#
Multipurpose Laser Instrument for Interplanetary Ranging, Time Transfer, and Wideband Communications^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

^{−4}(where R is the range), for decades, only three large meter-class telescopes, located, respectively, on mountaintops in southern France and NASA-supported sites at the University of Texas and the University of Hawaii, were capable of detecting return signals. Subsequently, a large telescope in Matera, Italy was added to the roster, but the larger 3.5 m telescope at Apache Point Observatory in Sunspot, New Mexico, USA made a huge difference in data yield as well as providing unprecedented ranging precision at the few millimeter level [5].

## 2. Two-Way Laser Transponders for Interplanetary Ranging and Time Transfer

^{−2}instead of R

^{−4}as in SLR to passive reflectors. Figure 2 illustrates the manner in which range and relative time can be transferred between Earth and the spacecraft. Subsequent to this concept, range and time offsets between an Earth-based clock, located at the 1.2 m telescope at NASA Goddard Space Flight Center, and the Mercury Laser Altimeter (MLA) mission, enroute to Mercury at a distance of roughly 22 million km, with an estimated 20 cm range accuracy [7]. A few months later, over 500 laser pulses transmitted by the same 1.2 m Earth station were observed by NASA’s Mars Orbiter Laser Altimeter (MOLA) at a distance of 80 million km. MOLA had previously mapped the surface of Mars, but, unfortunately, the onboard laser was no longer operational, and a return laser signal was not possible [8]. With the exception of a wideband optical transceiver operating in the MHz to GHz range, the hardware and operational requirements are similar, and the various operations can be consolidated within a single interplanetary instrument. The addition of the transceiver also permits the ability to transfer a coded value of the time at the start of the coded sequence from Earth to the interplanetary spacecraft, and vice versa, while a series of coded signals traded between the two terminals can also provide the range rate, resulting in accurate atomic clock offsets, range, and range rate between the two terminals as described in Figure 2 [6].

## 3. The Advantages and Disadvantages of Lasers over Microwaves in Deep Space Operations

## 4. Advantages of Single Photon Detector (SPD) Arrays

## 5. Interplanetary Laser Communications

_{ave}, which under the assumption of quasi-circular orbits is equal to the orbital radius of the planet about the Sun. The actual range can vary within R

_{ave}− AU and R

_{ave}+ AU. However, as mentioned previously, at or near the minimum interplanetary distance, the Earth is viewed against the extremely bright background of the Sun, while at or near the maximum distance, the Sun is physically blocking the optical path between the Earth and the planet. We will also ignore any transmission or scattering losses in the atmosphere since these can be largely mitigated by utilizing an astronomical telescope on a mountaintop or alternatively a large orbiting telescope, such as NASA’s 2.4 m Hubble Telescope, which in polar orbit would not experience interruptions in service due to Earth rotation. As for the planetary terminal, the need for high bandwidth communications would suggest a satellite in a near-polar orbit outside the planetary atmosphere and oriented for maximum visibility to the Earth station.

_{rE}= n

_{tP}η

_{tP}G

_{tP}G

_{rE}η

_{rE}η

_{dE}R

_{PE}

^{−2}

- n
_{tP}= the number of photons per pulse/bit emitted by the planetary laser - ή
_{tP}= the optical efficiency of the planetary transmit optics - G
_{tP}= the transmitter gain of the planetary telescope (optical antenna) - G
_{rE}= the receiver gain of the Earth telescope (optical antenna) - η
_{rE}= the optical efficiency of the Earth receive optics - η
_{dE}= the optical efficiency of the Earth detector - R
_{PE}= range between the Earth and planetary terminals

_{tot}= 72 (0.97) (0.95) = 0.66.

_{T}is the area of the telescope primary mirror, λ is the laser wavelength, α

_{T}= a/ω where a is the physical radius of the transmitting primary mirror and ω is the Gaussian beam radius at the telescope exit aperture, γ

_{T}= b/a where b is the physical radius of the secondary mirror, X

_{T}= 2πa

_{T}sinφ/λ = πD

_{T}sinφ/λ where φ is the pointing error, D

_{T}is the diameter of the transmitting telescope, and β

_{T}= 0 unless the outgoing beam is purposely defocused to create a wider beam angle as might occur during initial acquisition of the opposite terminal. Thus, once the two terminals are locked onto each other, we can set X

_{T}= β

_{T}= 0 and the gain equation simplifies to

_{T}which maximizes the transmitter antenna gain, is given by

_{R}is the area of the receive telescope primary mirror, γ

_{R}is the receiver obstruction ratio of the secondary mirror, and η

_{RD}has a maximum value of 0.95 if πR

_{D}/λF

_{E}> 0.7 where R

_{D}is the detector radius and F

_{E}is the Earth telescope F-number, i.e., the ratio of the receive telescope focal length over the primary diameter [18].

_{b}, we generate the equation for the transmitted laser power from the planetary platform needed to generate the desired number of received photons per bit at the Earth station, i.e.,

_{rE}is the desired received power at the Earth station. For example, if we want to limit the Bit Error Rate (BER) to one per thousand in a KHz system, one per million in a MHz system, or one per billion in a GHz system, then, based on Figure 3, the desired laser power received at the Earth terminal, P

_{rE}is equal to the photon energy hν multiplied by the desired received photons per bit n

_{rE}and the bit frequency f

_{b}, e.g., 7 thousand (KHz), 14 million (MHz), or 21 billion (GHz).

_{tot}= 0.66 and η

_{dE}= 0.7 into Equation (8) and further assume that a secondary mirror is not required for the smaller planetary telescope. The latter assumption implies γ

_{tP}= 0 and g

_{tP}= 0.81 from Figure 3. If we further assume an orbiting Earth telescope, like NASA’s 2.4 m diameter Hubble Space Telescope, the value of γ

_{rE}= 0.3 m/2.4 m = 0.125 or (1 − γ

_{rE}

^{2}) = 0.984.

^{2}or D

_{tP}= 1 m

^{2}/D

_{rE}= 1 m

^{2}/2.4 m = 0.42 m. Then a 10 W laser at 532 nm combined with a 42 cm diameter planetary telescope would allow roughly 900 MHz communications from Mercury or Venus, 700 MHz from Mars, 70 MHz from Jupiter, 10 MHz from Saturn, 6 MHz from Uranus, 1 MHz from Neptune, and 900 kHz from Pluto. Using Equation (8), the required power and telescope diameters for other laser wavelengths can easily be determined from Figure 5 by multiplying the y-axis result by the square of the wavelength ratio, (λ/532 nm)

^{2}, which equals 4 for a wavelength of 1064 nm (Nd:YAG) and 8.5 at 1550 nm.

## 6. Opposite Terminal Acquisition and Tracking

_{E}and R

_{P}are the orbital radii, and therefore the Earth–planet distance at time t is equal to

_{P}and ω

_{E}are the angular rates of the two planetary orbits. The cosine in Equation (10) can now be approximated by

_{P}and ω

_{E}) and the narrow laser beam divergences (which are 4 to 5 orders of magnitude smaller than conventional microwave systems), can complicate the initial acquisition and subsequent tracking of the opposite terminal. One attractive acquisition approach would be to have each terminal initially track the sunlit image of the opposite planet in order to narrow the search angle and then, based on our excellent knowledge of the orbital velocities and eccentricities (if any), point ahead of the viewed position to compensate for the two-way time delay.

_{0}is the time a light signal was transmitted by the planetary terminal, t

_{1}= RPE1/c is the time that signal was observed at the Earth station, and t

_{2}= (RPE1 + RPE2)/c is the time that the Earth response reaches the planetary terminal; then, the cosine of the point ahead angle for the Earth station is given by the dot product of the interplanetary range vectors at times t

_{0}and t

_{2}divided by their respective magnitudes, RPE1 and RPE2. This leads to the following set of equations for the planetary positions at time t = t

_{0}:

_{1}and t

_{2},

_{1}and t

_{2}

_{E}and ω

_{P}are the angular revolution rates of the Earth and planet about the Sun. The latter are obtained by dividing the orbit circumference, 2πR

_{P}, by the orbital period in Table 1. The value for Earth is ω

_{E}= 0.199 μrad/s. The vectors between the Earth and planetary terminals at the beginning and end of the roundtrip are in turn given by

_{P0}where, due to the assumed circular symmetry, we can arbitrarily set θ

_{E}= 0 deg. For most planetary geometries, the point ahead angle is a fraction of a milliradian but still orders of magnitude greater than the angular radii of the planet as seen from Earth, as listed in Column 8, Table 1. It should also be noted that orbital geometries where the point ahead angle drops to near zero in Figure 6 would be optimum locations to initiate opposite terminal acquisition. These opportunities would occur twice per Earth year for all of the planets but with different time intervals between them.

_{P0}= 180 degrees occurs for two reasons: (1) the relative planetary orbital velocities are additive because they point in opposite directions; and (2) the planets are at their maximum distance during the two-way light transit time between t

_{0}and t

_{2}. The height of the central peak falls for planets farther from the Sun because they revolve more slowly and therefore add less to the Earth angular velocity contribution. In decreasing order, the peaks in Figure 6 correspond to Mercury (black), Venus (red), Mars (green, Jupiter (pink), Saturn (aqua), Uranus (brown), Neptune (black), and Pluto (red). In the case of the outer planets (Mars and beyond), the Earth’s orbital angular velocity dominates, whereas the angular velocities of Mercury and Venus exceed that of Earth and tend to increase the point ahead angle.

## 7. Effects of Planetary Rotation or Planetary Orbits

_{P0}= 0 or 180 degrees) when the Sun would either blind the planetary terminal or block the beams entirely. In addition, the initial angular area of uncertainty for the location of the planetary orbiter would be constrained to a narrow circular rim defined by the orbital altitude above the planet’s surface, i.e., A

_{O}= πDh where D is the angular diameter of the planet as viewed by the opposite terminal and h << D is the maximum altitude of the satellite. A land-based terminal, on the other hand, could be located anywhere within the angular disk, i.e., A

_{L}= πD

^{2}/4, as listed in Columns 8 and 9 of Table 1, a factor D/4h larger. The look-ahead angle for a satellite in polar orbit about a planet of angular diameter D is roughly equal to πD/τ

_{orb}and is plotted in Figure 7 for the various planets as a function of the orbital period.

_{E}, is highly likely to be much larger than the planetary telescope diameter, D

_{P}, requiring the Earth terminal pointing to be much more accurate in transmission mode for a two-way communications link. It is therefore extremely important to either maintain a very tight coalignment of the transmit and receive telescope optical axes or increase the laser power to compensate for the optical loss. We will now discuss a possible solution.

^{2}/8(λR) where D is the diameter of the telescope primary mirror and λR is again the product of the laser wavelength and the range to the opposite terminal. Figure 5 in [17] suggests that choosing the value β’ = 2.4 would increase the planetary beam spread in the far field by a factor of 7 relative to the original central lobe. This would increase the transmitted beam area for acquisition by a factor of 49, thereby greatly accelerating acquisition of the opposite terminal. However, the mean reduction in signal strength due to defocusing would be about 2 orders of magnitude. If the received photons per bit was set at 21 photons as recommended earlier for the 1 Gbps system, an off-axis detector of the same size would collect only 0.2 photons per bit. However, by summing over 100 bits (100 ns) using an integrating circuit, one could record the same number of photons as in the focused case. An attractive concept to the author would be an NxN square array (N odd) of equally sized detectors with the central communications detector sized to collect all of the light entering the telescope parallel to the optical axis. At a minimum (N = 3), the central detector would be surrounded by eight equally sized integrating detectors summing over 100 pulses and guiding the detected beam to the central detector. Other detectors with longer integration times could be added to the outer boundaries of the array (N = 5, 7, etc) if needed to further widen the FOV for faster target acquisition.

## 8. Summary

_{T}(D

_{P}D

_{E})

^{2}(laser power times the square of diameters of gain-optimized transmit and receive telescopes) needed to achieve a particular bit error rate was determined for all of the planets and is proportional to (λR)

^{2}where λ is the wavelength and R is the distance between the Earth and the planet. At the extreme outer edges of our solar system, R can be as large as 40 AU (Pluto), resulting in a two-way light transit time of up to 11 hours! During such long time intervals, any (1) relative angular motion between Earth and the subject planet in their respective voyages about the Sun, (2) rotations of each planet about its axis in the case of ground-based terminals, or alternatively (3) orbital motions of the communications terminals about their respective planets will result in a combination of multiple look-ahead angles in highly diverse directions that must be taken into account in order to maintain coalignment of the two telescope axes and the required signal strength for wideband communications in the MHz to GHz range with low bit error rates (BERs). In this paper, the approximate magnitudes of all of these look-ahead angles have been determined under the assumption of perfectly circular, coplanar planetary orbits about the Sun and circular orbits of both terminals about their respective planets. It has been noted that for all of the planets there are two time intervals per Earth year when no look-ahead angles are required to compensate for planetary orbital velocities about the Sun, making them optimum times to initiate acquisition of the opposite terminal. It is further anticipated that during future interplanetary operations both terminals will have access to the most precise planetary orbit models as well as the ability to periodically synchronize both relative position and time through the use of the two-way transponder capabilities of the optical link, as discussed in Section 2 of this paper.

^{−4}signal strength dependence of satellite laser ranging (SLR) as opposed to the R

^{−2}dependence of the two-way transponder and communications applications considered here, certain satellites in the ILRS constellation can mimic the signal strengths expected from various planets throughout the solar system. These are listed in Table 2.

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Computation of the instantaneous range R and the clock offset dt via Asynchronous Laser Ranging and Time Transfer. Multiple measurements of the range provide the time derivative of R between the Earth and spaceborne clocks that appears in the equation for the clock offset, dt.

**Figure 3.**A plot of the number of received photons per bit vs. the probability that a “one” will not be properly detected in a wideband OOK communications system equipped with single-photon sensitive detectors. For example, with 14 photons received per bit, only 1 in a million (MHz) “ones” would be missed, while with 21 photons received per bit, only 1 in a billion (GHz) “ones” would be missed. To account for internal instrument or background light noise, one can set a photon threshold below which a “zero” bit is highly likely.

**Figure 4.**Maximizing the far field gain of the transmitting antenna. The left hand graph gives the ratio of the primary mirror radius to the laser Gaussian beam radius, i.e., α

_{T}= a

_{T}/ω, which yields maximum on-axis far field gain as a function of the secondary mirror obscuration ratio γ

_{T}= b

_{T}/a

_{T}. The second graph shows the resulting reduction in the peak far field transmitter gain relative to 4πA

_{T}/λ

^{2}where A

_{T}is the area of the primary mirror. The relatively minor effects of secondary mirror support struts on the far field pattern can be minimized by mounting the secondary mirror on an AR-coated window the same diameter as the primary or alternatively using thin supporting blades that are attached to and run parallel to the telescope tube.

**Figure 5.**The product of the transmitted laser power emitted by the planetary probe and the two telescope diameters squared (y-axis) is plotted as a function of the planetary distance (x-axis) for a wavelength of 532 nm and four candidate bit rates: 1 MHz (black), 10 MHz (red), 100 MHz (brown), and 1 GHz (pink). The dots along the lines indicate the average distance of the planet from Earth, as listed in Table 1. The chart can be used for other wavelengths by multiplying the y-axis number by (λ/532 nm)

^{2}.

**Figure 6.**Terminal point ahead angles in microradians for the various planets in the solar system versus the sum of their angular positions in their orbits about the Sun. Maximum point ahead angle occurs when Earth and the planet are on opposite sides of the Sun (180°) due to the fact that: (1) the range between them, and therefore the light travel time, is maximized; and (2) their orbital velocities I are in opposite directions and therefore the relative velocity is additive. The point ahead angles decrease for the outer planets because of their slower orbital angular velocities. Smaller secondary peaks occur at 0° (or 360°) for all the planets because: (1) the orbital velocities are in the same direction and therefore the relative velocity is reduced; and (2) the light travel time is minimized. Intermediate angles where the point ahead angle drops to near zero would be advantageous for mutual acquisition of the two terminals and occur twice per Earth year.

**Figure 7.**Additional point ahead angles required to compensate for the two-way light transit times between the Earth and a terminal in a polar orbit about the subject planet and in a plane approximately perpendicular to the Earth line-of-sight as a function of the orbital period. Such an orbit would: (1) provide access to the entire surface and atmosphere of the planet under study; (2) greatly reduce the angular uncertainty of the terminal location during initial acquisition; and, (3) with quasi-parallel orientation of the orbits, provide very long periods of uninterrupted access between the orbiting planetary and Earth communications terminals before orbital orientation adjustments would be required.

**Table 1.**Planetary parameters relevant to the acquisition and tracking of the opposite terminal during wideband communications between Earth and the planet under investigation. The angular radii for Earth and the planet it is communicating with corresponds to the angular spread seen by the opposite terminal at the average interplanetary distance. The actual distance can vary between RPE

_{ave}+/− 1 AU.

Planet Name | Solar Distance (AU) | Planet Diameter (km) | Planet Orbital Period (Years) | Planet Rotational Speed (km/h) | Mean Earth to Planet Distance (AU) | Mean One-Way Light Transit Time (min) | Mean Planet Angular Radius (µrad) | Mean Earth Angular Radius (µrad) |
---|---|---|---|---|---|---|---|---|

Mercury | 0.38 | 4879 | 0.2 | 10.83 | 1 | 8.3 | 16.42 | 40.93 |

Venus | 0.72 | 12,104 | 0.6 | 6.52 | 1 | 8.3 | 40.73 | 42.93 |

Earth | 1.00 | 12,758 | 1.0 | 1574 | 0 | 0 | NA | NA |

Mars | 1.52 | 6792 | 1.9 | 866 | 1.52 | 12.6 | 15.04 | 28.24 |

Jupiter | 5.2 | 142,984 | 11.9 | 45,583 | 5.2 | 43.0 | 92.52 | 8.25 |

Saturn | 9.54 | 120,536 | 29.5 | 36,840 | 9.54 | 78.8 | 42.51 | 4.50 |

Uranus | 19.2 | 51,118 | 84 | 14,794 | 19.2 | 158.6 | 8.96 | 2.24 |

Neptune | 30.1 | 48,528 | 164.8 | 9719 | 30.1 | 248.3 | 5.43 | 1.43 |

Pluto | 39.5 | 2376 | 248 | 47.18 | 39.5 | 326.3 | 0.20 | 1.09 |

**Table 2.**Satellites currently tracked by the International Laser Ranging Service (ILRS) that can mimic interplanetary links in the testing of laser transponders and communications. Because the satellite returns are only visible within a certain range of the source of the laser radiation, the Earth and planetary terminals must be collocated during the planetary simulation.

Satellite | Altitude (km) | Mean Target Cross-Section 10 ^{6} m^{2} | Minimum Transponder Range (AU) | Maximum Transponder Range (AU) |
---|---|---|---|---|

LAGEOS | 6000 | 15 | 0.263 | 0.771 |

GLONASS | 19,000 | 55 | 1.38 | 2.72 |

GPS | 20,000 | 19 | 2.60 | 5.06 |

LRE (elliptical) | 25,000 | 2 | 12.52 | 23.12 |

Apollo 15 (Moon) | 384,000 | 1400 | 111.6 |

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## Share and Cite

**MDPI and ACS Style**

Degnan, J.J.
Multipurpose Laser Instrument for Interplanetary Ranging, Time Transfer, and Wideband Communications. *Photonics* **2023**, *10*, 98.
https://doi.org/10.3390/photonics10020098

**AMA Style**

Degnan JJ.
Multipurpose Laser Instrument for Interplanetary Ranging, Time Transfer, and Wideband Communications. *Photonics*. 2023; 10(2):98.
https://doi.org/10.3390/photonics10020098

**Chicago/Turabian Style**

Degnan, John J.
2023. "Multipurpose Laser Instrument for Interplanetary Ranging, Time Transfer, and Wideband Communications" *Photonics* 10, no. 2: 98.
https://doi.org/10.3390/photonics10020098