Complex X-Ray Holography of GaAs crystal

● Principles of Holographic Imaging

● Barton's Algorithm and other Fourier Transforms

● Synchrotron Techniques

● Experimental Setup

● Image results

● Use in imaging and understanding magnetic structure

Holography in a nutshell

● Interference allows third degree of freedom encoded on detector.

● Scattered light can be reconstructed via reference beam which supplies phase information.

● Think of any 3D image as a 2D image with many possible reference points.

● Interference between reference beam and scattered beam

● Normally a lenseless technique

Complex X-ray Holography

2k =bk b−a k a

f Y' ' A−f Y

' ' B

1k =C kC −bk B

f Y' C−f Y

' B

● Phase equation for Holography

● Holograms 1 and 2

where chi is, f is, phi is

● Redifined Holograms

∣U oU r2∣=U oU r

¿∣U r

2∣∣Uo2∣U o

¿U r

B−C=2re f 1B−f 1

C j

cosa j

a j

B−A=2re f 2A−f 2

B j

sina j

a j

Barton's Algorithm

U k r =∫ e−ikr1k i1k d

complex k =1k i2k

Measure inputX-ray intensity

Rotate StageΔΘ , ΔΦ

Apply Barton'sAlgorithm find Emitter position

Output X-ray Intensity and Stage position

X-ray Fluorescence Technique

● Internal Source

flourescent rays from sample and reference from scattered incident rays

● Internal detector

Both sample atom and reference atom are illuminated.

● Si PiN diode used to monitor intensity

● 2 θ and Φ stages for rotations from 0-360 and 25 -70

● N2 cryostream cooled to 100 K

● 3 holograms recorded at 11.872 Kev, 11.865 KeV and 11.767 KeV.

● Beam focussed via cylidnrical graphite analyzer in IDH geometry

The BL37XU Beamline

Beamline Branch A Branch B

EnergyRange

5-37 Kev Si(111) 75.5Kev

ResolutionΔE / E

2 x 10-4 2 x 10-4

Flux at sample

10 12 – 10 13 photons

10 10 – 10 12 photons

Beam sizeAt sample

.7 x .2 mm(vert) (hori)

.5 x 3 mm

Higher Harmonics

<1 x 10 -4 <1 x 10 -4

● 3rd generation source

● Super Photon Ring 8 Gev (Spring-8)

● Harima, Hyogo, Japan

● .9-1.5 / 8 Gev in / out

● 64 bending magnets,

Spring-8 Source

● 3D reconstruction with Ga in center, As as purple and orange as next Ga

● Complex reconstruction technique lacking the twin images

Why use Spring-8?

● Coherence necessary, which requires large flux● Large flux reduces experiment time● Tunable energy needed for fluorescence● Very fine stage rotation angle● Special conditions needed for sample

Unique applications

● Removes twin image problem● Requires no lenses● Can detect magnetic scattering by polarizing

the light

references

● Wikipedia : Holography visited 4/15/12

● Wikipedia : Diffraction visited 4/15/12

● J.J. Barton Phys. Rev. Lett. 67 (1991) 3106-3109

● Takahashi, Yukio Phys Rev B 71 134107 (2005)

● Takahashi, Yukio. Sci Tech Adv Materials 4 (2003) 409 -414

● http://www.spring8.or.jp/en/facilities/accelerators/storage_ring/

● http://www.spring8.or.jp/en/facilities/accelerators/synchrotron/

● http://www.spring8.or.jp/wkg/BL37XU/instrument/lang-en/INS-0000000591/instrument_summary_view