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6. Data Reduction Methods Used in Experiment Cold

As is clear from what was said above, various types of interference (which differ a great deal in their characteristics) appear when observing on different spatial scales. Therefore, the problem of approaching the sensitivity of an "ideal" radiometer must be solved differently depending on the scale we are interested in. We shall discuss three cases here: scales comparable to the beamwidth of the radio telescope, scales of order 10 arcmin (10 beamwidths), and large scales (a few degrees and larger).
 

6.1. Point Sources, i.e., Scales Comparable to the Beam of the Radio Telescope

Research on these scales involves point sources, their distribution on the sky as well as in distance, and as well as their identification and physical properties. The main things which interfere with the identification of sources are noise spikes, confusion noise, and, to some extent, anomalous low-frequency noise.

6.1.1. Noise Spikes. Noise spikes can be divided into two categories: short noise spikes (d-functions), and noise spikes comparable in duration to the time required for the sky to pass through one beamwidth. In order to be able to identify and remove the short noise spikes, some oversampling was retained in the sampling rate as it was increased. Because of this, an isolated outlier (for example, a malfunction in the data collection system, etc.) cannot be a radio source, since a source with T_A = 5s should occur in three adjacent pieces of data (at 7.6 cm) when the interval between readings is decreased to 1^s.8. Isolated outliers were removed both automatically and by the observer. While examining the compressed data set on a computer screen, the observer gives the numbers of the neighboring readings, and the computer interpolates and replaces the outliers by the average of the neighboring readings. At this point, one should remember that a d-function has a white-noise spectrum wherever it is located in the set of data. Therefore, spectral cleaning methods are totally inapplicable to noise spikes (as well as the problem of removing discrete sources from the data set). The energy of a noise spike is distributed over all frequencies and no spectral filter is able to remove the interference. This is the hidden danger in the blind use of Fourier methods by the inexperienced observer when reducing data (without preparing the data beforehand). Therefore, special methods of dealing with localized interference must be used in addition to Fourier methods for interference distributed throughout the data set. Interference of longer duration (which could be mistaken for a source) was removed by correlating all the signals above the Scan level on two independent scans of the same section of the sky. If a signal was present on only one scan, it was discarded and replaced by an interpolated value. For the section of sky 13^h < a < 14^h, this procedure was carried out by comparing all of the individual scans with one another and removing all of the sufficiently strong outliers using the coincidence principle. One type of interference √ faulty automobile ignitions √ instilled great fear and, as was noted above, we expected to use the 31-cm observations to clean the 7.6-cm records. However, it turned out that this interference was generally not observed at 7.6 cm, since this type of interference has a very steep spectrum and the antenna was protected by antinoise screens.
 
 

6.1.2. Confusion noise and the number of sources √ faux density Relationship It seemed as if confusion noise would be the main limitation in our observations of both point sources and the background radiation. To illustrate this effect, a scan (obtained at 6cm on the Bonn 100-meter radio telescope in a two-beam observing mode (Wall et al., 1982)), which looks like a broad noise tracing with a root-mean-square fluctuation of 2 √ 3 mJy, is shown in Fig. 6.1(a). A simple extrapolation (using the formulae given in Section 4.3) to the observations with the north sector of the RATAN indicates that this effect should amount to approximately 2mJy. However, the confusion noise unexpectedly turned out to be significantly lower, because of the following: first, the excess resolution of the sector in the Experiment Cold observing mode, and second, the fact that the eOect is significantly different at flux levels of 1 mJy, and a simple extrapolation according to the recommended formulae (which are based on rougher surveys) leads to an overestimate of the confusion noise.

Radio astronomers have become accustomed to the idea that faint sources are much more numerous than strong sources; the numerical ratio is determined by the log N √ log P curve. However, a direct count of the faint sources in Experiment Cold indicated that we are on a rather flat section of the cumulative log N √ log P curve (Fig. 6.5),

 so that the situation is reversed. Thus, in a scan of the section of sky with right ascension 13^h < a < 14^h within the band surveyed (10' wide in declination at d = 4^o 54') averaged over 2 months, the maximum number of peaks due to sources is at amplitudes of 2 √ 3 mJy, and there are significantly fewer peaks at a level of 1 m Jy! Direct measurements of the log N √ log P curve at fluxes of about 1 mJy have only recently begun. The first such counts were obtained in Experiment Cold-1 in the spring of 1980 (Berlin, et al., 1980). They yielded a significant difterence (up to a factor of 10) toward a smaller number of sources than in the extrapolated estimates. VLA observations (Kellerman, 1982) with a sensitivity several times higher, but based on a smaller statistical sample (a small region with 13 sources), confirmed our results in the 1 mJy flux range (see Fig. 7.10). If one assumes that most sources have a nearly normal spectrum (there is no direct information on the spectra of such faint sources), data at longer wavelengths also confirm our conclusion that the number of sources with fluxes of ~1 may at a wavelength of 7.6cm is small. This explains the pronounced difference in the appearance of the drift curves in the "Cold" cycle compared with Fig. 6.1(a), for example. The average and half-difference of two independent averages over 11 days of observations are shown in Fig. 6.1(6); it follows from these two averages that essentially all of the peaks visible in the scan are sources. Moreover, regions free of sources exist, since only 20% of the space on the scans is occupied by the radio images of sources at the RATAN-600's beamwidth (1 are-minute) and a sensitivity of approximately 1 √ 3 mJy; the fluctuations determined by the system noise temperature T_n dominate (the size of the fluctuations can be calculated from Eq. (4.1)) between the sources. This is also demonstrated in Fig. 6.2, where the upper curve is an average of 38 days' observations of the section of sky between right ascensions 13^h 52^m and 13^h 54^m, and the lower is the same section after removal of low-frequency noise. Seven sources, as well as regions free from sources with root-mean-square fluctuations of approximately 0.5mJy (which corresponds to the radiometer noise) are visible in this section. Thus, the sources are separated from one another and can be singled out for individual study or, if we are interested in the larger scales (see Section 4.4), they can be removed from the scan.

 
6.2. Suppressing Anomalous Low-Frequency Noise

Thus, a qualitative analysis of the scans showed that the fluctuations in

Figure 6.2 A small section of a scan at 7.6 cm (average of 38 scans). It is also clearly evident here that the sky is "empty" between the sources, and that the radiometer noise dominates, with a dispersion of about 0.5 millijanskys. The upper curve is the initial data set, while the bottom is after removal of the low-frequency background.
 

the region between the discrete sources do not differ strongly from those expected from Table V.I, if one overlooks the low-frequency fluctuations. We shall now discuss what procedures can be used to get closer to the "ideal" sensitivity, and make a quantitative estimate of what signal-to-noise ratio (S/N) can be obtained in practice. In this section, we are interested in small scales, so that the most troublesome interference √ the anomalous low-frequency fluctuations √ can be filtered out up to a rather high frequency √ approximately 0.025 Hz (which corresponds to scales of ~ 10 l/D). Of course, high frequencies beyond the cutoff frequency of the antenna, must also be filtered out. The preparation of the initial set of data recorded at 7.6 cm with a time constant of 1.3 s ccnsisted of decreasing the interval between readings to 1.8 s and removing the noise spikes (Section 6.1). The filtering itself can be carried out by various methods; one of them, proposed by Heeschen, consists of the following operations:

-removing a linear baseline;
-clipping (at a level of 10 mK);
-fitting a polynomial to the clipped background;
-constructing the dift'erence between the initial data set and the baseline determined above; and
√ smoothing with the function (sin x/x) (suppressing frequencies above f_c).
 

√ smoothing with the function (sin x/x) (suppressing frequencies above f_c).
The basic operations which were carried out on the Experiment Cold scans in an analogous data reduction method are shown in Figs. 6.3 and 6.4.
Another convenient method of identifying the sources and suppressing the low-frequency fluctuations is the second-diAerence method. We shall discuss this method in more detail √ what kind of filter it corresponds to, and what -ind of S/N ratio is obtained. The procedure of constructing the second differences of the initial set of data

corresponds to convolving the initial set of data with delta functions distributed as shown in Fig. 6.5(a). The frequency response curve of such a filter is the Fourier transform of this pattern of delta functions

   (6.1)

The basic operations which were carried out on the Experiment Cold scans in an analogous data reduction method are shown in Figs. 6.3 and 6.4.

The following are shown in Fig. 6.5(b): (1) the spectrum of a signal corresponding to the antenna frequency response; (2) the noise spectrum, with a sharp increase at low frequencies; (3) the frequency response of filter (Eq. (6.1)). The maximum of the frequency response curve obtained in this way lies at a frequency 1/2 f_c this is nearly the optimum for the combination of noise and signal spectra under discussion. We remind the reader that the signal spectrum at the output of the radiotelescope and radiometer is the spectrum of the response of the antenna to the passage of a point source. If the response is a function of the form (sin x/x), which corresponds to the idealized case of a uniform electric field distribution over the antenna aperture,* the signal spectrum J(F) is described by the function (curve I in Fig. 6.5(6))
 

---

The cutofT frequency of the spatial frequency response curve of the antenna, f_c = D/l; in the spectrum ot the radiometer output signal, this corresponds to a frequency F_c = f_c w_o , where w_o is the rate at which a source moves through the antenna pattern.

 

      (6.2)

 For a signal with this spectrum, the optimum output filter yielding the maximum signal-to-noise ratio under ideal conditions (i.e., in the absence of anomalous low-frequency fluctuations) would be one like (Eq. (6.2)); see also Table VI.I. As we shall show below, using a filter with a response curve which suppresses both low and high frequencies (Eq. (6.1)) allows one to come very close to the "ideal" sensitivity in problems involving observations of sources with small angular diameters. However, such a filter would be optimum if the useful signal possessed a spectrum of the same form, with a steep slope at low (near zero) and high frequencies. The expected fluctuations in the temperature of the cosmic background DT_B/T_BB have a spectrum of this type (in one variant), with a maximum on scales of 5 √ 10arcmin (Fig. 6.6). Moreover, this range of scales is the least aA'ected by external interference (see Fig. 5.1). This is why an attempt was made to search for fluctuations in the cosmic background on these particular scales within the framework of Experiment Cold.
Returning to the problem of identifying point sources, we shall now find out whether we lose much in signal-to-noise (relative to observations
 

under ideal conditions, when the noise is thermal (i.e., in comparison with Table V.I) by using a filter of the form (6.1) under conditions in which there is an anomalous increase in the noise at low frequencies. In order to find this out, we use the equation for the signal-to-noise ratio at the output of a radiometer for a given (arbitrary) type of output bandpass and signal spectrum (Esepkina, Korol'kov, and Pariiskii, 1973 (Chapter II, Eq. 20)):

       (6.3)

where J is the signal spectrum, i.e., the Fourier transform of the outputsignal current i_out; K²( f) is the shape of the output bandpass in terms of power;- s/n is the signal-to-noise ratio at the radiometer output  is the high-frequency bandwidth of the radiometer, and a(t) is the normalized signal function (the flux of the signal as a point source drifts through the antenna pattern). Since we are interested in relative values of the signal-to-noise ratio  ,  we shall write Eq. (6.3) in the form

       (6.4)

and calculate relative values of  for various types of output filters, and assuming that _rect = 1 for a filter with a rectangular frequency response curve and a cutoff frequency equal to that of the antenna, f_c = D/l. The results of the calculations are given in Table VI.I. It follows from this table that by using a second-difterence filter to remove the anomalous low-frequency fluctuations, we lose about 30% in sensitivity compared to the optimum filter under ideal conditions, but the gain due to suppressing the low frequency fluctuations amounts to several orders of magnitude. This is evidently the limit which the observer should strive to reach under real conditions. Other methods of filtering out the low frequency noise should yield similar results. To conclude this section, we show the procedure of transforming the output noise spectrum at successive stages in the filtering process in Fig. 6.7. The first stage in this process is performed in analog form by an RC filter at the radiometer output, the next is the procedure of compressing the readings (equivalent to multiplying the spectrum by (sin f)/f), followed by convolution with a function of the form (sin x)/x, which is equivalent to multiplication by a boxcar function in frequency space, and, finally, filtering by the second-difference method. In Fig. 6.8, the output noise spectrum is shown at various stages in the filtering performed by V. V. Vitkovskii on one section of an actual scan in the course of reducing the materials from Experiment Cold.
 

6.3. Conclusion  

Removing the noise spikes and filtering out the low-frequency anomalous noise allow us to successfully identify point sources when the log N √ log P curve is extremely flat, obtaining system sensitivities which come very close to the ideal sensitivity in the process. It is clear

 
that the observer should not expect an increase in the signal-to-noise ratio above that of the standard optimal filtering methods for the ideal case (i.e., thermal noise alone). Moreover, he should make sure that he has not "over-filtered" his data.

A classical, well-studied example of a method for the optimal removal of thermal noise at the radiotelescope output (when searching for faint point sources) is convolution with the point source response. However, as we pointed out above, the whole problem is that the noise at the radiometer output has nothing in common with classical thermal noise, and, in the opinion of many experienced observers, the lion's share of

the difficulties in data reduction occur in "editing" (rather than reducing) the initial data set, i.e., in fact, in the process of making the noise approximately thermal and in correctly determining the "weights" of the harmonics in the spatial-frequency spectrum.

 
6.4. Protocluster Scales, i.e., on the Order of 10 Arcmin
 

These scales are important because they are similar to the scales of "protoclusters" of galaxies, the sizes of the background X-ray emission in nearby galaxy clusters, and the scales of the halos around strong radio sources. These scales diH'er from the smaller ones because of the necessity of filtering out the anomalous low-frequency fluctuations more carefully, and because of the absence of sufficiently reliable a priori information on the form of the signal function, as in the case of point sources (the antenna pattern). The major sources of interference on these scales are:

(a) noise spikes;
(b) radio sources observed by the method in Section 6.1, which must be removed from the scan;
(c) drifts and slow variations of various kinds;
(d) powerful low-frequency fluctuations in the atmospheric emission.

6.4.1. Preparation of the data set The preparatory operations included removing noise spikes and increasing the sampling rate (to roughly twice the characteristic sampling rate of the radio telescope), i.e., as in Section 6.1. An additional preparatory operation at this stage is the removal of radio sources. The point sources can be taken into account fairly confidently when they pass through the center of the beam (with dimensions of 1' x 10'). Identifying such sources was, in fact, the goal of the work described in the preceding section. We are now interested in the larger scales, and strong sources far away from the beam in declination, which pass through the edge of the antenna beam, make the situation more complicated. They correspond to features in the scans whose dimensions may reach tens of arcminutes. In order to identify and remove such sources, observations of the same band of sky were carried out using a sector of the RATAN shifted in azimuth by 30^o. After determining the declination of the feature from the observations at the meridian (azimuth 0") and at an azimuth of 30^o (as was done for the right ascension interval between 13^h and 14^h), it was possible to verify whether the observed apparent size of the feature agreed with the calculated size (the calculated antenna pattern is shown in Fig. 3.8). The majority of the features observed satisfy this theoretical relationship. Thus, it turned out to be possible to remove not only the sources identified by the method of Eq. (6.1), but a significant fraction of the distant interfering sources as well.

(a) partitioning the scan into boxes smaller than or equal to the size of the background (or source) being sought;
(h) constructing the distribution function of the amplitudes of the readings in each box;
(c) "normalizing" these distributions using a method similar to Chauvenet's method, i.e., throwing out all of the readings exceeding the 3s- level. When necessary, this procedure can be repeated;
(d) for the remaining "normalized" data set, the mathematical expectation (rather than the simple mean) was calculated, taking our a priori knowledge of the statistics of thermal noise into account. In practice, this was carried out by convolving the normalized distribution of amplitudes over the boxes with a theoretical amplitude distribution for Gaussian noise with the same dispersion (using the experimental parameters of the thermal noise at the radiometer output);
(e) the curve prepared from the average values over each box were filtered by the Fourier method; all harmonics below 1/2f_c an arbitrary critical source frequency (f_c  1/q_s), were thrown out. This blanking of up to 50% of the frequency bandwidth occupied by signal was performed because we wished to remove the anomalous low-frequency noise (atmospheric emission, etc.) as thoroughly as possible. The odd harmonics in the noise were also removed from the remaining spectrum (an assumption about the symmetry of the source). All of these procedures taken together allowed the measurement accuracy to be greatly increased, since most of the noise energy on protocluster scales is due to either discrete sources and sources of interference or with low- frequency atmospheric noise.

 
the entire low-frequency portion of the signal spectrum from 0 to √1/2 f_c as well as the high frequencies above f_c is removed (integrating from √1/2 f_c to f_c). We then obtain an identical result for the case of the optimal filter and the filter with a rectangular frequency response:

         (6.5)

i.e., because of the strong cut-off of the low-frequency portion, we lose almost a factor of three compared to the ideal case; however, in the process, we decrease the original dispersion on protocluster scales by several orders of magnitude. We believe that this method of "normalizing" over boxes comparable to the characteristic "intrinsic time interval" of the object under study is similar to the well-known "rank criteria" for dealing with interference, and has an adequate logical basis.

When using sufficiently powerful computers, a two-dimensional statistical analysis can be carried out. Extremely deep studies, as a rule, are carried out via many repeated observations of the same region of sky. It is always possible to represent the results of such observations in the form of a rectangular matrix of numbers, where each row contains readings spacing by the "intrinsic time interval" of the antenna and each column gives the values of the antenna temperature for the same region of sky, but at difterent times. Thus, a matrix with dimensions m x n (where m is the number of independent readings in a realization, and n is the number of realizations) is constructed. For the clusters, we performed a statistical analysis (removing the normal noise) along the rows. After removing the low-frequency noise on all the scans, it is possible to carry out an analogous procedure along the columns as well √ all of the deviations from the mean reading must follow a normal distribution. The departures should be ascribed to interference, and the corresponding readings on the appropriate scans should be replaced by the average value of the column. For white noise, the parameters of the normal law should be identical for the rows and columns. Therefore, observers in the US use this circumstance to apply the Fisher criterion when searching for Gaussian noise from the 3-degree background.
 

6.5. Large Scales √ The Background Emission of the Galaxy

The main problems here were the large-scale fluctuations in the cosmic background radiation and the background emission of the Galaxy. The chief source of interference is the unstable emission from the atmosphere. On very large scales, the emission of the Galaxy itself becomes perceptible. The first and second harmonics of the brightness distribution in the band 0^h < a < 24^h  are due to the emission of the Milky Way, and they dominate the spatial frequency spectrum of the Galaxy, while the tropospheric structure function becomes saturated on scales of √ 15^o (for an average wind velocity ~ 7 km s^-1).

On these same scales, numerous instrumental drifts due to variations in the ambient temperature and the temperature in the input circuits, as well as the stability of the amplifiers, were present. Much effort was expended, and the ingenuity of those who developed the radiometer was manifested in the struggle for the internal stability of the radiometer (Berlin and Gol'nev, 1982). Then, a correlation between the hourly fluctuations and the temperature inside the receiver cabin was noticed. It was later noticed that these fluctuations were significantly higher at the output of the 8.2-cm radiometer, for which the losses at the input are higher. This allowed these fluctuations to be interpreted as variations in the emission from the feed horns themselves. The unacceptable ripple at the radiometer output, with a period of 1.3 s (the refrigerator cycle), and the instability in the temperature within the parametric amplifier cryostat (which led to drifts with an amplitude of up to 100mK) were removed. An attempt to take the atmospheric conditions into account using sensors for the outside temperature, pressure, and humidity (which were recorded every hour by the observers on duty during the entire deep survey cycle) turned out to be unsuccessful (perhaps the observations were not accurate enough). Nevertheless, we were able to show that the dominant drifts on time scales of 1^h are not connected with these parameters. We note that the eftorts of the engineers in their work on the receiver were clearly successful; fluctuations of unknown nature, with a characteristic time scale of order 1 h and a rather low amplitude (<=100mK) are what we are discussing here. An example of a night-time scan many hours long made in good weather (Fig. 3.2) bears rather eloquent testimony to this fact, since it is clear that these are features of "celestial" origin.

One of the strongest sources of interference on large scales is the effect of the direct incidence of solar radio emission on the primary feed of the radio telescope. The contribution from this effect may reach 100 mk at unfavorable times and leads to rapid changes in the signal level at sunrise and sunset, as well as when the sun goes behind and comes out from behind the secondary mirror of the radio telescope. Evidently, this effect can be decreased by using a primary feed with less scattering, and by adding simple screens to the edges of the secondary mirror which are matched to the field distribution in this region (see the results of the work of Maiorova, Korol'kov, and Stotskii in Section 3.4). In Experiment Cold, it was also necessary to stop observing for about two hours as the sun passed through the meridian. This region of the sky was illuminated by the sun through the sidelobes of the antenna pattern (see Ignat'eva et al., 1982). Some of the eftects may be due to surface errors and the cracks between the elements; in Experiment Cold, the cracks were screened to reduce the antenna noise temperature, but the screens introduced phase errors and therefore also increased the scattering near the main beam of the antenna pattern. In Experiment Cold, only 175 elements of the north sector were used, rather than the entire sector (225 elements); the secondary mirror was

 
designed to illuminate 225 elements. This led to a sharp decrease in the field distribution over the aperture, which also increased the amount of scattering near the main beam of the antenna.

Despite all of the difhculties listed above, we attempted to construct a complete 24-h profile of the antenna temperature distribution along our band on the sky. We "sewed together" the points within 1 h before and 1 h after the culmination of the Sun, as well as the 2 √ 3 min gaps for calibration and compensation at the end of each hour of observations. The two quietest records in the entire set (19 and 24 March, 1980), which turned out to be similar (except for the strong features which vary with solar time and are almost a fortiori connected with the disappearance of the feed into the "shadow" of the secondary mirror), were selected. These 24-h-long scans are shown in Fig. 6.10. The repeatability of the curves is encouraging. The next stage consisted of carefully classifying all of the scans according to quality; the average curve resulting from selecting the 13 best 24-hour-long curves was used to analyze the large-scale distribution of the background emission of the Galaxy (Fig. 8.2). The Galactic component of the background will be discussed in more detail in Section 8, but we shall note here that on individual 24-h-long scans under good atmospheric conditions, the Galactic emission dominates on scales of 30^o √ 360^oC. We also note that in Experiment Cold, a complete cross-section through the Galaxy at centimeter wavelengths was obtained for the first time. Our experience in identifying the Galactic background showed that by using methods for removing the atmospheric emission, one can hope to make the accuracy of ground-based background observations close to that of space-based studies (at least at centimeter wavelengths), and actually obtain the sensitivity of the new-generation radiometers in practice. Moreover, this suggests that it is necessary to use shorter wavelengths to study the extragalactic background radiation on larger scales.

 
6.6. Scales Comparable with the Size of the Horizon at the Recombination Epoch (0.5 √ 2^o)

 These scales are of particular interest in connection with the fundamental question of the causal relationship between sections of the Universe on scales larger than the size of the horizon at the recombination epoch, and touch on key problems of singularities, as well as modern "Grand Unification Theories" (see, for example Novikov, 1983). Diffuse Galactic objects (H II regions and SNR's), superclusters, and the "voids" in the Universe also occur on these same scales. On these scales, we intended to use a procedure for removing atmospheric

However, it unexpectedly turned out that the dominant noise energy on these scales at 7.6 cm was due to real features on the sky, repeatable from one observation to another; these features were also visible at 31cm (see Fig. 6.11). The correlation between these wavelengths becomes even more obvious if the discrete sources and the very-low-frequency noise (on scales larger than 5^o) are removed (see Fig. 6.12(a)). We therefore initially decided to remove the noise which was correlated at wavelengths of 31 and 7.6 cm from the scans (Fig.6.12(b)). It was

Figure 6.12 The effectiveness of the removal of Galactic noise from the 7.6-cm data. (a) Establishing the correlation between the fluctuations at 31 cm (average of 65 days) and 7.6 cm (average of 22 days). The correlation coefficient is greater than 0.8. (b) The result of subtracting the 3 l-cm data from the 7.6-cm data using the slope determined from the regression curve in (a). Noise remains on scales of 0.^o8- 5^o.

possible to select an amplitude for the filtered scan at 31 cm such that simply subtracting it from a scan of the same section of sky at 7.6 cm led to almost a factor of ten decrease in the dispersion at 7.6cm on scales of 1^o √ 2^o. It was immediately observed that after taking the experimental correction for the spillover loss at 31 and 7.6cm into account, the procedure for choosing the amplitude is identical to the assumption that the emission from the features visible in Fig. 6.11 is synchrotron in nature, with a brightness temperature spectral index of 2.55, which is very similar to the spectral index of the Galactic background emission at latitudes greater than 10^o(see Section 8). We attribute these features to structure in the Galactic background emission. Their characteristic size is approximately 1^o √ 2^o, and their amplitude at 7.6cm is about 1 mK. Their relative amplitude in the section 13^h < a < 14^h (latitude of approximately 60^o) is approximately 1 √ 2% of the brightness of the Galaxy in this direction.

Such fluctuations in the sky brightness place substantial limitations on the sensitivity of radiotelescopes to scales of 1^o√ 2^o even in the coldest region of the Galaxy. Thus, for single-frequency observations, we encountered a limit of ~ 1 mK, which is 50 √ 100 times worse than the expected thermal noise for Experiment Cold.

As is evident from Fig. 6.12(b), we succeeded in almost completely removing this "Galactic" noise by using the 31-cm data. The remaining emission at 7.6 cm is correlated (as was expected) with the emission at shorter wavelengths. The regression curve for the relationship between the remaining emission at 7.6 cm and the emission at 2cm is shown in Fig. 6.13(a). Noting the high correlation coefficient, we subtracted the 2-cm data from the 7.6-cm data using the slope of the regression curve (Fig. 6.13(b)). As a result, we obtained the curve in Fig. 6.13(c). Here, s  50 mK, i.e., the dispersion is only a few times greater than that expected in the ideal case (Table V.I).

In order to successfully make progress in dealing with the atmospheric noise, the Galactic noise, and the noise from the ground, it is necessary to have several extremely sensitive radiometers observing simultaneously, and highly accurate temperature, pressure, and humidity sensors. Taking all of these sources of noise into account can only be carried out by the method of least squares, choosing the correlation coefficients with the other wavelengths in such a way that the mean square deviation at the wavelength being studied is a minimum. Naturally, this should be done after removing the uncorrelated interference and the discrete sources.

In order to attract experts to this important problem, we remind the
 

 
reader that in solving this problem rather efficiently, we simultaneously solve the no less fundamental problem of the phase correction of images in interferometer networks. Since , and

 
6.7. Conclusions
 

We shall now summarize the analysis of a data set averaged over 22 days of observations under good and fair conditions.

When studying point sources at 7.6 cm at intermediate elevations in the standard mode, it should be kept in mind that about 20% of the sky is filled with radio sources with flux density greater than 1 √ 2mJy. Regions where the thermal radiometer noise dominates up to fractions of a mJy are frequently visible between the sources.

Finally, there are drifts on scales of 1 h, which were not successfully identified and whose amplitude is at least ~10mK (sometimes reaching 100mK) under good atmospheric conditions.

In order to come as close as possible to the noise of an "ideal" radiometer (more precisely, the "ideal" noise of a real radiometer at 7.6 cm) the RATAN-600 should be equipped with several new-genera-tion radiometers. Then, in a multi-frequency observing mode, it is possible to develop the mathematical method needed to realize the potential of the RATAN-600. Partial success can already be achieved using such a mathematical method with the present set of radiometers.

Finally, we saw that it is dangerous for the observer to try to dodge the problems in the struggle to approach the sensitivity in Table V.I. The general methodological lesson of Experiment Cold is that the noise from all of the sources of interference should be studied and methods for removing them should be evaluated first, and then it should be decided whether it is realistic to propose a certain experiment. From the experience of Experiment Cold, we believe that a search for the optimum radio-astronomical wavelength region for solving a particular problem should include a discussion of the methods of dealing with the sources of interference (dealing with Ss_i , rather than the components of T_sys).