PART II: THE FOCAL PLANE FAULT
II.1 Basic concepts
Bicep2 focal plane is populated with small (physically and electrically) slot antennas cut in a metal plane in a rectangular grid arrangement. There are some 500 such slots in the focal plane. The slots are alternately “horizontal” (parallel to the x axis say) and “vertical” (y axis) – to receive two orthogonal polarizations.
The horizontal slots receive vertically polarized radiation and the vertical slots are horizontally polarized radiation.
Consider two nearby antennas that are orthogonal to each other. They look at the same spot in the sky and receive the same sky polarization.
If the horizontal antenna detects maximum power and the vertical antenna detects zero power, the incident sky polarization is vertical.
If the horizontal antenna detects zero power and the vertical antenna detects maximum power, the incident sky polarization is horizontal.
If both antennas detect the same power, the incident sky polarization is at 45 degree angle (or 135 degree angle).
When the two antennas record different amounts of nonzero power, the sky polarization angle can be calculated.
Any ambiguity in the angle is resolved by adding other information and coordinating across the entire imaging plane.
This is the basic principle of Bicep2 polarimetry we need to know. Of course the practice is far more complicated.
The main points for our purpose are:
1. Each location a in the focal plane corresponds to a location A in the sky. If a moves, A moves.
2. The antennas must be identical in their electromagnetic properties. What this means for our specific purpose is that for the same amount of co-polarized power incident on an antenna, each antenna must report exactly the same amount of energy. When I say exactly, I mean there is very little tolerance, probably only a small fraction of 1%.
Note that the Bicep2 telescope can be rotated about its axis. We assume that the imaging plane is rigidly fixed to the body of the telescope so that it rotates with the telescope.
II.2 The antenna fault
Now let us refer to Figure 2 which shows the flipside of the Bicep2 focal plane. You can see the horizontal and the vertical slots and the associated microstrip circuitry connecting the antennas to the detectors (not shown).
The design of a slot antenna requires that the microstrip transmission lines on the circuit board stay clear of the antenna to some distance around it – as shown in the case of the vertical antennas. However, this principle was not followed for the horizontal antennas.
As a result, the properties of the horizontal and the vertical antennas are different. They will report different amounts of power when the same amount of copolarized power is incident on them. As I have explained, such a difference translated to a polarization angle ascribed to the incoming sky wave.
Thus, an intrinsic instrumental polarization is introduced at all circuit board locations a.
This instrumental polarization is introduced all across the board and are ascribed to all corresponding sky points A being observed.
Furthermore, the difference in the power reported varies across the board because of the way the circuit has been designed.
So the instrumental polarization has an entire polarization map (mosaic) of itself.
If there is any polarization in the sky, the map Bicep2 obtains is some kind of convolution of the instrumental map and the actual sky map.
If the focal plane (the telescope) is rotated, the location of a in the telescope changes with respect to the sky. And so the location A in the sky changes. Thus the instrumental map of the sky rotates with the telescope.
Therefore, when the telescope is rotated, the sky image reported by Bicep2 structurally rotates.
This what was implied in the humor in this figure.
Remember that Bicep2 was looking for the smallest of small signals. There needed to be not even an appearance that the horizontal and the vertical antennas are different. Instead, we have this clear design violation!
1 The horizontal and the vertical antennas are not the same.
2 The focal plane has a clear directionality.
3 The focal plane properties become convoluted with any actual sky map the telescope is observing to provide an artifactual sky map.
II.3 The array fault
Let us now turn to the antenna array, a portion of which is shown in Figure 3. The progress of the Bicep2 class telescopes has been driven by packing more and more antenna elements into this area, reportedly to provide higher resolution and faster imaging of the sky.
One of the fundamental limitations of Electromagnetic Theory is that electromagnetic waves cannot resolve (discern, discriminate) structures that are smaller in size than ~ λ/3 ( λ= the wavelength, in this case 2 mm).
What this means in the present context is that to the incoming wave, antennas placed closer than this length do not act as independent detectors of radiation. So this is like providing more pixels to an image after it has been fully resolved. All that happens is that the data file gets bigger and bigger with no practical benefit added.
But in the Bicep2 case, this is not only needless increase of the number of antenna elements. It can also be detrimental because of cross-talk between antennas that are assumed by the researchers to be independent.
For experts, you can read between the lines and see some of the roots of misunderstandings in this scientific design approach statement from the Bicep2 camp below. They gave up the most crucial need for aperture area to accommodate the mistaken idea that more and more antennas can be packed to get more and more capability!
Traditionally,bolometers have been used with horns to match the detectors’ optical response to the camera/telescope optics. At Caltech, we have developed an entirely planar equivalent with an integrated, printable, phased array antenna. Whereas technology from circa 2005 allowed for 50 pixels in the progenitor camera BICEP-1, we recently deployed over 1500 pixels in the Keck-array and BICEP-2 cameras, providing 8.5uK sqrt(s) sensitivity. In December of 2013, we will bring another 1500 detectors to the field in the BICEP-3 camera, which will expand our coverage from just 150GHz to 90GHz so we can discriminate CMB photons from galactic foregrounds. The balloon bourn SPIDER will also fly December 2013, with a mixture of 90 and 150GHz, but a comparable number of pixels as Keck. We realistically expect that the data sets from these experiments over the next few years will let us constrain the tensor-scalar ratio r of modes from inflation to r=0.01. The key behind this rapid scale-up has been to use small aperture cameras with just enough resolution to see the 2-degree primordial B-mode peak (an aperture of 26cm at 150GHz), thus making the design scalable to multiple cameras.
Somebody needs to do something about what is going on here under the guise of advanced research.
II.4 Bicep2 observation technique
It is clear that the Bicep2 team were not aware of the issues I have discussed above. They have in fact bandied around images of the focal plane all over the place with great parental pride. These images contained clear visual signal of what was wrong.
However, it seems that they concluded that some type of attention needed to be given to the angular position of the telescope about its axis. This is how they described this:
To make accurate measurements over a wide area, the challenge is to control false signals. … Finally, to remove from the system any effects that might arise from having a preferred direction, we spin our telescope around its axis every day.
So it seems that some type of angle-averaging or angle randomization with regard to some unknown suspected directionality in the telescope underlies the Bicep2 sky maps unveiled.
This is most curious in a state-of-the-art, pioneering experiment attempting to make the grandest of discoveries.
If there is a suspected directionality, would you not want to examine this? Especially when it takes no more effort than making sky images with the telescope fixed at 0, 45 and 90 degrees position (for example).
What does it mean exactly to average maps if they were structurally rotating?
So the Bicep2 team had the burden to produce those angle-specific sky maps before publishing their discovery. This crucial scientific burden for the Bicepe2 experiment cannot be avoided with statements like We compared Bicep2 with other telescopes and everything is fine.
II.5 The proof offered: Bicep1 vs Bicep2
Let us nevertheless consider the self-explanatory Figure 4. Here we see that for the E-mode polarization, there is some correspondence between Bicep1 and Bicep2. (Not so for B-mode). Specifically, the directionality in the map seems to be the same.
Note that Bicep1 did not have the grid type focal plane. It had tried and true polarized horns in its focal plane.
So we end up with a contradiction between basic physics principles in the textbooks and astronomical observations reported by the Bicep2 team
SCIENTIFIC DESIGN ANALYSIS: The telescope is not capable of measuring polarization features in the CMB radiation because of its small aperture. The imaging plane has a pronounced directionality, and adds an instrumental polarization component across the sky map. Tighter packing of antennas cannot lead to higher resolution beyond a certain point – which was crossed by a great extent. When that happens, even the limiting resolution is lost.
OBSERVATION REPORTED: The telescope is reporting crisp high resolution polarization sky maps that do not depend on the angle of the telescope.
SCIENTIFIC ESTABLISHMENT RECEPTION: The astronomical discovery has been accepted in toto and without any qualification. The only debate concerns the interpretation of this observation.
Where have we seen these three steps unfold before?!