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A laboratory experiment
to measure the intensity profile of a
luminous light source
Walter Y. Mok
Allen Fisher and Jeff Corbett
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The Riddle
• How to measure the luminous intensity
distribution of an object that is far away
with a small angular spread?
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Summary of the journey of discovery
• The Young’s double pin-holes interference
• The definition of visibility = the degree of coherence
• The visibility curve of the Young’s experiment is similar to
the diffraction pattern from the an aperture (the extended
source )-- illuminated with a monochromatic light
producing the same light intensity distribution over the
aperture – Von Citterut & Zernike
• The visibility curve of the Young’s experiment does not
change with propagation through lens - Zernike
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Definition of coherence
• The degree of coherence of two light
vibrations shall be equal to the visibility of
the interference fringes that may be
obtained from them under the best
circumstances.
I max – I min
I max + I min
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Design of the experiment
• Monochromatic light source– LED
• Two slits separated at variable distance –
Alan wrench double slit.
• Recording the interference pattern – CCD
camera
• Lens to
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Synchrotron Light Interferometer
SR light, X-ray beam Block, Double slit, Polarizer, Filter, CCD camera
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Laboratory simulationFigure 1: Interferometer setup with CCD camera
Slit #1 change the size of the
aperture of the light source
Slit # 2 two slit with variable center
to center distance
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Construction of a double slit
Alan Wrench
on magnetic
baseJAW
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Typical interferogram on the
camera
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Example of interferogram
D=40mm, l=400nm
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Measurement of visibility
Imax
Imin
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Plotting of visibility vs. slit
separation (size of Alan wrench)
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Three ways to measure beam size
• From one visibility data point
• Gaussian approximation of beam profile
• Fourier Transform
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1-D van Citterut-Zernike’s
theorem
Where is the complex degree of spatial coherence
is the beam profile as a function of y
is distance between source beam and the double slit
D is the distance between the slit
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Small beam size measurement by means of
Gaussian Approximation of beam profile
The RMS beam size is related to the RMS width of
the visibility curve.
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Calculate the beam size from one
data point of visibility
Ref: T.Mitsuhashi, “Beam Profile and Size Measurement by SR interferometer” in
Beam measurement, Ed. By S. Kurokawa, PP 399-427, World Scientific (1999).
Where F= source to slit, D=center to center slit separation
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Practical consideration in
interferometry
• Wave front error introduced by the optical
components deformation due to heat
• Imbalance of intensities of photons passing
through a double slit
• Linearity of the CCD camera-calibration is
needed.
• We are measuring a time averaged result.