Observing Transfer Observing Transfer FunctionsFunctions

For Multimode SpectrometersFor Multimode Spectrometers

What is a Transfer FunctionWhat 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.

Ideal situationsIdeal 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.

Measurement Setups Measurement Setups

Measurement SetupsMeasurement Setups

Measurement SetupsMeasurement Setups

Point Mapped Spectral Response Point Mapped Spectral Response of Photonic Crystalsof 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.

Point Mapped Spectral Response Point Mapped Spectral Response of Photonic Crystalsof Photonic Crystals

Difficulties with Setups 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.

Output of Holographic FiltersOutput 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

Basic Holographic responseBasic Holographic response

Source

hologram

Detector

A white light input is broken into its spectral components and spread acrossa large spatial area. If the input component has infinite spatial extent and infiniteangular variation the output will wash out and become white light.

Examples of position dependent Examples of position dependent Response (Brag Matching)Response (Brag Matching)

Note:100=.04in, tests done with a white lightPoint source

Notes on Masked InputNotes 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

Response of Photonic CrystalsResponse 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.

Basic Photonic Crystal ResponseBasic 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

Simplicity Of a Photonic crystal Simplicity Of a Photonic crystal SpectrometerSpectrometer

The final goal of a photonic crystalspectrometer is to mount it directly to thefocal plane of a camera and take the nearfield image of its spectral response.

We hope to get more variance and a betterunderstanding of the filter properties ofphotonic crystals by looking at its near fieldresponse. Also finer resolution with new equipment (monochromatic and cameras) willenable us to use the transfer properties to completeA spectrometer.

Future WorkFuture 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.