Observing Transfer Functions For Multimode Spectrometers

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.

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.

Measurement Setups

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.

Point Mapped Spectral Response of Photonic Crystals

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 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 response Source hologram Detector 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.

Examples of position dependent Response (Brag Matching) Note:100=.04in, tests done with a white light Point source

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

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.

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

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.

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.