is inferred.

Close modal

In this case, the noise in the film-based framed image precludes computation of the LSF by direct differentiation. The resulting resolution is estimated by comparison of a lineout of the grid image with a convolved grid pattern [Fig. 7(b)]. The convolved pattern matches the observed lineout for a Gaussian-shaped blurring of ∼3 μm–4 μm (FWHM). Since the image plane resolution of the framing camera is limited to ∼50 μm–60 μm, with a magnification of 21.97, the resolution at the object should be limited to ∼2.3 μm–2.7 μm, even for perfect imaging resolution, so that obtained is only slightly less well resolved than the best obtainable with a framing camera at this magnification. Since the emitting region is now much larger than the FZP, the zeroth-order contribution extends well outside the first-order–image region and is relatively constant within.

A series of experiments known as the Revolver experiments,24 whose principal investigators are the Los Alamos National Laboratory co-authors of this paper, were performed on the OMEGA target chamber. Both Ti and Fe backlighters were used to radiograph a set of concentric, double-shell implosions, where the outer shell was ∼1200 μm in diameter and the inner shell was ∼400 μm in diameter. The inner shell consisted of a 15- to 2-μm-thick Cr shell, held in place by a two-photon polymerization, 3D-printed lattice with a volume-averaged density of 50 mg/cm3–200 mg/cm3. The outer 25-μm-thick CH shell was driven by 40 beams with 11.4 kJ of UV light in a 1-ns pulse. Two backlighter foils were used per double-shell implosion. One foil backlit a pinhole array in front of a framing camera, and the other backlight the single FZP in front of a framing camera. Six beams were used to illuminate the pinhole imaged framing camera backlighter and eight beams for the FZP-imaged framing camera backlighter. All backlighter beams were ∼423 J/beam in a 1-ns pulse. The experiments with the Fe foil backlighters had the highest contrast when imaged by the FZP as the principal emission line is the Fe Heα line at 6.701 keV. The ratio of order contributions ε1/ε0 is nearly a maximum at this energy and is ∼15× greater at 6.7 keV than at 4.75 keV [Fig. 2(b)], an important advantage for observing lower signal-to-noise features.

Example images obtained with the FZP using a high-speed framing camera at the image plane of the FZP (rear of TIM) are shown in Fig. 8. The image of the earliest frame time (one per target shot) at t = 1.9 ns is shown in Fig. 8(a). Here, the outer shell has not yet undergone a collision with the inner shell and the shell is still nearly uncompressed. A perfectly round limb is seen with a region near but not at the middle having a very low zeroth-order background. This arises from the fact that the inner shell is effectively opaque, and with a size larger than the FZP, it is blocking the zeroth order from the outer parts of the backlighter. The position of the minimum is determined by the relative alignment of the backlighter, central target, and FZP. If they were all centered on a line, the minimum would have been centered on the image of the inner shell. The image is seen to fall on a single strip of the four-strip framing camera, with only small regions of the limb falling outside the strip. For this case, the imaging conditions were L = 3646.6 mm, f = 214.24 mm, p = 228.57 mm, q = 3418.03 mm, and M = 14.95 mm. The detector limiting resolution is expected to be ∼3.3 μm–4.0 μm. Large departures from circular symmetry, i.e., projected spherical symmetry, are seen in the later frame times after the shell collision [Figs. 8(b)8(d)]. These are a consequence of the perturbations caused by a combination of drive variation and a likely much larger induced perturbation caused by variations of the 3D-printed lattice.

FIG. 8.

Framed FZP images of Fe-foil backlit (6.70-keV) Revolver double-shell implosions on OMEGA with one image per shot onto a single strip of a four-strip high-speed framing camera: (a) shot 96 150 at t = 1.9 ns, (b) shot 96 152 at t = 4.0 ns, (c) shot 96 153 at t = 4.5 ns, and (d) shot 96 154 at t = 4.0 ns.

FIG. 8.

Framed FZP images of Fe-foil backlit (6.70-keV) Revolver double-shell implosions on OMEGA with one image per shot onto a single strip of a four-strip high-speed framing camera: (a) shot 96 150 at t = 1.9 ns, (b) shot 96 152 at t = 4.0 ns, (c) shot 96 153 at t = 4.5 ns, and (d) shot 96 154 at t = 4.0 ns.

Close modal

Finally, Fig. 9 shows a qualitative comparison between an Fe backlit image obtained with the pinhole arrays and an image obtained with the FZP. The image from the FZP is shown in Fig. 9(a), and the pinhole image is shown in Fig. 9(b) (both at t = 4.5 ns). The expected resolution of the framed FZP image is ∼3.3 μm–4.0 μm if limited solely by the framing camera. The pinhole image was acquired with a 15-μm-diam pinhole dph at a magnification of 4. The two TIM-based framing cameras were nearly orthogonal to each other on the target chamber sphere, so only a qualitative comparison between the resolution of features is possible. The pinhole image was geometrically limited to a resolution of (M + 1)dph/M = 18.75 μm. The framing camera increases that to ∼22.5 μm–27.0 μm, when taken in quadrature. Figure 9(c) shows the FZP image blurred to the approximate resolution of the pinhole image, dramatically illustrating the loss of detail in the pinhole image as compared to the FZP image. Since it is an undiffracted image (i.e., zeroth order), it does not have another component competing with it, so no background is seen in the middle of the inner shell radiograph in the pinhole image.

FIG. 9.

Comparison of a framed FZP image and pinhole image of a Revolver double-shell implosion on OMEGA, each backlit by Fe-foil emission (6.70 keV) at t = 4.5 ns: (a) the FZP image (XRFC1 in TIM-4 with FZP), (b) the pinhole image (SFC4 TIM-3 with 15-nm pinholes), and (c) the FZP image blurred to the resolution of the pinhole image.

FIG. 9.

Comparison of a framed FZP image and pinhole image of a Revolver double-shell implosion on OMEGA, each backlit by Fe-foil emission (6.70 keV) at t = 4.5 ns: (a) the FZP image (XRFC1 in TIM-4 with FZP), (b) the pinhole image (SFC4 TIM-3 with 15-nm pinholes), and (c) the FZP image blurred to the resolution of the pinhole image.

Close modal

Fresnel zone plate x-ray imaging has been developed at the Laboratory for Laser Energetics by incorporating single zone plates into assemblies used until now exclusively for single pinholes or pinhole arrays. Unlike the pinholes, the FZP’s must be placed in the focus condition for the principal line emission being imaged. This is straightforward with current positioning methods. The FZP’s are currently being used for x-ray radiography using laser-generated x-ray line emission, which is sufficiently monochromatic to obtain well-focused x-ray images with FZP’s without the need to use a monochromator element. This has been demonstrated in this work with x-ray emission lines from Ti, V, and Fe sources, both e-beam and laser-plasma generated.

The ability to resolve features in the object, with scale sizes as small as ∼1.5 μm, has been quantified with resolution targets, and when used in conjunction with high-speed framing cameras, imploding objects have been both spatially resolved to ∼3 μm–4 μm scales and time resolved to ∼30 ps. Framing camera imaging with FZP’s can obtain increased resolution by increasing the magnification, a possibility well within the scope of this method. The relative magnitude of the undiffracted zeroth-order contribution to the diffracted first-order image has been shown to be a function of both the relative size of the emission region and the ratio of the first- to zeroth-order efficiency ε1/ε0. Both maximizing the ratio and minimizing the source area, when possible, can increase the contrast of the first-order image. A central block can eliminate the zeroth-order in a select region but was not explored in this work expect by calculation.

An additional simplicity of adopting FZP use without monochromators is the possibility of placing multiple zone plates together in an array. This can allow the FZP’s to be used to advantage to either obtain multiple nearby images of the same object or to couple the images to multi-strip framing cameras, thereby allowing for time-resolved imaging of the object. Nevertheless, monochromators provide an additional means by which the x rays passing through the FZP can be limited to a narrow, well-focused energy range. This can increase the resolution obtainable and is extremely important in the case where the object being radiographed is a strong x-ray emitter as well. Laser implosion of spherical shells, the current favored method of achieving nuclear fusion ignition, is an important case where the subject emits strongly both during laser ablation and during the stagnation phase of the compression.

In order to use FZP’s to radiograph a highly compressed deuterium–tritium (DT) plasma at stagnation, a monochromator must be used to limit self-emission. Until now, this has been pursued at LLE by using spherical crystal imaging,25 a method that provides both a monochromatic throughput and spatial resolution. However, the technique has been unable to resolve the compressed DT fusion fuel as a consequence of limited spatial resolution (∼15 μm) and a subject whose scale size at compression is expected to be even smaller than the resolution of the spherical crystal imager. An FZP, or an array of such, could provide the necessary resolution to diagnose the compressed plasma conditions at scales approaching 1 μm.

The authors acknowledge with gratitude the efforts of the staff at the Laboratory for Laser Energetics and of the operations personnel of the OMEGA and OMEGA EP Laser Systems. This material is based on work supported by the Department of Energy National Nuclear Security Administration under Award No. DE-NA0003856, the University of Rochester, and the New York State Energy Research and Development Authority.

This report was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of the authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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