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Synchrotron Light Interferometer Project at Jefferson Lab Pavel Chevtsov February 21, 2003 - Properties of Light - Synchrotron Radiation - Beam Diagnostics with Synchrotron Light - Synchrotron Light Interferometer at Jefferson Lab with some

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Synchrotron Light Interferometer Project at Jefferson Lab

Pavel Chevtsov

February 21, 2003

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  • Properties of Light
  • Synchrotron Radiation
  • Beam Diagnostics with Synchrotron Light
  • Synchrotron Light Interferometer at Jefferson Lab

with some Experimental Results

  • Conclusions
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Properties of Light

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Diffraction

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Diffraction describes how light interacts with its physical environment. Diffraction is the spreading of waves around obstacles.

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.

y L

a

S I(y) = I(0) sin( ) = kay/(2L) k = 2 /

[ ]

2

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Resolving power of image-forming systems Diffraction of light limits the resolution of optical systems. The images of two objects, which are very close to each

  • ther, overlap.

How close two points can be brought together before they can no longer be distinguished as separate ?

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L The Rayleigh criterion states that two similar diffraction patterns can just be resolved if the first zero of one pattern falls on the central peak of the other.

min =

a s R = ( )min R

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Interference

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Interference is the net effect of the combination of two or more wave trains. Interference results from the superposition

  • f electromagnetic waves. It is the mechanism

by which light interacts with light.

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The intensity pattern is given by: y

a

D

L

.

S sin( )]

2

[ 1 + cos(kDy/L) ]

I 0 [

I(y) = = kay/(2L)

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If the light source is not “point-like”

.

.

S

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sin( )]

2

[ 1 + V cos(kDy/L + ) ] I0[ I(y) = = kay/(2L) V = Imax - Imin Imax + Imin visibility (fringe contrast) And the visibility and the “phase shift” are connected with the degree of coherence : V = | | , = f (arg )

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Theorem of van Cittert – Zernike

The degree of coherence is given by the Fourier transform

  • f the intensity distribution of the source object.

( ) = I( ) exp{ -i 2 } d

∫

= D R

  • the visibility of the interference fringe picture from a point source is equal to 1
  • a small source object gives a good visibility (fringe contrast)
  • a large source object gives a poor visibility (fringe contrast)

( ) (0) =

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What is about the resolution of such a double slit assembly (interferometer) ? Following Rayleigh’s criterion,

min = 2D

s R = ( )min y

a

D

L The resolution can be made very high …

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… but only if

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.P1

.

P2 S P1 and P2 remain correlated: for all typical points S in the source | SP1 – SP2 | << 0

2/ 2/

is the coherence length for the bandwidth

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sin( )]

2

[ 1 + V cos(kDy/L + ) ]

[

I(y) = = kay/(2L) Behavior of the function:

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sin( )]

2

[ 1 + V cos(kDy/L + ) ]

[

I(y) = = kay/(2L)

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sin( )]

2

[ 1 + V cos(kDy/L + ) ]

[

I(y) = sin( )]

2

[ 1 ± V ]

[

Env1,2(y) =

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sin( )]

2

[ 1 + V cos(kDy/L + ) ]

[

I(y) =

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sin( )]

2

[ 1 + V cos(kDy/L + ) ]

[

I(y) =

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Synchrotron Radiation

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History - 1940th Theory of radiation from relativistic particles Pomeranchuk, Ivanenko, Sokolov, Ternov (USSR) Schwinger (USA) Synchrotron ideas - 1945 Veksler (USSR), McMillan (USA)

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The first visual observation of synchrotron radiation was in 1947 from the General Electric synchrotron in the USA.

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Synchrotron radiation (SR) is emitted from relativistic charged particles when their paths are changed. By the magnetic field, for example. Everywhere further we will consider

  • nly the synchrotron radiation from

electrons generated in the bending magnets.

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~ 1/ (5 GeV electrons -> 10-4 )

Because of the relativistic effect, the synchrotron radiation is emitted in a narrow cone in the forward direction, at a tangent to the orbit

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~ 1/ (5 GeV electrons -> 10-4 ) 2 cm ? ~ 100 m !

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Synchrotron radiation

  • highly polarized (E and E )
  • has a wide energy spectrum (from infrared to -rays)
  • extremely intense and highly collimated
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A typical energy spectrum of synchrotron radiation The critical wavelength ’ (or c) divides the radiated power into two equal parts: one-half of the power is radiated above this wavelength and one-half below.

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c =

4 3 3 The critical wavelength [A. Hofmann] Example: 5 GeV electrons, = 40 m

c = 0.16 nm

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At low frequencies the properties of synchrotron radiation are independent of the particle energy and depend only

  • n the radius
  • f the curvature.

The rms opening angle for >>

c

  • rms = 0.41 ( / )1/3
  • rms = 0.55 ( / )1/3

Example: = 630 nm, = 40 m

  • rms = 10-3
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  • rms = 10-3

2 cm ? ~ 10 m

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Synchrotron Radiation Beam Diagnostics

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e¯ detector lens

Imaging of the beam cross section with synchrotron radiation - SLM

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The natural opening angle of the emitted light sets a limit to the resolution of the SLM

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The diffraction limited resolution of synchrotron light imaging systems in the visible part of the spectrum [A.Hofmann]:

S ≈ 0.3 (λ2ρ)1/3

Example: λ = 630 nm, ρ = 40 m

S ≈ 0.1 mm

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Can we build a synchrotron light interferometer and use its data to measure smaller beam sizes ?

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  • T. Mitsuhashi, Photon Factory, KEK, Japan
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Problems

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Synchrotron radiation is like a moving narrow searchlight in horizontal direction.

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We observe photons coming from different positions when the electron moves from point A to point B. We must sum these photons.

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A B S1 S2 When an electron is moving from point A to point B, the light is sweeping from slit S1 to slit S2.

  • The intensities of two modes of light illuminating

the slits are different.

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  • T. Mitsuhashi has modified the van Cittert-Zernike

theorem and developed the method to calculate the beam size on the basis of the interference picture for the synchrotron light emitted by the beam. “Beam Profile and Size Measurement by the Use

  • f the Synchrotron Light Interferometer”
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  • OK. Now we build our interferometer.
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S Synchrotron Light Source Lens CCD

R L Synchrotron Radiation Interferometer

Image

Double slit assembly D a

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Problems

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Two polarized components

  • f the synchrotron light

(p and s) are “in anti-phase”. Their superposition will not give us the interference fringes at all.

  • > We get just a sort of a “SLM”.
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The synchrotron light is not monochromatic. range is the whole visible spectrum !

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S Synchrotron Light Source Lens CCD

R L

Synchrotron Radiation Interferometer

Image

Double slit assembly Polarization filter Band pass filter ( 0 ± )

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Beam Size Calculation

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In case of a gaussian beam shape it is easy: sin( )]

2

[ 1 + V cos(kDy/L + ) ] I0[ = kay/2L I(y) = V = exp(- 2 2 D2

2 beam 2 R2

) =

V(D) ( ) = I( ) exp{ -i 2 } d

∫

( ) (0) =

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Methods to calculate the beam size

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  • 1. We measure (experimentally) the contrast of the interferogram

as a function of the slit separation D. Then we define the RMS

  • f the visibility curve

V . beam =

R 2

V

D V ..

. . ...

V

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  • 2. We can also measure the RMS beam size from one data of

visibility which is measured at a fixed separation of a double slit assembly

beam =

R D √ 0.5 ln(1/V)

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V = 0.8

S = 0.12 mm

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Synchrotron Light Interferometer at Jefferson Lab Main Components

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S Synchrotron Light Source Lens CCD

R L

Synchrotron Radiation Interferometer at Jefferson Lab

Synchrotron Light Interference Picture

Double slit assembly Polarization filter Band pass filter ( 0 ± )

R = 9.18 m L = 1.12 m 0 = 630 nm = 40 m

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1C12

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Resolution of our synchrotron light interferometer

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Our Synchrotron Light Interferometer Main Control Components

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Common Serial Driver Multiplexed Maxvideo Library Stepper-motor Control Software Video Camera Control Software EPICS Distributed Database Control Software Structure

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Very First Experimental Results

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(exposure time = 2 sec)

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V = 0.8

S = 0.12 mm

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SLI Data After 2002 Summer Shutdown

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(exposure time = 50 sec)

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(exposure time = 10 sec)

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Recent Data

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(exposure time = 15 sec)

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Very Last Data

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Summary

  • Jefferson Lab has a modern beam diagnostic device

based on non-invasive technology

  • Jefferson Lab has a great experience in design and

installation of such a device

  • The resolution of this device can be made less than 10 m
  • The device’s operational current range:

a few microamps –> milliamps

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SLI team:

  • P. Chevtsov, J.-C. Denard, R. Hicks, K. Capek, D. Hardy,
  • D. Wetherholt, Z. Kurzun

Many thanks to:

  • S. Suhring, M. Spata, O. Garza, all accelerator operators and

technicians. Special thanks to:

  • M. Tiefenback, G. Krafft, H. Areti, L. Merminga, J. Benesch,
  • A. Bogacz, A. Freyberger, Y. Derbenev, A. Hutton, K. White.
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