A Proposed Method for a Photon-counting Laser Coherence Detection System to Complement Optical SETI (2025)

Laser radiation does not occur naturally, thus any detection of laser radiation implies an intent to put this radiation to use. In astrophysical terms the detection of laser radiation is a strong indicator of intelligence and technology: a so-called technosignature (Tarter 2006). This was pointed out at the early inception of the maser (Schwartz & Townes 1961). There are many potential technosignatures that have been actively searched for (Tarter 2001), but the predominant medium of searches for extra terrestrial intelligence (ETI) signals has been the radio spectrum. Recent years have seen more efforts directed toward optical detection methods (Howard et al. 2007; Werthimer et al. 2001; Reines & Marcy 2002; Tellis & Marcy 2017). A particular advantage arises from the low divergence of higher frequency beams—such as optical and infra red lasers—that concentrates the signal, making it easier to detect, but only if it is well directed (i.e., there is an intent). It also reduces the required power in the laser, making it technologically easier to implement. Detecting any laser signal has relied on the enhanced spectral brightness of the laser or the enhanced temporal brightness that pulsed lasers achieve. Detection of continuous lasers by their spectroscopic signature involves looking for peaks of enhanced brightness against blackbody emission containing absorption dips (Reines & Marcy 2002; Tellis & Marcy 2017; Stone et al. 2005), which has involved algorithmic-based searches of stellar spectra in collected databases. They concentrate on looking for narrow emission peaks amidst high-resolution absorption spectra. Given the spectral resolution and the detector sensitivity it is estimated that ETI lasers in the MegaWatt range would be detected with powers of 10's of kW also possibly detectable in some circumstances. As yet, no laser signatures have been found.

Arguably, the preferred approach has been to look for short optical pulses—modulation being another technosignature—that would be created by a laser to achieve the required brightness more easily than with continuous sources. Short pulses (10nS or less) can be observed by looking for two- and three-way coincidences in photon-sensitive detectors (Werthimer et al. 2001; Maire et al. 2014; Schuetz et al. 2016; Schuetz 2018). This has been performed over a number of years with telescopes typically of a scale 1 m (Wright et al. 2001), and we would expect to see photon densities of around 10 photons per pulse. Abeysekara et al. (2016) made alternate use of a larger ground-based gamma observatory to detect optical pulses with a sensitivity of 1 photon m⁻².

Borra (2012) considered that the effect of a train of short optical pulses upon a detected spectrum would be to produce an optical comb in frequency space. This would show up as a periodic signal when the spectrum was Fourier transformed. Indeed, such signals were observed (Borra & Trottier 2016), but their origin is yet to be established with Hippke (2019), postulating that they arise from nonrandom spectral absorption features. Leeb et al. (2013) considered detecting periodic pulsed signals in the temporal domain, but ruled out looking for continuous signals: "We rule out a continuous signal (i.e., zero modulation), as this cannot easily be discriminated against natural light sources." The case for using coherence when using heterodyne or homodyne detection techniques was delivered robustly by Kingsley (1993).

The detection techniques used are looking for different things: pulse detection cannot detect continuous sources. Spectroscopic detection integrates over time and cannot distinguish pulsed from continuous lasers. A table of indicative performance values is given in Table 1, with more examples given in Schuetz et al. (2016). The two techniques are not directly comparable as the pulsed detection technique can in principle detect a single pulse, which would be significant when the false alarm rate is low—as is the case with more than two detectors and the relevant quantity is the number of photons per pulse per square meter of detection area. This signal does not integrate due to the threshold of detection for coincidences. The spectroscopic technique looks for signal not against the received flux but against the photon noise and therefore requires integration. There is then a threshold of received photons per square meter per second relative to the background, which is dependent upon the star type and the spectral bandwidth. It is proposed in this paper that a method for detecting truly coherent, continuous laser sources is a realistic and effective way to look for ETI laser signals. This technique is most comparable to the spectroscopic observations as it requires integration but has the potential for flexibility in detecting both continuous and pulsed sources in post processing of events.

Earthly laser detection systems tend to concentrate on the intensity characteristics of laser radiation; that is, to look for enhanced spectral intensity or high temporal brightness and the same is true for OSETI. Recently, a technique based on detecting coherence has been used by Benton (2017) to positively detect faint laser radiation against a bright incoherent background, which is of course the same problem faced by OSETI. The utilization of coherence with OSETI was mentioned by Kingsley (1993), who discussed the possibility of heterodyne detection. He also mentioned homodyne detection but dismissed it due to unspecified difficulties.

The concept being proposed here involves the use of an asymmetric Mach Zehnder interferometer (MZI). The MZI divides incoming wavefronts along two paths using a beamsplitter, which are subsequently recombined with a second beamsplitter (Hecht 2002) shown schematically in Figure 1. If in traveling along either path, the optical phase is shifted then this manifests itself as an intensity variation when the light from the 2 arms is recombined and then detected. The detected intensity varies according to

where I_d(t) is the time varying detected intensity, λ is the optical wavelength, and ϕ(t) is the time varying phase occurring in one of the interferometer arms. G(Δλ) is a complex temporal coherence function related to the spectral power density of the source (Goodman 2015). A star with a wide spectral bandwidth has a very short coherence length (<1 μm), whereas lasers typically have coherence lengths of many cms or more. The approach taken by Benton for laser detection was to introduce a fixed path length difference between the interferometer arms and then to sinusoidally modulate the length of one of the arms with a piezo-mounted mirror. The modulation of the path length (a temporal change of relative phase ϕ(t)) gives rise to an intensity modulation only if the source coherence length exceeds the fixed path length difference. Thus the detection of a modulating signal implies the presence of a coherent source.

This technique can be applied to the search for ETI lasers with account taken of the intensities and timescales involved. Looking for continuous ETI sources draws comparisons with a spectroscopic detection approach. Tellis & Marcy (2017) indicate that there are issues that arise as a consequence of using an Echelle spectrograph such as found on the Keck Telescope used to look for laser emission in stellar spectra. First, there are examples of atomic emission lines being detected such as can happen in solar flares (Singh et al. 2006). These would be indistinguishable from laser emission as their spectral width is less than the resolution of the spectrometer. Such emissions are identified by a spectral analysis algorithm and must be discarded by manual intervention. Second the long integration time sees rapid events such as cosmic ray interactions with the spectrograph CCD leaving a localized signature which can also give a false positive to the analysis algorithm. This too can be excluded after manual examination. In principle, both of these issues would not cause a problem for a suitably designed coherence detection system. A third issue is the need for a reference spectrum to be taken to observe changes. Other techniques, such as multi-pulse coincidence detection will work only if the laser source is pulsed. Applying the concept of coherence detection using interferometry would involve looking for a modulation of the output intensity. This modulation is observed by sampling the output signal and extracting an amplitude at the modulation frequency. In the case of stellar interferometry, the photon flux is so low that photon-sensitive detectors, such as avalanche photodiodes (APDs) are required. In this paper, a new method for coherence detection with a photon-sensing coherence detector using an MZI is described. At each of the two output ports of the MZI is located a photon-sensitive detector such as a silicon APD. Every photon detected is recorded with its time of detection accurate to sub 1nS, called a time tag. Processing can be done offline using the time tags. Path length modulation can be provided by a piezo-mounted mirror in one of the arms driven with a sinusoidal signal. The amplitude of the modulation causes a phase shift, which is of course wavelength dependent, so must be chosen to maximize the signal for expected signal wavelength. To discriminate emission lines the requirement for the asymmetry in path length difference between the arms must exceed the expected coherence length, which can be determined from the emission line width. The coherence length l_c of an emission with a Gaussian profile is given by

where λ is the source wavelength and Δλ is the spectral line width (Akcay et al. 2002). Examining the spectral width of the strongest Fraunhofer lines from the Sun, the narrowest line has a width of 0.006 nm (Fe I 525.0216 nm) which has a coherence length of 43 mm. This, however, is not an emission line and most lines are much broader than this. Emission lines can arise from coronal loops (Singh et al. 2006) where the narrowest observed lines are 0.05 nm. Thus, coherence lengths for wavelengths around 656 nm (Hα) would be around 8 mm.¹ On the very reasonable assumption that lasers have narrower linewidths than this then introducing a path length difference of 10 mm or more should prevent emission lines from giving rise to a modulating output and only lasers would cause intensity modulation.

The expected stellar background intensity levels can be estimated in relation to the solar photon flux, which is approximately 4×10¹⁸ photons s⁻¹ m⁻² nm⁻¹ in the visible region (Smestad et al. 2008). The photon flux scales with the inverse square of the distance so for a Sun-like star at a distance of 1 kPc the received flux would be

where F_s is the solar photon flux. The total received background photons are calculated from

where A is the telescope receiver area, t is the observation time, and Δλ is the spectral bandwidth. The OSETI spectral examinations made using the 10 m Keck telescope provide us with measurement of expected level of stellar background photons (Tellis & Marcy 2017). The Echelle spectrometer used has a pixel resolution of λ/Δλ=250,000 and is operated for around a 10 min observation time to give somewhere between 10,000 to 40,000 photons per pixel (dependent upon the signal-to-noise ratio (S/N) required). Choosing an in-between value of 30,000 photons in 600 s this gives around 50 photons s⁻¹. At a wavelength of 500 nm, one pixel represents 0.002 nm; this gives 500 pixels per nm and of the order 25,000 photons s⁻¹ nm⁻¹. This is the same order as the estimated photon flux in Equation (3), which gives 9000 photons nm⁻¹ but will vary significantly depending upon the stellar luminosity and distance. As is the case for spectral measurements, any laser signal needs to be discerned against the photon noise not against the absolute background signal.

The intensity at a detector placed at one of the output ports of the MZI follows a cosinusoidal modulation (Hecht 2002; Benton 2017) as described in Equation (1):

where I₀ is the input intensity; γ(λ) is a wavelength-dependent factor representing reflection coefficients at both beamsplitters and also incorporates losses; k=2π/λ; and ΔL is the difference between the length of the interferometer arms L₁−L₂(t).

Modulating the arm length with a piezo mirror with a modulation voltage of amplitude v_m at a frequency f_m the path length difference is

where p is the response of the piezo in μ m/V, and v_off is an offset voltage. With careful choice of offset voltage the intensity at a detector can be written as

Sampling the detector signal over a period of time, and taking the Fourier transform shows power concentrated in the modulation frequency and is an indicator of coherent input. The signals at each of the output ports are 180° out of phase thus subtracting the 2 signals increases the S/N.

Estimation of detectability of laser signals was performed by modeling Poissonian photon-count distributions for noise and laser signals. Within the model, the modulation frequency of a piezo-mounted mirror was chosen to be 2 kHz for the following reasons. Source intensity modulations of incoherent background appear as modulations in the detector outputs, and this can arise from atmospheric scintillation (Osborn et al. 2015). The atmospheric scintillation frequency spectrum extends to around 1 kHz, so the modulation frequency is placed beyond this level to reduce background noise. This is dependent on telescope size and is less prevalent in large telescopes. With a sparse photon rate, the number of events per cycle is best maximized to reduce the high-frequency contributions of discrete event-based signals (Kingsley 1993). It was found that sampling at 8 kHz worked well. The noise and signal Poisson distributions were produced from the average photon detection rate per sample period based upon an expected photon level for the Keck telescope, as discussed earlier (25000/s background with 8 kHz sample rate has an average of 0.31 photons per sample). The laser signal distribution was multiplied by the interferometer modulation function, , and then added to the noise. In the case of using two detectors, one at each output port of the MZI, the signal photons are directed to particular detectors depending on the phase of the modulation function. This was determined by comparing the absolute amplitude of the modulation function with a function 180° out of phase with it. Dark count rates in APDs are so low (and non Poissonian) as to be negligible, and were not included. There are a number of ways to analyze a set of photon events, but here consistency is kept with the author's earlier approach of summing FFTs (Benton 2017). A data set of counts per sample time for each detector x_n(t) was Fourier Transformed () and then these two transform sets were subtracted, and the magnitude of the result taken

Example plots of the generated counts and the FT signals are shown in Figure 2. This data shows a subset of a 20,000 sample set where the background rate was 25 k photons s⁻¹, and the laser signal rate is 500 photons s⁻¹ distributed between the two detectors (this is chosen to give observable signal from a single set for demonstration purposes). The sample rate was 8 kHz, and the modulation frequency was 2 kHz. A section of the FT amplitude spectrum is given in the central plot with the modulation frequency in the center of the region. It can be seen that the amplitudes at the modulation frequency show opposite signs in the two detectors because they are out of phase. The lower plot shows the resulting power spectrum from the subtraction of the amplitude spectra from the two detectors with a clear peak at the modulation frequency. The height of this peak is extracted and compared with the noise level throughout the frequency space.

This was repeated and sets of magnitude values were summed with the power level at the modulation frequency extracted along with the background level. Initially, sample sets of 20,000 points were transformed with 300 sets summed yielding an observation time of 750 s, a similar scale to the spectroscopy measurements (Tellis & Marcy 2017). Modeling explored the effect of sample size and spectral bandwidth on the detectability of laser signals of varying amounts. Increasing the size of the sample set increases resolution and thereby improves the S/N as long as the reference modulation is stable. This can be seen in the plots shown in Figure 3 where the better resolution resulting from a larger number of points gives rise to stronger signals. These plots all represent an observation time of 750 s. In this case, the potential laser signal rate was varied and repeated 10 times to estimate the signal level uncertainty. The dotted line on the plots represents five standard deviations from the mean level of the background and is treated as a reliable detection threshold. The background rate was set at 2.5 k to represent a 0.1 nm spectral bandwidth in a Keck-sized telescope. A 600 k point FFT results in an improved detection threshold c.f. an equivalent observation time with 20 k FFT sets. A single FFT for the entire data set—6 million sample points would represent the ultimate resolution and be equivalent to the sensitivity obtained from a lock in amplifier with a long integration time. The spectral bandwidth determines background photon rate and also the photon noise against which any laser signal must be detected. A spectral bandwidth of 1 nm would be roughly equivalent to 25 k counts per second. Models of the signal level versus the incident laser photon rate were conducted for 0.1 nm, 1 nm, and 10 nm spectral bandwidths (assuming perfect collection and detection). This can be seen in Figure 4, where the detectable laser signal level is around 130 photons s⁻¹ with a 10 nm bandwidth, 40 s⁻¹ with a 1 nm bandwidth and around 20 s⁻¹ with a 0.1 nm bandwidth. These plots were made using 600 k point FFTs summed to give a total observation time of 750 s.

This modeling so far has assumed perfect optics and detectors. The effect of loss and detector quantum efficiency is shown in the plots of Figure 5, where a comparison is made between perfect collection and 30% efficiency. Some of the most sensitive scenarios seen here have a sum of 10 sets of 600 k point FFTs (750 s observation time) showing a detectable signal with 10–20 laser photons/s (100% efficiency) with a background level of 2500 s⁻¹ equivalent to a filtered spectral bandwidth of 0.1 nm, a total of some 15,000 photons. This approach as a whole compares favorably with the sensitivity of the spectroscopy approach (Tellis & Marcy 2017), which expects a threshold of 50,000 photons and claims 83 photons per second threshold for pulse detection with a typical 10-minute observation. Expected sensitivities are shown in Table 2. It is worth considering that the use of a Keck-type telescope represents a high level bespoke investigation, whereas there is a more accessible scale of investigation which is more broadly applicable. Modeling for a reduced scale telescope with a 1-m diameter mirror, assuming the same parameters (600 k FFT, 750 s observation time) results in a detection threshold of around 400 photons s⁻¹ using a 1 nm spectral bandwidth.

A system to implement this concept could operate as follows and is shown in Figure 6. A MZI with an extended length arm must sit in a section of collimated light, as could be provided by a parabolic mirror post collection telescope. The required spectral resolution can be obtained using a diffraction grating directing dispersed light onto two arrays of single-photon detectors. The collimated light from both arms should interact with the same diffraction grating to ensure consistent resolution between detector arrays. An array able to give complete spectral coverage would be a large and involved system with potentially thousands of independent detection and timing channels replicated at both output ports. This would represent the state of the art in APD arrays (Bruschini et al. 2017), but an array of 1024 APDs is certainly feasible. It is worth noting that the throughput of photon detections is the same no matter the number of channels (provided they are not saturated), but more channels means better resolution and reduced spectral bandwidth per channel, which reduces the threshold for detection. Providing wide spectral coverage within a single detector is currently beyond single-photon detector technology and several detection wavebands would be required with different APD technologies. A more targeted approach may be required making use of the "magic colors for OSETI" (Narusawa et al. 2018; Hippke 2018). This could use small arrays of APDs with quantum efficiencies matched to the required wavelength. Such wavelengths have been suggested matching Nd:YAG laser wavelengths (a rather anthropomorphic approach). Other suggestions include using specific absorption wavelengths that would be universal, but may be less intense lasers. A system which has a tunable wavelength filter could be considered but may require excessive observation time for comprehensive spectral coverage.

4.1.Power Requirements

4.2.Effectiveness

The coherence detection technique is discussed in comparison to the dispersive spectroscopic techniques because it is the the only alternative method that can detect continuous laser sources. The values for expected sensitivity given in Table 2 compare favorably with the spectroscopy measurements with sensitivities below 1 photon s⁻¹ m⁻², but should be considered only as indicative of the potential of the technique. The spectroscopic method as described by Tellis & Marcy (2017) has the signal spread over multiple detecting pixels (a point-spread function (PSF) width of 4.3 pixels), which is fundamentally limited by the system optics. With coherence detection the signal is spread across frequency and is limited by the resolution of the FFT, hence signal improves with increasing sample size. Comparison of the detected number of laser photons with the expected Poissonian noise level is shown in the Ratio column and approaches unity because the signal is spread over few frequency channels: it is effectively a narrower PSF. Thus, the threshold as calculated here could be improved by a longer observation time and also by a larger FFT size. Of course the clumping of counts into sampling periods is an artifice, made for convenient use of the FFT. The data exists as discrete events with a timing resolution determined by detector deadtime and more sophisticated analysis algorithms can be conceived to make use of this. The timing resolution also makes it possible to detect pulsed laser sources by looking for coincidences between the two detectors. This would work best if the pulse repetition rate is greater than the modulation frequency. The interferometer tends to direct coherent photons down the same arm so coincidences between arms are unlikely. This could be rectified by placing two detectors in each arm and looking for coincidences that occur in the correct arm relative to the interferometer setting. If, however, the detectors were photon number counting detectors, this would not be an issue and a mean photon bunch can be extracted from information contained by the two detectors. This should also lead to a determination of the pulse repetition rate. The data rate generated by such a system is given by the number of photons detected which is dependent upon the overall bandwidth and collection area. The critical factor is the spectral bandwidth per channel as this defines the noise level that must be exceeded, hence a modest spectrometer with a resolution of 0.1 nm and an array of APDs ought to be both cost effective and very sensitive. The fifth row of Table 2 shows a modeling outcome assuming a collection area of 1 m². This has a higher sensitivity of 5.26 photons s⁻¹ m⁻², but the ratio to the Poisson level is still good. The Poisson nature of the statistics means that many such small systems could be added together to achieve an equivalent sensitivity to the larger telescope system. The economy of scale gained from developing many smaller systems might suggest the search could move away from large telescopes and equip an array of smaller telescopes with a photon-sensitive coherence detector.

4.3.Issues