Ground Layer Laser Seeing Meter

Transcription

1 PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 16:31 318, 014 March 014. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A. Ground Layer Laser Seeing Meter S. CAVAZZANI, 1 G. RODEGHIERO, 1 I. CAPRARO, S. ORTOLANI, 1,3 C. BARBIERI, 1,3 AND V. ZITELLI 4 Received 013 June 06; accepted 014 February 18; published 014 March 19 ABSTRACT. The seeing calculation and its evolution during the night is a key point for the operation of telescopes and adaptive optics systems. Currently, there are various instruments able to measure the seeing, for example, the DIMM (differential image motion monitor) and the MASS (multi aperture scintillation sensor). This paper describes a new tool for the local ground layer seeing measurement. In particular, we want to derive the Fried parameter r 0 through a laser beam horizontal propagation. This is a new method for the experimental study of low-altitude atmospheric turbulence. Finally, we sketch an experimental setup for the Asiago Ekar Observatory and its possible applications. Online material: color figure 1. INTRODUCTION Atmospheric turbulence is one of the main limitations of astronomical observations from the ground. The generally accepted physical analysis of this phenomenon is based on the Kolmogorov theory (Kolmogorov 1941) and its subsequent developments. In astronomical applications, the study of turbulence is closely related to the phenomena causing perturbations on incoming wavefronts, generally called seeing. One of the main parameters of astronomical seeing is Fried s radius r 0, which corresponds to the equivalent size of the turbulent cell seen by an optical instrument. The Fried parameter is not a local variable, but the result of an integration along the light path. Thus, it depends on the path length as well as on the refractive index structure constant C n. It is well known that seeing is very often dominated by the turbulence near the ground, mixing layers with a strong thermal gradient. Knowledge of the contribution of these layers to seeing is fundamental for the design of modern telescopes and their adaptive optics (AO) systems. It is also important to understand the statistical distribution of atmospheric parameters, such as the seasonal trends, to plan observations in advance, as well as determine their feasibility. Until now, there have been many studies on the vertical component of the optical turbulence distribution, while the data on the horizontal distribution has been sparse; for instance, Masciadri et al. 1 Department of Astronomy, University of Padova, Vicolo dell Osservatorio 3, I-351, Padova, Italy; stefano.cavazzani@unipd.it. National Council Research (CNR)-National Institute for the Physics of the Matter (INFM)-Laboratory for Ultraviolet and X-Ray Optical Research (LUXOR) Lab and Adaptica s.r.l, Via Tommaseo 77, I-35131, Padova, Italy. 3 INAF-Osservatorio Astronomico di Padova, Vicolo dell Osservatorio 5, I-351, Padova, Italy. 4 National Institute for Astrophysics (INAF)-Osservatorio Astronomico di Bologna, Via Ranzani 1, I-4017, Bologna, Italy. (00) showed the finite size of the horizontal turbulence layer. The measurement of the horizontal component is also useful for characterizing sites hosting large-area telescopes through a continuous monitoring of the layers above the main mirror. The instrument described in this paper (called Laser Seeing Meter, LSM) is able to obtain a direct measurement of the turbulence near the ground through a horizontal laser beam propagation, to be compared with the r 0 obtained by measuring the temperature gradient fluctuations. The concept of horizontal turbulence is very similar to the vertical turbulence concept. The main physical difference is that vertical turbulence varies with altitude, while horizontal turbulence remains virtually constant along the integration paths of the model. This makes the instrument highly sensitive to variations in the ground layer. Through comparison with seeing calculated by traditional methods, it will be possible to describe a variety of turbulence phenomena, in particular the comparison of the turbulence in the ground layer to the turbulence in the layers at higher altitude. Finally, detectors with very high temporal resolution can provide useful information for single photon propagation for quantum astronomy and quantum communications (see, for instance, Cavazzani et al. 011; Corvaja et al. 011; and Capraro et al. 011). The LSM is formed by two towers with mobile platforms. The height and distance of the towers are parameters needed for the theoretical description of the instrument. One platform is equipped with a laser transmitter, and the other is equipped with a receiver (Fig. 1). Two temperature sensors are also mounted on the platforms, together with a weather station.. FRIED PARAMETER AND SEEING Fried has shown (Fried 1965), within the limits of the validity of the Kolmogoroff law, that r 0 is expressed by the formula: 31

2 GROUND LAYER LASER SEEING METER 313 The light from the point source is spread over an area having a full width at half-maximum (FWHM) given in arcseconds by: FWHM ¼ 0:98 λ r 0 : (6) The amplitude of this effect for relatively long exposure times is independent of the pupil diameter. We consider the image smearing of a horizontal laser beam to calculate the atmospheric r 0. Then, we can calculate the value of the refractive index structure parameter C n. FIG. 1. Laser seeing meter concept: a laser beam is emitted by the top of an 10 m tower toward another platform hosting the detection module. A weather station records the environmental data that are correlated with the beam spot measurement. Z 0:43 4π 1 λ cosðθ zen Þ C ndz 3=5; (1) where C n is the refractive index structure parameter: C n ¼ P C T T ; () and P and T are the atmospheric pressure and temperature, measured in millibars and kelvins. The temperature structure parameter C T ðxþ is defined through the formula: C T ðxþ ¼ ½TðxÞ T ðx þ ΔxÞŠ : (3) Δx =3 This parameter, measured in ð CÞ m =3, expresses the temperature variations between two locations at distance Δx. The indicate an average over time. Atmospheric turbulence produces scintillation, smearing and motion of the image. Roddier (Roddier 1981) has obtained the following approximate expressions for the calculation of these three effects: The image scintillation, as function of C n, is given by the following formula: σ Z I I 1 D 7=3 ðcosðθ zen ÞÞ 3 C nðzþz dz; (4) where D is the diameter of the telescope. The motion of the image, as function of λ, D and r 0, is given in arcseconds by: σ ðxþ ¼σ ðyþ ¼0:18λ D 1=3 r 5=3 0 : (5) 3. INVERSION MODEL TO CALCULATE THE FRIED RADIUS We recall that r 0 is an atmospheric integrated measure. In the present model, it is calculated on the distance between the two instrument s columns. The C n is then calculated accordingly on the same distance. Through equation (6), we get the radius of a point-like laser spot after horizontal propagation in the atmosphere: R Sp ¼ d sin 0:98 λr0 ; (7) where d is the distance between the towers. If instead the laser beam has a diameter D L, the radius of the laser spot after horizontal propagation is given by: R Sp ðd L Þ¼dsin 0:98 λr0 þ D L : (8) We assume that, for a short integration path, the spectrum of the modes is moved towards the lowest order atmospheric turbulence modes; in this case, the contribution of high-order atmospheric turbulence modes to the model assumptions is negligible. We remember that the integration path is on the order of tens of meters or a few hundred meters. Reversing equation (8) we get: 0:98λ arcsin h RSp ðd L Þ D L = d Considering that r 0 is given by the formula: Z 0:43 4π 1 λ cos ϕ we can calculate the value of C n: i : (9) C ndz 3=5; (10) C n ¼ 4:73 λ 4π r 5=3 0 d ; (11) where cosðϕþ ¼1 because we are in a horizontal path. Now we have to isolate the contribution due to the propagation 014 PASP, 16:31 318

3 314 CAVAZZANI ET AL. characteristics of a laser beam. Any beam propagates in vacuum according to the relation: WðzÞ ¼W 0 ½1 þðz=z R Þ Š 1= ; (1) where WðzÞ is the beam radius (to 1=e of the intensity onaxis), W 0 is the beam radius at waist (z ¼ 0), and Z R is the Rayleigh length that defines near and far field, respectively, when z<z R and when z>z R. The Rayleigh range is defined as follows: Z R ¼ πðw 0 Þ =λ; (13) and the half-angle of divergence of the beam in far field, obtained from equation (1) when z Z R, is θ ¼ λ=πw 0. The two parameters λ and W 0 define all the characteristics of the beam. Assuming Gaussian propagation of the beam, equation (9) becomes: 0:98λ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi arcsin½ðr Sp ðd L Þ ðd L =Þ 1 þðd=z R Þ Þ=dŠ ; (14) where Z R is defined by the formula: Z R ¼ π ðd L=Þ : λ Table 1 and Figure show the results of a LSM simulation. We calculate r 0 through the R Sp observation. This simulation is done with the following parameters: transmitter laser diameter D ¼ 1 cm, d ¼ 00 m and d ¼ 50 m, λ ¼ 0:63 μm. We note that r 0 increases with a decrease in R Sp and that the instrument sensitivity decreases with a decrease in the distance (d) between the two towers. To increase the sensitivity for short distances, one has to increase the transmitter laser diameter D, as shown by Figure 3 for two transmitter laser diameters, D ¼ 10 cm and D ¼ 5 cm. These trends are related to the theoretical r 0 variation from 5 cm to 30 cm Calculation of r 0 through C T We can calculate the C T with temperature sensors mounted on the LSM through equation (3). Through the inverse of equation (3) we can calculate the temperature variation average: FIG.. Laser seeing meter simulation (transmitter laser diameter ¼ 1 cm, d ¼ 50 m and d ¼ 00 m, λ ¼ 0:63 μm). We report the values in Table 1. The black line represents the R Sp variation with a distance of 00 m between the two towers. The gray line represents the R Sp variation with a distance of 50 m between the two towers. These trends are related to the r 0 variation from 5 to 35 cm. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½T ðxþ TðxþΔxÞŠ ¼ Δx =3 C T ðxþ : (15) Table and Figure 4 show the results of a simulation: d ¼ 00 m, λ ¼ 0:63 μm and D L ¼ 1 cm. These values are related to the r 0 variation from 5 cm to 30 cm. We note that D L variations of the order of millimeters correspond to variations of the order of C. This is an interesting result because it compares theoretical values of temperature with the induced distortion of a laser beam for fixed r 0 values. 4. FANTE AND YURA MODEL If we take into consideration propagation through a random media such as the turbulent atmosphere, we have to modify our model in order to take this into account. This has been done by Fante (1975) and, subsequently, by Dios et al. (004), where they calculate the long-term (LT) beam radius as a sum of two factors, the normal diffraction one (short term; ST) and the one given by the turbulence-induced spreading of the beam: W LT ðzþ ¼W ST ðzþþ β ; (16) where β is the second-order moment of beam displacement. Following the work by Fante (1975), this formula yields the following for collimated beams: TABLE 1 LASER SEEING METER (LSM) SIMULATION (TRANSMITTER LASER Diameter ¼ 1 cm, d ¼ 00 m AND d ¼ 50 m, λ ¼ 0:63 μm) r 0 (cm) R Sp... d ¼ 00 m (mm) R Sp... d ¼ 50 m (mm) NOTES. We calculate the Fried radius (r 0 ) through the laser spot radius (R Sp ) observation. We note that instrument sensitivity decreases with a decrease in the integration path (d ¼ 00 m d ¼ 50 m). The tool becomes less sensitive to variations of the R Sp when the integration path decreases. 014 PASP, 16:31 318

4 GROUND LAYER LASER SEEING METER 315 FIG. 3. Laser seeing meter simulation (transmitter laser diameter D ¼ 10 cm and D ¼ 5 cm, d ¼ 100 m, λ ¼ 0:63 μm). The black line represents the R Sp variation with a transmitter laser diameter of 10 cm. The gray line represents the R Sp variation with a transmitter laser diameter of 5 cm. These trends are related to the r 0 variation from 5 to 30 cm. W LT ðz ¼ LÞ ¼W 0 1 þ L Z R 4L ; þ (17) where k 0 ¼ π=λ. In Tyson (011), we see that r 0 (Fried s coherence length) and r 0 ;s(fried s coherence length for spherical waves) are given respectively by the formulas: and r 0 ;s¼ 0:43k secðβþ 0:43k secðβþ Z L 0 Z L C n 0 C ndz 3=5 (18) z 3=5: dz (19) L In a horizontal path, secðβþ ¼1, and the integration path L coincides with the value of z, so in this case r 0 r 0 ;s. Another accepted approximation is related to the work by Yura (1973) for the short-term beam spread: TABLE COMPARISON BETWEEN THE D Sp VARIATIONS AND ΔT (M C) TEMPERATURE VARIATIONS: d ¼ 00 m, λ ¼ 0:63 μm AND D L ¼ 1 cm r 0 (cm) D Sp (cm) ΔT (m C) NOTE. In the first column we have the r 0 fixed values (cm), in the second column we have the D Sp variations (cm), and in the third column we have the corresponding ΔT values ð10 3 CÞ. FIG. 4. Trends of the values listed in Table. The black line represents the D Sp variation (left axis) as a function of r 0. The dashed line represents the ΔT variation (right axis) as a function of r 0. W ST ¼ W 0 1 þ L 4:L r0 1=3 ; Z þ 1 0:6 R W 0 (0) valid when 0:6ðr 0 =W 0 Þ COMPARISON OF DIFFERENT MODELS In this section, we compare the models. The calculation of the spot radius is done through the following formulas: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D L R Sp ðfanteþ ¼ 1 þ d 4d þ (1) with the Fante model, R Sp ðyuraþ ¼D L 1 þ d 4:d þ with the Yura model, and Z R Z R 1 0:6 R Sp ðcavazzaniþ ¼d sin 0:98 λr0 þ D L r0 1=3 () D L = sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d 1 þ Z R (3) with our model. Table 3 and Figure 5 show the values of a simulation with the three models for different values of the Fried radius: d ¼ 00 m, λ ¼ 0:63 μm and D L ¼ 1 cm. We note that the model described in this article is much more sensitive than the other models. One possible explanation is that the two previous models are optimized for long distances (on the order of several kilometers). Our model is extremely sensitive over 014 PASP, 16:31 318

5 316 CAVAZZANI ET AL. TABLE 3 SIMULATION WITH THE THREE MODELS FOR DIFFERENT VALUES OF THE FRIED RADIUS: d ¼ 00 m, λ ¼ 0:63 μm AND D L ¼ 1 cm r 0 (cm) R Sp (Fante).... (mm) R Sp (Yura).... (mm) R Sp (Cavazzani).... (mm) short distances (e.g., d ¼ 00 m) and shows a significant difference compared to Fante s and Yura s models. This difference decreases with an increase in r 0. This important result gives the instrument good theoretical sensitivity to ground layer r 0 variations. We stress that the instrument is not intended as a wavefront sensor but as a seeing meter. 6. DETECTION AND MEASUREMENT OF BEAM DIAMETER In a setup where a laser is about 300 m away from a target, one can think several possible ways to detect its diameter. Since the system is designed to obtain a spot diameter on the order of 3 to 0 cm, it is possible to place a white screen and a calibrated camera in order to get an estimate of the beam diameter, as shown in Figure 6 (panel 1). The beam diameter is estimated as an average of the diameter along each axis centered on the spot centroid and using equation (4). A similar realization, which removes the problem of spot projection, is easily implemented by using a tiny smeared-out thin glass instead of the white screen. The camera is positioned along the laser beam axis beyond the glass, and it observes the transmitted beam spot; see Figure 6 (panel 3). Another solution that gives a greater sensitivity is the use of a matrix of photodiodes placed directly on the receiving screen, as shown in Figure 6 (panel ). Atmospheric turbulence induces a beam distortion; in addition to the shape FIG. 5. Comparison between the three models and the trends of the values listed in Table 3 (d ¼ 00 m, λ ¼ 0:63 μm and D L ¼ 1 cm). We note that for short distances our model is more sensitive than the Fante s and Yura s models. This difference decreases with an increase in r 0. The gray line with triangles represents the trend of our model, the dashed line with circles represents the trend of Fante s model, and the black line with crosses represents the trend of Yura s model. distortion, we will also have the phenomenon of scintillation but, for the theoretical model described in this paper, this phenomenon is irrelevant: the r 0 measurement occurs through the average diameter calculation of the surface on the screen. According to the astronomical theory of turbulence, the atmosphere keeps constant conditions for about 60 s (Roddier 1981). This assumption is valid in the case of the seeing measurement; for wavefront sensors, the correct timescale for atmospheric variations on laser propagation is on the order of the beam diameter or wind speed (Andrews et al. 005). With this assumption, for the astronomical turbulence study, it will be sufficient to have surface measures integrated on the order of seconds, while for wavefront sensor or quantum applications higher temporal resolutions are needed. We then consider the mean surface of the spot A, and the D Sp is calculated using the formula: rffiffiffiffi A D Spot ¼ : (4) π The obtained D Sp will be used for the r 0 calculation. 7. PILOT EXPERIMENT With reference to the above presented LSM concept we propose a pilot and cost effective experiment that could be carried out at the Asiago Ekar Observatory (longitude E , latitude N , altitude 1366 m) to verify the likelihood of the model introduced in the previous sections. A prototype of the LSM would be installed at Mount Ekar between the Schmidt 67/9 and the 18 cm Copernico telescope domes along the east-west direction. The towers, hosting the transmitter (laser) and the receiver (detector), should be about 10 m high, in order to sound the portion of the atmosphere s ground layer around the domes. The flat plateau at the top of Mount Ekar in the E-W direction is about 30 m and limits the distance between the two towers to this upper value (see Fig. 7). The separation can be extended if we accept an increase in the altitude of one of the two towers, but since the proposed model is sensitive over short distances, this range seems to be adequate to give rise detectable effects. The height of the two towers prevents the laser beam from crossing spaces where the observatory personnel operate, and it doesn t interfere with the observations of the two telescopes. The orientation of the LSM corresponds approximately to the direction of the prevailing winds. The installation of the 014 PASP, 16:31 318

6 GROUND LAYER LASER SEEING METER 317 FIG. 6. 1) LSM detection module with the off-axis camera observing the beam spot on a white screen. ) LSM detection module equipped with a matrix of photodiodes to detect and sample the impinging laser beam. 3) Alternative set up with a semitransparent screen and the on-axis camera observing the transmitted beam spot. LSM at Mount Ekar Observatory would ensure easy and constant accessibility to the experimental setup for observations and maintenance of the whole system. There is also an interesting consequence of installing the LSM close to an astronomical observatory; the control software of the Schmidt and Copernico telescopes for system tracking and image acquisition performs an estimation of the point-spread function (PSF) FWHM at rate of 1 Hz. This continuative PSF sampling could be recorded in a serendipity modality during the nights of parallel astronomical observations and LSM operations. An offline data analysis of the FWHM of the stars retrieved by the control software of the telescopes would allow a cross-correlation with the LSM FWHM measurements. In principle, this cross-correlation leads to a comparison between the turbulence regime that develops FIG.7. Conceptual laser seeing meter set up between the Schmidt 67/9 and 18 cm Copernico domes. See the electronic edition of the PASP for a color version of this figure. along the horizontal direction with that of the orthogonal direction propagating upward toward the sky. Even if the stars FWHM acquisition is subjected to the scheduled observing program with variable elevations depending on the observed object, the correlation is equally important and meaningful since it sounds a rather different portion of the atmosphere from that explored by the LSM. In addition, the observatory has a weather station equipped with an all-sky camera. 5 These data provide a comprehensive study of turbulence and how this is related to all weather phenomena. 8. CONCLUSION In this paper, we have described a new tool for the r 0 calculation for near-ground layers through the propagation of a horizontal laser beam. The instrument is also equipped with high-resolution temperature sensors. This allows, in theory, a comparison between the two values: the r 0 measured with our model and the r 0 calculated with the C T (see 3). The value calculated through the temperature gradient is based on discrete data and a theoretical model, while the value calculated using the laser is based on continuous data and requires more limited assumptions. This allows a greater sensitivity to fluctuations and leads to a new study of atmospheric turbulence. The paper also compares two models currently used to study the propagation of a laser beam to our model. Theoretically, our model is more sensitive over short distances; this of course remains to be experimentally tested (see 5). Finally, we propose a LSM prototype to be installed at the Asiago Ekar Observatory in order PASP, 16:31 318

7 318 CAVAZZANI ET AL. to test the proposed model (see 7). Aweather station will allow study of the correlations of the seeing effects with the major atmospheric phenomena, in particular, wind and humidity. We plan to improve this model using satellite data. We could compare the data obtained with the LSM beam with satellite data, in particular, the seeing values (see, for instance, Cavazzani et al. [011]). This is a crucial step for the new site testing methodologies. Furthermore, this can be very helpful for sky observations as well as for quantum communication. This activity is supported by Strategic University of Padova funding by title QUANTUM FUTURE and by INAF, Astronomical Observatory of Padova. REFERENCES Andrews, L. C., & Phillips, R. L. 005, Laser Beam Propagation Through Random Media, Vol. 15 (nd ed.; Bellingham: SPIE) Capraro, I., Tomaello, A., Dall Arche, A., & Villoresi, P. 011, Proc. SPIE, 8161, C Cavazzani, S., Ortolani, S., & Barbieri, C. 011, MNRAS, 411, 171 Cavazzani, S., Ortolani, S., & Zitelli, V. 011, MNRAS, 419, 3080 Corvaja, R., et al. 011, in Proc. 4th Int. Symp. on Applied Sciences in Biomedical and Communication Technologies (New York: ACM), 187 Dios, F., Rubio, J. A., Rodríguez, A., & Comerón, A. 004, Appl. Opt., 43, 3866 Fante, R. L. 1975, Proc. IEEE, 63, 1669 Fried, D. L. 1965, J. Opt. Soc. Am., 55, 147 Kolmogorov, A. N. 1941, Proc. USSR Acad. Sci., 30, Masciadri, E., Avila, R., & Snchez, L. J. 00, A&A, 38, 378 Roddier, F. 1981, Prog. Opt., 19, 81 Tyson, R. 011, Principles of Adaptive Optics (3rd ed.; Boca Raton: CRC) Yura, H. T. 1973, J. Opt. Soc. Am., 63, PASP, 16:31 318