Small radio interference array visibility simulation and FITS generation method and system

Abstract

The invention discloses a small radio interference array visibility simulation and FITS generation method and system, and relates to the technical field of radio astronomy. The method comprises the following steps: firstly, constructing a small interference array consisting of at least four antennas, generating a time domain voltage signal of each antenna by simulating a target celestial body signal and background noise, and performing accurate time shifting according to geometric delay; then, carrying out segmented Fourier transform on the time domain signal to generate a dynamic frequency spectrum, and calculating a complex visibility function through cross-correlation operation between the antenna pairs; finally, the visibility data, the antenna position, the observation frequency, the calculated UVW coordinates and other information are packaged and output according to a standard FITS file format. According to the invention, a complete process from signal simulation to standard data format generation is realized, a standardized solution is provided for data processing, archiving and imaging of a small radio interference array, and the method is especially suitable for research on rapid interference measurement and mapping positioning of a temporary source.

Description

Technical Field

[0001] This invention relates to the field of radio astronomy observation and data processing technology, and more specifically, to a method and system for simulating, calculating, and generating standard astronomical data files for visibility functions applicable to small radio interferometer arrays. Background Technology

[0002] Interferometry is a core technology in radio astronomy. It simulates the observational capabilities of a giant telescope by combining multiple independent antennas, thereby achieving extremely high angular resolution. Traditional large interferometric arrays (such as VLA and ALMA) have mature data processing pipelines and standards. However, small interferometric arrays built for scientific research, teaching, or specific scientific objectives (such as transient source detection) often lack a complete and automated process from simulating raw signals to generating standard data formats. In existing technologies, data processing for small arrays typically relies on non-standard custom scripts, making their data incompatible with mainstream astronomical software (such as CASA and AIPS), which is detrimental to long-term archiving, sharing, and in-depth analysis of the data. Therefore, there is an urgent need for a method to generate standard format data files for small radio interferometric arrays to lower the data processing threshold and improve data utilization. Summary of the Invention

[0003] To address the problems existing in the prior art, the present invention aims to provide a method and system for simulating visibility and generating FITS for small radio interferometer arrays, thereby solving the problems of non-standard data processing procedures and incompatible data formats for small radio interferometer arrays.

[0004] To achieve the above objectives, this invention provides a method and system for visibility simulation and FITS generation of a small radio interferometer array. The technical solution of this invention includes three core parts: signal simulation, visibility calculation, and FITS file generation. In the signal simulation stage, a small radio interferometer array is first constructed, with a preferred embodiment employing an array layout consisting of four antennas. The direction of the target celestial object is set, determined by the azimuth and elevation angles. One antenna is used as a reference, with its geometric delay set to 0. Based on the baseline length between each antenna and the target sky position, the geometric delay of the signal reaching the other antennas relative to the reference antenna is accurately calculated. The formula for calculating the geometric delay is: τ = (d·s) / c, where d is the baseline vector, s is the unit vector of the wave source direction, and c is the speed of light. Subsequently, a time-domain voltage signal containing background noise and the target signal is generated. The background noise is generated using a white noise generation function, and the target signal is loaded from an actual observation data file. The target signal is embedded into a specific time window of the background noise, and the time-domain voltage signal of each antenna is generated using a signal generation function. The reference antenna signal remains unchanged, while the signals of other antennas are precisely time-shifted using a signal time-shift function based on the calculated geometric delay to simulate the wavefront arrival time difference. The time-shifted signal is represented as: t_i_shifted = np.roll(t_i, shift_samples), where shift_samples is the number of sampling points calculated based on the geometric delay and sampling rate.

[0005] Furthermore, in the visibility calculation stage, a piecewise Fast Fourier Transform (FFT) is performed on the time-domain signal of each antenna to generate a frequency-time two-dimensional dynamic spectrum. The long time-domain data is divided into multiple fixed-length time intervals, and an FFT is performed on each interval to obtain a two-dimensional complex dynamic spectrum array for each antenna. The dimensions of the dynamic spectrum are [number of frequency channels, number of time sampling points]. For all possible baseline pairs, point-by-point complex multiplication is performed on the dynamic spectra of the corresponding two antennas. The formula for calculating the complex visibility function is: visibility = t1_w * np.conjugate(t2_w), where t1_w and t2_w are the dynamic spectra of the two antennas, and np.conjugate represents taking the conjugate complex number. Through this operation, the complex visibility function of each baseline is obtained. To simplify processing, the visibility data can be superimposed on the frequency dimension to obtain a sequence of visibility changes over time for a single frequency channel. The stacking method is to average along the frequency dimension: v_single_freq = np.mean(v, axis = 0), where axis = 0 means averaging along the frequency dimension.

[0006] Furthermore, in the FITS file generation stage, a FITS file structure is first created, containing a main header unit and multiple extended data units. The main header unit stores metadata such as observation time, source coordinates, and frequency parameters. The observation time is converted to Julian day format for storage, the source coordinates include right ascension and declination, and the frequency parameters include center frequency and bandwidth. Based on the antenna position, observation time, and source coordinates, the (u,v,w) coordinates of each baseline at each time sampling point are calculated. The UVWCOMPUTING function is called, with input parameters including the antenna position matrix, the observation time array, and the source coordinates, and the output is an array of UVW coordinates for each baseline. The calculation of UVW coordinates is based on the Earth's rotation and the array geometry. In the main HDU, the data is organized in a "random group" structure. For each UV sampling point, three parts of information are stored: complex visibility (real and imaginary parts), weight (initially set to 1.0), and the corresponding (u,v,w) coordinates and modified Julian day. The data storage format is a binary table, with each row corresponding to a time sampling point. A frequency HDU is created to record detailed frequency setting information, including the number of frequency channels, frequency resolution, center frequency, etc. Create an antenna HDU, recording the name, location coordinates (X, Y, Z), and number of each antenna. Antenna location information is stored in tabular form for easy retrieval by subsequent data processing software. Write the complete data model to disk, generating a standard UVFITS format file. The file conforms to the FITS standard format, containing a 2880-byte block structure to ensure cross-platform compatibility. The generated FITS file can be directly recognized and imported by professional astronomical software such as CASA and AIPS using the importuvfits task.

[0007] This invention offers the following advantages: it realizes a complete process from signal simulation to standard data format generation, solving the problem of inconsistent data processing procedures for small radio interferometer arrays; the generated UVFITS files conform to international standards and can be directly recognized and processed by mainstream astronomical software, facilitating data sharing and long-term archiving; it supports different array configurations and observation parameter configurations, allowing adjustment of parameters such as the number of antennas, baseline length, and observation frequency according to actual needs; the system adopts a modular design, with each functional module capable of independent expansion and optimization, facilitating subsequent functional upgrades and performance improvements; it is particularly suitable for teaching demonstrations, testing and verification of small radio interferometer arrays, as well as rapid interferometric measurement and localization research of transient sources, possessing significant practical value and promising prospects for widespread application. Attached Figure Description

[0008] Figure 1 This is a simulated layout of four small antennas;

[0009] Figure 2 The time delay of the synthesized signal across the four antennas;

[0010] Figure 3The interference fringes (bottom right) are obtained between antenna 2 (reference antenna) and antenna 4;

[0011] Figure 4 The UV coverage of the Crab giant pulse synthesis data (integration time of less than 1 second) by the four antennas;

[0012] Figure 5 The corresponding dirty beam of Crab giant pulse synthesis data (integration time of less than 1 second) from the four antennas;

[0013] Figure 6 A dirty plot of Crab giant pulse synthesis data (integration time less than 1 second) from four antennas;

[0014] Figure 7 The UV coverage is integrated over 10 hours using four antennas to a constant, continuous source (analog data).

[0015] Figure 8 The corresponding dirty beam is integrated for 10 hours from a constant, continuous source (analog data) using four antennas;

[0016] Figure 9 Cleaning diagram for integrating four antennas with a constant, continuous source (analog data) for 10 hours. Detailed Implementation

[0017] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0019] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0020] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0021] The following is combined Figures 1-9 The embodiments described herein will be described in detail. It should be understood that the specific implementation methods described herein are for illustrative and explanatory purposes only and are not intended to limit the scope of the invention.

[0022] Example 1: Visibility simulation and FITS file generation for a small radio interferometer array;

[0023] This embodiment uses a small radio interferometer array consisting of four antennas, with the array configuration as follows: Figure 1 As shown. The four antennas are labeled Antenna 1, Antenna 2, Antenna 3, and Antenna 4, with Antenna 2 serving as the reference point. The antenna position coordinates are as follows: Antenna 1 (0,0,0), Antenna 2 (100,0,0), Antenna 3 (0,100,0), Antenna 4 (100,100,0), in meters.

[0024] First, signal simulation is performed, with the direction of the target celestial body determined by its azimuth (target_phi) and elevation (target_theta). Antenna 2 is used as a reference, and its geometric delay is set to 0. Based on the baseline lengths between the antennas and the target's position in the sky, the geometric delay of the signal reaching other antennas relative to the reference antenna is precisely calculated. The formula for calculating the geometric delay is:

[0025]

[0026] in, is the baseline vector, and c is the speed of light (3×10⁸ m / s).

[0027] The geometric delay of antenna 1 relative to antenna 2 is calculated as follows:

[0028]

[0029] Where (x1, y1, z1) are the position coordinates of antenna 1, (x2, y2, z2) are the position coordinates of antenna 2, and θ is the elevation angle. It is the azimuth angle.

[0030] When generating the time-domain voltage signal, the background noise is generated using a white noise generation function, and the target signal is loaded from the actual observation data file (e.g., GP_bs.npy). The target signal is embedded into a specific time window (t_start to t_end) of the background noise, and the time-domain voltage signals t_1, t_2, t_3, and t_4 of the four antennas are generated using a signal generation function. The reference antenna signal t_2 remains unchanged, and the signals of the other antennas are precisely time-shifted according to the calculated geometric delay to simulate the wavefront arrival time difference. The time delay is as follows: Figure 2 As shown.

[0031] A piecewise Fast Fourier Transform (FFT) is performed on the time-domain signal of each antenna to generate a two-dimensional dynamic spectrum in frequency and time. The long time-domain data is divided into multiple time intervals of length FFT_length, and an FFT is performed on each time interval to obtain a two-dimensional complex dynamic spectrum array (t1_w, t2_w, etc.) for each antenna. The dimensions of the dynamic spectrum are [number of frequency channels, number of time sampling points].

[0032] For all possible baseline pairs (four antennas can form six independent baselines), a point-by-point complex multiplication operation is performed on the dynamic spectrum of the corresponding two antennas. The formula for calculating the complex visibility function is: visibility = t1_w * np.conjugate(t2_w). Through this operation, the complex visibility functions (v12, v13, v14, v23, v24, v34) of the six baselines are obtained. To simplify the processing, the visibility data can be superimposed in the frequency dimension to obtain a sequence of visibility changes over time for a single frequency channel.

[0033] Finally, a FITS file structure is created, containing a main header unit and multiple extended data units. The main header unit stores metadata such as observation time, source coordinates, and frequency parameters. Observation time is converted to Julian day format for storage, source coordinates include right ascension and declination, and frequency parameters include center frequency and bandwidth. Based on antenna position, observation time, and source coordinates, the (u,v,w) coordinates of each baseline at each time sampling point are calculated. The UVWCOMPUTING function is called, with input parameters including the antenna position matrix, observation time array, and source coordinates, and the output is an array of UVW coordinates for each baseline. In the main HDU, the data is organized in a "random group" structure. For each UV sampling point, the complex visibility, weight, and corresponding (u,v,w) coordinates and modified Julian day are stored. Frequency HDUs and antenna HDUs are created, recording detailed frequency setting information and antenna position information. The complete data model is written to disk, generating a standard UVFITS format file.

[0034] Example 2: Implementation methods for different array configurations;

[0035] This embodiment employs an interferometric array consisting of six antennas in a Y-shaped configuration. The six antennas are labeled Antenna 1 through Antenna 6, with Antenna 1 serving as the reference. The antenna position coordinates are as follows: Antenna 1 (0,0,0), Antenna 2 (86.6,50,0), Antenna 3 (-86.6,50,0), Antenna 4 (0,100,0), Antenna 5 (86.6,150,0), Antenna 6 (-86.6,150,0), in meters. The signal simulation and visibility calculation steps are the same as in Embodiment 1, but the number of baselines is increased to 15. When generating the FITS file, the visibility data and UVW coordinate information of all 15 baselines need to be stored.

[0036] Example 3: Implementation of multi-frequency channels;

[0037] This embodiment employs an interferometric array consisting of four antennas, with an observation frequency range of 1.2-1.6 GHz, divided into eight frequency channels, each with a bandwidth of 50 MHz. During signal simulation, time-domain signals for each frequency channel are generated. During visibility calculation, frequency dimensions are kept separate, generating visibility data for all eight frequency channels. When generating the FITS file, detailed frequency channel information is recorded in the frequency HDU, including the center frequency, bandwidth, and frequency resolution of each channel.

[0038] Example 4: Implementation method for long-term integration observation;

[0039] This embodiment employs an interferometric array consisting of four antennas to perform long-term integration observations of a continuous source for 10 hours. During signal simulation, a 10-hour time-domain signal is generated. For visibility calculation, the time-domain signal is divided into multiple time segments, each 10 seconds long, resulting in 3600 time sampling points. When generating the FITS file, visibility data and UVW coordinate information for all time sampling points are stored.

[0040] Example 5: Implementation of Rapid Observation of Transient Sources This example uses an interferometric array consisting of four antennas to rapidly observe transient sources, with an integration time of less than 1 second. During signal simulation, a 1-second time-domain signal is generated, and the target signal duration is approximately 10 milliseconds. For visibility calculation, the time-domain signal is divided into multiple time segments, each 1 millisecond in length, for a total of 1000 time sampling points. When generating the FITS file, the visibility data and UVW coordinate information of all time sampling points are stored.

[0041] Through the implementation of the above embodiments, those skilled in the art can clearly understand the technical solution and implementation methods of the present invention, and can make corresponding adjustments and optimizations according to actual needs. The present invention realizes a complete process from signal simulation to standard data format generation, providing a standardized solution for data processing, archiving, and imaging of small radio interferometer arrays, and has significant practical value and promising prospects for application.

[0042] Any process or method described in the flowcharts of this invention or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a particular logical function or process, which can be implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device. The computer-readable medium can be any medium containing a program for storage, communication, propagation, or transmission for use by an execution system, apparatus, or device, including read-only memory, magnetic disks, or optical disks.

[0043] In the description of this specification, references to terms such as "embodiment," "example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, those skilled in the art can combine or combine the different embodiments or examples described in this specification and the features therein without causing contradiction.

[0044] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Therefore, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for simulating visibility and generating FITS for a small radio interferometer array, characterized in that, Includes the following steps: Signal simulation: Set the coordinates of the target celestial body and the configuration of a small radio interferometer array, calculate the geometric delay of each antenna relative to the reference antenna based on the baseline length and target direction; generate a time-domain voltage signal containing background noise and target signal, and time-shift the signal of the non-reference antenna according to the geometric delay to obtain the final time-domain signal of each antenna; Visibility calculation: Perform piecewise fast Fourier transform on the time-domain signal of each antenna to obtain the frequency-time dynamic spectrum of each antenna; for all possible baseline pairs, perform complex cross-correlation on the dynamic spectra of the corresponding two antennas to obtain the complex visibility function of each baseline; FITS file generation: Create a FITS file structure and write observation time, source coordinates, and frequency parameter metadata; calculate the UVW coordinates of each baseline based on antenna position and observation time; store visibility data, weights, UVW coordinates, and associated time information in the main data unit of the FITS file in a random group format; at the same time, create an extended data unit containing antenna information and frequency information; finally, output a standard format UVFITS file.

2. The method as described in claim 1, characterized in that, In the signal simulation, the target signal is a transient source pulse signal extracted from actual observation data.

3. The method as described in claim 1, characterized in that, In the signal simulation, a small radio interferometer array is first constructed, using an array layout consisting of several antennas.

4. The method as described in claim 3, characterized in that, In the signal simulation, the direction of the target celestial body is set, which is determined by the azimuth and elevation angles; one of the antennas is used as a reference, and the geometric delay of the signal reaching other antennas relative to the reference antenna is accurately calculated based on the baseline length between each antenna and the target sky position.

5. The method as described in claim 4, characterized in that, The formula for calculating geometric delay is: τ=(d·s) / c, where d is the baseline vector, s is the unit vector of the wave source direction, and c is the speed of light.

6. The method as described in claim 5, characterized in that, Subsequently, a time-domain voltage signal containing background noise and target signal is generated. The background noise is generated using a white noise generation function, and the target signal is loaded from the actual observation data file. The target signal is embedded into a specific time window of the background noise, and the time-domain voltage signal of each antenna is generated through a signal generation function.

7. The method as described in claim 1, characterized in that, After the visibility calculation, the visibility data is superimposed on the frequency dimension to obtain a visibility sequence for a single frequency channel.

8. The method as described in claim 1, characterized in that, In the generation of the FITS file, the UVW coordinates are calculated by calling the UVWCOMPUTING function, combined with the observation time, antenna position, and source coordinates.

9. The method as described in claim 1, characterized in that, The small radio interferometer array consists of four antennas.

10. A system for simulating visibility of a small radio interferometer array and generating FITS, characterized in that, The system is used to implement the method as described in any one of claims 1-9, the system comprising: The signal simulation module is used to calculate the geometric delay and generate a time-domain voltage signal that includes time shift. The visibility processing module is used to generate dynamic spectrum and calculate cross-correlation visibility; The FITS file building module is used to initialize the file structure, calculate metadata, populate data, and output the final file.

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