Data sets obtained are standard for observations with the “CHARA Classic” beam combiner. These files consist of roughly 200 scans of the dither mirror, which oscillates back and forth through 142.0µm of delay at a frequency of 150 Hz in the region that the fringe packets are detected. The scan accumulation time is limited to about 5 minutes. In theory, objects could be observed for a longer period of time, but data sets obtained in this fashion have consistently crashed the data reduction code.
CHARA records data using two detector channels, the first of which records the transmissive component of the beam from one telescope and the reflective compo- nent of the beam from the other telescope, while the second records the opposite. CHARA’s detectors record the photon count and the dither mirror position once per millisecond. The dither mirror positions can be used to break the data into individ- ual scans by finding every instance in which the mirror changed direction. For the purposes of data reduction, the x-axis for all scans is left as time in ms, rather than converting to µm of delay space or mas of angular distance. The recording process is bookended by shutter sequences (visible in Figure 3.1 as the dips in the flux level) which help measure the noise levels and the flux ratio between the two telescopes. The first and third areas of the shutter sequence represent the flux levels of the in- dividual telescopes. The shutter for one telescope is closed in the first region and the shutter for the other telescope is closed for the third region. The second region represents the dark noise scans, where the shutters for both telescopes are closed.
The first step in reducing these data is to account for the dark level, which is ac- complished by calculating the average flux value from all dark noise scans in both the “before” and “after” noise scans and subtracting that value from all points in Figure 3.1. Data with the dark noise subtracted is presented in Figure 3.2. After breaking up the data into individual scans, a low-pass filter can be applied to normalize each scan, as shown in Figure 3.3. After obtaining the normalized functions of intensity with respect to time for both detectors, the visibility as a function of time can be
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determined. From Benson et al. (1995), the normalized intensities of both detectors are known: IA,N(t) = 1 + 2√αβ α+βV(t) (3.1) IB,N(t) = 1− 2√αβ 1 +αβV(t) (3.2) V(t) =V sin(π∆σvgt) (π∆σvgt) cos(2πσ0vgt+φ) (3.3)
where α = I2/I1, the intensity ratio between the two telescopes, β = R/T, the
ratio between the reflectance and transmittance of the beam splitter, V(t) is the visibility as a function of time, V is the visibility amplitude, ∆σ is the inverse of the coherence length (Λ−1
coh), vg is the group velocity of the dither mirror, t is time, σ0
is the wavenumber, and φ is the phase. By rearranging equations 3.1 and 3.2, the time-dependent visibility can be written as a function of the intensities of the two detectors: V(t) = 0.5(αβ)−0.5( 1 α+β + 1 1 +αβ) −1(I A,N(t)−IB,N(t)). (3.4)
The flux reaching the detectors during the shutter sequence allows for the determina- tion of the quantitiesα and β. When shutter S1 is closed, the flux reaching detector
A, indicated as IAS1, is I2T, while the flux reaching detector B (IBS1) is I2R. Simi-
larly, when shutter S2 is closed, the fluxes reaching detector A and B are, respectively,
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sequences. For example, to determine the value of IAS1 for a particular data set, the
average of all points in the designated regions in Figure 3.2 is calculated. From the aforementioned definition of α and β, the following can be derived:
α= IAS1 IBS2 = IBS1 IAS2 (3.5) and β = IBS1 IAS1 = IAS2 IBS2 . (3.6)
Once the coefficients αandβ have been determined, a “visibility scan” can finally be calculated from equation 3.4. Next, the scan is smoothed by isolating the fringe frequency in the scan’s power spectrum. Taking the Fourier Transform of a scan gives the characterization of the fringe packets in the frequency domain. The peak of this power spectrum is ideally located at the frequency set during observation, which, for this project, is generally 150 Hz, but can occasionally be 100 Hz for fainter targets. After locating the peak, a bandpass filter of 60 Hz is applied to enhance the fringe signal relative to the noise present at other frequencies. Bandpass-filtering is equivalent to multiplying the power spectrum by a box function whose box width is 60 Hz. This enhanced signal is inverse Fourier Transformed to obtain the smoothed visibility scan. The power spectrum for an example scan has been presented in Figure 3.4 along with the boundaries for the bandpass-filtering. Figure 3.5 shows the results of bandpass-filtering, with the smoothed scan offset from the unsmoothed scan for
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Figure. 3.3: Normalization. This shows the method of normalizing a CHARA data scan.
clarity. The bandpass-filtered scan is the final product that is now used to evaluate the presence of SFPs.
Figure. 3.4: Bandpass filtering. The vertical lines show the boundaries of bandpass filtering.
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Figure. 3.5: Bandpass-filtered scan. The top half of the plot shows the normalized scan in the lower plot of Figure 3.3. After applying the 60-Hz bandpass filter shown in Figure 3.4, the result is the smoothed scan in the lower half of the plot.