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An Infrared Fourier Transform Spectrometer
for Millimeter to Far Infrared Wavelengths
Motive:
We are currently involved in the construction of an infrared Fourier transform spectrometer (IRFTS) for microwave to far-infrared wavelengths. This device is necessary in order to determine the accuracy of the MAT telescope's current and future generations of CMB detectors. It is essential that the detectors "respond" only to a select band of frequencies because the CMB data is extremely faint in amplitude compared with low frequency noise, noise from dust and noise from atmospheric oxygen spectral lines. An IRFTS with a blackbody source spectrum can be used to produce an interferogram (a plot of power versus interferometric path difference), the Fourier transform of which will determine the frequency response of MAT's detectors.Optics Design:
The FTS is essentially a Michelson-Morley interferometer (without rotational freedom--we're not worried about the aether wind). Divergent rays of light emitted from a blackbody point source are collected by a 90° off-axis parabolic mirror. This new, parallel beam then encounters a mylar beamsplitter (a thickness of about 10 mils makes a fairly efficient beamsplitter) at a 45° angle to the beam path. This splits the beam into two halves; one goes on to reflect off of a stationary flat mirror, the other reflects off of a traveling flat mirror. Initially, both flat mirrors are at the same path difference from the beamsplitter. Both beams are then recombined and projected onto a second 90° off-axis parabolic mirror, which converges the combined parallel beams back down to a focus, where we place a bolometer inside of a Dewar to measure intensity. As the traveling mirror increases its path distance from the beamsplitter, the intensity of the combined beams (measured by the bolometer) reflects the changing phases of the different wavelength components in the blackbody source spectrum. By plotting the intensity of the recombined beams as a function of path difference (between the stationary and traveling mirrors), and then taking the Fourier transform of this plot, we change from the time domain (since we move the mirror at a constant velocity and keep track of its position) to its reciprocal--the frequency domain, thus creating a power spectrum.By first taking the power spectrum of the interferometer system without any filter/detector in front of the bolometer and then dividing this spectrum by that of the interferometer with an added filter/detector, we can determine the absorption spectrum of the filter. The entire system is encased in a plexiglass casing so that we can purge the system with Nitrogen gas and thus eliminate water and oxygen inside, since oxygen has a spectral line in the bandwidth of interest.
Interferogram Simulation:
We have written a computer program to simulate how the actual IRFTS will work, as detailed above. (A blackbody source emits waves which we reflect off of an off-axis parabolic mirror in order to make the radiation beam parallel, and then split the beam as it passes through a mylar beamsplitter. Half of the original beam gets reflected off of a flat mirror, and comes straight back to the beamsplitter, while the other half of the beam gets reflected off of a moving flat mirror, which is placed perpendicular to the other flat mirror (see diagram). This causes the path difference between the 2 mirrors to change, which results in a changing interference upon recombination, as the 2 halves of the beams recombine constructively and destructively at the beamsplitter. The recombined beam is redirected by another off-axis parabolic mirror, and the power of the beams (intensity squared) is measured by the detectors. The frequency dependence of a blackbody source is defined as:where n is frequency, k is the Boltzmann constant, c is the speed of light, and T is the temperature of the blackbody source. In an ideal situation, the power detected from a blackbody source, as a function of frequency, would look like: (insert graph of BB vs f)
In real life, however, there are many other factors that influence the power that the detectors pick up, such as the beamsplitter and various bandpass filters. The blackbody intensity, with a square wave filter between 136 and 159 GHz (G(n)), has a frequency response as seen here: (insert graph of BB*g vs f)
Another factor that affects what the detectors pick up is the beamsplitter. When the beam of radiation hits the mylar, some fraction is reflected, while another fraction is transmitted. The transmission intensity (T(n)) is determined from the following equations:
The fraction of waves transmitted through the beamsplitter is 1 - R, where R is the fraction of waves reflected from the beam splitter. Here, n1 is the index of refraction of the environmental medium and n2 is that of the beamsplitter. Theta is the angle of incidence of the beam onto the beamsplitter, in our case 45°. A sample of the wave-transmission plot is:
The equation for the intensity of interfered waves is given as: where A(n) = G(n)B(n)T(n). When we perform a Fourier transform, we convert time-dependent data (power vs frequency) into space-dependent data (power vs path-difference). In the case of the mounted mirror traveling 200 cm, with data taken every 0.06 cm, a squarewave bandpass between 136 and 159 GHz, blackbody temperature 1300 K, and a Mylar 0.01 cm thick beamsplitter, we have the following simulation: (picture coming soon...)
Software Control:
We are using ValueMotion Vis from LabView as elements in our motion program which control the movement of the mirror mounted onto a cart driven by a stepper motor and worm-gear track while simultaneously taking data from the bolometer. Starting at a predetermined "zero-path" position, the mirror is then slowly moved at constant velocity, until it reaches a distance that corresponds with the desired precision of the interferogram. Bolometer and chopper data are run into a National Instruments DAQ board. A separate NI motion control board communicates with the stepper motor driver.The Fourier transform spectrometer will record the position of the moving mirror, (x), and the intensity of the recombined waves, (I). We have written a computer program that simulates the interference of waves and runs a Fourier transform on the space-dependent data, converting it to time-dependent data, which reveals the frequency response of the cryogenic detectors. The equation for the intensity of interfered waves is given as:
where A(n) = G(n)J(n)B(n). B(n) is the Blackbody spectrum, where n is frequency, k is the Boltzmann constant, c is the speed of light, and T is the temperature of the blackbody source. J(n) is the fraction of waves transmitted through the beamsplitter, at each frequency. Its parameters are the thickness of the beamsplitter, index of refraction of the mylar, and the angle of incidence of the beams. G(n) is a bandpass function.
The transmission intensity is determined from the following equations:
The fraction of waves transmitted through the beamsplitter is 1 - R, where R is the fraction of waves reflected from the beam splitter. Here, n1 is the index of refraction of the environmental medium and n2 is that of the beamsplitter. Theta is the angle of incidence of the beam onto the beamsplitter, in our case 45°.
In the case of the mounted mirror travelling 200 cm, with data taken every 0.06 cm, a squarewave bandpass between 136 and 159 GHz, blackbody temperature 1300 K, and a Mylar 0.01 cm thick beamsplitter, we have the following simulation:
We are using ValueMotion Vis from LabView as elements in our motion program which control the movement of the mirror mounted onto a cart driven by a stepper motor and worm-gear track while simultaneously taking data from the bolometer. Starting at a predetermined "zero-path" position, the mirror is then slowly moved at constant velocity, until it reaches a distance that corresponds with the desired precision of the interferogram. Bolometer and chopper data are run into a National Instruments DAQ board. A separate NI motion control board communicates with the stepper motor driver.
Mirror Production:
Because the blackbody source emits more or less divergent rays, we must first adjust these to be parallel ray if we hope to not lose power as path distance increases. Also, the beam must be reflected out of the way of subsequent optical elements. The most convenient layout to use is right angles. Thus, a 90° off-axis parabolic mirror is needed to collect the incoming divergent source rays, set at the mirror's focal distance, and turn them 90°, emerging collectively as a parallel beam. Two such off-axis paraboloid mirrors were needed: one to convert the source point into a beam, and another to convert the beam back down to a point for purposes of detection.We manufactured these mirrors out of aluminum plate stock by mounting them (the mirror "blanks") at a 45° angle inside of a CNC programmable milling machine where we programmed a G-code loop to create increasing radii as a function of one displacement axis parallel to the base of the milling machine. Corrections for the milling tool shape in the formula for the rate of increase of the radii of our paraboloid mirror were in fact made. Using this process, we produced two 9-inch diameter square aluminum mirrors. With extra polishing, the surfaces achieved a near-optical quality--far better than we needed for infrared wavelengths.
Cryogenics:
The dewar consists mainly of three parts: Outer wall, heat shield and inner tank. The coldplate is directly soldered to the inner tank, so its temperature is always same as the inner tank which is filled with liquid nitrogen or liquid helium. The Winston horn, used to collect IR photons and decide the observation direction, and bolometer are mounted to the coldplate to get cooled. There are two Allen Brailey resistors mounted to the bolometer and coldplate, respectively, in order to monitor their temperatures.The bolometer is made from Neutron Transmutation Doped (NTD) Germanium. In very low absolute temperature, e.g around 4K, its resistance can be expressed roughly as R(T)=R0*EXP(T0/T)^a. So we can get a nonlinear resistance change corresponding to temperature change, i.e. dR/dT is not constant.
After the bolometer absorbs the combined intensity of Infrared, it will be heated up, leading to a change of resistance. A bias current is added on the ends of bolometer through two 10-megaohm load resisters. So there will be a voltage change on the ends of bolometer. A very low noise pair JFET follower is used to measure this voltage. After a 1000-gain eletronic circuit, we can get the DC-output (static voltage on the ends of bolometer), AC-output (Infrared intensity signals), and Bias-output (directly measuring the Bias voltage).
All Current Plans:
Currently, all the optics are in place including traveling mirror motion hardware, plexiglass casing, and simple detector. A Micron blackbody source has been acquired as well as a Stanford chopper, LabVIEW DAQ and motion control boards. For the purposes of testing, we have put up an HP sweeper set to a steady monochrome frequency along with a simple power meter as detector, and we have successfully produced our first interferogram of a pure, clean sine wave with noise accounting for non-zero "null" points. After properly integrating the Cryogenics into our spectrometer and completing the analysis software, we will mount the blackbody source and hopefully get the first blackbody interferogram.Click here to return to the undergraduate research page.