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Characterizing transverse coherence of an ultra-intense focused X-ray free-electron laser by an extended Young's experiment.

Inoue I, Tono K, Joti Y, Kameshima T, Ogawa K, Shinohara Y, Amemiya Y, Yabashi M - IUCrJ (2015)

Bottom Line: For a focused X-ray spot as small as 1.8 µm (horizontal) × 1.3 µm (vertical) with an ultrahigh intensity that exceeds 10(18) W cm(-2) from the SPring-8 Ångstrom Compact free-electron LAser (SACLA), the coherence lengths were estimated to be 1.7 ± 0.2 µm (horizontal) and 1.3 ± 0.1 µm (vertical).The ratios between the coherence lengths and the focused beam sizes are almost the same in the horizontal and vertical directions, indicating that the transverse coherence properties of unfocused XFEL pulses are isotropic.The experiment presented here enables measurements free from radiation damage and will be readily applicable to the analysis of the transverse coherence of ultra-intense nanometre-sized focused XFEL beams.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan ; RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan.

ABSTRACT
Characterization of transverse coherence is one of the most critical themes for advanced X-ray sources and their applications in many fields of science. However, for hard X-ray free-electron laser (XFEL) sources there is very little knowledge available on their transverse coherence characteristics, despite their extreme importance. This is because the unique characteristics of the sources, such as the ultra-intense nature of XFEL radiation and the shot-by-shot fluctuations in the intensity distribution, make it difficult to apply conventional techniques. Here, an extended Young's interference experiment using a stream of bimodal gold particles is shown to achieve a direct measurement of the modulus of the complex degree of coherence of XFEL pulses. The use of interference patterns from two differently sized particles enables analysis of the transverse coherence on a single-shot basis without a priori knowledge of the instantaneous intensity ratio at the particles. For a focused X-ray spot as small as 1.8 µm (horizontal) × 1.3 µm (vertical) with an ultrahigh intensity that exceeds 10(18) W cm(-2) from the SPring-8 Ångstrom Compact free-electron LAser (SACLA), the coherence lengths were estimated to be 1.7 ± 0.2 µm (horizontal) and 1.3 ± 0.1 µm (vertical). The ratios between the coherence lengths and the focused beam sizes are almost the same in the horizontal and vertical directions, indicating that the transverse coherence properties of unfocused XFEL pulses are isotropic. The experiment presented here enables measurements free from radiation damage and will be readily applicable to the analysis of the transverse coherence of ultra-intense nanometre-sized focused XFEL beams.

No MeSH data available.


Related in: MedlinePlus

(a), (b) The dependence of η and the visibility of scattering patterns on the scattering vector q for I1/I2 = 1/25, 1/5, 1, 5 and 25 for two spherical particles of radii R1 = 75 nm and R2 = 50 nm. η(q) takes any value greater than or equal to zero, and thus the maximum value of the visibility corresponds to the complex degree of coherence. In part (a), q1 and q2 satisfy η(q1) = 0 and η(q2) = +∞, respectively. For I1/I2 = 1/5, 1, 5 and 25, the visibility shows a peak in q < q1. For I1/I2 = 1/25, the visibility shows a peak in q1 < q < q2. For all cases, the first peak value in the visibility along the q direction (q > 0) corresponds to /γ(r1, r2; 0)/. (c), (d) The dependence of the visibility of scattering patterns on the scattering vector q for I1/I2 = 1/25, 1/5, 1, 5 and 25 for two spherical particles of similar size [for part (c), R1 = 51 nm and R2 = 50 nm; for part (d), R1 = 76.5 nm and R2 = 75 nm].
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fig1: (a), (b) The dependence of η and the visibility of scattering patterns on the scattering vector q for I1/I2 = 1/25, 1/5, 1, 5 and 25 for two spherical particles of radii R1 = 75 nm and R2 = 50 nm. η(q) takes any value greater than or equal to zero, and thus the maximum value of the visibility corresponds to the complex degree of coherence. In part (a), q1 and q2 satisfy η(q1) = 0 and η(q2) = +∞, respectively. For I1/I2 = 1/5, 1, 5 and 25, the visibility shows a peak in q < q1. For I1/I2 = 1/25, the visibility shows a peak in q1 < q < q2. For all cases, the first peak value in the visibility along the q direction (q > 0) corresponds to /γ(r1, r2; 0)/. (c), (d) The dependence of the visibility of scattering patterns on the scattering vector q for I1/I2 = 1/25, 1/5, 1, 5 and 25 for two spherical particles of similar size [for part (c), R1 = 51 nm and R2 = 50 nm; for part (d), R1 = 76.5 nm and R2 = 75 nm].

Mentions: When a narrow bandwidth XFEL pulse with mean frequency ω irradiates a large-sized particle of radius R1 at position r1 and a small particle of radius R2 at r2, the intensity of the interference fringes, except for a constant factor, can be expressed as (Mandel & Wolf, 1995 ▸)withandwhere I1 and I2 are the intensities of the incident beam at r1 and r2, respectively. In the equations above, q is the magnitude of the scattering vector transfer q [q = (4π/λ)sinθ, where θ is half the scattering angle and λ is the wavelength of the incident radiation], and F(q, R) = 3[sin(qR) − qRcos(qR)]/(qR)3 and V(R) are the form factor and the volume of a spherical particle of radius R, respectively. τ is the time delay at q for the scattering waves originating from the two particles, γ(r1, r2; τ) is the complex degree of coherence, and α12 is the phase of γ(r1, r2; τ). Assuming that the longitudinal coherence time is much longer than τ, /γ(r1, r2; τ)/ and α12(τ) are approximated to be /γ(r1, r2; 0)/ and α12(0), respectively (Mandel & Wolf, 1995 ▸). Then, the visibility of the interference fringes at q, v(q) = B(q)/A(q), is given bywhere η(q) = R12(q)(I1/I2)1/2, with η(q) takes any value greater than or equal to zero. One can find certain scattering vectors satisfying η(q) = 1, and thus the maximum value of v(q) equals /γ(r1, r2; 0)/. As an example, Fig. 1 ▸(a) shows η(q) for several values of I1/I2 in the case of R1 = 75 nm and R2 = 50 nm. Note that η(q) is positive infinity when q satisfies F(q, R2) = 0 (e.g.q = q2 in Fig. 1 ▸a), while η(q) takes a minimum value of zero when q satisfies F(q, R1) = 0 (e.g.q = q1 in Fig. 1 ▸a). Fig. 1 ▸(b) shows the visibility divided by /γ(r1, r2; 0)/ calculated from equation (4) at the same condition. In every case, the first peak value of v(q) along q (q > 0) corresponds to the maximum visibility and equals /γ(r1, r2; 0)/. Therefore, by calculating the visibility of the interference fringes for each q and finding its first peak along q, we can determine the modulus of the complex degree of coherence without a priori knowledge of I1/I2.


Characterizing transverse coherence of an ultra-intense focused X-ray free-electron laser by an extended Young's experiment.

Inoue I, Tono K, Joti Y, Kameshima T, Ogawa K, Shinohara Y, Amemiya Y, Yabashi M - IUCrJ (2015)

(a), (b) The dependence of η and the visibility of scattering patterns on the scattering vector q for I1/I2 = 1/25, 1/5, 1, 5 and 25 for two spherical particles of radii R1 = 75 nm and R2 = 50 nm. η(q) takes any value greater than or equal to zero, and thus the maximum value of the visibility corresponds to the complex degree of coherence. In part (a), q1 and q2 satisfy η(q1) = 0 and η(q2) = +∞, respectively. For I1/I2 = 1/5, 1, 5 and 25, the visibility shows a peak in q < q1. For I1/I2 = 1/25, the visibility shows a peak in q1 < q < q2. For all cases, the first peak value in the visibility along the q direction (q > 0) corresponds to /γ(r1, r2; 0)/. (c), (d) The dependence of the visibility of scattering patterns on the scattering vector q for I1/I2 = 1/25, 1/5, 1, 5 and 25 for two spherical particles of similar size [for part (c), R1 = 51 nm and R2 = 50 nm; for part (d), R1 = 76.5 nm and R2 = 75 nm].
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fig1: (a), (b) The dependence of η and the visibility of scattering patterns on the scattering vector q for I1/I2 = 1/25, 1/5, 1, 5 and 25 for two spherical particles of radii R1 = 75 nm and R2 = 50 nm. η(q) takes any value greater than or equal to zero, and thus the maximum value of the visibility corresponds to the complex degree of coherence. In part (a), q1 and q2 satisfy η(q1) = 0 and η(q2) = +∞, respectively. For I1/I2 = 1/5, 1, 5 and 25, the visibility shows a peak in q < q1. For I1/I2 = 1/25, the visibility shows a peak in q1 < q < q2. For all cases, the first peak value in the visibility along the q direction (q > 0) corresponds to /γ(r1, r2; 0)/. (c), (d) The dependence of the visibility of scattering patterns on the scattering vector q for I1/I2 = 1/25, 1/5, 1, 5 and 25 for two spherical particles of similar size [for part (c), R1 = 51 nm and R2 = 50 nm; for part (d), R1 = 76.5 nm and R2 = 75 nm].
Mentions: When a narrow bandwidth XFEL pulse with mean frequency ω irradiates a large-sized particle of radius R1 at position r1 and a small particle of radius R2 at r2, the intensity of the interference fringes, except for a constant factor, can be expressed as (Mandel & Wolf, 1995 ▸)withandwhere I1 and I2 are the intensities of the incident beam at r1 and r2, respectively. In the equations above, q is the magnitude of the scattering vector transfer q [q = (4π/λ)sinθ, where θ is half the scattering angle and λ is the wavelength of the incident radiation], and F(q, R) = 3[sin(qR) − qRcos(qR)]/(qR)3 and V(R) are the form factor and the volume of a spherical particle of radius R, respectively. τ is the time delay at q for the scattering waves originating from the two particles, γ(r1, r2; τ) is the complex degree of coherence, and α12 is the phase of γ(r1, r2; τ). Assuming that the longitudinal coherence time is much longer than τ, /γ(r1, r2; τ)/ and α12(τ) are approximated to be /γ(r1, r2; 0)/ and α12(0), respectively (Mandel & Wolf, 1995 ▸). Then, the visibility of the interference fringes at q, v(q) = B(q)/A(q), is given bywhere η(q) = R12(q)(I1/I2)1/2, with η(q) takes any value greater than or equal to zero. One can find certain scattering vectors satisfying η(q) = 1, and thus the maximum value of v(q) equals /γ(r1, r2; 0)/. As an example, Fig. 1 ▸(a) shows η(q) for several values of I1/I2 in the case of R1 = 75 nm and R2 = 50 nm. Note that η(q) is positive infinity when q satisfies F(q, R2) = 0 (e.g.q = q2 in Fig. 1 ▸a), while η(q) takes a minimum value of zero when q satisfies F(q, R1) = 0 (e.g.q = q1 in Fig. 1 ▸a). Fig. 1 ▸(b) shows the visibility divided by /γ(r1, r2; 0)/ calculated from equation (4) at the same condition. In every case, the first peak value of v(q) along q (q > 0) corresponds to the maximum visibility and equals /γ(r1, r2; 0)/. Therefore, by calculating the visibility of the interference fringes for each q and finding its first peak along q, we can determine the modulus of the complex degree of coherence without a priori knowledge of I1/I2.

Bottom Line: For a focused X-ray spot as small as 1.8 µm (horizontal) × 1.3 µm (vertical) with an ultrahigh intensity that exceeds 10(18) W cm(-2) from the SPring-8 Ångstrom Compact free-electron LAser (SACLA), the coherence lengths were estimated to be 1.7 ± 0.2 µm (horizontal) and 1.3 ± 0.1 µm (vertical).The ratios between the coherence lengths and the focused beam sizes are almost the same in the horizontal and vertical directions, indicating that the transverse coherence properties of unfocused XFEL pulses are isotropic.The experiment presented here enables measurements free from radiation damage and will be readily applicable to the analysis of the transverse coherence of ultra-intense nanometre-sized focused XFEL beams.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan ; RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan.

ABSTRACT
Characterization of transverse coherence is one of the most critical themes for advanced X-ray sources and their applications in many fields of science. However, for hard X-ray free-electron laser (XFEL) sources there is very little knowledge available on their transverse coherence characteristics, despite their extreme importance. This is because the unique characteristics of the sources, such as the ultra-intense nature of XFEL radiation and the shot-by-shot fluctuations in the intensity distribution, make it difficult to apply conventional techniques. Here, an extended Young's interference experiment using a stream of bimodal gold particles is shown to achieve a direct measurement of the modulus of the complex degree of coherence of XFEL pulses. The use of interference patterns from two differently sized particles enables analysis of the transverse coherence on a single-shot basis without a priori knowledge of the instantaneous intensity ratio at the particles. For a focused X-ray spot as small as 1.8 µm (horizontal) × 1.3 µm (vertical) with an ultrahigh intensity that exceeds 10(18) W cm(-2) from the SPring-8 Ångstrom Compact free-electron LAser (SACLA), the coherence lengths were estimated to be 1.7 ± 0.2 µm (horizontal) and 1.3 ± 0.1 µm (vertical). The ratios between the coherence lengths and the focused beam sizes are almost the same in the horizontal and vertical directions, indicating that the transverse coherence properties of unfocused XFEL pulses are isotropic. The experiment presented here enables measurements free from radiation damage and will be readily applicable to the analysis of the transverse coherence of ultra-intense nanometre-sized focused XFEL beams.

No MeSH data available.


Related in: MedlinePlus