Baseline ripples
I : the 30-MHz component

Abstract

This is the first in a series of reports that will analyze the various components seen in the baseline ripple, with amplitudes that depend on the observation mode. Besides the familiar 7MHz baseline ripple, a component of 30MHz period appears in certain modes of observation. The origin of the 30MHz component of the baseline ripple is investigated. It is shown that it arises not from the observation itself but from the calibration; more specifically from the mismatch at the amb/cold system calibration loads. The consequences for astronomical observations are :

1. a baseline ripple proportional to the continuum offset present in the data;
2. a gain modulation of approx +/- 3%

We present the results of some specific tests to determine the origin of these ripples, and some first attempts towards improvement. Some possible cures are proposed. Some feedback from astronomers is kindly requested on the following points : a) how much of a nuisance do these ripples actually represent; b) is a software remedy (FFT editing, BASE SIN fitting) adequate?

The symptom

A component in the baseline ripple with approx 30MHz has been reported by M.Guelin in PSW observations of M31. A similar baseline ripple component was noted by B.L. during technical tests specifically aimed at baseline ripples (will be reported elsewhere).

We present below in fig.1 a spectrum obtained in PSW mode with a reference position 30' away, defined in the "M31" coordinate system; the orientation in Az-El of the displacement beween source and reference was therefore arbitrary.

To determine the round trip distance of the standing waves, we can apply the FFT command in CLASS. The result is presented in Figure 2. At the available resolution, the round trip distance can be estimated to be between 9.33m and 9.95m. In the future, if similar measurements are repeated, it would be better to use a 230 receiver channel, together with the filterbanks in 1GHz mode, which would give a more accurate determination of the round trip distance, possibly helpful to pinpoint the location of the reflection.

Geometry

The period indicates a round trip distance of 10m, i.e. a distance of 5m between obstacles. The table below shows the estimates for relevant optical path distances, derived from tape measures and consultation of the blueprints, and rounded to the nearest cm. The optical travel path between the dewar window and the mixer entrance (believed to be inherently mismatched) has been estimated at 20cm.

The round trip distance is close to that indicated by the periodicity of the ripples. This constitutes circumstancial evidence that reflections in the calibration loads contribute to the observed ripple. An experimental confirmation is presented below.

Experiments

Measurement of the power spectrum delivered by the system calibration loads.

Because the spectrometer channels have arbitrary electronic gains, and, at least in the case of filterbanks, arbitrary offsets, the measurement of a power spectrum requires both a reference and a calibration (just like for astronomical observations). We have therefore performed the following measurements, using the WAIT button to pause between acquisition phases. Each measurement was made against either one of the system calibration loads, or against a hand-held load (ambient or cold) located either in front of the dewar window, or just in front of the system calibration load. Self-explanatory short names are used.

The CAL COLD performed in scan 8866 is intended to provide a "clean" calibration for the subsequent scans. Because the loads were within ~25cm of the mixer, one can rule out modulation of power (and therefore of the inferred gains), at least with periodicities comparable with 30MHz. The next four scans each compare with a "clean" reference (DewarCold) an ambient or cold load, system or manual. The observations were processed with CLASS in the standard way. This means that the temperature scale is not the scale of blackbody temperature at the dewar window. From the power present during the "Sky" phase of calibration, the software has deduced a tau_Z=0.0915. The temperature scale is therefore scaled by :

But that is not our prime concern in the present context. Figure 3 below shows, on that temperature scale, the power spectra of the HandCold and SysCold loads, referred to DewarCold. Figure 4 likewise shows the power spectra of HandAmb and SysAmb. The 30MHz ripple is present in the spectra of both system loads; and appears to be absent from the hand loads. This does not prove that it is actually absent with the hand loads, because even small motions during the integration period could have smeared out ripples, but that is not the main point. Some ripple is also present in the hand loads, with a lower amplitude and a ~90MHz period.

Impact on a simulated observation

There remains to assess the impact on the calibrated spectra of the ripples present in the calibration. The main effect is believed to be the modulation of the gains. Rather than perform the algebra, we observed a simulated astronomical CAL COLD (scan 8873), with the system loads in the Amb and Cold subscans, and a DewarCold load (following the previous measurements, it can be assumed to be free from ripples) during the "Sky" subscan. Using the CAL program, we applied that simulated calibration to PSW scan 8872, where the "On" is a HandAmb, and the "Off" a DewarCold. Following the results above, scan 8872 is presumably exempt from intrinsic ripples. The result is shown in figure 5 below.

On our pseudo-Ta* scale, the ripple amplitude is about 10K peak for a 285K mean continuum level. This corresponds to a 3.5% peak (7%pp) gain modulation. This is consistent with the "real-life" spectrum shown in figure 1 above, where the mean On-Off continuum is ~2K, and the ripple amplitude is ~0.12K peak-to-peak, corresponding to a +/-3% gain modulation of the continuum.

Further measurements

Further tests were performed during technical time on Fri, Dec 11. Pyramidal absorber was installed on the system ambient load, and surrounding the system cold load. A CalCold (9286) and four PSW scans (9287, 88, 90, 91) were acquired following the same procedure as described above for scans 8866-8872. A fifth PSW scan was acquired, similar to scans 9787 and 8867, i.e. SysCold-DewarCold, but with a lens placed in front of the calibration cold load; the intent being to defocus the reflected beam, and thus decrease the undulation in the power spectrum.

Fig.6 below : SysCold versus DewarCold, after surrounding the SysCold with pyramidal absorber. The offset has changed from that in fig. 3, possibly because the DewarCold load was colder; but that is not important.

Fig. 7 below. Same as fig. 6, for the system ambient load.

Fig. 8 below. Same as fig. 6, but with a lens in front of the window of the calibration dewar.

Summary of results

In order to provide a quantitative measure of the ripple amplitudes in the various experiments described above, we have noted for each scan the rms amplitude relative to a polynomial baseline, with a degree (generally 2-3) chosen to eliminate large scale baseline undulations. As noted previously, these measurements are on an arbitrary, but uniform, pseudo-Ta^* scale. Rms values can be converted to peak-peak multiplying by 2.8. One can see from the table below that the change to pyramidal absorber reduced the ripple on the SysAmb load by a factor of 3, but that surrounding SysCold with the same type of absorber did not bring any significant improvement. Furthermore, the addition of a lens in front of the SysCold window actually increased the amplitude of the ripple. Taken at face value, this result (which needs to be confirmed and carefully analyzed) might indicate that the reflection does not primarily take place at the window, but on the cold load itself.

The tests are incomplete

Ideally, we should have tested both polarizations and both frequency bands. We tested one receiver only to save time and obtain results promptly. Other tests (measurement of image gain, to be reported separately) give indications that the values reported here are representative.

Estimate of the reflection coefficient on the loads

Borrowing an equation that will be derived in a forthcoming report on the 7-MHz ripples, the normalized peak-to-peak amplitude of gain ripple is given by :

where r_m and r_l are the amplitude reflection coeffcients at the mixer and the load respectively. Assuming r_m approx 0.4, one can infer that r_l is approx. 0.044, corresponding to -27dB return loss, which is intrinsically not so bad.

Consequences in real observations

1. Baseline ripple, whenever some continuum (source or atmospheric in origin) is present in the data, as shown at the beginning of this report.
2. Systematic calibration errors of narrow lines, up to +/-3%. While this may not sound like much, we should worry about errors at that level if we want to improve the spectroscopic calibration, which is especially crucial when line ratios are used to derive physical conditions in the source.

Conclusions

We propose that we should attempt to improve the spectral flatness of the calibration system. Possible actions :

• Replace the sys ambient load with black pyramidal absorber, believed to be among the best available at millimeter frequencies. (done)
• Replace the window of the cold load with a lens having both surfaces curved. In the present setup, a flat window is placed near a waist of the beam, which maximizes the coupling of the reflection to the time-reversed beam. The curved surfaces of a lens would throw the reflected beam off-focus, while not changing substantially the coupling to the cold load of the transmitted beam. At the same time, we should switch to circular grooves, which hopefully would result in equal effective temperatures for both linear polarizations. (tried, inconclusive)
• Or, alternatively, implement a flat window inclined w/r to the main axis. However, this would require more substantial mechanical modifications. (to be discussed further).