St. Cloud State University
REU program-Summer 2008
Univ. of Wisconsin - Madison
Madison, WI 53706
Research projects of other REU students
Useful links
My conclusions
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Brody Fuchs St. Cloud State University
REU program-Summer 2008 |
Research projects of other REU students Useful links My conclusions |
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Schematic diagram of the WHAM instrument (fig. 1)
Above is a diagram of the WHAM instrument, it is a large Fabry-Perot spectrometer coupled to a telescope (all-sky siderostat). The dual-etalon system allows for very high resolving powers. After the etalons is where the filter is inserted into the system. The filter lives in a filter wheel which can hold up to a total of 16 filters, allowing for observations of multiple lines during one night. The aforementioned dual etalon system uses two Fabry-Perot etalons in succession to select one order to transmit while suppressing neighboring orders, this results in greater resolving power. In the figure below, (a) is the transmission function of the first etalon, (b) is the transmission function of the second etalon, (c) is the transmission function of the system and the dotted line is the transmission function of the filter. It is easy to see that the dual etalon system does a good job of locally transmitting only one order, but orders are going to line up again somewhere far away which is where the filter comes in, to block out any unwanted orders.
Transmission functions of etalons and interference filter (fig. 2)
Because interference filters consist of glass with dielectric layers deposited
on the surface, this creates multiple beam interference within the glass,
causing the filters to act like etalons. With multiple beam
interfernce, peaks are found where the condition for constructive interference
is met: 
, where m is the order,
lambda is the wavelength, n is the index of refraction between surfaces, l is
the gap width, and theta is the incident angle.
The purpose of this project was to design, construct and test an instrument that could determine key parameters of 3 inch WHAM filters:
We need to know these parameters for a few reasons such as correct WHAM data interpretation, testing new filters to ensure that they meet manufacturers specifications, testing older filters to make sure that they are still in working quality because these filters can deteriorate over time for various reasons such as humidity, dust, fingerprints, etc.
Side 1 of tested, deteriorated filter (fig. 3) |
Side 2 of filter (fig. 4) |
We started by taking an existing Ebert monochromator as shown below
Diagram of Ebert monochromator (fig. 5)
Diagram of Ebert spectrometer (fig. 6)
A dispersion test was performed to ensure that the Ebert spectrometer was in working condition. The following figures show the results of the dispersion test.
ThAr spectrum with peaks highlighted (fig. 7) |
Dispersion plot of peak wavelength vs. peak pixel number (fig. 8) |
Comparing this spectrum with a Kitt Peak ThAr spectral atlas, the peaks have similar separations and relative intensities. The dispersion plot shows that the dispersion is linear and it is also consistent throughout the visible range.
The actual spectral data needed sits on a platform of noise. This noise is in the form of dark current and CCD bias. There are also intensity differences among pixels which is a multiplicative factor. The way to get rid of all noise is by subtracting an average dark/bias image from both the data image and the flat field image, then divide the corrected data image by the corrected flat field image. This noise needs to be removed before the data interpretation stage.
Crude ThAr Spectrum With Average Dark (fig. 9) |
Dark Corrected Spectrum (fig. 10) |
White light images were produced by illuminating the entrance slit with a diffused white light source. White light images are needed for flat field images as well as to calculate the bandpass of the system. The bandpass (and exit slit) edge is where the intensity starts to fall from maximum intensity due to diffraction. The bandpass is useful to know because it needs to be large enough for the filters that are being tested. In this case it is large enough because the typical fiter width is ~20A and the system's bandpass is 92A. I have marked the edges of the exit slit on the figure below.
White Light Intensity Spectrum (fig. 11)
One more test was run before the profiling could begin, the FWHM dependence of a ThAr line on the width of the entrance slit. Since the ThAr lamp was not very bright a trade-off had to be made. When the entrance slit was smaller, the line resolution was better but the lines were more intense and broad when the slit was opened up. A happy medium was found somewhere in between.
Once the key parameters were determined to be satisfactory, the profiling could be started
The experimental schematic is shown below. The two alignment mirrors are used to align the light source on the input iris. The input iris is diffused because the light source is very bright. The diffuser scatters light in all directions, but only a small range of angles pass through the system. The lens L2 collimtates the light and the beam iris can select the size and/or portion of the beam to illuminate the filter. Only a small range of wavelengths centered on 6566A are transmitted by the filter, these parallel rays are focused by a lens that is confocal with the spherical mirror inside the spectrometer to keep a consistent F/10 beam. The grating inside the spectrometer can be rotated to select a different range of passing wavelengths from the exit slit. The exit slit is then imaged onto the CCD detector for analysis.
Crude Paint Diagram of Experiment Setup (fig. 12)
The first test that is carried out is the center and FWHM of the filter bandpass. The way this is done is by tuning the spectrometer to the expected center wavelength of the filter. The desired filter is then placed in the beam of white light and the entrance slit is illuminated with the filtered light. The image of the exit plane is then captured on the CCD detector and then processed and noise-filtered in IDL (below is a sample profile intensity plot). When the profile is obtained in IDL, the curve is fit with a "Gaussfit" procedure which returns such parameters as center wavelength, peak value and width of Gaussian. When the location of the peak (in pixel number) is given, that number is plugged into the dispersion equation to convert it into a wavelength (in angstroms).
Sample IDL filter intensity profile (fig. 13)
Filter uniformity is very important for precise and accurate measurements. Uniformity means having the same transmission characteristics anywhere on the filter. We can test uniformity in two different ways, by illuminating the center of the filter and varying the beam diameter and illuminating a small part of the filter and moving the beam from one side of the filter to the other. The first test is testing the center of the filter, we start by illuminating the filter center with a 10mm beam (the smallest beam that produces enough signal) and look at the transmission profile. We image profiles for each beam size (10, 20, 30, 40, 50mm) and compare profiles to ensure that it is the same for every beam size. To test the edges of the filter, a 10mm beam was used to illuminate different parts of the filter from one side to the other.
Schematics of filter tests (fig. 14)
Tuning the filter's peak wavelength can be very convenient. Tuning is done by
rotating the filter so that angle on incidence is not 0. The test was done by
rotating the stage that houses the filter by 2 degree increments and capturing
data at each step. Data was taken up to 10 degrees on each side. Since
multiple beam interference is governed by , it does not matter which way you rotate
the filter because the cosine function is even. Another thing to note is when
the incident angle is 0, the cosine term is 1 and the peak wavelength is as
red as it can get. When the filter is rotated and the cosine term drops off
from 1, the peak get shifted towards the blue so the filter can only be tuned
towards the blue.
Filter and holder on rotation stage (fig. 15) |
Filter profiles at different angles (0 degrees=solid, shorter wavelengths on left) (fig.16) |
Look at the results of peak dependence on various parameters was as expected. The peak did not depend on the iris diameter or the 10mm region tested which shows that this filter is very uniform. The incident angle dependence resembles a cosine function which is consistent with the multiple beam interference equation. The result are shown below.
Peak vs. Angle (fig. 17) |
Peak vs. Beam diameter (fig.18) |
Peak vs. Region (fig. 19) |
The tests on the FWHM did not show dependence on any parameters but did reveal some non-uniformity in this filter. Results can be seen below.
Width vs. Angle (fig. 20) |
Width vs. Beam diameter (fig.21) |
Width vs. Region (fig. 22) |
The tests that are run are effective in characterizing these filters for correct data interpretation as well as ensuring all filters are up to standards. Future progress with this instrument include fabricating a new filter holder for the 3 inch WHAM filters. Replacing the lenses and mirrors with newer, higher quality parts. Improving the region test by using the same 10mm beam, but designing a way to translate the filter. This will eliminate any problem with a non-collimated beam since the same beam will be used to test the whole filter (figure below). Offband blocking also needs to be tested. This is needed because unwanted orders may be passing through the filter in an area that is untested, which would cause errors in the WHAM data. Offband blocking is also what the filter is designed to do in the first place.
Problems with using different parts of beam (fig. 23)
I would like to give a special thanks to those who have assisted me throughout the summer.
This work was funded by a REU supplement to the NSF WHAM Grant (PI Haffner).