Spatial resolution measurement

The spatial and temporal resolutions of the cameras were measured. A tailored Au PC was used instead of an X-ray PC to measure the spatial resolution at different off-axis distances. The Au PCs were fabricated by depositing an 80 nm Au film on a quartz substrate. Photolithography was used to develop a resolution mask for each PC [34]. The resolution mask comprised several slits with dimensions of 3 mm × 3 mm. The slits had various spatial frequencies, namely 500, 200, 100, 66, 50, 40, 33 and 28 μm. Two slits, whose directions were parallel and perpendicular to the PC transmission line, were used for each spatial frequency. Eight spatial frequencies with sixteen slits are formed to a slit group. Several slit groups were deposited repetitively along each PC to measure the spatial resolution at different off-axis distances.

The spatial resolution of the camera, which is determined by the combined magnetic lenses and MCP imager, can be expressed as [19, 22]: $\delta =\sqrt{{\left({\delta }_{\text{drift}}\right)}^2+{\left({\delta }_{\text{MCP}}\times M_{\text{S}}\right)}^2}.$ (1)

Here, δ_drift is the spatial resolution of the combined magnetic lenses; δ_MCP = 50 μm is the spatial resolution of the MCP imager; and the spatial magnification ratio M_s is 1. As δ_MCP and M_s are fixed, δ is primarily influenced by the combined magnetic lenses.

The spatial resolution was simulated as follows. Lorentz3DEM software was used to simulate the electromagnetic field from the PC to the MCP of the camera, and the resulting electron trajectories were traced. The spatial resolution of each off-axis position was obtained using the Rayleigh criterion. Two photoelectron beams were emitted at specific positions on the PC, and their corresponding image points on the MCP were obtained. The minimum distinguishable distance between the two image points was obtained using the Rayleigh criterion, and the corresponding gap between the two photoelectron beams on the PC was determined as the spatial resolution.

The static spatial resolution measurements were performed using a DC ultraviolet source. A static DC voltage was applied to both the PC and MCP. The PC converted the incident ultraviolet light to a photoelectron image with a mask. The photoelectron image was then imaged onto the MCP by combined magnetic lenses and converted to a visible image by the MCP imager. Finally, a CCD was used to capture the visible images.

The spatial resolution characteristics of the cameras with different numbers of magnetic lenses were compared. The number of magnetic lenses was increased, and the static image of the corresponding camera was obtained. When the camera consists of one magnetic lens, the static image on the Gaussian plane of the middle transmission PC is shown in Fig. 2(a). Static images with resolution masks when the camera comprises two, three, and four magnetic lenses are shown in Figs. 2(b), (c), and (d), respectively. The spatial resolution is obtained from the static image, and the modulations of the slits for different spatial frequencies are given by $M=\frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }}.$ (2)

Fig. 2Full-screen View

(a) Static image with a resolution mask on the Gaussian plane of the middle PC when the camera has one magnetic lens. Static images corresponding to the cases when the camera comprises (b) two, (c) three, and (d) four magnetic lenses

Here, I, I_max, and I_min denote the corresponding intensity of the slit image, maximum intensity, and minimum intensity, respectively. The measured and simulated results were compared.

The 200 μm mask for various off-axis distances and magnetic lens numbers are shown in Fig. 3(a), and their corresponding modulations are shown in Fig. 3(b). The lines and points represent the simulated and measured results, respectively. The camera with one magnetic lens exhibits the worst imaging quality. The modulation decreases rapidly with increasing off-axis distances. It cannot distinguish 200 μm when the off-axis distance exceeds 13.5 mm. The camera with two, three, or four magnetic lenses exhibits considerably better imaging quality than the single magnetic lens camera. The camera that uses four magnetic lenses exhibits better spatial resolution than that using two or three lenses. In the camera with four magnetic lenses, the entire effective working area with diameter of 60 mm delivers a spatial resolution better than 200 μm. The measurement and simulation results are consistent, and show that the modulation worsens with increasing off-axis distance. Therefore, the spatial resolution decreases with increasing off-axis distance.

Fig. 3Full-screen View

(Color online) (a) 200 μm mask on Gaussian plane for different off-axis distances and various numbers of magnetic lenses. (b) Modulation of the 200 μm mask in (a) versus the off-axis distance. (c) Modulation of the 100 μm mask on the Gaussian plane with various off-axis distances

The modulations of the 100 μm masks on the Gaussian plane versus off-axis distances are shown in Fig. 3(c). The visibility of the 100 μm mask reduces when the off-axis distance increases. The 100 μm mask can be distinguished within the area with radius of 4.5 mm when one magnetic lens is used. The imaging quality significantly improves when the camera uses four magnetic lenses. However, the 100 μm mask in the PC off-axis 26.5 mm does not exhibit visible modulation. The camera cannot have a working area with a radius of 26.5 mm for 100 μm spatial resolution on the Gaussian plane. Furthermore, the modulation for the 100-μm mask descends faster than that for the 200- μm mask along the off-axis distance.

The off-axis spatial resolution is primarily influenced by the field curvature, which is a type of aberration that transforms an imaging plane into a curved surface. The curvature close to the axis is approximately spherical. In the magnet–lens imaging system, the curvature radius r_p of the image surface is given by [35] $\frac{1}{r_{\text{p}}}=-\frac{e}{4m{V}^{\frac{3}{4}}}{\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}{B}^2\text{ dz}}.$ (3)

Here, e and m are the electron charge and mass, respectively; V is the voltage between the PC and the mesh; B is the magnetic field strength in the drift tube; and z is the axial direction variable.

The field curvature is a complex parameter because the curvature radius r_p varies with the off-axis distance. The imaging surface was simulated using the Lorentz3DEM software. The curved imaging surfaces for cameras consisting of various numbers of lenses and their two-dimensional projections are shown in Fig. 4(a) and Fig. 4(b), respectively. The lines represent the simulation results for a PC with a simulation area diameter of 60 mm. The parameter L is the distance from the imaging surface to the PC along the axis, which represents the position of the imaging surface for each off-axis point. The simulation results show that the imaging surface is curved when the PC voltage is fixed. Although the object point has a larger off-axis distance, its corresponding L is smaller, which indicates that the imaging point is located closer to the PC for a farther off-axis object point.

Fig. 4Full-screen View

(Color online) (a) Simulation of field curvatures with different magnetic lenses. (b) Two-dimensional projections of the field curvature: plane A is the Gaussian plane and plane B is another imaging plane to achieve a larger PC-sensitive area and reduce the spatial resolution differences in the working area

In the experiment, the imaging surface was detected using a planar MCP, and the distance between the PC and MCP was fixed in the camera. Therefore, the position of the imaging point for each off-axis object point could not be simultaneously obtained in an experiment with the same PC voltage. The imaging-point positions were obtained from different experiments using different PC voltages. The PC voltage was adjusted in turn, resulting in a sequence of the clearest areas of the image on the MCP. Subsequently, the PC voltage for each object point on the PC that was imaged clearly on the MCP was obtained. In the camera with four magnetic lenses, the experimental results demonstrated that the distance between the object plane and image surface reduced by approximately 0.14 mm when the PC voltage increased by 1 V. Similar results were obtained for the other magnetic lens imaging systems. Therefore, the variation in PC voltage can be used to obtain the imaging point position of each PC object and its corresponding variation [35]. The experimental results of the position of the imaging point versus the off-axis distance of the PC object point are shown in Fig. 4(b). In Fig. 4, the lines and points represent the simulation and experimental results, respectively. The experimental results are consistent with the simulation results. The position of the imaging point is moved to the PC when the off-axis distance of the object point is increased, leading to a curved imaging surface. However, the detector of the curved imaging surface is a planar MCP; consequently, the spatial resolution varies with the off-axis distance of the electrons emitted from the PC. Therefore, the uniformity of the spatial resolution over the entire sensitive area of the PC was reduced.

In Fig. 4(b), plane A is the Gaussian plane, and the curved imaging surfaces are the Petzval surfaces [35]. S₁, S₂, S₃, and S₄ are the axial deviations between the Gaussian plane and Petzval surface with an aperture radius of 30 mm. The maximum in the camera with one magnetic lens, S_1, is approximately 13 cm. The deviation S₂ decreases to 5 cm when two magnetic lenses are used. A better curvature is achieved by using three magnetic lenses, and the deviation S₃ is approximately 2.5 cm. The field curvature further improves in the camera with four magnetic lenses, and deviation S₄ improves to less than 2 cm. The improvement in the field curvature enhances the spatial resolution with an increasing number of magnetic lenses, which explains the experimental results shown in Fig. 3.

The location of the Gaussian plane A for the camera imaging system was adjusted to improve the uniformity of the spatial resolution in the entire sensitive area of the PC. The PC voltage of −3 kV was fixed, while the magnetic lens excitation currents were reduced. The Gaussian plane A was moved farther from the PC. The spatial resolution differences in the working area improved when the plane B in Fig. 4(b) was moved to overlap with the MCP plane. Fig. 5(a) shows the 200 μm static images of the slits on the imaging plane B, while Fig. 5(b) shows its modulations varying with off-axis distance. Compared to the results for the Gaussian plane A in Fig. 3(a), the off-axis spatial resolution of off-axis 25.5 mm is significantly improved. The 200-μm mask on the radius of 25.5 mm was distinguishable in the camera with four and three magnetic lenses. Fig. 5(b) shows that changing the imaging plane from A to B improves the modulation for the off-axis region. However, the modulation of the on-axis area decreases. Fortunately, the spatial resolution differences over the entire working area improve. Comparing the modulation difference of plane B in Fig. 5(b) with that of plane A in Fig. 3(b), the modulation difference among the points within a 30 mm off-axis distance in plane B is better than that in plane A. Therefore, the uniformity of the spatial resolution of the entire working area for plane B is better than that for plane A.

Fig. 5Full-screen View

(Color online) (a) Static images of 200 μm masks on imaging plane B. (b) Modulations of 200 μm masks on imaging plane B for various off-axis distances. (c) Modulations of the 100 μm masks on imaging plane B versus off-axis distance

The modulations of the 100 μm slits for the static images on the imaging plane B are shown in Fig. 5(c). The 100 μm spatial resolution with radius of 26.5 mm is distinguishable in the camera with four magnetic lenses. Further, multiple combined magnetic lenses produce better imaging quality than a single magnetic lens. The camera with four combined magnetic lenses achieved a spatial resolution of 100 μm in a sensitive area with a diameter of 53 mm.

Temporal resolution measurement

The energy spread at the mesh results in temporal magnification of the electron pulse in the drift tube, which greatly improves the temporal resolution. The temporal resolution T of the pulse-dilation framing camera is mainly determined by the temporal resolution T_MCP of the MCP imager and the pulse-dilation temporal magnification factor M, which is given by [21] $T\approx \frac{T_{\text{MCP}}}{M},$ (4)

The pulse dilation temporal magnification factor M is determined by the PC voltage, PC dilation pulse slope, and drift tube length [26]. Because of the small distance from the PC to the mesh and the negligible initial electron energy spread at the PC, the electrons that enter the drift tube at time t_i reach the MCP at time $t^{\prime }$ as follows [25]: ${t^{\prime }}_i=\frac{L_{\text{pm}}}{\sqrt{2e\varphi \left(t_i\right)/m}}+t_i,$ (5) where L_pm is the 550 mm length of the drift tube. Between the two time steps, the temporal magnification factor M can be expressed as [33] $\begin{array}{c}M\left(t_{i+1},t_i\right)=\frac{{t^{\prime }}_{i+1}-{t^{\prime }}_i}{t_{i+1}-t_i}\\ =1+\frac{L_{\text{pm}}}{\sqrt{2e/m}}\frac{\varphi {\left(t_{i+1}\right)}^{-1/2}-\varphi {\left(t_i\right)}^{-1/2}}{t_{i+1}-t_i}\\ \approx 1+\frac{L_{\text{pm}}}{\sqrt{2e/m}}{\left[\varphi {\left(t\right)}^{-1/2}\right]}^{\prime }.\end{array}$ (6)

In general, the drift tube length is determined when the pulse-dilation framing tube is designed. The temporal resolution T is primarily determined by the PC voltage, PC dilation pulse slope, and MCP imager resolution [26]. As shown in Fig. 6, the variation of the temporal resolution T of the camera with the PC dilation pulse slope and its relationship with the PC voltage were studied when the temporal resolution of the MCP imager was 100 ps. The temporal resolution improves with increasing PC dilation pulse slope. This is because the temporal magnification factor M increases with the PC dilation pulse slope. In Fig. 6(a), a voltage of −2.5 kV is applied to the PC. As shown in Fig. 6(b), the PC dilation pulse slope is 2.5 V/ps. Figure 6(b) shows that the temporal resolution improves with decreasing the accelerating voltage. The accelerating voltage is an important parameter for the camera because both the electron transit time spread from the PC to the anode mesh and the spatial resolution improve with increasing acceleration voltage [31, 32]. The acceleration voltages of the pulse-dilation framing cameras are typically higher than 2.5 kV [21, 36].

Fig. 6Full-screen View

(a) Temporal resolution of the camera varying with PC dilation pulse slope. (b) Temporal resolution of the camera versus accelerating voltage

The temporal resolution was measured using a femtosecond laser and fiber bundle. The measurement setup included a Ti-sapphire femtosecond laser system, an optical time adjustment system, a fiber bundle, an optical imaging system, an electric trigger signal generator, an electric delay circuit, and the pulse-dilation framing camera, as shown in Fig. 7(a). Two laser beams with wavelengths of 266 nm and 800 nm were emitted by the femtosecond laser system. The 266 nm UV light was used to excite photoelectrons, while 800 nm infrared light served as a synchronous trigger signal. UV light with a pulse width of 130 fs was reflected by a total reflection mirror M₁, and the spot size of the UV light was then enlarged by a concave lens L₁. The fiber bundle was composed of 30 fibers and was used to separate the input UV laser into 30 light points. The lengths of the 30 fibers were increased with an equal difference of 2 mm, and the error was less than 0.2 mm. Therefore, 30 UV light points were generated at various times. A delay of approximately 10 ps was achieved for each pair of adjacent light points. Photographs of the fiber bundle and an array diagram of the fiber output port are shown in Fig. 7 (b) and (c), respectively. The 30 UV light points obtained from the fiber bundle are imaged onto the PC using lenses L₂ and L₃, which generates 30 photoelectron pulses. The emission time interval for each pair of neighboring photoelectron pulses is approximately 10 ps.

Fig. 7Full-screen View

(Color online) (a) Schematic of the experimental setup for temporal resolution measurement. (b) Photograph of the fiber bundle. (c) Output port array of the fiber bundle. Fiber 1 is the shortest fiber. The centers of neighboring fibers are separated by a gap of 0.2 mm

First, the static image of 30 laser pulses was acquired, as shown in Fig. 8(a). The PC and MCP were subjected to static DC voltages of −3 kV and −700 V, respectively. The top-right image point is imaged from the shortest fiber, and each pair of neighboring images is 0.5 mm apart. The static image represents the light intensity uniformity of the 30 light points, which is used as a normalized background image for the gating image.

Fig. 8Full-screen View

(Color online) (a) Static image of the 30 laser pulses corresponding to static DC voltages of −3 kV and −700 V applied to PC and MCP, respectively. (b) Gating image of the 30 laser pulses for the camera without pulse-dilation. Only a −2.5 kV DC voltage is applied to the PC, while a −483 V DC bias plus the gating pulse described above are applied to the MCP. (c) Gating image of 30 laser pulses for the camera with pulse-dilation. A −3 kV DC bias overlaid by the 2.5 V/ps PC dilation pulse are applied to the PC, while a −483 V DC bias and the gating pulse are applied to the MCP. (d) Measured results of the temporal resolution; the red and blue data are the results without pulse dilation for (b) and those with pulse dilation for (c), respectively

The gated image of the camera without pulse dilation (Fig. 8(b)) was measured by applying a −2.5 kV static DC voltage on the PC and a −483 V DC bias plus the gating pulse as described above for the MCP. When a static DC bias was applied to the PC, the electron beam was not temporally dilated. The MCP was driven by the gating pulse and the electron signal was sampled by the MCP imager. Thus, we measured the gate width of the MCP imager. Figs. 8(a) and (b) show two raw CCD images. To reduce the effect of the nonuniform light intensity distribution, the static results from Fig. 8(a) were used to correct the gating results in Fig. 8(b). A lineout of the corrected data is shown in red in Fig. 8(d). The solid red block points represent the experimental results, which were Gaussian fitted to obtain the intensity versus time curve. The full width at half maximum (FWHM) of the Gaussian curve is defined as the temporal resolution of the camera. Fig. 8(d) shows that, while the electron signal is not dilated, the temporal resolution is approximately 100 ps, which is the temporal-resolution T_MCP of the MCP imager.

Finally, the gated image for the camera with pulse dilation was measured, as shown in Fig. 8(c). The MCP was gated, and subjected to a −483 V DC bias and the gating pulse. The PC was excited by a dilation pulse and −3 kV DC bias. Therefore, the photoelectron pulses were temporally dilated and the temporal resolution of the camera improved significantly, as shown in Equation (4). To obtain pulse dilation, all or part of the 30 photoelectron pulses were synchronized with the rising edge of the PC dilation pulse. In this experiment, the arrival time of the laser pulses at the PC was constant, and the timing of the PC dilation pulse was accurately adjusted using a delay circuit to synchronize the PC dilation pulse with the photoelectron pulses. A good synchronization position was achieved in many of the experiments, which was approximately 235 ps relative to the starting time of the PC dilation pulse. The PC voltage at this synchronization position is approximately −2.5 kV. The measured gated image of the camera with pulse dilation when the synchronization position is 235 ps and the photoelectron pulses are dilated is shown in Fig. 8(c). The lineouts of the results from Fig. 8(c) are indicated in blue in Fig. 8(d), which shows that the temporal resolution T of the pulse-dilation framing camera is approximately 10 ps. The temporal magnification factor M was acquired from the PC voltage, temporal resolution T_MCP of the MCP imager, and temporal resolution T of the pulse-dilation framing camera. The measured M was 10, which was consistent with the theoretical result of 10.2 calculated using Eq. (6).