Observing Transfer Functions

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Observing Transfer Functions

• For Multimode Spectrometers

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What is a Transfer Function

• This is an expression for the final output of a
  system that depends on the spatial and spectral
  characteristics of the input.
• H is of course the function that we are looking
  for.

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Ideal situations

• The ideal filter for a multi-mode spectrometer is
  independent of the Input position and takes an
  averaging of the spectral distribution of the
  input plane.
• Random photonic crystals could possibly achieve
  this ideal situation.
• Volume holograms will always be dependent on the
  input position and form of the source.

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Measurement Setups
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Measurement Setups
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Measurement Setups
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Point Mapped Spectral Response of Photonic
Crystals

• This setup is not yet built due to the fact that
  any serious measurement will require the computer
  controlled actuators that are on the way. It
  simply consists of a broad band white light
  illumination incident on a photonic crystal and a
  spectrometer behind the filter measuring its
  response.

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Point Mapped Spectral Response of Photonic
Crystals
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Difficulties with Setups

• Holograms need to be aligned in XYZ, two axis of
  tilt and in an axis of rotation. If you have any
  of these angles misaligned you diffracted beam
  will go off in odd directions and be difficult to
  map on a detector.

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Output of Holographic Filters

• 2D Holograph filters give a liner shift in
  wavelength acting as a dispersive element.
• 3D Holographic filters have the standard response
  coupled with a brag matching condition. This
  condition although it can contribute to a greater
  spectral diversity makes it much more difficult
  to understand the transfer function of the
  material

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Basic Holographic response
A white light input is broken into its spectral
components and spread across a large spatial
area. If the input component has infinite spatial
extent and infinite angular variation the output
will wash out and become white light.
Source
hologram
Detector
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Examples of position dependent Response (Brag
Matching)
Note100.04in, tests done with a white
light Point source
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Notes on Masked Input

• With the holographic systems we are building a
  mask that will interact with the calculated
  transfer function of a hologram. This transfer
  function will be a liner shift function with a
  brag matched condition. The final inversion of
  the data to make a spectrometer will be a known
  calculation and will not involve a calibration

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Response of Photonic Crystals

• Response of photonic Crystals is not dependent on
  the position of the Input function and is best
  expressed as a display of spectral variances.

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Basic Photonic Crystal Response

• Randomly arranged photonic domains allow
  different wavelengths of light to pass or even to
  be stopped all together making for a diverse
  output

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Simplicity Of a Photonic crystal Spectrometer
The final goal of a photonic crystal spectrometer
is to mount it directly to the focal plane of a
camera and take the near field image of its
spectral response. We hope to get more variance
and a better understanding of the filter
properties of photonic crystals by looking at its
near field response. Also finer resolution with
new equipment (monochromatic and cameras)
will enable us to use the transfer properties to
complete A spectrometer.
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Future Work

• To complete permanent testing stations, with
  automated scanning of the inputs and outputs.
  This will enable a very detailed mapping of the
  point response of holograms, the point mapped
  spectral response of photonic crystals and the
  impulse response of both filtering mediums.