A paper about Planar Interferometer Arrays

In summary, it appears that the matrix A is used to calculate the direction of the source from a given relative phase measurement vector. This is done by determining the unmeasured integer portions of the relative phase measurements between all antennas pairs.
  • #1
senmeis
69
2
Hello,

I have attached a paper about Planar Interferometer Arrays. Now I’m trying to understand this paper but something confuses me. I am very thankful if somebody can help me with it.

1:
By using multiple antenna-pairs in a suitable geometric configuration, it is a simple matter to ensure that the mapping from the set of possible direction cosine pairs onto the set of relative phase measurement vectors is one-to-one and therefore invertible by a doa estimation algorithm.
It seems to me that direction cosines and phase differences are 1:1 correspondent, that is, a phase difference can lead to a fixed direction cosine. Is it correct?

2:
Determining a unique source direction from a given relative phase measurement vector involves, at least implicitly, determining the unmeasured integer portions of the relative phase measurements between all antennas pairs.
What is meant by „unmeasured integer portions of the relative phase measurements between all antennas pairs“? Does it have something to do with resolving ambiguities?

Senmeis
 

Attachments

  • 01172129.pdf
    110.9 KB · Views: 438
Engineering news on Phys.org
  • #2
The phase difference between two antennas specifies the cosine of the angle of arrival. But with only one pair of antennas the source is only known to be on the surface of a cone with it's axis through the two antennas. With sufficient antenna pairs the direction of intersection of many cones can be computed. All cones form circles on the spherical map of all possible DOA.

Since phase differences are modulo 360°, when the dimensions of the array exceed one wavelength, there are ambiguous phase solutions. It is necessary to identify the integer number of cycles that are missing and apply them when computing the cosines of the angles.

Your observation 1: “that a phase difference can lead to a fixed direction cosine”, is correct only if the ambiguity is not present, probably because the array is small.

Your observation 2: “unmeasured integer portions of the relative phase measurements between all antennas pairs”, is referring to the missing complete cycles.

That work was in 1983. Since then, computers have gained sufficient speed to predict the phases expected from every point on a one degree grid in space, then search the DOA space for the least squares best match to the current measured differential phases. There is no ambiguity because the ambiguous results are suppressed by the least squares score. In 1989 I was doing that on an array of 18 antennas, with an Intel 386. Things have changed.
 
  • #3
Thank you Baluncore.

Under equation 1 I observe: 0 ≤ øi < 1. I think it is a mistake, the right one should be: 0 ≤ øi < 2∏.

Maybe it is a print error?

I still can’t understand how the matrix A is defined. This definition is made under equation 9 on page 354. Has anyone any idea about this definition?

Senmeis
 
  • #4
That is because radio engineers like to measure things in wavelengths, not radians.

The baselines between the elements of the array are being measured in wavelengths.
That is shown a few lines above the 0 ≤ øi < 1, where the d. vector is defined in wavelengths.
 
  • #5
,

Thank you for sharing this paper on Planar Interferometer Arrays. It is a complex topic, but I will do my best to clarify your confusion.

1: You are correct in your understanding that direction cosines and phase differences are 1:1 correspondent. This means that for a given set of direction cosines, there is only one possible phase difference measurement that can be obtained. This is important in doa estimation algorithms because it allows for a unique mapping between the two sets, making it easier to determine the source direction from the phase measurements.

2: The "unmeasured integer portions" refer to the fact that the relative phase measurements between antenna pairs can only be measured to a certain precision. There will always be a small margin of error in the measurement, which may result in a fractional value for the phase difference. This fraction is what is meant by the "unmeasured integer portion." To determine the exact direction of the source, these fractions must be rounded up or down to the nearest integer, which is why it is referred to as "implicit" in the doa estimation process. This process helps to resolve any ambiguities and obtain a unique source direction.

I hope this helps to clarify your understanding of the paper. If you have any further questions, please let me know. As a fellow scientist, I am always happy to discuss and assist in understanding complex topics.
 

1. What is a Planar Interferometer Array?

A Planar Interferometer Array is a type of optical instrument that uses multiple optical paths to measure the phase difference between two beams of light. By using multiple paths, it can increase the sensitivity and resolution of traditional interferometers.

2. How does a Planar Interferometer Array work?

A Planar Interferometer Array works by splitting a beam of light into multiple paths, each with a different length. The beams are then recombined, and the resulting interference pattern is measured. The phase difference between the beams is then calculated and used to determine properties of the light source, such as wavelength or refractive index.

3. What are the advantages of using a Planar Interferometer Array?

One advantage of using a Planar Interferometer Array is its increased sensitivity and resolution compared to traditional interferometers. Additionally, it is compact and can be integrated into existing systems easily, making it a versatile instrument for a variety of applications.

4. What are some applications of Planar Interferometer Arrays?

Planar Interferometer Arrays have a wide range of applications, including measuring the refractive index of materials, detecting small surface defects, and characterizing the properties of light sources such as lasers. They are also used in the field of astronomy for imaging and spectroscopy.

5. What are some limitations of Planar Interferometer Arrays?

One limitation of Planar Interferometer Arrays is that they are sensitive to environmental disturbances, such as vibrations or temperature changes. They also require precise alignment and calibration for accurate measurements. Additionally, they may not be suitable for measuring highly divergent or incoherent light sources.

Similar threads

  • Electrical Engineering
Replies
17
Views
2K
Replies
49
Views
2K
  • Beyond the Standard Models
Replies
11
Views
982
  • Introductory Physics Homework Help
Replies
8
Views
4K
  • Quantum Interpretations and Foundations
Replies
3
Views
1K
Replies
1
Views
2K
Replies
8
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Special and General Relativity
Replies
29
Views
5K
Replies
12
Views
2K
Back
Top