Development of a Lunar Scintillometer as part of the national large optical telescope site survey

Abstract

Ground layer turbulence is a very important site characterization parameter used to assess the quality of an astronomical site. The Lunar Scintillometer is a simple and effective site-testing device for measuring the ground layer turbulence. It consists of a linear array of photodiodes which are sensitive to the slight variations in the moon’s brightness due to scintillation by the lower layers of the Earth’s atmosphere. The covariance of intensity values between the non-redundant photodiode baselines can be used to measure the turbulence profile from the ground up to a height determined by the furthest pair of detectors. The six channel lunar scintillometer that has been developed at the Indian Institute of Astrophysics is based closely on an instrument built by the team led by Andrei Tokovinin of Cerro Tololo Inter-American Observatory (CTIO), Chile (Tokovinin et al., Mon. Not. R. Astron. Soc. 404(3), 1186–1196 2010). We have fabricated the instrument based on the existing electronic design, and have worked on the noise analysis, an EMI (Electromagnetic Induction) resistant PCB design and the software pipeline for analyzing the data from the same. The results from the instrument’s multi-year campaign at Mount Saraswati, Hanle is also presented.

Appendix: Computation of the Signal-to-noise Ratio Due to Photon Noise

The extremely low signal strength requires us to ascertain the contribution of photon noise and the associated signal-to-noise ratio. Important parameters like the photocurrent generated by the full moon and the signal output due to the weakest of scintillations are also computed in this section.

Cramer et al. [3] has created a spectral irradiance profile of the moon with a combined standard uncertainty of less than 1%, between the wavelengths of 420 nm to 1000 nm, unaffected by strong molecular absorption. Although the differences in the locations of observation and the corresponding sky conditions will result in a difference in the observed spectral irradiance, we can use the spectral response generated in Cramer et al. [3] to estimate a rough value of the signal-to-noise ratio at the lower limits of the covariance of normalized intensity fluctuations (close to 10^− 4). The upper plot in Fig. 19 shows the spectral irradiance of moonlight (the data for which is derived from Cramer et al. [3]) in units of μW m^− 2 nm^− 1, and the responsivity of the FDS1010 photdiode (the data for which is derived from the FDS1010 datasheet [18]) in units of A/W. The lower plot in Fig. 19 shows the spectral response of the photodiode to moonlight, in units of A nm^− 1, which is the product of the spectral irradiance of moonlight with the responsivity of the FDS1010 photodiode (both of which are given in the upper plot of Fig. 19) and the area of the photodiode (10^− 4 m²). The area under the curve shown in the lower plot (of Fig. 19) would give an approximation of the current generated by the unbiased FDS1010 photodiode when exposed to the full moon at zenith. The area under the curve gives a current of I _{d c} = 52.36 nA. The spectral irradiance data given in Cramer et al. [3] only covers the wavelength range of 420 - 1000 nm. Hence, the actual current generated will be higher than the calculated DC photocurrent (I _{d c} ) due to the full moon, if we include the photoelectrons generated for the wavelengths at which the data is not available. For the sake of computing the signal-to-noise ratio, we have taken the I _{d c} , which is computed for the area under the curve shown in the lower plot of Fig. 19.

Fig. 19

Upper plot shows the spectral irradiance of moonlight (in μW m^− 2 nm^− 1) and the responsivity of the FDS1010 photdiode (in A/W). The lower plot shows the spectral response of the photodiode to moonlight (in A nm^− 1)

For an integration time of t =  2 ms, the total photoelectrons generated by the direct current,

$$\begin{array}{@{}rcl@{}} N_{s}&=& \frac{I_{dc} \times t}{e}=\frac{52.36 \times 10^{-9} \times 0.002}{1.6 \times 10^{-19}} \\ &=&6.55 \times 10^{8} \end{array} $$

(5)

The number of photoelectrons contributing to photon noise is given by,

$$\begin{array}{@{}rcl@{}} \sigma&=&\sqrt{N_{s}}= 2.56 \times 10^{4}, \end{array} $$

(6)

$$\begin{array}{@{}rcl@{}} I_{\sigma}&=&\frac{\sigma \times e}{t}= 2.05 \times 10^{-12}A \end{array} $$

(7)

The output voltage contribution of the photon noise (after amplification) is given by,

$$\begin{array}{@{}rcl@{}} V_{o\sigma}&=&I_{\sigma} \times K_{trans} \times K_{ac} \\ &=&2.05 \times 10^{-12} \times 9.1 \times 10^{6} {\Omega} \times 90 \\ &=&1.68 mV, \end{array} $$

(8)

where K _{t r a n s} is the gain of the transimpedance amplifier and K _{a c} is the AC gain of the inverting amplifier.

The amplitude of scintillations can be as low as 10^− 4 times the average flux amplitude of the moon. From (5), the number of photoelectrons generated by the smallest of scintillations can be given by,

$$\begin{array}{@{}rcl@{}} N_{sc}&=&N_{s} \times 10^{-4} \\ &=&6.55 \times 10^{4} \end{array} $$

(9)

From (7) and (9), for the lowest range of scintillation amplitudes, the signal-to-noise ratio (SNR) because of photon noise is given by

$$ S_{p}=\frac{N_{sc}}{\sigma}= 3.2 $$

(10)