We present an advanced schematic arrangement of the radio-wave spectrometer with a few parallel optical arms for processing the data flow. This arrangement includes two principal novelties. First of them consists in the proposed design, where each individual optical arm exhibits its original performances providing parallel multi-band observations within a few different scales simultaneously. These optical arms have the beam shapers providing both the needed incident light polarization and apodization to increase the dynamic range. After parallel acousto-optical processing, data flows of all the optical arms are united by the joint CCD matrix on the stage of the combined electronic data processing. The second novelty is in usage of unique wide-aperture bastron-based acousto-optical cell providing one of the best performances at the middle-frequencies (about 500 MHz) in comparison with the other available crystalline materials in this range. Such multi-band capabilities have a number of applications in astrophysical scenarios at different scales: from objects in the distant universe to planetary atmospheres in the Solar system. Thus one yields the united versatile instrument, which provides comprehensive studies of astrophysical objects simultaneously with precise synchronization in various frequency ranges.
Spectroscopic techniques have been a powerful tool for investigating the physics of astronomical phenomena since its very first use in stellar classification by father Angelo Secchi in the mid-1800s. To date, this technique is used pan-chromatically. From space it has been possible to investigate the absorption and emission line spectra of highly ionized multi-electronic atoms (Fe, Si, O, Mg, Ne, etc.) whose prints appear mainly at X-ray and Extreme Ultraviolet regimes. At lower frequencies, molecular (electronic, vibrational, and rotational) transitions dominate the infrared and (sub-)millimeter spectra on a variety of celestial bodies and have been studied from the ground at the available atmospheric windows, as well as from space when the atmospheric opacity precludes ground based observations.
The analysis of spectra at radio frequencies (1 - 250 GHz) is of particular importance for the investigation of the physical and chemical properties of astronomical objects in a number of astrophysical scenarios; from studies of the high red-shift universe to planetary atmospheres in the solar system. Different astrophysical contexts require, in general, different capabilities. For instance, at large distances when extragalactic objects cannot be resolved, a rather coarse resolution (of a few 10s of MHz) is sufficient to detect the most prominent molecular emission lines (CO, HCN). In this particular frame- work, the detection of emission lines not only allows the investigation of the physical properties of the gas (such as density), but also to determine, through the wavelength displacement of the spectral lines, the red-shift of the objects and hence their distances (see, e.g. [
In the nearby extragalactic universe, the resolution requirements are more demanding, since in many cases, spectral lines are less broadened by velocity dispersion. In this intermediate scale context, some of the current investigations are focused in identifying faint molecular lines that can contribute in tracing the effects of significantly distinct environments in the star formation rate of galaxies with prominent star formation (Starbursts and Active Galactic Nuclei) [
More locally, galactic studies on the gas content of star forming regions and around young and relatively mature stars require higher resolutions (of a few KHz). For these global cases the bandwidth needs are also different, although it should be mentioned that it is desirable to have the largest possible bandwidth to collect data on several molecular species simultaneously. These requirements have been nicely summarized in figure 8.12 of Ref. [
As indicated above, the resolution requirements increases from left to right, from about 30 MHz needed for high-z galaxies, to the very high resolution demanded by analyses of molecular gas in galactic scenarios. The necessary bandwidth for each case is depicted by the two vertical axes given in frequency and km/s units on the left and right axes, respectively. Correspondingly, the vertical and horizontal lines provide a rough indication of the resolution and bandwidth, denoted in the figure as RSB (Red- shift Search Receiver Band, see below), WB (wide band) and NB (narrow band). The
circles and squares indicate, respectively, these requirements for two representative wavelength bands: 1 and 3 millimeters.
In general, the different demands are fulfilled by independent instruments working at a given astronomical facility. Such is the case, for example, of the two spectrometers, the Red-shift Search Receiver (RSR) [
Whilst there are currently a number of multi-band radio wave continuum cameras in operation at different astronomical infrastructures, such as the SCUBA-2 at the James Clerk Maxwell Telescope [
Within this article, a pioneer approach to designing a prototype of the acousto-optic spectrometer for radio-astronomy is schematically analyzed as well as preliminary confirmed by both the practical estimations and proof-of-principal experiments. The advances under this proposal reflect the next step in a progress in this field that includes principally higher level of parallelism in a wideband analogue signal processing with various frequency performances simultaneously and selecting the most appropriate AO materials for the desirable algorithm of processing.
As it had been described recently [
The principal difference of the schematic arrangement presented here in comparison with the one described in [
Finally, after parallel AO processing, all these data flow are united by the joint matrix CCD photo-detector already on the stage of a high-bit-rate combined electronic data processing. After parallel AO processing, data flows of all the optical arms are united by the joint CCD matrix on the stage of the combined electronic data processing. At this point one yields at the united versatile instrument, which provides comprehensive studies of astrophysical objects simultaneously with precise synchronization in various frequency scales. At the moment, we have restricted ourselves by only the three similar spatial optical arms for data processing (see
The first spatial arm of data processing represents almost a replica of the optoelectronic scheme described previously [
The third arm of processing is intended for direct spectrum analysis of UHF radio- wave signals whose the central frequencies exceed 1.5 GHz and the frequency bandwidth are over 300 MHz. At the moment, the third spatial arm oriented to an AO cell based on rather specific cut of a lithium niobate (LiNbO3) crystal providing the anomalous regime of light scattering in the near infrared range at λ ≈ 1150 nm. Potentially, one can already have imagined the fourth spatial arm directed to reaching the frequency bandwidths over 1 GHz with the corresponding growth of the central frequencies. In practice, the most adequate approach for providing such bandwidths can
be based on either the phased-array technique [
Each of the enumerated spatial optical arms for spectrum analysis within the prototype under discussion consists of a few optical or optoelectronic sub-systems, namely:
1) Rather powerful coherent light source controlling the linear polarization state and operating in a single frequency regime with small (about 1 - 3 mrad) beam divergence;
2) Beam shaper providing the desirable degree of linear polarization as well as the needed expansion and apodization of that beam;
3) The AO cell represents by itself specifically operating opto-electronic sub-systems, which determine the main performances of taken spatial arm;
4) Fourier-transform system including the integrating lens with an individual row of the CCD-matrix (see
The three AO cells are key components of an advanced spectrometer under proposal, since exactly this triplet of devices is responsible for the efficiency of data processing, the frequency resolution and bandwidth of analysis, i.e. the precision of radio-signals detection. There are various criteria for choosing optimal AO cells crystalline materials; one can require, for example, a large light scattering efficiency or an increased angular range of optical beam scanning, or a minimized acoustic losses to provide the highest possible frequencies of operation, etc.
Together with this, even an individual spatially one-channel AO cell provides a multi-channel (a thousand channels or more) parallel processing in the frequency domain in such a way that practical frequency range of AO cell’s operation can be varied in wide limits to be adequate to the observational needs of modern radio-astronomy. These needs are widely varied from the frequency bandwidth ∆f ≈ 40 MHz and the frequency resolution δf ≥ 15 KHz to ∆f ≈ 300 MHz or more and δf ≥ 100 KHz with the number of parallel processing channels in the frequency domain (or, equivalently, the number of resolvable spots) N ≈ (2 − 3) × 103 as the case requires. These performances can be achieved at the top of modern technology exploiting specially designed AO cells based on specifically selected crystalline materials and regimes of their operations as it has been noted above.
Within our today’s aims, one can mention first of all the successful arrangement and detailed characterization of the above-mentioned sub-systems for the second arm with the specially designed wide-aperture AO cell based on the bastron single crystal, which is unique for practical applications.
This pioneer AO cell works at optical wavelength λ = 671 nm, which combines the convenience of operating in just the visible range with good enough transparency of this material with dark red light, from the single frequency solid-state laser CL-671- 050-S (Crysta Laser). The bastron-based AO cell of 6 cm aperture is theoretically able (see section 3) to manage the UHF radio-wave signals whose best performances can be estimated at the central frequency about of 500 MHz, frequency bandwidth close to 260 MHz and frequency resolution better 92 KHz providing the number N ≈ 2.7 × 103 of resolvable spots or, what is the same, the number of parallel frequency channels for spectral data processing.
The beam shaper included a variable optical attenuator, a Glan-Taylor linear polarizer, and a specially designed 4-prism beam expander for achieving the apodization by the tunable Gaussian profile. During its characterization rather precise adjusting the incident light beam had been realized. The processing part of this spatial arm embraces three key components. The first of them is the above-mentioned unique bastron AO cell with active optical aperture 60 × 2 mm. The second one is a fragment of the 3-inch achromatic doublet lens (Edmund Optics) with the focal length of about 85 cm, while the third component represents the second row of at least a 3-row multi-pixel CCD- matrix whose pixel has not more than 7 µm width. The performed characterization demonstrates that each individual optical beam can shape a spot whose main lobe has about 14 - 21 µm width, so that such a lobe lights usually two or three pixels in the corresponding row of CCD-matrix providing optimal resolution from viewpoint of the sampling theorem. General optical scheme of the second, i.e. the middle-frequency spatial arm for a new prototype under consideration, is depicted in
The AO interaction leads to deflection of the incident light beam by an angle that is directly proportional to the frequency of the applied electric and, consequently, acoustic signal. One of the most important parameters for an AO cell, included into the Fourier processing, is the number of resolvable spots N in the image plane, which corresponds to the number of resolvable frequencies in the Fourier-transform plane. The number N can be determined as a ratio of the maximal light beam deflection angle ∆θ to the beam divergence δθ ≈ λ/D (with the refractive index n ≈ 1 for the air), where D is the linear size of that beam, i.e. N = ∆θ(λ/D). The above-noted proportionality inherent in the Fourier transform makes it possible to explain ∆θ = λ∆f/V in terms of the frequency bandwidth ∆f and acoustic wave velocity V. Then, due to the transition time of passing an acoustic wave through an AOC with an aperture coinciding with D is τ = D/V, one can write
It is seen from Equation (1) that if both the AO cell’s-aperture D and, consequently, the transition time τ are fixed, so that growing the number N can only be provided by increasing the bandwidth ∆f. In so doing, the highest efficiency of light scattering is extremely desirable of course. However, the scattered light intensity depends on the angular-frequency mismatch η as well, which is conditioned by a wide range of varying the wave vectors of acoustic waves. The dependencies of the maximum scattered light intensity on the squared acoustic power parameter
One can find that the efficiencies about 50% are approximately the same for all the taken values of the relative frequency bandwidth when σ2 ≈ π/4. By this it means that the maximum scattered light intensity will be almost the same for every frequency component under analysis with σ2 ≈ π/4 or, in the other words, the magnitude σ2 ≈ π/4 provides minimal variations of the scattered light intensity versus the applied frequency of a signal within the bandwidth ∆f at the cost of decreasing the interaction efficiency by about 50%.
The above-mentioned number of resolvable spots N characterizes either the number of frequency channels for parallel analysis or the frequency resolution inherent in processing optical system. The frequency bandwidth ∆f of each AO cell depends on the chosen regime of light scattering. In the case of normal regime associated with a one-fold non- collinear light scattering, one can assume that the angle θ0 of light incidence is rather small, so that cosθ0 ≈ 1, and the frequency bandwidth of a one-fold light can be expressed as
Now, one can analyze a few factors limiting the number of resolvable spots as a function of the frequency parameters [
Within such an analysis the bastron (Sr0.75Ba0.25Nb2O6) had been chosen for the application to the second spatial optical arm. The selection of tetragonal Sr0.75Ba0.25Nb2O6- crystal (its point-symmetry group is 4 mm) is conditioned first of all by its quite acceptable figure of merit
These estimations show that N does not exceed the values of about 1500 or 3000 as a maximum for any crystal. This is why the obtained numbers N reflect evidently the physical limitation peculiar to the normal regime of an AO interaction in anisotropic materials.
To provide direct spectrum analysis of UHF radio-wave signals the LiNbO3-based AO cell operating in the anomalous light scattering regime with wide-bandwidth tangential phase matching with so-called “optimal matching” can be chosen. As it had been shown in [
(a), (b) (2)
where n is the average refractive index and L = L0 is the initial length of AO interaction.
Expression for ΔfA in Equation (2) does not include the frequency fC in the contrast with the corresponding formula for ΔfN ~ 1/fC, leading to fast increasing ΔfN when the central frequency fC grows.
The above-mentioned approach can be illustrated by the following numerical estimations for a one-fold light scattering in lithium niobate crystalline AO cell operating in the regime of anomalous light scattering with wide-bandwidth tangential phase matching.
The main values NE and NO of the refractive indices inherent in a lithium niobate crystal are markedly dispersive; for instance, NE ≈ 2.208, NO ≈ 2.967 at λ = 633 nm and NE ≈ 2.152, NO ≈ 2.227 at λ = 1150 nm [
In this case, N is again limited by the independent agents mentioned previously, but they have to be partially modified because now the above-exploited in section 3 approximation Δf ≈ f0/2 cannot be applied. In so doing, one can use the expression
which does not depend on the frequency. The second limitation is not actual now due to the Klein-Cook parameter is high enough even at the minimal frequency in the range of processing. The second limitation is not actual practically due to the carried out above estimation of the Klein-Cook parameter even at the minimal frequency in the range of processing. At the same time, the acoustic attenuation can be extremely important for acoustic waves at the UHF. One can take B ≈ 10 dB/aperture as an acceptable level of acoustic losses along the AO cell’s aperture and find an allowable aperture D as
due to Γ ≈ 1 dB/(cm∙GHz2) [
By this it means that one can expect N ≥ 3500 resolvable spots with the LiNbO3-cell under consideration, while the corresponding frequency resolution δf = V/D is close to about 100 KHz.
The efficiency of anomalous AO interaction with wide-bandwidth tangential phase matching in a crystal can be characterized by the modified figure of merit
One can find from this plot that LiNbO3-based AO cell under discussion is able potentially to provide the efficiency of light scattering up to 36% per one Watt of the applied acoustic power within a 0.405 level of a maximum frequency bandwidth close to 300 MHz.
The bastron-based AO cell of 6 cm aperture is able theoretically (see section 3) to manage the radio-wave signals whose the best performances can be estimated at the central
frequency about 500 MHz, frequency bandwidth close to 250 MHz and frequency resolution about 91.7 KHz providing potentially N ≈ 2720 resolvable spots. Testing of the second spatial optical arm of a new prototype under consideration, had been preliminary carried out with the currently available Bragg AO cell made of the bastron single crystal, which had an active optical aperture of 60 × 2 mm. To minimize the optical absorption in this material the dark-red light (the wavelength is 671 nm, the refractive index n ≈ 2.3) with linear polarization state of the incident light had been chosen. The normal process of light scattering by pure longitudinal elastic mode propagating along the [
Within the first part of experiments, specially designed wide-aperture AO cell based on the unique bastron (Sr0.75Ba0.25Nb2O6) single crystal had been inserted in the above- described second spatial optical arm of that schematic arrangement representing a layout of an AO spectrometer (see section 2). Namely, it consists of the solid-state laser CL-671-050-S/CrystaLaser/(λ = 671 nm, the output optical power about 50 mW); the bastron-based AO cell of 6 cm aperture that is able potentially to manage the UHF radio-wave signals at the central frequency ~500 MHz; a four-prism beam expander, a large-aperture 3-inch achromatic doublet lens (Edmund Optics), and a multi-pixel CCD linear photo-detector. A bastron-based AO cell was illuminated by the single- frequency light beam expanded and polarized linearly in a plane of light scattering, which includes the acoustic beam inside the bastron-based AO cell. Such a state of polarization gave maximal transmission and desirable Gaussian apodization of the prism beam expander because the plane of optical beam expansion was coinciding with the plane of light polarization. Moreover, this polarization state provided the highest efficiency of light scattering within the chosen orientation of a crystal.
The Bragg regime of AO interaction can be provided only if the angle of light incidence on undoutedly thick dynamic acoustic grating satisfies the necessary Bragg condition as well as if the Klein-Cook parameter Q realizes the inequality
The piezoelectric transducer of that AO cell with the interaction length L = 1.0 cm had been made of a thin lithium niobate (Y + 36˚)-cut crystalline plate. It generated pure longitudinal acoustic mode with rather low losses of electro-acoustic conversion slightly exceeding 2 dB, due to a fact that the acoustic impedance of this lithium-ni- obate crystal cut is equal to
The electronic scheme for optimal connection of the sweep-generator with that port of the AO cell’s, i.e. in fact with the lithium niobate transducer, included a two-section wide-band matching circuit of the lumped electronic components accompanied by a two-cascade resistance step-down transformer assembled out of micro-coaxial cables. This electronic circuit was used to make as wide and uniform as possible the frequency band-shape even at the coast of decreasing the efficiency of the AO cell in part. The single-frequency longitudinal mode with the acoustic power density up to 0.3 mW/mm2 was generated at the swept carrier frequency during the experiments. The efficiency of AO interaction with the pure longitudinal acoustic mode was limited by about 10% to keep the linearity of potential analysis.
Estimating the frequency resolution peculiar to the bastron-based AO cell within the frames of the above-described optical system (including the multi-pixel CCD-array
with 7 µm × 200 µm pixels) had been performed at the wavelength 671 nm as well. Two types of measurements had been carried out with a loaded AO cell, i.e. with radio-wave signal applied at the electronic port of that bastron-based AO cell. The first type of measurements had been performed at the central acoustic frequency 500 MHz with total acoustic wave attenuation
Our experimental results had been obtained using the achromatic integrating lens (Edmund Optics) with F = 85 cm at the light wavelength 671 nm, so that theoretically
The second type of measurements had been carried out using Gaussian apodization of the incident light distribution to demonstrate an opportunity of suppressing side lobes and increasing potential dynamic range of data processing within the second spatial optical arm of a prototype under design. In so doing, a few profiles for Gaussian apodization had been shaped exploiting the above-mentioned 4-prism beam expander due to rotating each prism individually and adjusting rather large angles of light incidence as accurate as possible. At the output of expander, these profiles had been checked
using a linear diaphragm of about 30 microns width in combination with a wide-aper- ture silicon photo-detector sliding together along a 60 mm optical aperture of the expander’s last prism. Two typical light distributions for the cases β ≈ 2 and β ≈ 6 are presented in
In this case, the acoustic carrier frequency was again about fM ≈ 500 MHz with total acoustic wave attenuation close to B ≈ 6 dB/aperture.
In this paper, we have presented an innovative design of a multi-band acousto-optic spectrometer with a few spatially parallel optical arms for the combined processing of
their data flow. Similar schematic arrangement permits the simultaneous exploitation of three or more bands at different resolutions and bandwidths, which makes it a highly versatile instrument in a number of astrophysical scenarios. The design is based on the use of a few, currently the three, different AO cells, and one of them, which is based on unique bastron crystal, represents specific subject of our interest as well as the object of advanced studies at the current stage of development.
This pioneer AO cell worked at optical wavelength λ = 671 nm, which combines the convenience of operating in just the visible range with good enough transparency of this material with dark red light. It has been demonstrated experimentally that the bastron- based AO cell of 6 cm aperture is practically able to manage the UHF radio-wave signals at the central frequency about fM ≈ 500 MHz within the frequency bandwidth ~258 MHz at the frequency resolution about 113.5 kHz providing the number N ≈ 2174 of resolvable spots or parallel frequency channels for spectral data analysis. Together with this, the potential of a UHF lithium niobate AO cell, operating in the anomalous light scattering regime with wide-bandwidth tangential phase matching has been estimated theoretically. The progressed characterization has shown a possibility of exploiting such an AO cell directly at the central frequency fM ≈ 500 MHz within the frequency bandwidth ~260 MHz with the needed efficiency. Additionally, practical aspects of realizing the Gaussian apodization in a multi-band AO spectrometer have been experimentally examined as well.
Finally, one can note that, as it has been indicated in the introductory section, the proposed design of a multi-band spectrometer will allow us the construction of a versatile instrument that can be used in virtually every astronomical context, with the advantage that data in three or even more bands can be obtained at the same time. This not only reduces time overheads associated with instrument changes, but allows us to extract valuable data in at least two distinct wave bands. It becomes achievable for the first time to our knowledge due to after parallel acousto-optical processing, data flows of all the optical arms are united by the joint CCD matrix on the stage of the combined electronic data processing. At this point, one yields at the really united astrophysical instrument, which provides comprehensive studies of astronomical objects simultaneously with precise synchronization in various frequency scales.
We would like to thank CONACyT for financial support through grant CB-256961 and 61237.
Shcherbakov, A.S., Dagostino, M.C., Arellanes, A.O. and Tepichin, E. (2016) An Advanced Multi-Band Acousto-Optical Radio-Wave Spectrometer with Multi-Channel Frequency Processing for Astrophysical Studies. International Journal of Astronomy and Astrophysics, 6, 393- 409. http://dx.doi.org/10.4236/ijaa.2016.64032