Projection phase contrast microscopy with a hard x-ray nanofocused beam: Defocus and contrast transfer

We report a projection phase contrast microscopy experiment using hard x-ray pink beam undulator radiation focused by an adaptive mirror system to 100–200 nm spot size. This source is used to illuminate a lithographic test pattern with a well-controlled range of spatial frequencies. The oscillatory nature of the contrast transfer function with source-to-sample distance in this holographic imaging scheme is quantified and the validity of the weak phase object approximation is confirmed for the experimental conditions.

Figure 1

Contrast transfer functions for phase and amplitude objects as a function of the normalized spatial frequency $\sqrt{\lambda z}\nu$.

Figure 2

(a) Micrograph of the lithographic test sample. (b) Setup of in-line holography.

Figure 3

(Color) (a) Hologram (projection image) recorded at $z_1=15\text{mm}$ after division by the empty beam. Circles indicate the radii where the CTF is zero. (b) The position of the circles was determined from evaluating the rms deviation of the intensity values from the mean for each pixel radius from the center. The cusps indicate the positions of the circles. The source-to-sample distance $z_1$ is then scanned, changing field of view and the positions of the CTF minima. For illustration, holograms recorded at (c) $z_1=15\text{mm}$ (star centered), (d) $z_1=5\text{mm}$, and (e) $z_1=3\text{mm}$ are shown to illustrate the effect of varied defocus $z$. The images were divided by the empty beam. Grey scale is scales in the interval [0,2] for (a), (d), and (e) and [0.7,1.3] for (c).

Figure 4

Spatial frequency of zero contrast for the first order obtained from the radii in the holograms where the contrast undergoes an inversion, normalized to the position at the start of the scan along with the predicted curve $z^{-0.5}$. The insert shows the $\sqrt{n}$ scaling of the first four orders determined from Fig. 3.

Figure 5

One-step holographic reconstruction by Fresnel-Kirchhoff back propagation of the hologram shown Fig. 3. By identification of the void stripes in the center with the lithographic design (see Fig. 2), one recognizes contrast transfer down to about 200–100 nm, as expected. However, reconstruction from one hologram alone introduces artifacts at those spatial frequencies which are not transferred; see the blurred outer rings.